APPLIED PHYSICS REVIEWS Semi-insulating semiconductor heterostructures: Optoelectronic ... ·...

JOURNAL OF APPLIED PHYSICS VOLUME 85, NUMBER 9 1 MAY 1999

APPLIED PHYSICS REVIEWS

Semi-insulating semiconductor heterostructures: Optoelectronicproperties and applications

David D. Noltea)

Department of Physics, Purdue University, West Lafayette, Indiana 47907-1396

~Received 11 September 1998; accepted for publication 25 January 1999!

This review covers a spectrum of optoelectronic properties of and uses for semi-insulatingsemiconductor heterostructures and thin films, including epilayers and quantum wells.Compensation by doping, implantation, and nonstoichiometric growth are described in terms of theproperties of point defects and Fermi level stabilization and pinning. The principal optical andoptoelectronic properties of semi-insulating epilayers and heterostructures, such as excitonicelectroabsorption of quantum-confined excitons, are described, in addition to optical absorption bymetallic or semimetallic precipitates in these layers. Low-temperature grown quantum wells thathave an arsenic-rich nonstoichiometry and a supersaturated concentration of grown-in vacancies arediscussed. These heterostructures experience transient enhanced diffusion and superlatticedisordering. The review discusses the performance of optoelectronic heterostructures andmicrocavities that contain semi-insulating layers, such as buried heterostructure stripe lasers,vertical cavity surface emitting lasers, and optical electroabsorption modulators. Short time-scaleapplications arise from the ultrashort carrier lifetimes in semi-insulating materials, such as inphotoconductors for terahertz generation, and in saturable absorbers for mode-locking solid statelasers. This review also comprehensively describes the properties and applications ofphotorefractive heterostructures. The low dark-carrier concentrations of semi-insulatingheterostructures make these materials highly sensitive as dynamic holographic thin films that areuseful for adaptive optics applications. The high mobilities of free carriers in photorefractiveheterostructures produce fast dielectric relaxation rates that allow light-induced space-chargegratings to adapt to rapidly varying optical fringe patterns, canceling out environmental noise duringinterferometric detection in laser-based ultrasound, and in optical coherence tomography. They arealso the functional layers in high-sensitivity dynamic holographic materials that replace staticholograms in Fourier imaging systems and in experimental Tbit/s optical systems. Semi-insulatingheterostructures and their applications have attained a degree of maturity, but many critical materialsscience issues remain unexplored. ©1999 American Institute of Physics.@S0021-8979~99!07209-6#

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TABLE OF CONTENTS

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . .6259II. FULLY COMPENSATED SEMICONDUCTORS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6260III. SEMI-INSULATING EPILAYERS AND

HETEROSTRUCTURES. .. . . . . . . . . . . . . . . . . . . 6261A. Ion implantation of heterostructures. . . . . . . . . . 6261B. Compensated doping during epitaxy. . . . . . . . . . 6263C. Nonstoichiometric growth of heterostructures. . 62D. Transient enhanced diffusion in

nonstoichiometric quantum wells. . . . . . . . . . . . 6266IV. OPTOELECTRONIC SEMI-INSULATING

HETEROSTRUCTURES. . . . . . . . . . . . . . . . . . . . .6267A. Heterostructure stripe lasers. . . . . . . . . . . . . . . . . 6267B. Vertical cavity surface emitting lasers. . . . . . . . 6269C. Optical modulators. . . . . . . . . . . . . . . . . . . . . . . .6269

6250021-8979/99/85(9)/6259/31/$15.00

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D. Semi-insulating heterostructures for ultrafastoptoelectronics. . . . . . . . . . . . . . . . . . . . . . . . . . .6270

E. Semi-insulating heterostructures formode-locking solid state lasers. . . . . . . . . . . . . . 6272

V. PHOTOREFRACTIVE SEMICONDUCTORHETEROSTRUCTURES. . . . . . . . . . . . . . . . . . . . .6273A. Dynamic holography in quantum wells. . . . . . . . 6274B. Photorefractive heterostructure geometries. . . . . 6275C. Photorefractive optical microcavities. . . . . . . . . . 6280D. Photorefractive quantum well applications. . . . . 62

I. INTRODUCTION

Semi-insulating semiconductors constitute a speclass of semiconductor materials because they possess acial limiting behavior: they exhibit close to the minimum

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9 © 1999 American Institute of Physics

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dark carrier density permissible for a given band gap. Whthe low carrier density of the semi-insulating semiconductgives these materials extremely high resistivities in the dathey may have significant photoconductivity under illumintion because of their typically high carrier mobilities. Theproperties make these highly resistive materials valuableapplications that lie at the other end of the spectrum frapplications for highly conducting doped semiconductor mterials and devices. The semi-insulating semiconductorsvalued for their high resistivity, high defect densities, ashort carrier lifetimes. They provide insulating device isotion for integrated circuits and provide current blocking laers for heterostructure lasers. They exhibit strong photofractive effects, and are of interest for use as ultrafphotodetectors, among other interesting effects and apptions, many of which are described in this Review.

Semi-insulating bulk semiconductor crystals have lobeen the mainstay of III–V integrated circuit technology bcause high-resistivity substrates partially replace the funcof the oxide in silicon devices to isolate discrete deviceslayers within an integrated circuit. Common examplessemi-insulating semiconductors are chromium-doped G~GaAs:Cr! and GaAs compensated by the so-called EL2fect ~GaAs:EL2! as well as iron-doped InP~InP:Fe!. Thesesemi-insulating materials are formed by either intentiodoping with transition–metal impurities during growth frothe melt, or by relying on the formation of native defecduring crystal growth, such as the arsenic antisite defeccompensate residual shallow dopants.

In the past ten years, interest in semi-insulating materhas expanded to included the growth or fabrication of seinsulating epilayers or heterostructures. This extensionsemi-insulating materials into heterostructures was a natevolution, because the semi-insulating heterostructures wused in the traditional role as high-resistivity insulatingtransport blocking layers for electronic devices and lasBut new applications for semi-insulating heterostructuhave emerged that are unique to the heterostructures. Tinclude photorefractive quantum wells, which are hographic thin films in which self-adapting holograms canwritten that respond dynamically to changing light intenties. Related devices that rely on the semi-insulating propties of thin semiconductor films are photoconductive receers for laser-based ultrasound detection. In addition, thetechnique of low-temperature molecular beam epitaxyinaugurated a subclass of semi-insulating semiconductorterials that have extremely high intrinsic defect densitiThese low-temperature-growth~LTG! materials have gainedattention because of their ultrashort carrier lifetimes, whmake them useful for terahertz electromagnetic wave gention, ultrafast photodetectors, and as saturable absorbermode-locking lasers.

This review covers the full spectrum of properties auses for semi-insulating semiconductor heterostructuresthin films, beginning with the growth and processing of tfilms, including implantation, doping, and nonstoichiometgrowth. The principal optical and optoelectronic propertof semi-insulating epilayers and heterostructures, such ascitonic electroabsorption, are described. This is followed

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a discussion of the performance of optoelectronic hetestructure devices that incorporate semi-insulating layerspart of their structures, including heterostructure stripesers, vertical cavity surface emitting lasers, and optical etroabsorption modulators. This review also covers ultrafapplications that arise from the ultrashort carrier lifetimessemi-insulating materials, including ultrafast photocondutors, terahertz generation, and saturable absorbers for mlocking lasers. The properties and applications of photofractive heterostructures are comprehensively describethe last section.

II. FULLY COMPENSATED SEMICONDUCTORS

Fully compensated semiconductors are formed whedominant deep-level defect cancels the net charges fother defect and dopant levels. In this case the Fermi levepinned at an energy near the dominant deep level enewhich can be located in principal, anywhere within the bastructure. Only in the case when the Fermi level is pinnnear the middle of the band gap will the material haveminimum dark carrier density, and only in the case of semconductors with larger band gaps will the materialstrongly semi-insulating.

The most common defects used for intentional compsation are the transition metal defects.1,2 These are chosenbecause they are easily incorporated substitutionally intosemiconductor host, they produce both donor and accelevels, and there is a wide variety to choose from. The denergy levels for transition metals from the first row of tperiodic table are shown in Fig. 1 for several of the III–semiconductors.3 The figure is plotted to emphasize the iteresting and useful invariance of the transition metal enelevels among this class of homovalent semiconductors. Tinvariance has been used to predict heterostructure boffsets4–7 as well as to experimentally measure band-edhydrostatic deformation potentials.8,9 The donor and acceptolevels show clear trends in their energy levels astransition–metal ion progresses from Ti through Ni. Ttransition metal Mn is a special case, because it has a hoccupiedd shell that makes it more stable than the oth

FIG. 1. Transition–metal energy levels in the III–V semiconductors GGaAs, and InP. The levels are plotted to show the relative band offsets~Ref.3! among these isovalent semiconductors.

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6261J. Appl. Phys., Vol. 85, No. 9, 1 May 1999 Appl. Phys. Rev.: David D. Nolte

ions. The Mn ions are also the most important constituenfor the study of semimagnetic semiconductors among tII–VI semiconductors.10

An alternate approach to the formation of fully compensated semiconductors is the use of radiation or implant daage. Damage of almost any kind leads to the formationdefects within the semiconductor characterized by danglibonds. As increasing densities of these deep defects are pduced by radiation, the Fermi level moves within the bangap. An important property of many semiconductors is thnearly universal convergence of the Fermi level to the Ferlevel stabilization energy11 of a given material, independentof the type of radiation. This convergence to a universenergy can be explained through an autocompensatmechanism, in which the energies of the dangling-bond dfects lie within a band of energies centered on the averadangling bond energy in that specific material. The defecinclude both donors and acceptors, which compensate eother. The Fermi level stabilization energy of several of thcommon semiconductors is shown in Fig. 2. Like Fig. 1, thplot emphasizes the similarities across the disparate matals, which allows the stabilization energy to be used to prdict heterojunction band offsets.

A less common compensation mechanism is the copensation of charge around small metallic precipitates. Theprecipitates can be formed through implantation of metions, followed by annealing,12–15 or can be formed directlyby molecular beam epitaxy at low substrate temperatures flowed by annealing.16–19The metal inclusions act as internaSchottky contacts that deplete charge of either sign inspherical depletion region.20 It has also been shown thatvoids can compensate charge in a manner completely anagous to the metal precipitates,21 and illustrates the universalcharge-compensation capability of any internal semicondutor interface that leaves states unfilled. A complication in th

FIG. 2. Characteristic Fermi level pinning energies in several semicondutors showing Schottky pinning energies, charge-neutrality levels, and Felevel stabilization energies~Ref. 11!.

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interpretation of the compensation mechanism in nonsichiometric ~LTG! GaAs is the presence of high concentrtions of arsenic antisites. These defects are deep donorscompensate acceptors in a manner similar to bulk seinsulating GaAs:EL2. However, the LTG materials showevolution of compensation properties from the defect limitas-grown or weakly annealed materials, to metallic prectates in more strongly annealed materials. The detailsLTG materials and their compensation mechanisms arescribed in Sec. III C.

Fully compensated materials are sometimes erroneolabeled as ‘‘intrinsic’’ because the Fermi level rests nearmiddle of the band gap, where it would occur in the textbocase of an intrinsic semiconductor without defects. Howevthis word is misleading because Fermi levels in all semicductors~at usual temperatures! are pinned by the compensation of donors by acceptors, or vice versa. Furthermospace-charge effects and carrier lifetimes in fully compsated semiconductors are far different than the propertiestributed to intrinsic semiconductors. Therefore, the use ofterm intrinsic is discouraged when referring to highly compensated materials.

III. SEMI-INSULATING EPILAYERS ANDHETEROSTRUCTURES

A. Ion implantation of heterostructures

Heterostructure devices and materials are typically oseveral microns thick. This thickness is compatible with iimplantation ranges for many ion species. Therefore, hetstructures are uniquely suited for the use of ion implantatto produce compensated semiconductor material. This cadone by implantation of compensating dopants, or by dirradiation damage through the implantation of ions suchoxygen or hydrogen.

1. Proton implantation

It was discovered in 1966 that proton bombardmentGaAs produces high resistivity material,22 but the first prac-tical application did not occur until 1969 when it was usedisolate junction devices based on the ability to convert bn- and p-type conducting material23 to high resistivity.Shortly thereafter Dymentet al.demonstrated the use of proton implantation to form the narrow current-confinemestripes needed for low-threshold-current diode laser24

These initial discoveries and applications of proton iplanted GaAs were followed by extensive studies ofelectronic25–28 and optical29,30 properties. Proton implantation has been commonly used for optoelectronic applicatisuch as buried heterostructure diode lasers, vertical casurface emitting lasers, photorefractive quantum wells,ultrafast photoconductors, all of which are discussed in lasections in this Review.

Proton implantation compensates residual impuritthrough two effects. First, the knockout atoms and vacanproduced during the implantation have dangling bonds tcompensate charge of either sign. Second, the protons~hy-drogen! can passivate shallow dopants by forming neutcomplexes with shallow acceptors or donors.31 Compensa-tion by radiation damage is the dominant mechanism wit

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the implant range of the proton, while hydrogen passivatiwhich is a considerably weaker effect, can extend sevmicrons deeper into the material, especially after weaknealing at 300–600 °C.32 This extended diffusion of hydrogen into the device can have important consequencesoptoelectronic applications.33 Details concerning the range oprotons and the degree of damage produced depend on dand dose rates, as well as on the temperature of the deduring implantation.28 For instance, cold implants are moeffective in producing compensation than room-temperaimplantation by nearly a factor of two.

The range for proton implantation into GaAs is shownFig. 3 as a function of proton energy, along with longitudinstraggle, calculated using the software packageTRIM.34 Foran implant energy of 175 keV, the proton range is 1.3mmwith a longitudinal straggle of 0.2mm. The density profile ofvacancies produced by 175 keV protons is shown in FigOn average, there are about 40–50 vacancies produceimplanted proton. Many of these vacancies recombineform neutral complexes, leaving only a fraction of the radtion damage to compensate shallow dopants. Proton imptation studies inton-type GaAs have shown that protons wian energy in the range of 150 keV remove approximatthree conduction electrons per proton.35 Implantation intop-type GaAs requires a higher dose by approximately a

FIG. 3. Range and longitudinal straggle for proton and oxygen implantGaAs calculated usingTRIM simulator~Ref. 34!.

FIG. 4. Vacancy density profile for 175 keV proton implantation into GaA

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Compensation by radiation damage can be removedthermal annealing. The conductivity in dopedn- andp-typeGaAs and AlGaAs can be recovered using annealing tperatures of 600 °C or higher, although the recovery teperatures vary with dopant species and concentrations.29,36Inthe p-type materials, the final resistivity after recoverytypically smaller by about a factor of five than before implantation. Because radiation damage can be removed bynealing at sufficiently high temperatures, this preventsuse of high-temperature processing stages for proton-isoldevices after the implantation step. This restriction hdriven the search for other implanted ion species thatretain their compensating properties even after annealOne of these alternative choices is oxygen implantation.

2. Oxygen implantation

Oxygen implantation into GaAs and AlGaAs sharsome similarities with proton implantation. For instance aimplanted materials are highly resistive because of radiadamage, which anneals away above 600 °C, but after htemperature annealing the mechanisms for compensaspace charge are different. While hydrogen is mobile, apassivates shallow dopants by forming neutral complexoxygen is thought to be relatively immobile and to produthermally stable deep levels that compensate charge fshallow dopants. Favennecet al.37 first reported the forma-tion of high resistivity GaAs by oxygen implantation. It warecognized quickly that the doping effects and higtemperature stability38 made these implants superior to prton implantation for certain optoelectronic applications fwhich device lifetimes were critical issues, such as hetejunction diode lasers.39 Because of the larger mass of oxygecompared with the proton, significantly larger implant engies are needed to penetrate into heterostructures. Fostance a range of only 0.3mm requires an implant energy oapproximately 200 keV. The higher energy and mass acontribute to many more knockout atoms per ion thanprotons.

Studies that compare oxygen implantation into AlGawith implantation into GaAs have found that oxygen implatation of n-type GaAs does not produce thermally stabsemi-insulating material, but that implantedn-type AlGaAsdoes form stable semi-insulating material, possibly by foring AlO defect complexes that act as electron traps.40

3. Transition metal implantation

An alternative to oxygen implantation~which relies ondefects of unknown identity to compensate charge! is directimplantation of impurities to produce known deep leveThe transition metals present a wide variety of optionsion implantation, and produce stable deep level defects wincorporated substitutionally in the lattice. One of the mothoroughly studied transition metal implants is iroimplanted InP because of the technological importanceInP:Fe for optoelectronic devices that operate at wavelenbeyond 1mm.

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High-resistivity layers inn-type InP produced by Fe implantation were first demonstrated by Donnelly aHurwitz.41 After annealing at 725 °C for 15 min, the matericould reach a resistivity greater than 13107 V cm. Thedepth of the implanted region was noted to be greater tthat predicted by implantation theory, indicating that Fe dfused into the substrate during annealing. Detailed studiethe implanted and annealed materials showed that implation at room temperature with a dose of 1014cm22 lead toamorphitization of the implanted layer. The layer couldrecrystallized by annealing, but produced a pileup of irand extended defects at the amorphous–crystainterface.42 Implants with the substrate held at 200 °showed that the InP remained crystalline and preventedhomogeneous Fe distributions after annealing.43 This workformed the basis of a novel buried heterostructure InGaAInP laser that employed a buried Fe implanted layer for crent confinement.44 Extensive studies of related diode strutures containing an Fe-implanted layer were madeunderstand charge transport issues in these structures.45,46

B. Compensated doping during epitaxy

Epitaxial growth techniques offer unprecedented conover the introduction of impurities into semiconductor marial. All the epitaxial growth processes~excluding liquid–phase epitaxy! occur far from equilibrium. This makes ipossible to incorporate impurities at concentration levelscould not be sustained in equilibrium. In addition, it is retively easy to introduce dopant precursors into the growprocess, as in the use of transition–metal organic precurin metal organic chemical vapor deposition~MOCVD!growth. It is therefore possible to directly grow compensasemiconductor materials during the epitaxial process itse

Because of the importance of semi-insulating materfor III–V integrated circuits and optoelectronic devices, tfirst growth of semi-insulating InP using MOCVD in 198represented a significant breakthrough.47,48 This wasachieved using ferrocene as the dopant source, with msured resistivities approaching 23108 V cm. Space-chargelimited currents were observed in this material for fields o104 V/cm.48

After this first demonstration, the regrowth of seminsulating InP as the current–confinement layers of burheterostructure lasers became one of the standard laserrication procedures. The high-resistivity layer replacreverse-biasedp-n junctions as the current blocking layersthese lasers, giving smaller parasitic capacitance resultinhigher modulation bandwidth. An extensive literature hasscribed many aspects of the growth and tailoring of seinsulating layers as current blocking layers in lasers. Hoever, Fe-doped InP loses its semi-insulating character udouble injection of electrons and holes, which degrades laperformance. Therefore, alternative semi-insulating layhave also been explored for the buried heterostructure laFor instance, compensated epilayers of InP incorporatinghave been grown using the MOVPE technique.49 This workfollowed earlier work that used MOVPE to grow Cr-dopeGaAs.50 Deep donor concentrations up to 331016cm23 in

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Molecular beam epitaxy~MBE! has been used to growtransition–metal-doped semi-insulating epilayers. Forample Cr-doped GaAs/AlGaAs photorefractive quantuwell structures were grown by MBE.52 For the photorefrac-tive application, very high concentrations of deep carrtraps are needed. MBE has also been used for extremelydoping of GaAs with Fe, leading to the spontaneous formtion of Fe3GaAs precipitates.53 These metallic~and mag-netic! precipitates share some properties in common wintrinsic precipitates of arsenic in nonstoichiometric GaAs

C. Nonstoichiometric growth of heterostructures

The pursuit of semi-insulating III–V heterostructures aquired a new tool in the arsenal of growth and processtechniques when it was discovered that nonstoichiomearsenic-rich GaAs can be semi-insulating. Epitaxial growtechniques are inherently far from equilibrium, makingpossible to grow materials with no bulk analog. In the caof MBE growth of GaAs, lowering the substrate temperatuduring growth causes excess arsenic to be incorporatedthe lattice as arsenic antisite defects and as gallium vacies. Under high-temperature annealing, the excess arsforms semimetallic precipitates. These point and semimelic defects can compensate charge from shallow dopants~andfrom each other! and render the material semi-insulatinthrough a complicated interplay of compensation mecnisms. Nonstoichiometric materials have therefore beenimportant new addition to the list of MBE materials for botheir technological importance, as well as their interestphysical behavior.

1. Low-temperature-grown GaAs

The growth of high-quality GaAs by MBE is typicallyperformed on substrates held at a temperature near 60but there is a long history of MBE at lower substrate teperatures. Low-temperature conditions lead to the growthpolycrystalline material, with some early notable exceptioIn 1978 Murotaniet al.54 discovered that MBE growth oGaAs at substrate temperatures near 400 °C producestalline GaAs that was semi-insulating. Growth of excellequality GaAs at even lower temperatures down to 200was shown to be possible using a modification of MBcalled ‘‘migration enhanced epitaxy.’’55,56The MEE materi-als had superior optical performance compared with ordinMBE materials, but were not semi-insulating. Lowtemperature growth of semi-insulating material gained atttion with the work by Smithet al.57 who found that backgat-ing of metal–semiconductor–field-effect transist~MESFET! devices could be eliminated when grown on LTGaAs. This launched considerable activity in the study ofmaterial and its potential applications. A complete overviof work on LTG materials can be found in Ref. 58.

Low-temperature-grown GaAs is nonstoichiometric wan excess of arsenic that is taken up by point defects inas-grown materials.59 The most common point defects a

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the arsenic antisite defects AsGa, arsenic interstitials Asi , andgallium vacanciesVGa. The arsenic antisite defects are simlar ~or identical! to the so-called EL2 electron trap in GaAand the defect properties observed in LTG materialssimilar to the known properties of EL2.60,61For layers grownat 200 °C, the as-grown antisite concentrations are apprmately 1019cm23.62 The gallium vacancy concentrationlower by approximately a factor of 10 for this growttemperature,63 but is still far above equilibrium values, leading to interesting annealing behavior.64,65 The presence ogallium vacancies in LTG GaAs has extremely importaconsequences in terms of device thermal stability and oating lifetimes, because the vacancy is mobile and isdominant mechanism for superlattice intermixing as wellimpurity diffusion. The high as-grown vacancy concenttions in LTG materials lead to transient enhanced diffus~described in Sec. III D 2! which can degrade optical anelectronic device performance.

It was discovered by Mellochet al.16 that the excessarsenic formed precipitates when LTG GaAs was annealetemperatures above 600 °C. The precipitate size distribuwas not homogeneous, but did have well-defined aversizes and spacings that increased with increasing annetemperature and times. Subsequent studies of the precition process showed that it could be controlled with a hdegree of specificity, leading to the term ‘‘precipitaengineering.’’66 For instance, the precipitates were foundnucleate and grow more readily in GaAs than AlGaAs,67 andin n-type material than inp-type material.17,67,68By combin-ing different doping and compositional layers in a hetestructure, and by controlling the growth and annealtemperatures,69 the precipitates could be induced to growonly in selected regions or planes. The presence of thecipitates in annealed LTG GaAs changes the electronicoptical properties of the material.

2. Nonstoichiometric quantum wells

The growth of quantum well structures at low substrtemperatures has been developed since the mid-1980’s.initial growths were performed at low substrate temperatudown to 200 °C using migration enhanced MBE in which Gor Al atoms are evaporated onto a clean GaAs surface inAs-free atmosphere.55,56,70 The atoms are mobile down tlow temperature, and migrate across the growth surface.produces high-quality materials that remain stoichiometricspite of the low growth temperature. The good stoichiomeof the material is also indicated by the insensitivity of tquantum wells to annealing up to 800 °C.71 In nonstoichio-metric quantum wells grown by MBE at low temperaturethe quantum wells intermix rapidly because of high grownvacancy concentrations.72

The first study of optoelectronic properties of nonsichiometric quantum wells grown at low substrate tempetures was performed by Knoxet al.73 The AlGaAs/GaAsquantum wells were grown at 300 °C and exhibited broened excitonic resonances. With annealing, the excitotransition broadened further and shifted to higher energyAlAs/GaAs multiple quantum wells grown at 310 °C rel

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tively sharp excitonic features were observed in the as-gromaterials.74,75 This material was semi-insulating and showexcellent quantum-confined Stark effects74 that were usefulfor photorefractive quantum well applications.76–79 Theproperties of LTG quantum wells continues to be an areaactive research,80,81 and in particular the diffusion propertieunder annealing have attracted attention because ofstrong transient enhanced diffusion exhibited in thematerials.72,82–84

3. Optical and electro-optic properties of LTGmaterials

Nonstoichiometric GaAs and related materials have hdefect densities of a variety of species, includiVGa, Asi , AsGa, as well as arsenic precipitates. All these dfect and precipitate species influence the optical propertiethe material. As the material is increasingly annealed,concentrations of point defects decrease while the sizespacing of the arsenic precipitates increase.17 These trendsare reflected in the optical properties of the material. Becaof the great variety of species and the different time depdencies, unraveling the specific contributions to the optiproperties by each species is a challenging task thatcaused some discussion and controversy in the literature.presence of defects and precipitates directly influencesabsorption and refractive index of the composite LTG marial. These primary properties, in turn, are involved in seondary effects, such as sub-band-gap photoconductivity,citonic electroabsorption, and resonant optical nonlinearit

The optical absorption of as-grown LTG materials hastrong extrinsic contribution both below and above the bagap. The spectrum of the absorption below the bandshows striking similarities to the absorption spectrum ofarsenic antisite AsGa, which has been attributed to the defelevel EL2. Some differences are found between the Lspectrum and the EL2 spectrum, but these may be accoufor by the stronger perturbations that exist in the LTG marials compared to semi-insulating LEC GaAs.85 Using near-infrared absorption calibrated to the EL2 defect86 and mag-netic circular dichroism87 it is possible to quantify theconcentrations of neutral@AsGa

0 # and charged@AsGa1 # in the

LTG materials.62 In samples grown at 200 °C, this studfound initial concentrations of@AsGa

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0 #5331018cm23 and@AsGa

1 #5331017cm23. The concentration of ionized AsGa istherefore approximately an order of magnitude smaller ththe concentration of the neutral species. This makes a stargument that the Fermi level is pinned by the arsenic asite defects in as-grown materials. With increasing anneing, both concentrations decrease with an activation enebetween 1.3 and 1.4 eV. These optical techniques losesitivity to the defect concentrations for annealing abo600 °C, which is expected to be the crossover temperafrom defect-dominated compensation to precipitadominated compensation mechanisms.

The absorption spectrum below and above the bandis shown in Fig. 5 for a sample grown at 250 °C and anneaat successively higher annealing temperatures from 40

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600 °C for 1 min.88 The initial excess absorption is greatthan 15 000 cm21, but decreases rapidly with increasing anealing as the arsenic antisite concentration decays. Cobutions to the refractive index have also been studied afunction of growth and annealing89,90 using ellipsometry andFabry–Perot oscillations. The defects make a positive ctribution to the refractive index by as much asDn50.25 atthe band gap at 870 nm, but decrease the refractive indeapproximately the same amount at theE1 critical point near450 nm.

As the point-defect density is reduced with increasannealing, semimetallic arsenic precipitates becomedominant source of extra absorption in LTG GaAs. Theclusions represent a heterogeneity in the complex dielecfunction of the material, leading to characteristic absorptthat is unrelated to photoionization of point defects. A meinclusion in a dielectric will absorb light because of the ecitation of electric current in response to the electromagnfield. This effect is classical, and can be viewed as enedissipated through joule heating. Semiclassically, the lighabsorbed by surface plasmons that are~in principle! observ-able as Fro¨hlich resonances in the absorption spectrum.91,92

In the case of arsenic precipitates, the inclusions are osemimetallic, and the Fro¨hlich resonance is severely broaened by the large imaginary component of the complexelectric function of arsenic. This leads to a very broad afeatureless absorption spectrum that extends above andlow the GaAs band gap.93 An interesting challenge is to distinguish between the sub-band-gap absorption due to pretates, and the absorption due to photoionization of podefects, because both lead to sub-band-gap absorption. Ispecial case of silver precipitates in Ag-implanted AlGaAthe Frohlich resonance can be large and sharp because sbehaves almost like a free-electron metal but the resonawill only be observable if the precipitates are nearly sphecal in shape.93 The size and shape distribution of experimetally observed Ag precipitates has been found to be nonform, again leading to a featureless absorption spectbelow the band gap.15 It is important to note that althougthe arsenic and silver precipitates both lead experimentallqualitatively similar absorption spectra, the origins are dferent. The absorption in the case of the arsenic precipit

FIG. 5. The absorption coefficient of LTG GaAs~grown at 250 °C! for 1min annealings at increasing temperature~Ref. 8!. The absorption of a GaAsreference sample is shown for comparison.

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is homogeneously broadened, while the absorption incase of silver precipitates is inhomogeneously broadenThese differences should therefore be accessible to optechniques that differentiate between homogeneous andhomogeneous broadening, such as photon echo techniquspectral hole burning.

In addition to energy dissipation by joule heating, italso possible to observe photoemission of electrons fromarsenic precipitates. This is a quantum–mechanical prothat generates photoconductivity for light below the bagap. This effect has practical application for use as an extsic photoconductor. The photoemission properties of arseprecipitates have been studied in GaAs94 as well asAlGaAs95 in p- i -n diode structures. The wavelength anvoltage dependence of the photocurrent is consistent withemission barrier given by the energy separation of the Felevel in the precipitates from the conduction band edge.

Excitonic electroabsorption caused by the FranKeldysh effect96 has been studied in LTG materials in tranverse geometries with coplanar metal–semiconductor–m~MSM! contacts with wide gaps97 and with interdigitatedelectrodes.98 In samples of LTG AlGaAs annealed at 750 °for 30 s, the excitonic electroabsorption showed a stroasymmetry and an enhancement relative to an AlGasample grown at ordinary temperatures. The electroabstion spectra are compared in Fig. 6. The enhanced electrsorption in the LTG materials has been attributedtransport-driven charge accumulation on the precipitawhich produce strongly inhomogeneous local electric fiearound the precipitates.99,100 The electro-optic effect in theLTG epilayers has been used for a demonstration of hographic storage with small pixel size in thin epilayers.101 Thehigh resistivity of annealed LTG materials has also madpossible to study the polarization dependence of the FraKeldysh effect under high fields in thin samples of GaAs.102

Franz–Keldysh oscillations are still observable in the LTmaterials despite the broader excitonic linewidth, althousamples with a weak annealing at 600 °C for 1 min did nshow significantly enhanced electroabsorption.

As described in Sec. III C 2, it has been shown that qutum wells with sharp excitonic features can be grown at l

FIG. 6. Electroabsorption spectra in response to a dc electric field okV/cm that was applied across coplanar contacts for standard-temperand low-temperature grown Al0.2Ga0.8As ~Ref. 97!.

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temperatures,74 providing fast photoconductive materiawith good quantum-confined Stark shifts. When used inp- i -n structure~with mild in situ annealing at 450 °C for 24min during the growth of the topp layer!, the device showsan excellent quantum-confined Stark effect. However, wincreasing annealing, the electroabsorption quickly degraas shown in Fig. 7. The rapid broadening with increasannealing is much more pronounced than for stoichiomequantum wells. This enhanced broadening is caused bysupersaturated concentration of group III vacancies inLTG materials that causes transient enhanced diffusion innonstoichiometric quantum wells.

D. Transient enhanced diffusion in nonstoichiometricquantum wells

1. Gallium vacancy migration

The diffusion of gallium vacancies is suspected to bedominant self-diffusion mechanism in GaAs accountingthe migration of group III elements. Gallium vacancies mgrate only on the gallium sublattice, and do not communicwith the arsenic sublattice.103 Vacancy diffusion is particu-larly effective for inducing intermixing of heterojunctions iheterostructures or superlattices. For example, when a gIII vacancy migrates on its sublattice and passes througheterojunction interface between GaAs and AlAs, a galliand an aluminum atom swap places. Successive passvacancies across the interface produce a continuous imixing, drawing aluminum into the GaAs and gallium inthe AlAs. Considerable literature on quantum-well interming has documented this process.104,105Differences betweenthe migration probabilities of group III vacancies in GaArelative to AlAs can produce nonlinear diffusion profiles bcause of the dependence of the diffusion coefficient on ccentration. However, experiments on isotopic superlattihave helped quantify the equilibrium properties of galliuself-diffusion in stoichiometric GaAs free of concentratiodependent effects,106 establishing the equilibrium diffusionproperties of GaAs with a high degree of certainty.

FIG. 7. The quantum-confined Stark effect in LTG AlAs/GaAs multipquantum wells vs annealing temperature for 30 s~Ref. 74!.

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2. Nonequilibrium intermixing

In low-temperature-grown heterostructures the mateis produced far out of equilibrium, and in addition to thexcess arsenic that is incorporated in the material, theralso a deficiency of group III atoms, leading to a supersarated concentration of group III vacancies, such as thelium vacancyVGa. The concentration of gallium vacanciein LTG materials has been calibrated against growth teperature using positron annihilation spectroscopy,63 shown inFig. 8. This excess concentration of vacancies produces lenhancements in the interdiffusion of quantum wellsmany orders of magnitude relative to equilibrium diffusio

The first indication of enhanced diffusion in LTG quatum wells was found in the quantum-confined Stark effecLTG AlAs/GaAs quantum wells annealed at successivhigher temperatures between 600 and 900 °C.82 In addition tothe broadening of the quantum-confined excitons due toterface roughening, which had been noticed previousl73

there was also a shift to higher energy for the excitonic trsition. This was caused by the diffusion of aluminum into tGaAs wells, which increased the average band gap.

The enhanced interdiffusion of LTG quantum wells dgrades the performance of devices in some applications.instance, laser diode structures that have incorporated sLTG layers showed enhanced intermixing degradation oflaser junction.107 Additional aspects related to the perfomance of electroabsorption modulators and photorefracquantum wells have been discussed in the literature.73,74,77,84

Related observations of anomalous diffusion of gallium habeen made in arsenic-deficientGaAs, produced at the surfacby laser annealing.108

The annealing-induced band-gap shift in the nonsichiometric quantum wells was several orders of magnitularger than the shifts induced by equivalent annealing in sichiometric superlattices. Furthermore, the dependence oenhanced diffusion on temperature was anomalously smproducing a small effective migration enthalpy for the intemixing process that did not at first appear to be consiswith the migration enthalpy for vacancy diffusion.82 None-

FIG. 8. Gallium vacancy concentration vs growth temperature in LTG Gaobtained from positron annihilation measurements~Ref. 63!.

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theless, subsequent studies have explained the small etive migration enthalpy for intermixing in LTG quantumwells in the context of the transient decay kinetics of texcess vacancy concentration as it relaxes to equilibrium

3. Transient decay of supersaturated vacancyconcentration

The time-dependent decay of the excess vacancycentration in LTG materials can take many forms. Forstance, if the formation of divacancy complexes is the donant decay mechanism, then the decay would show secorder kinetics. Similarly, if the vacancies are annihilatedarsenic interstitials to form arsenic antisites, or if the vaccies form complexes with other point defects, then the dewould not be single exponential, but would exhibit stretchexponential behavior as the concentrations of all defectscrease with increasing annealing. On the other hand, mthermodynamic relaxation processes do approximate siexponential behavior. In the case of single exponentialcay, the time-dependent diffusion length is

LD2 ~ t !5D0t exp@2~H f1Hm!/kBT#1D1ta

3exp~2Hm /kBT!@12exp~2t/ta!#, ~1!

whereH f andHm are the formation and migration enthalpiof the vacancies, respectively, and the annihilation timethe excess vacancy concentrationta is also assumed to bthermally activated by

1/ta5na exp~2Ha /kBT!, ~2!

whereHa is the annihilation enthalpy andna is the attemptrate for annihilation of a vacancy. For long annealing timthe second term in Eq.~1!, which describes the enhancemedecays to zero, leaving the equilibrium term.

A strong case can be made forHa5Hm in Eq. ~2! be-cause a vacancy must first migrate in order to annihilaUnder this condition, the effective migration enthalpy cvanish, leading to a diffusion process that appears atherwhich was observed experimentally in the enhanced dision of the LTG quantum wells.72,82 Detailed studies havebeen performed on the transient enhanced diffusion in Lquantum wells using phototransmittance experiments.diffusion data are shown in Fig. 9 compared with the theretical curves from Eq.~1!.109 For high-temperature anneaing for long times, the transient behavior relaxes to the eqlibrium diffusion coefficient. At short annealing times anlow temperatures, the curves asymptotically approacslope given by the vacancy migration enthalpy. At intermdiate temperatures, the data fall on a family of isochrocurves. The small slope in this intermediate regime is a csequence ofHa'Hm .

IV. OPTOELECTRONIC SEMI-INSULATINGHETEROSTRUCTURES

Many heterostructures laser and modulator architecturequire high-resistivity regions to confine current to specifiareas, or to isolate devices or parts of devices from oneother. Therefore, the growth or formation of semi-insulati

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layers in optoelectronic heterostructures has played anportant role in the history and ongoing development of thdevices.

A. Heterostructure stripe lasers

The goal of practical in-plane heterostructure lasersigns is to laterally confine current, carriers, and photoThis is achieved most readily in stripe laser geometrieswhich a narrow strip of active region defines the laser axThe narrow strip can be formed using many different aproaches, some of which use semi-insulating materials. Seral stripe laser designs are shown in Fig. 10, including seinsulating,p-n blocking layer structures, and simple oxidstripe. The oxide is usually SiO2 that confines the current toa small strip near the top contact. The oxide stripe laserlateral current confinement, but no charge or photon confiment, making its commercial value limited. Implanted strilasers use ion implantation to form semi-insulating regio

FIG. 9. Transient enhanced diffusion coefficient in LTG AlAs/GaAs quatum wells for an array of isochronal and isothermal annealings, plottedthe square of the diffusion length divided by the annealing time~Ref. 109!.

FIG. 10. Stripe laser geometries showing semi-insulating,p-n reversedjunction and oxide stripe structures.

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that extend to thep-n junction on either side of the stripeProton or oxygen implantation has been used in this geetry. Protons produce semi-insulating material throughintroduction of radiation damage, which is not stable unhigh-temperature annealing, and which can migrate toactive region during long-term operation of the laser. Onother hand, oxygen implantation in AlGaAs forms seminsulating material that is stable even for annealing o600 °C. Oxygen can also be used to induce superlatticeordering in the implant region by postimplant annealingprovide lateral optical confinement as well as charge confiment.

Much stronger optical and charge lateral confinemcan be achieved in buried heterostructure~BH! lasers. Buriedheterostructure injection lasers have filamentary activegions that are completely buried inside a higher-band-semiconductor material, producing an optical waveguideometry that has both excellent current and opticonfinement.110 Much of the development of buried heterstructure lasers has focused on the design and fabricatiothe blocking layers on either side of the stripe to have lcapacitance and low leakage currents.

The most common approach to producing a currblocking layer is to incorporate reverse-biasedp-n junctionsin the blocking layer. However, these junctions can be leand allow current to flow along the edge of the active laaround thep-n junction, especially at high power. Furthemore, the reverse-biased junction has a high capacitancecontributes to the total capacitance of the laser, limitmodulation speeds. An alternative material approach toproblem of the blocking layer has been to regrow seinsulating materials around a stripe mesa to form a plastructure. The semi-insulating planar buried heterostruc~SI-PBH! lasers have high resistivity, and do not suffer froserious junction capacitance. These advantages have lethe development of semi-insulating-embedded buried hetstructure lasers in both AlGaAs/GaAs devices and InP-balonger-wavelength devices.

1. GaAs-based heterostructure stripe lasers

Proton implantation was used among the earliest currconfinement stripe laser geometries to electrically isolatelaser and to confine the current to a narrow stripe.24,111,112

The proton implantation was convenient, produced hiresistivity materials, could be performed after all growsteps to prevent annealing of the radiation damage, and cdefine stripe widths below 10mm. It became one of thestandard fabrication techniques for early double heterostture lasers, and produced lasers with acceptable threscurrents.113–115Optimal performance was achieved by reduing the proton implant range to use only the tail of the iplant distribution to reach to the active junction.116–118How-ever, these DH lasers had no lateral charge confinement119 oroptical confinement, which kept threshold currents relativhigh, and long-term operation of the lasers could causeimplantation damage to migrate, leading to decreased califetimes in the active region, and ultimately to devicfailure.

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Replacing proton implantation with oxygen implantatioincreased the operating lifetime of the implanted stripe lasby removing the reliance on mobile defects, such as vaccies, to form semi-insulating material. Oxygen implantatiinto n-GaAs and AlGaAs produces semi-insulating materthat remains semi-insulating after annealing abo600 °C.38,40 The first demonstration of an oxygen-implantestripe laser was made by Blumet al.39 The oxygen-implanted stripe lasers showed early improvements in thmal resistance over conventional SiO2 current-confinementgeometries.120 Later refinements led to significant reductioin threshold currents of oxygen-implanted devices compawith conventional oxide geometries.121 Figure 11 shows thelight power–current (L – I ) curve for two identical 10-mm-stripe structures, one with SiO2 confinement, and the othewith oxygen-implant confinement. In addition to the curreconfinement effects of the semi-insulating implant regiothe improvement was also attributed to compositional disdering that provided lateral charge and optical confinemeThe improvement in oxygen-implanted stripe lasers wstudied as a function of stripe width.122 It was found thatoxygen doses that were necessary to produce disordeand therefore optical confinement, produced detrimentalfects for lasers with stripe widths less than 5mm, such as themigration of the implant damage into the active stripe.

BH lasers have superior lateral confinement for currecharge, and photons relative to the implanted laser structbecause the blocking layer can have a significantly higband gap than the active region. In addition to better confiment of current and charge, the higher band gap has a lorefractive index, and produces strong index guiding. A bied heterostructure GaAs/AlGaAs laser was demonstrateTsang and Logan by forming the blocking layer using Gdoped Al0.65Ga0.35As regrowth by liquid–phase epitaxy.123

Ge-doped AlGaAs is highly resistive124 and forms a high-gapcurrent blocking layer. Subsequent BH laser growths wperformed using MOCVD125,126and MOVPE.127 In the caseof MOCVD, the semi-insulating AlGaAs layer was grown breducing the reactor pressure and increasing the Vratio.126

FIG. 11. L – I curve for SiO2 stripe laser compared with oxygen-implantelaser~Ref. 121!.

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2. InP-based buried-heterostructure stripe lasers

Buried heterostructure diode lasers that operate at wlengths beyond 1mm are commonly based on InP technoogy. Examples of these heterostructures include the lband-gap materials InGaAs/InP and InGaAsP/InP. The loband gaps allow higher thermal leakage currents in Ibased devices, which leads to high threshold current,differential quantum efficiency, abnormal temperaturependence of the threshold current, and rollover of the ligcurrent characteristic. These problems place severe reqments on the blocking layers in the long-wavelength burheterostructure designs. In addition, ion implantation canrender these materials semi-insulating~as demonstrated inFig. 2!. The radiation damage produces a self-compensset of defects that pin the Fermi level near the conducband. Therefore semi-insulating blocking layers mustgrown or fabricated postgrowth through implantation.

The first InGaAsP buried heterostructure using seinsulating current confinement was fabricated by Fimplantation inton-InP.44 The implantation, followed byhigh temperature annealing, produced material with a retivity as high as 108 V cm.41 The single-channel device usein situ annealing after the implantation and before the fiLPE regrowth. Detailed studies were made of the roletransport in the implanted layer and how it affected the traport properties of the laser.45 But the Fe-implantation depthwas limited to only 0.3mm using two implant energies o275 and 400 keV, giving the devices only moderate bredown voltages.

Devices with higher breakdown voltages were achievby selectively regrowing semi-insulating InP into thickblocking layers. The first demonstration of a semi-insulatembedded buried heterostructure laser was made usingride VPE of InP without iron,128 which attained resistivitiesof 104 V cm in the blocking layer. The device consisted oplanar structure that is compatible with circuit integratioand exhibited low parasitic capacitance. Successive devwere fabricated using selective regrowth of Fe-dopedwith MOCVD,129–131and MOVPE.132–134

Extensive simulations of the current confinement charteristics of semi-insulating-embedded buried heterostruclasers have been performed for the semi-insulating Fe-doInP-based structures.135,136Despite the excellent low capactance in the structures, leakage currents could not be cpletely eliminated by the semi-insulating layers in simpgeometries. More complicated structures with additiofunctionality have lead to an extensive literature.

B. Vertical cavity surface emitting lasers

Vertical cavity surface emitting lasers~VCSEL! showpromise for laser optoelectronic systems because theythe potential for low thresholds,137 for integrability intodense two-dimensional arrays, and for their good mode qity for efficient fiber or free-space coupling.138 The firstVCSEL was fabricated in 1979 in the GaInAsP/Insystem,139 but serious progress was not made in this technogy until the late 1980’s when the routine growth of higquality semiconductor Bragg mirrors became available.140

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Proton implantation for current confinement playedcritical role in the VCSEL development in much the samway as it had for current-confinement in stripe lasers. EaVCSEL designs used deep proton implantation to the aclayer to confine current in small active windows typical10–20mm in diameter.141–143As in the case of proton im-plantation for the stripe lasers, a chief concern in the protimplanted VCSEL is the effect of the radiation-induced dfects on the luminescence efficiency of the active regionwell as the effect on laser operating lifetimes because oflateral migration of the radiation defects. It was found thpostimplantation annealing~of a 1015cm22 proton implantwith energies up to 300 keV at 450 °C! for 150 s restored theluminescence intensity without removing the curreisolation.144 This annealing step was compatible with typicannealing steps for AuGeNi metallization processing comon in GaAs technology. However, proton-implanted devdegradation over long-term operation remained. Shalloproton implants were shown to remove part of the probleyielding devices that had predicted lifetimes greater th105 h at 10 mA at an ambient temperature of 40 °C.145 Againas in the case of the stripe lasers, alternative current isolaapproaches have been explored, including the use of mstable oxygen implantation.146

C. Optical modulators

Semiconductor optical modulator structures are ofclosely related to laser structures. They absorb light ratthan emit light. Therefore, the structures can draw from silar functions of semi-insulating material for current confinment or current reduction in lasers, as well as the formatof guided wave structures.

The semi-insulating regrowth processes that were deoped for buried-heterostructure lasers can also be usedelectroabsorption modulators. InP-based multiple-quantuwell buried-mesa electroabsorption optical modulators wfabricated by first growing a diode structure that was pterned into a mesa. The walls of the mesa were then buby selective regrowth of Fe-doped InP using MOCVD. Tuse of semi-insulating material reduced the parasitic captance and improved high-frequency performance up toGHz in an InGaAs/InP structure,147,148and up to 11 GHz ina GaInAsP/InP structure.149

Proton implantation contributed to improvementswaveguide and modulator structures by removing free caers from doped or optically excited GaAs. Optical waguides for 1.15mm light were fabricated by proton implantion around a stripe in GaAs.150 The implant damage removed carriers and reduced the refractive index. The hresistivity of proton-implanted GaAs heterostructures halso been used to form suppressed photocurrent opmodulators.151

A class of optoelectronic device that shares many ofcharacteristics of excitonic electroabsorption modulatorsthe photorefractive quantum well structures.152,153These de-vices rely on the same electroabsorption properties as insity modulators. However, unlike the modulators~that arereticulated using mesa etches or implant isolation! photore-

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fractive quantum wells are unreticulated broad-area seinsulating thin films that record holographic space-chagratings. These devices are described in detail in Sec. V

D. Semi-insulating heterostructures for ultrafastoptoelectronics

The high defect densities associated with semi-insulamaterials lead to short free-carrier lifetimes by providingficient nonradiative recombination pathways. The short crier lifetimes make these materials attractive for the genetion and detection of ultrafast ~picosecond andsubpicosecond! electromagnetic pulses by combining utrafast optical excitation with the ultrashort carrier lifetimin photoconductive circuits.

1. Picosecond free-carrier decay in films andheterostructures

The three photoconductive materials most commoused for ultrafast applications are implanted silicon-osapphire~SOS!, implanted GaAs and related multiple quatum wells, and LTG GaAs and related heterostructures. Eof these materials has reasonably good transport propecombined with fast free-carrier decay. The quantum well mterials have the additional useful property of large electoptic effects associated with quantum-confined excitons.

Silicon-on-sapphire exhibits decreasing carrier lifetimwith increasing doses of implanted oxygen.154 The lifetimesdecrease to as short as 600 fs for oxygen implantation dapproaching 1014cm22. Higher doses begin to degrade thmaterial transport properties, and do not significantly iprove the material speed,155 as shown in Fig. 12.

The carrier lifetimes of GaAs can also be brought inthe ps regime through implantation. The lifetimeshydrogen-implanted GaAs are shown in Fig. 12 as a funcof hydrogen implant dosage,156–158compared with the speedof SOS with oxygen implantation. It has also been possto achieve subpicosecond lifetimes in arsenic-ion implanGaAs.12 Implantation with MeV Ga and oxygen ions leadsps lifetimes and semi-insulating GaAs material,159 as doesthe use of neutron irradiation of AlGaAs/GaAs quantuwells.160 The relatively universal ability of radiation damagto create semi-insulating GaAs and related heterostruct

FIG. 12. Carrier lifetimes for oxygen-implanted silicon-on-sapphire~SOS!and proton-implanted GaAs~Refs. 155, 156, 157, and 158!.

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without strong dependence on the implant species is a simconsequence of the Fermi level pinning process illustrateFig. 2 in Sec. I. In all cases, the carrier lifetimes canreduced to approximately 1 ps under the highest doses.

Carrier lifetimes in LTG materials can be designed wconsiderable flexibility because it is possible to indepedently vary the excess arsenic concentrations, the intrindefect densities, and the precipitate sizes and densitievarying growth temperature, annealing times, and anneatemperatures. Carrier lifetimes in LTG materials below acosecond can be achieved with the incorporation of laexcess arsenic concentrations by growing at 200 °Cbelow.161–163 The combination of fast carrier lifetimes anhigh resistivity is achieved only after postgrowth annealinwhich is needed to reduce the hopping conduction inas-grown materials.

Several systematic studies have been performed to rethe carrier lifetimes in LTG GaAs to the amount of excearsenic incorporated in the material during low-temperatgrowth.164,165The lifetimes for 30 s isochronal annealing ashown in Fig. 13 as a function of annealing temperature fofamily of three different excess arsenic concentrations0.52%, 0.25%, and 0.02%.165 These arsenic concentrationare only moderate, leading to greater than ps decay timbut illustrate the importance of calibrating the excess arseconcentrations.

2. Ultrafast photoconductive switches andtransmission lines

As the speeds of electronic circuits continually increait becomes difficult to find traditional drive electronics thare fast enough to test the performance of the circuits. Alnate methods for the generation of fast electrical transiemust be used, such as combining ultrafast laser pulseselectronic photoconductive circuits to produce a hybrid otoelectronic technology.

Fast electronic switches generated by fast laser pucan be made using a simple photoconductive gap in acrostrip line that is illuminated by an ultrafast laspulse.166,167 The initial work was performed on bulk semconductors such as silicon, but it was recognized that s

FIG. 13. Electron free carrier lifetimes vs annealing temperature for LGaAs containing different excess arsenic concentrations~Ref. 165!.


FIG. 14. Ultrafast optoelectronic switches~a! Auston switch;~b! micro-stripline geometries;~c! coplanar stripline geometry;~d! sliding contact coplanarstripline.

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optical absorption depths of above-band-gap light madpossible to operate the switches using highly resistive ptoconducting thin films.168 The short recombination lifetimeof amorphous silicon deposited by CVD on fused silica wused to produce rapid relaxation of the switch. The low mbilities of amorphous silicon limited device speed, but improved performance was found using radiation-damasilicon-on-sapphire.154 The increasing speed of the photocoductive switches made it necessary to use optoelectrmethods to measure the electronic transient. These metincluded using a second photoconductive gap to performtoelectronic sampling,169 as well as using electro-optic crystals to sense the transient fields.170

The original configurations of the Auston switches168

used single strip lines on a substrate with a uniform grouelectrode on the bottom surface, shown in Fig. 14~a! withvariations on the microstrip geometry, shown in Fig. 14~b!.The propagation of picosecond pulses on these transmislines exhibited severe mode dispersion. To reduce the dission effects, coplanar striplines superseded the single sline designs.171 The coplanar strip lines, shown in Fig. 14~c!have negligible capacitance172 and less severe dispersioThese features make it possible for the device response sto depend only on the intrinsic properties of the photocducting material, rather than on the device geometry. Usthe coplanar strip lines, electrical transients with subpicosond duration were generated and detected.171,173 The incor-poration of a ‘‘sliding contact’’ coplanar strip line configuration, shown in Fig. 14~d! significantly increased theflexibility of ‘‘excite–sample’’ experiments173 by allowingthe excitation pulse to move. Additional excite–sample fleibility was made possible by using proton-implanted seminsulating multiple quantum wells as the photoconduct

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material,174 and using the built-in excitonic electroabsorptioto perform electroabsorption sampling.175

The development of low-temperature-grown~LTG!GaAs provided the optoelectronic switches with a matewell-suited for integration with high speed GaAs electroniThis advantage was recognized early after the developmof LTG57 material because it combined high mobilities wiultrashort lifetimes. Electrical transients with full width ahalf maximum ~FWHM! of 1.6 ps were generated fromphotoconductive gap and coplanar strip lines fabricatedLTG material.176 The high breakdown voltage of LTG materials has also been used for picosecond switching of hivoltage pulses exceeding 800 V.177

3. THz pulse generation and detection

The propagation of fast electrical transients on convtional transmission lines, including the coplanar strip linproduce significant distortion arising from dispersion afrequency-dependent losses. An alternative approach is fspace propagation of the electromagnetic transient by uphotoconductive switches as Hertzian dipoles to radiateelectromagnetic pulses directly into free space. The radiaelectromagnetic pulses could likewise be detected usingother photoconductive switch. A free-space electromagntransient with a 1.6-ps–pulse duration was successfully donstrated using silicon-on-sapphire as the photoconducthin film.178 The designs of the radiating and detectingpoles were further improved to produce single cycle trasients with a bandwidth of 2 THz.179 The ability to manipu-late and direct the THz transients was considerably advan

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with the introduction of THz optics.180,181 Additional en-hancements in the THz bandwidth were achieved usdefect-enhanced electric fields at the edge of the microsanode.182,183 The use of LTG materials in the antennas halso been demonstrated,184 and the LTG materials havlargely replaced implanted silicon-on-sapphire in recentplications. For instance, LTG materials were used as ultratransient mirrors to produce infrared ps pulses at a walength of 10.6mm.185

4. Metal –semiconductor –metal ultrafastphotodetectors

Ultrafast metal–semiconductor–metal~MSM! detectorsare formed by placing coplanar electrical contacts on seinsulating photoconductors. The contacts are usually indigitated to increase the device responsivity~by decreasingthe carrier transit time!, and to decrease the resistance, aare coplanar to reduce capacitance. The low capacitancelow resistance of the interdigitated MSM detectors ensthat the RC time constants are short and that the MSMtector speed is limited by either the carrier transit timor the carrier recombination time. These attributes makeMSM detectors attractive for optoelectronic applicatiosuch as communications, chip connects, and high-spsampling.186–190

In semi-insulating materials, recombination lifetimes cbe subpicosecond, producing ultrafast MSM photodetectThe initial fabrication of a 375 GHz bandwidth detector wiinterdigitated contacts on LTG GaAs191 launched a period odevelopment by many groups,192–196 with bandwidths ap-proaching a THz. Similar ultrafast detectors have been fricated using InP:Fe.197

E. Semi-insulating heterostructures for mode-lockingsolid state lasers

The significant flexibility in the properties of lowtemperature grown GaAs and related materials, especthe ability to tune carrier lifetimes by choosing growth aannealing conditions, has made the LTG materials key cponents in semi-insulating heterostructures for use in molocking solid state lasers. Ultrafast pulse formation in sostate lasers using only passive components requires fastlinearities such as saturable absorption. Carrier thermation in highly excited semiconductors has long been recnized as an important and fast nonlinearity~approximately100 fs relaxation time! that can be used for passive molocking. Furthermore, the fast carrier recombination timesLTG materials are ideal for the typically high repetition ratof mode-locked lasers, allowing the materials to fully relprior to the next pulse.

An interesting aspect of the use of saturable absorpin LTG materials to mode-lock lasers is the relatively lorecombination time of the carriers relative to the durationthe optical pulse. For instance, in recent demonstrationmode locking of Ti:sapphire lasers, LTG semiconducsaturable absorbers with lifetimes greater than 10 ps wused to produce pulses with 6.5 fs duration.198 Severalmechanisms by which slow saturable absorbers can pro

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ultrashort mode-locked pulses are illustrated in Fig. 15.the first example, a slow saturable absorber coupled witslow gain recovery can produce fast optical pulses duringshort time that the gain exceeds the loss. However, in msolid-state lasers, the gain remains relatively constant,the mode-locking dynamics must rely entirely on the slosaturable absorber. This has been shown to be possiblethe stabilization of soliton-like pulses with slow saturababsorbers,199 illustrated in the second example in Fig. 15.this case, the fast component of the saturable absorptiosufficient to form a soliton-like pulse in the laser cavity.

One drawback of simple semiconductor saturablesorbers is the incompatibility of the band-edge resonant nlinearities with the need for broadband tuning of popusolid-state lasers, and with the large bandwidths of ultrapulses. An early solution to this problem was the develoment of a broadband saturable absorber based on a gragap structure of LTG AlGaAs. The design is shown in F16~a! for its implementation in a self-starting passivemode-locked Ti:sapphire laser.200 The graded gap spans thwavelength range from 870 nm atx50 to 723 nm atx50.22. This structure had a significantly wider bandwidthan previous LTG quantum-well saturable absorbers, alloing continuous tuning of sub-10-ps pulses over 100 nm fr760 to 860 nm. This specific saturable absorber was incporated in a resonant passive mode-locking~RPM! configu-ration in which the saturable absorber resides in a weacoupled external cavity shown in Fig. 16~b!.

Mode-locking stability was significantly improved witthe development of antiresonant semiconductor Fabry–Psaturable absorbers that could reside intracavity.201 This wasmade possible by the use of an antiresonant design thaduced the intensity inside the semiconductor device andcreased the saturation intensity. By bringing the saturaabsorption intracavity, difficulties with active stabilizatiowere removed and the laser designs became more comThe antiresonant Fabry–Perot saturable absorber designfirst demonstrated for mode locking a Nd:YLF laser. The tand bottom reflectors were composed of 50 periodsAlGaAs/GaAs multilayer stacks grown at ordinary tempetures. The saturable absorber was composed of 62-Å-InG

FIG. 15. Ultrafast pulse shaping mechanisms with slow saturable absor~a! Slow loss and gain saturation;~b! soliton pulse formation.

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quantum wells (x529%) grown at low substrate tempertures~380 °C! with 60-Å-GaAs barriers. The carrier lifetimof the saturable absorber was measured at 69 ps.

The antiresonant Fabry–Perot saturable absorber resented the first in a growing class of semiconductor saturabsorber mirrors~SESAM!. The low modulation depth of theinitial SESAM lead to the development of an anti-reflectiocoated saturable absorber mirror.202 This structure shown inFig. 17 produced 34 fs pulses from Ti:sapphire with a 3msmode-locking buildup time.203 The saturable absorbermuch thinner in this design, consisting of only a sing150-Å-LTG GaAs well. The thin layer reduces the insertiloss of the device.

Broadband SESAM devices for broad tuning andability to support 10 fs pulses required more bandwidth thallowed by AlGaAs/AlAs Bragg stacks. These SESAM dvices were placed on Ag substrates that served as broadmirrors. Two devices were tested shown in Fig. 17, a lofinesse antiresonant Fabry–Perot and an antireflection coabsorber layer. The low-finesse structure produced 6.pulses from a Ti:sapphire laser. The interferometric autocrelation of the laser pulse is shown in Fig. 18.198

V. PHOTOREFRACTIVE SEMICONDUCTORHETEROSTRUCTURES

The photorefractive effect is an optical nonlinearity thtransforms gradients in light intensity into changes inoptical properties of the photorefractive material. The phorefractive effect is unique to semi-insulating materials, a

FIG. 16. ~a! Broadband saturable absorber design for resonant-pasmode-locking~RPM! using a graded-gap LTG AlGaAs layer;~b! use of asaturable absorber for RPM of a Ti: sapphire laser~from Ref. 200!.

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photorefractive heterostructures and quantum wells compa special class of photorefractive materials.204 These materi-als are useful for real-time hologram formation, and are uwith light intensities that are significantly lower than for odinary optical nonlinearities. Holograms in photorefractiquantum-well structures can be fully developed using omW/cm2 of light intensity,205 while maintaining hologramerase and rewrite rates over a kilohertz.

The photorefractive effect in heterostructures153 is basedon the accumulation of photogenerated space charge traat deep defects. The photogeneration process usuallyvolves two interfering laser beams that produce an interence intensity pattern on the device. Under an applied etric field, photocarriers generated in the bright interferenfringes move to and are trapped at defects in the dark fringThe separated space-charge produces a space-charge efield that modifies the optical properties of the semicondtor through electroabsorption. The spatially modulated eltroabsorption takes on the same spatial pattern as the i

FIG. 17. Semiconductor saturable absorber mirror~SESAM! devices thatincorporate LTG materials for fast recovery rates~Ref. 203!.

FIG. 18. Interferometric autocorrelation trace for a 6.5 fs pulse frommode-locked Ti: sapphire laser using the SESAM structure of Fig. 17~b!~from Ref. 198!.

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ference pattern, and constitutes the physical hologram.hologram can move in real time to track changes in the lipatterns up to rates comparable with the dielectric relaxatime of the semiconductor. This dynamic nature of the hograms make them ideal for adaptive optical applications.a more complete treatment of the photorefractive effectRef. 206.

Photorefractive quantum wells~PRQW! may be viewedquite generally as dynamic holographic thin films that canused to record moving holograms. Many applications ta

FIG. 19. Basick-vector geometries for Raman–Nath diffraction, includinmomentum vectors and field amplitudes for degenerate~self-diffraction! andnondegenerate readout.

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advantage of this dynamic and adaptive ability of the hograms. Several of the applications discussed at the end ofsection include adaptive laser-based ultrasound detecoptical imaging through turbid media with possible biomecal applications, and femtosecond pulse shaping and rtime dispersion compensation for ultrafast fiber optical apcations.

A. Dynamic holography in quantum wells

1. Grating geometries

The geometries for hologram writing and self-diffractioare shown in Fig. 19 for a hologram written by plane wavproducing a regular holographic grating in the thin film thdiffracts the writing beams into first-order diffracted beamBecause photorefractive quantum wells and heterostructoperate with an applied electric field, different orientationsthe incident writing beams and applied field produce thdistinct photorefractive grating geometries. These are shoin Fig. 20, and are classified by the orientations of the eltric field and hologram grating vector relative to the planethe thin film. When the electric field is applied in the planethe thin film, this is called the transverse-field geomewhich uses the Franz–Keldysh excitonic electroabsorptFor this reason, it is also called the Franz–Keldysh geoetry. When the electric field is applied perpendicular to tquantum wells, this is called the longitudinal-field geometor the quantum-confined Stark geometry. When the wbeams are incident from the same side of the structure,beams write a transmission grating. When the beams arecident from opposite sides, they write a volume reflectigrating.

FIG. 20. The three basic photorefractive quantum well geometries showing field directions and grating vector orientations~Ref. 153!.

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The dynamic charge transport processes that formspace-charge gratings are significantly different in the diffent geometries. The relative orientation of the grating vecand the direction of transport has a major impact onoperation of the device. For instance, in both the transvetransmission and longitudinal reflection geometries the traport is parallel to the grating vector. This leads to ‘‘normaspace-charge grating formation.153 However, for the longitu-dinal transmission geometry, the grating vector is perpdicular to the transport. This situation imposes differespace-charge grating dynamics compared with the otherometries. The physics of the grating formation dynamicseach of these geometries are discussed in more detaSec. V B.

2. Raman –Nath diffraction

Photorefractive thin films perform as planar diffractiogratings because the thickness of the film is typically smathan the hologram fringe spacing. This aspect of photoreftive quantum wells make them easier to operate than bphotorefractive crystals, especially during nondegenefour-wave mixing, because no alignment of the probe labeam is necessary to observe a diffraction order. The pciples of diffraction from thin films are described by thRaman–Nath diffraction theory that was originally devoped to describe diffraction of light by sound waves207 ~as inacousto-optic modulators208! and undulating surfaces.209–211

Raman–Nath diffraction in photorefractive quantum wecauses two-wave mixing in addition to diffraction into mutiple higher orders.

The space-charge gratings in the semi-insulating hetstructures produce space-charge electric fields that mothe dielectric function of the structure. The associated dietric grating consists of both an index grating and an absotion grating because of the causal connection throKramers–Kronig of the excitonic electroabsorption with telectrorefraction. Therefore, photorefractive quantum whave absorption and index gratings that contribute apprmately equally to the diffracted signal, although the conbutions tradeoff with different wavelengths, and are only apreciable for wavelengths within one or two excitonlinewidths of the band gap. The spatially modulated comprefractive index under sinusoidal excitation is given by

n~x!5n01n1 cos~Kx1f!, ~3!

where the phase shiftf is the photorefractive phase shift threpresents the spatial shift of the index grating relative tointerference fringe pattern writing the grating. Finite spatshifts lead to finite energy transfer during photorefracttwo-wave mixing. A plane wave transmitted through the thfilm experiences a complex amplitude modulation given

Et~x!5Eiei @d01d1 cos~Kx1f!# ~4!

with the complex phase factors given by

d j52pnjL

l cosu81 i

a jL

2 cosu8, ~5!

wherenj anda j are the Fourier coefficients for the index anabsorption gratings,L is the thickness of the film, andu8 is

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the internal angle where sinu85(1/n0)sinu . The diffractionefficiency is defined as the ratio of the diffracted intensrelative to the incident intensity. In photorefractive quantuwells the diffraction efficiency is typically smaller than 5%The first-order signal is largest and therefore the most inesting for applications. To good approximation for photofractive quantum wells, the diffraction efficiency neglectinsurface reflections is

h615F S pn1L

l cosu8D2

1S a1L

4 cosu8D2GexpS 2a0L

cosu8 D . ~6!

3. Two-wave mixing

During the hologram writing process, if the wavelengof the writing beams is tuned close to the excitonic transitenergy, the same beams that write the grating are diffracby the grating. This is sometimes called a degenerate wamixing process, in which all the write and read beams hathe same wavelength. Because the wavelengths are idena first-order diffraction from each write beam will propagain the direction of the other write beam. This causes a linsuperposition of a transmitted with a diffracted beam. Trelative phases of the transmitted and diffracted waves argeneral different, leading to interesting interference effesuch as nonreciprocal energy transfer in which one begains energy at the expense of the other. This interferebetween transmitted and diffracted waves is called two-wmixing.

The intensityI 1 of the combined transmitted and difracted beams after passing through the dielectric film is

I 1~L !5e2a0LF I 1~0!1AI 1~0!I 2~0!

3S 62pn1L

l cosu8sinf1

a1L

2 cosu8cosf D G . ~7!

The most important consequence of Eq.~7! is the differencein sign in front of the index term in the brackets. When tphotorefractive phase shiftf is nonzero, there is a nonreciprocal transfer of energy from one beam to the other. Tfeature makes it possible to measure the contributions fthe absorption and index gratings separately. Photorefracgain in a photorefractive thin film can be expressed in terof the ratio of the mixed intensity to the unmixed intensitThe gain ratio is expressed in terms of the beam intenratio b5I 2(0)/I 1(0) as

g5I 1~L !

I 1~0!e2a0L

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where the maximum grating amplitudes for unity modulatiarenm andam .

B. Photorefractive heterostructure geometries

1. Transverse-transmission geometry

A typical MBE layer structure for a transverse-field phtorefractive quantum well is shown in Fig. 21. The electr

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optic layer of the device is the multiple quantum we~MQW! structure composed of 100 periods of 70-Å-Gawells and 60-Å-Al 0.3Ga0.7As barriers. The MQW layer issandwiched between two Al0.2Ga0.8As buffer layers. The series of GaAs, AlAs, and Al0.5Ga0.5As layers on the bottomare for substrate removal using either epitaxial liftoff tecniques or direct etching of the substrate. The entire strucis typically grown on a semi-insulating substrate, althouthis is removed in transmission devices, and therefore dnot participate in the photorefractive structure.

The fabrication of the transmission PRQW begins wproton implantation of the device. A double implantation1012cm22 at 160 keV and 531011cm22 at 80 keV providesa relatively uniform defect density in the device to a depthapproximately 1.5mm. After implantation, TiAu or AuGecoplanar contacts with a 1–3 mm gap are deposited on tplayer. The structure is then epoxied to a glass or sappsubstrate, and the semiconductor substrate is removed.nal proton implantation can be performed on the free surfas the final step to ensure uniform semi-insulating behathrough the entire device. The completed transverse-fiPRQW device is shown in Fig. 22.

The transverse-field electroabsorption, or FranKeldysh effect, is shown in Fig. 23 for increasing applielectric fields.212 The large electroabsorption produces diffeential transmission that exceeds 100% for a field of 25 kcm. The electrorefraction is also shown in the figure callated from the electroabsorption using the Kramers–Krotransform. Absorption changes as large as 5000 cm21 andrefractive index changes of 1% are achieved under the mmum electric field. An important feature of the exciton

FIG. 21. MBE growth structure for a typical transverse-field photorefracquantum well.

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electroabsorption is the wavelength-dependent phase ocomplex dielectric function that is imprinted onto the dfracted beam through the dependence ofDa and Dn onwavelength. The excitonic spectral phase is shown in F23~c! as a function of wavelength and electric field. Thapproximately linear dependence of the phase on wavelehas important practical consequences for applications sucadaptive ultrasound receiving and femtosecond pulsecessing using the PRQW devices.

The symmetric two-wave mixing gainGa is shown inFig. 24 as a relative cross-beam modulation intensityDI /I .In addition to the symmetric term, there is also an asymmric two-wave mixing gainGn that constitutes nonreciprocatransfer of energy from one beam to the other when anpreciable photorefractive phase shift is present. No net ghas yet been achieved in the PRQW devices. The four-wmixing diffraction efficiency corresponding to the two-wavmixing is also shown in Fig. 24. An output diffraction efficiency of over 1% has been observed under the maximelectric field.

The transverse-field PRQW structures have shown aries of interesting effects. The first observation of four-wamixing in these devices was performed by Nolteet al.204

using ‘‘off-the-shelf’’ quantum well structures that wermade semi-insulating using proton implantation initially dveloped for ultrafast strip line studies.174,213 This first dem-onstration of the PRQW was followed by studies of twwave mixing,214 and other higher-order interference effecamong the many diffraction orders.215

The PRQW devices have many advantages over otraditional photorefractive devices such as the ferroelecoxides,216 which typically required high intensities of W/cm2

to achieve response rates on the order of a Hz. This hpower and low-speed characteristic of ferroelectrics was csidered to be an insurmountable barrier to eventual commcialization. The PRQW devices, on the other hand, perfounder low intensities down tomW/cm2 and by using high

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FIG. 22. Fabricated transverse-field PRQW device that operates in transsion after the substrate is removed and the contacts are applied.

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intensities achieve rates greater than 100 kHz. This lointensity and high-speed characteristic of the PRQW devhas improved the prospects for applications, opening up psibilities in image processing, ultrafast data generation, bmedical imaging, and laser-based ultrasound, describeSec. V D.

The low-intensity performance of the transverse-fiePRQW is shown in Fig. 25 for two wavelengths corresponing to zero crossings of the electroabsorption and electrfraction, respectively.205 The photorefractive gratings havsaturation intensities on the order of 10mW/cm2. The high-speed performance is shown in Fig. 26, which is obtainedmoving gratings using an acoustic-optic modulator. Tmaximum rate at which the photorefractive grating canspond is the response rate of the material. At a power ofmW, the response rate is 40 kHz. Many other aspects oftransverse-field geometry have been investigated, includperformance using write lasers with above-band-gphotons,217 effects of the high absorption,218,219 as well asphotorefractive properties of LTG epilayers and quantwells.80,81,101.

FIG. 23. Franz–Keldysh electroabsorptionDa, electrorefractionDn andexcitonic spectral phasec as functions of field and wavelength for 30%AlGaAs/GaAs multiple quantum wells~Ref. 276!.

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One intriguing aspects of the transverse-field PRQWvices is the presence of a nonzero photorefractive phasef in Eq. ~7! for these devices. The photorefractive phashift is caused by a spatial shift of the physical space-chagrating relative to the intensity pattern that writes the gratiThis spatial shift is an ordinary consequence of carrier difsion in traditional bulk photorefractive materials, but wexpected to vanish in the high-field drift-dominatetransverse-field PRQW devices. Nonetheless, substaphotorefractive phase shifts were observed.205,214The originof the phase shift remained a mystery for several years aits discovery by Wanget al.,214 but a strong clue to its originwas seen in a characteristic field of 3–4 kV/cm at whichturned on relatively abruptly. This field is similar to the fiethat initiates the Gunn effect in bulk conducting materiaHowever, our materials were semi-insulating, and therefcould not support Gunn domain formation.

The solution to this mystery was first proposetheoretically.220 It was observed that the formation of spacharge was intimately related to the dielectric relaxation rof the illuminated material. Therefore, transport effects taffected the dielectric relaxation would influence photofractive grating formation. Although the PRQW device

FIG. 24. Photorefractive two-wave mixing efficiency for a 30% AlGaAGaAs transverse-field PRQW~Ref. 212! and the associated output diffraction efficiency spectrum.

FIG. 25. Demonstration of the low-intensity performance of the transvefield PRQW geometry measuring two-beam coupling as a function of laintensity at two different wavelengths for which the mixing is entirely froabsorption gratings or index gratings~Ref. 205!.

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were semi-insulating, they experience electron heatingtransport in the high electric fields. The photogenerated etron population is heated to many hundreds of degreestransferring many of the electrons from the directG valley tothe lower-mobility indirect valleys. The electron velocitherefore saturates with increasing field. This transport nlinearity, which forms Gunn domains in conducting materichanges how the electrons respond to changes in elefields even in semi-insulating materials. The effective dieltric relaxation rate in the PRQW devices becomes

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which is small when the differential velocitydv/dE be-comes small due to the transport nonlinearity. This disabdielectric relaxation, and drives charge from bright fringesaccumulate in the dark fringes. The space-charge elefield in this situation is shifted by a quarter fringe spacirelative to the intensity, constituting ap/2 photorefractivephase shift. This theoretical mechanism was experimentverified by Brubakeret al. by correlating the onset of thphase shift with the transport nonlinearity in photorefractGaAs epilayers,221 shown in Fig. 27. The photorefractivphase shift is an important property that is relevant for maphotorefractive applications. The identification of this nemechanism for inducing a phase shift therefore could hbroad ramifications in the context of other photorefractmaterials.222

2. Longitudinal-transmission geometry

A cross-sectional view of a longitudinal PRQW is showin Fig. 28 across a few bright and dark fringes. In the asence of illumination, the electric field falls uniformly acrothe quantum well layer. When bright and dark fringes intsect the device plane, photogenerated carriers in the bfringes transport vertically to the cladding layers, where thare trapped at defects. The accumulated space-chargeduces a space-charge electric field that cancels the apfield in the bright fringe, but the applied field remains in t

FIG. 26. Demonstration of high-speed performance in the transverse-PRQW geometry measuring two-beam coupling as a function of Dopshift on one of the writing beams for different write intensities.

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dark fringe. Therefore, there is a spatial modulation offield across the device, producing dielectric gratings inquantum wells.

The situation in Fig. 28 is not a steady-state conditiobut represents a condition of optimal spatial modulationsome time after either the application of the electric fieldof the illumination. For longer times, the region of spaccharge expands laterally and at long times screens the efield, removing both the spatial modulation and the dielecgratings. Therefore, the longitudinal transmission geomeis a transient grating geometry. Steady-state diffraction unsteady-state field and illumination can only occur under scial circumstances.223 In the longitudinal geometry, it istherefore necessary to describe the device performanctransient terms, such as peak or time-average performan

The longitudinal transmission geometry was propossimultaneously with the demonstration of the transvetransmission geometry.204,213 It was first demonstrated in aII–VI CdZnTe/ZnTe quantum well structure,224,225and was

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FIG. 27. The hot-electron photorefractive phase shift compared with nohmic transport in a GaAs epilayer demonstrating the semi-insulating csequence of the Gunn effect~Ref. 221!.

FIG. 28. Cross section with fringes of the longitudinal transmission geoetry.

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FIG. 29. Longitudinal-field PRQW re-sponse for 2 and 4 WM vs frequencoffset in one of the write beams~Ref.78!. The maximum photorefractivegain coincides with the knee in the diffraction efficiency.

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later demonstrated in Cr-doped AlGaAs/GaAs quantum wstructures.52 Fabrication of the longitudinal-geometry devices remained difficult until an improved device designcorporated the photorefractive quantum well structure insa p- i -n diode that was an all-semiconductor structure wiout extra dielectric layers.76 Subsequent improvements anmodifications have included removing defects from tquantum wells,226 incorporating low-temperature-growtlayers in the cladding,52,76,226 as well as removing defectfrom the cladding layer and relying on trapping in the quatum wells that were grown at low temperature for thpurpose.77 Photorefractive quantum wells that operate attechnologically important wavelength 1.55mm have alsobeen developed in InGaAs/InGaAsP materials.227,228One ofthese long-wavelength devices took a novel approach bying quantum dots in the cladding layer to trap and storespace charge rather than relying on defects.229

Because of the complicated transient behavior of the lgitudinal geometry, it has been the subject of consideratheoretical modeling. Fringing fields were shown to playimportant role in the transient decay of the gratings and lited the spatial resolution by pulling carriers out of the brigfringes and into the dark fringes.230 Several models specifically addressed the transport issues in the devices.231,232 Amuch simpler approach modeled this structure as an equlent circuit.233 The equivalent circuit described all the reevant phenomenological behavior without needing to pform detailed transport calculations. It also made a cldistinction between transient and time-average diffractperformance.

Recent developments in the longitudinal transmissgeometry have focused on the behavior of moving or runnphotorefractive gratings. Nonstationary gratings result whthere is a time-dependent phase difference between thewriting beams. In the simplest case, a constant frequeoffset between the beams produces an interference pathat moves with constant velocity. Combining moving grings with the transient response of the longitudinal geome

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produces interesting and potentially useful behavior.For instance, with static interference gratings it is impo

sible to produce nonreciprocal energy transfer betweentwo writing beams during two-wave mixing because the logitudinal structure has a strictly local response to the intsity. An equivalent statement is that there is no asymmetrdefine a direction of energy transfer in the static case. Hoever, if the grating is moving, it breaks the left–right degeeracy, making energy transfer possible. The moving interence pattern produces a nonlocal optical nonlinearityforcing the space-charge grating to lag behind the illumition. This spatial lag constitutes a spatial shift and introdua photorefractive phase shift into Eq.~7!.

Forcing the space-charge grating to spatially lag thetical stimulus requires specific relationships betweengrating velocity and the dielectric relaxation time of the mterial. If the interference pattern moves too slowly, the spacharge grating can keep in step, and no energy transferbe observed. If the interference pattern moves too quicthen the space charge cannot respond to the spatial motion in the light intensity, and the device will have a homgeneously screened field. But when the interference patmoves approximately one fringe spacing in one dielecrelaxation time, an optimum condition exists that allowslarge spatial modulation in the space charge, as well aspatial lag of the grating by a quarter fringe spacing. Thefore an optimum grating velocity~frequency offset! will pro-duce a maximum nonreciprocal energy transfer betweentwo beams. This is shown in Fig. 29, together with the fowave mixing diffraction efficiency that was measured simtaneously, as functions of the frequency offset betweentwo write beams.78 The two-wave mixing energy transfer ismaximum when the grating strength~measured by four-wavemixing! begins to decay, marking the balance between ging velocity and dielectric relaxation time.

The interplay between the moving gratings and tpulsed electric field is potentially useful for Doppler velocmetry applications. The equivalent circuit model of the lo

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gitudinal geometry shows that the space-charge gratinwritten by the displacement currents associated withrapid change in the applied electric field.233 Therefore asingle step in the field produces a temporarily frozen gratiin spite of the fact that the interference pattern is moviOnce the grating is frozen by the electric strobe, the phasthe interference pattern produces an oscillatory coupling wa sinusoidally oscillating transfer of energy betweenbeams, first in one direction, and then in the opposite dirtion. This behavior is shown in Fig. 30. It is importantnote that the intensity shows oscillatory behavior even athe electric field is removed from the device as the strograting decays. The frequency of oscillation in the transmted beam intensity is identical to the frequency offsettween the writing beams. Therefore, measuring the osction frequency is equivalent to measuring the Doppler shif79

3. Longitudinal-reflection geometry

The longitudinal-reflection geometry~the third and lastgeometry shown in Fig. 20! is a traditional photorefractivegeometry because the electronic transport is parallel tograting vector. On the other hand it has the distinctionbeing the only PRQW geometry that operates with voluholographic gratings. Approximately ten fringes can becommodated in the small thickness of a typicalp- i -n quan-tum well diode structure. In spite of this small numberfringes, they are sufficient to produce a Bragg reflection. Teffect of the Bragg reflection has been observed in a twave mixing experiment as beam coupling caused byinterference between the transmitted beam and the diffrabeam.234

This geometry poses several challenges. The counpropagating beams produce interference fringes with ariod of only 0.12mm. This places severe requirementsmechanical stability to prevent washing out the gratingsfringe motion. The short fringe spacing also requires antremely high defect density to support enough space chto screen the applied electric field. To achieve this, the qutum wells were grown at low substrate temperature, incorrating high defect densities, but at the cost of degradingdevice sensitivity. These experimental difficulties with th

FIG. 30. Transient 2 WM during strobed operation of the longitudinalp- i -nphotorefractive diode in the presence of a Doppler-shifted writing beshowing optical interference oscillations after the field has been remo~Ref. 79!.

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geometry make it the least attractive for eventual applitions. However, a continued effort may be merited by tgeometry because it appears to be the only PRQW geomthat may achieve net gain.235

C. Photorefractive optical microcavities

Photorefractive quantum well devices have the advtages of high nonlinear optical sensitivity and fast dynamholographic speeds, but these advantages are offset in sapplications by diffraction efficiencies on the order of on1%. Therefore efforts to improve the diffraction efficiencare important for eventual commercialization of thesevices. The semiconductor quantum well structures ofPRQW geometries lend themselves to enhancements uoptical microcavity effects. The relevant microcavities aasymmetric Fabry–Perot structures that operate in reflectbecause the quantum wells have high absorption.

Asymmetric Fabry–Perot~ASFP! structures operatethrough a sensitive balance of phase and amplitude ofreflected partial waves.236,237These structures have been ivestigated extensively as high-contrast quantum well elecabsorption modulators.236–249Significant enhancements werpredicted theoretically in the holographic diffraction efciency of photorefractive quantum wells operating as ASdevices.250 One of the important findings was the relativinsensitivity of the enhanced diffraction on the exact cavbalance condition. Balancing the cavity was found to posevere difficulties for modulator arrays because the contratio can change significantly with only very small changin cavity length. This limited the usefulness of the ASFconcept for modulator arrays. However, in asymmetFabry–Perot devices that operate as dynamic hologr~shown in Fig. 31!, the diffraction enhancement is not highsensitive to the cavity length. Therefore, the asymmeFabry–Perot concept may be fundamentally more attracfor diffractive devices than for the modulator applications fwhich they were initially developed.

Fabry–Perot effects were investigated in the photofractive quantum wells first in transmission251 in partiallyasymmetric cavities, and then in reflection in fully asymmric cavities.252 In the latter case, the ratio of the diffracteintensity relative to the zero-order reflected intensity wasserved to be 2:1 in a single diffraction order. By consideri

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the energy in both first-order diffracted beams, 80% ofenergy scattered from the device appeared in the first difftion orders, and only 20% remained in the zero-orderflected beam. The output diffraction efficiency~defined asthe ratio of the diffracted intensity to the reflected intensi!is shown in Fig. 32 for two devices with different cavitconditions. The output diffraction efficiency in the best caattains a value of 200%. Longitudinal photorefractive quatum well devices using asymmetric Fabry–Perot cavithave been fabricated on semiconductor Bragg stack223

These longitudinal devices achieved peak transient inputfraction efficiencies of 1.2% under a bias of 20 V atintensity of 9 mW/cm2. Even higher output diffraction effi-ciencies may be attainable by carefully balancing the cato produce a phase grating that would quench the zero-oreflection.253 Input diffraction efficiencies~defined as the ratio of the diffracted intensity to the incident intensity! in thePRQW devices may approach several percent in idcases.250

D. Photorefractive quantum well applications

Applications for photorefractive quantum wells habroadened in recent years to contribute to such differenteas as femtosecond function generators, biomedical imasystems, and laser-based ultrasound receivers. Severthese applications are specifically suited to the PRQWvices and take advantage of their high-speed adaptive horaphy and their high sensitivity.

1. Optical correlation and image processing

The first applications for photorefractive quantum wewere optical correlation and image processing. A joint Forier transform optical correlator was implemented usingdoped GaAs/AlGaAs longitudinal-field photorefractivquantum well devices.254 This device performed an opticacorrelation using only 3mW of power, the correlation wasobtained in 1ms, and the image could be erased in 2ms. Thegrating writing process in the longitudinal geometry has s

FIG. 32. Output diffraction efficiency from two transverse-field PRQasymmetric Fabry–Perot structures, showing 200% output diffractionciency into one diffraction order for one device~Ref. 252!.

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eral features that give it unique characteristics that are usin optical correlators and image processing. The devihave gray-scale response to incident intensity, and havelinear and saturated regimes, depending on the applied fiand gate times.255 By controlling the saturation intensity othe device, it is possible to switch between image similarand image-area recognition.256

2. Three dimensional and biomedical imaging

Ultrafast laser pulses are convenient probes for distanresolved scanning because the ultrashort pulses can befor time-of-flight laser ranging with excellent depth resoltion. For instance, a laser pulse with a duration of 100 fsgive a depth resolution less than 50mm. Coherent laser ranging requires coincidence detection of the probe and a reence pulse. There are many ways to perform this detecfor point-by-point scanning. However, there is a consideraadvantage to obtaining a full image field that containsdepth information without the need to scan across the obj

Image-field 3D acquisition with 50mm-depth resolutionis possible using photorefractive quantum wells as a ‘‘cohence gate.’’257 When a probe pulse reflects from a thredimensional topology, the returning wavefront is dispersin time according to the roundtrip distance. When this sigwave interferes with a short reference pulse, it producesterference only when the probe and reference temporoverlap. Therefore, it is possible to make a hologramthose parts of an object located only at a specific depth.changing the delay of the reference pulse, the full depresolved image is acquired in successive layers like a tographic map. The optical schematic for the process is shoin Fig. 33, and the results of imaging a three-dimensioobject are shown in Fig. 34. The object is a machined mpart with 100mm step heights. The reconstruction is mafrom successive delays on the reference arm of the hgraphic writing system. The full-field acquisition in thidepth-resolved holography can be recorded directlyvideo,258 or can be digitized and stored for future computreconstruction.

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FIG. 33. Experimental arrangement for imaging through turbid media usa PRQW as a holographic coherence gate~Ref. 257!.

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Because the time-of-flight uses coherent pulses,same imaging system makes it possible to image throhighly scattering turbid media. This process of coheregating is called optical coherence tomography. Opticalherence tomography~OCT! is a well-established laser imaging technique for imaging through translucent media259 andhas been applied to shallow imaging through biologitissue.260–262 The difficulty of imaging through scatterinmedia is that the scattered light obscures the image of inest carried by the ballistic light. When laser light propagathrough a translucent medium, part of the light scattersoptical heterogeneities, while part continues to propagatescattered, and reflects off buried objects of interest. Thisscattered light is sometimes called ‘‘ballistic’’ light.263 Thescattered and unscattered light have one very diffeproperty—the unscattered light remains coherent withoriginal laser beam, while the scattered light~on average!does not. The process of OCT detects only the coherent lrejecting the incoherent scattered light. While conventioOCT is a promising optical technology for imaging into mdia that were previously inaccessible, it performs point-bpoint scanning, which is time consuming~as for confocalmicroscopy!, and is not compatible with direct imaging tvideo.

Imaging through scattering media with holography264

provides full-frame acquisition with the same depth resotion in turbid media as point-by-point scanning. Photorefrtive quantum wells are candidates for this process becaustheir high sensitivity and speed. They can record holograof coherent light buried in a high-intensity background,257

and they can operate at video rates.258 Recent experimentshave demonstrated imaging through 13 mean-free-p~roundtrip! of a turbid medium using transverse-field phot

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refractive quantum wells.258 This depth may be doubled boptimized design and growth of the quantum wells, makit feasible to image to the bottom of human epidermal laywith obvious applications for biomedical imaging.

3. Femtosecond pulse shaping and spectralholography

Shaping of laser pulses on the femtosecond~fs! timescale can be performed using optical Fourier synthesis teniques in which the amplitudes and phases of the optfrequency components of a fs pulse are individuamanipulated.265,266 Access to the individual Fourier components of an ultrafast pulse can be attained by spectrallypersing the pulse off an optical grating and transformingspectrum into the Fourier plane. This is shown in the opti

FIG. 34. Object and computer-reconstructed image demonstrating deresolved holographic imaging using the setup of Fig. 33~Ref. 257!.

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train in the horizontal plane of Fig. 35. This optical configration is called a zero-dispersion delay line in which a pudiffracts off grating G1 and is Fourier transformed by leF1 onto the Fourier plane, occupied by the PRQW infigure, which acts as a shaping element. In the absencthis shaping element, the pulse is again transformed byF2 and is reconstituted by grating G2 to produce the origpulse. When a shaping element is placed in the Fouplane, the phase and amplitude of each spectral compocan be controlled independently. Therefore, the output pcan be given any arbitrary pulse shape, limited withinspectral resolution of the zero-dispersion delay line. Tpulse shaper therefore can be viewed as a general-purpooptical function generator. Many different optical elemencan be used as the shaping element, including static amtude and phase masks, or by programmable spatial lmodulators. Dynamic holographic media, such as photofractive materials, are an important class of shaping elembecause they can be programmed optically in real time.

Photorefractive quantum wells have several featuresallow them to be compatible with holographic fsec pushaping. A key requirement for use of a holographic medifor fs pulse manipulation is the maintenance of transforlimited optical pulses after passing through the optical ement. Diffraction of 100 fs pulses from photorefractive quatum wells have been shown to be transform limited,267

although the limited bandwidth of the quantum-confinedciton transition lengthened the pulse duration to appromately 400 fs. The transform-limited diffraction from thquantum wells is a consequence of the approximately linfrequency dependence of the excitonic spectral phase, shin Fig. 23~c!. A linear phase imposed in the spectral domamerely constitutes a time delay in the time domain, but dnot lead to any distortion of the pulse.268 Photorefractivequantum wells are therefore compatible with fs pulse shing and manipulation experiments, and have previously bused for electric-field cross-correlation measurements,269 andfor time-to-space conversion experiments.270

The implementation of holographic fs pulse shapinging a transverse-field PRQW device is shown in Fig. 35. TPRQW is placed in the Fourier plane of the zero-dispersdelay line. The hologram is written in the PRQW usinbeams in a vertical plane relative to the plane of the deline. The hologram can be either a real-space image,Fourier image, depending on the focal length of theF lens.The probe pulse is consequently diffracted in the vertiplane of the pulse shaper while the unshaped transmpulse remains in the horizontal plane. These two pulsestherefore spatially separated.

The operation of the holographic pulse shaper drafrom aspects of Fourier optics. When theF lens in the holo-gram writing arm is used to image, then the temporashaped pulse will have the envelope corresponding toFourier transform of the object in the writing beam. WhtheF lens acts as a Fourier transform element, then the tporally shaped pulse will have the envelope correspondinthe object itself. In this later case, the process is called spto-time mapping, and the shaped pulse is called the tidomain image of the object in the writing beam.

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In holographic pulse shaping, the holograms are writby a separate laser from the manipulated pulse. Another cof application uses holographic media in which the hograms are written by the fs pulses themselves, called speholography.272 Considerably more functionality and direcuse of the dynamic nature of the photorefractive materialpossible with spectral holography. Photorefractive quantwells have been used to perform real-time dispersion copensation and have been demonstrated to remove arrtime drift.273

4. Laser-based velocimetry and ultrasound detection

The use of lasers to probe surface velocities andplacements has a long history based on the ability of inferometry to measure small changes in the relative phastwo coherent beams.274,275However, in most practical applications, the interrogated surface is nonspecular, and the

FIG. 36. Holographically shaped pulses showing~a! and odd pulse, and~b!a square pulse~Ref. 268!.

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turning wavefronts are typically distorted with significaspeckle. In addition, relative motion, vibrations or other pturbations in the interrogated surface or in the environmmake it difficult to maintain the appropriate phase bneeded for linear homodyne detection. One solution toproblem is the use of adaptive interferometers that compsate for speckle and adapt to slow changes in phase.namic holography is one example of an adaptive systemcan perform as an adaptive beam combiner in a compensinterferometer.

Photorefractive quantum wells have several advantaas dynamic holographic media that lend themselves to labased ultrasound detection, such as their high speedshigh sensitivities. The high speeds allow them to have hcompensation bandwidths, while the high sensitivities mthem attractive for use with very weak signals. Two specapplications have emerged that use PRQW devices. Labased adaptive velocimetry has been demonstrated ulongitudinal-field PRQW devices,79 while laser-based adaptive ultrasound detection has been demonstrated utransverse-field PRQW devices.276 Each device has uniquattributes, in addition to the speed and sensitivity, that pvide new avenues to compensated velocimetry and usound detection.

Doppler velocimetry using longitudinal-field PRQW dvices can be performed with a variation on the moving gring process described at the end of Sec. V B2. It was notthat the photorefractive gain continues to oscillate even athe electric field is turned off. Furthermore, the frequencyoscillation of the transient gain increased with increasingtuning of the signal beam relative to the reference beam. Tis shown in Fig. 37 for AO detuning frequencies from 1300 kHz for an intensity of 100 mW/cm2. By considering theprocess in terms of oscillatory mode coupling, it canshown that the measured oscillation frequency of the gaiequal to the frequency offset between the two write beam79

Because the two-wave mixing acts as an adaptive beam cbiner, this process can be used to perform Doppler hetdyne detection that automatically compensates for speand slow phase distortions.

FIG. 37. Oscillatory mode coupling between Doppler-shifted write beaduring two-wave mixing in a longitudinal-field PRQWp- i -n diode ~Ref.79!. The oscillation frequency is equal to the frequency shift betweenwrite beams.

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A potentially more useful application of adaptive beacombining is compensated laser-based ultrasound detecIn manufacturing environments and during the nondestrtive evaluation~NDE! of parts and infrastructure, it is oftenecessary to make remote measurements of surface dispments caused by ultrasound signals. But the speckle andbrations in these applications are prohibitive to the usestandard interferometers. The development of time-delay~orself-referencing! interferometers ~such as the confocaFabry-Perot277! allowed the processing of light scatterefrom a rough surface with a large field of view, but requirpath-length stabilization of the interferometer. Two-wamixing, performing as an adaptive beam combiner, solthis stabilization problem.278,279

The function of two-wave mixing in adaptive homodyndetection is shown in Fig. 38. The hologram in the PRQWwritten by the reference and the signal beams. Each bdiffracts from the hologram and copropagates in the dirtion of the other beam. An important feature of dynamholography is the matching of the wavefronts betweendirect and diffracted waves in each of the arms. The matcwavefronts make it possible to detect the homodyne sigusing a large-area detector. In addition, slow vibrations~be-low the compensation bandwidth of the holographic marial! are tracked by the dynamic holograms, removingneed for active stabilization. Therefore, dynamic holograpin this application compensates both speckle and lofrequency vibrations, while passing the high-frequency snal associated with the ultrasound.

The expression for the signal-to-noise ratio of the adtive beam combination is

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The unique feature of the transverse-field PRQWvices in this application is the ability to use the excitonspectral phase@shown in Fig. 23~c!# to tune the coherendetection to perfect quadrature. This is in contrast to theof bulk photorefractive crystals in this application whicmust separately control the photorefractive phase shift.example of a received homodyne signal generated by aezoelectric transducer and detected adaptively usingPRQW is shown in Fig. 40 for different wavelengths as tlaser is tuned through quadrature. The best linear detecoccurs for wavelengths near 837 nm.

FIG. 40. Time trace of an ultrasound signal measured through a transvfield PRQW device operating as an adaptive beam combiner~Ref. 276!.

FIG. 39. Noise–equivalent–surface displacement~NESD! for laser-basedultrasound detection using the adaptive PRQW~Ref. 276!.

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ACKNOWLEDGMENTS

The author gratefully acknowledges NSF ECS-97082that has been the primary and continuing source of supfor this work. Support from NSF DMR-9400415 and thBMDO Focused Research Initiative is also acknowledgThe help and support of M. R. Melloch, J. M. Woodall, E.Haller, W. Walukiewicz, and A. M. Glass over many yearsalso gratefully acknowledged and appreciated.

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