The generation of ultrashort laser pulses.pdf

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Rep. Prog. Piiys. 58 (1995) 169-267. Prinled in the UK

The generation of ultrashort laser pulsesP M W FrenchFemtosecond Oplin Group, Blackett Laboratory, Imperial College, Prince Consort Road. London,SW 7 ZBZ,UK

AbstractThis article is intended to provide an introduction to ultrafast laser development forscientists new to the field. It also aims to provide a snapshot of the state-of-the-art ofultrafast lasers and to indicate how this state evolved over the last thirty years. I n thefirst section, the main issues concerning ultrashort pulse generation are discussed andthe most important ultrafast laser media are briefly reviewed. An extensive historicalsurvey of mode-locking and pulse compression from 1964 until 1994 is then presentedwhich covers the most important developments and aims to put recent advances andstate-of-the-art femtosecond lasers in context. This review also anticipates future devel-opments in practical ultrafast lasers for real-world applications. The basic techniquesof mode-locking are then reviewed at a tutorial level. These include active mode-locking,passive mode-locking with real, resonant saturable absorbers and passive mode-lockingwith the optical Kerr effect. Emphasis is placed on ultrafast solid-state lasers, dye lasersand fibre lasers. Group velocity dispersion and self-phase modulation are introducedand their interaction discussed in some detail. Fibre-optic pulse compressionisdescribedand the significance of soliton shaping and solitary lasers is highlighted. Some of thephenomena limiting the minimum achievable duration of laser pulses are identified.The final section describes techniques for measuring ultrashort pulses including electro-optic streak cameras and second harmonic generation autocorrelation.This review was received in August 1994.

0034-4885/95/O20169 t 6%59.50 Q 1995 IOP Publishing Ltd 169


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I70 P M CV French

ContentsI . IntroductionI , I , General remarksI .2 . Issues in ultrashort pulse generation

1.3. Ultrafast laser media2. Historical overview2.1. Introduction2.2. First generation : picosecond lasers2.3. Second generation : femtosecond dye lasers2.4. Third generation : femtosecond solid-state lasers2.5. Fou rth generalion: useful ullrafast lasers3.1. Introduction3.2. Active mode-locking3.3. Passive mode-lock ing3.4. Hybrid mode-lockingultrafast lasers4. . G roup velocity dispersion4.2. Self phase m odulation4.3. Pulse com pression using SPM and GVD4.4. Soliton propagation and soliton shaping5.1. Introduction5.2. Linear techniques5.3. Second harmonic autocorrelationReferences

3 . Principles of mode-locking

4. Role of group velocity dispersion and self-phase modulation in

5. Measuremen t of ultrashort light pulses

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The generation of u h a s h o r t laser pulses 171

1. Introduction1.1, General remarksThis article is intended to review the physics an d technology concerned with the genera-tion of ultrashor t laser pulses. It will hopefully also convey some of the excitement th atthe dramatic advances of the last few years have provoked within the laser community.The recent advent of tunable femtosecond lasers which are reliable and user-friendlyhas already had a significant impact on spectroscopic studies within diverse areas ofphysics, chemistry and biology. In particular, the development of room-temperaturevibronic solid-state lasers and the exploitation of the optical Kerr effect for pulse shapingin ultrafast lasers have decoupled femtosecond pulses from dye lasers. One consequenceof the increased convenience of the technology is that comm ercial ultrafast laser systemsare now state-of-the-art and routinely outperform home-made research lasers for thefirst time. Progress contiuues to be extremely rapid and the keenly anticipated compact,diode-pumped, all-solid-state femtosecond lasers, tuning throughout the visible andnear infra-red spectral regions, will be of enormous importance fo r metrology, medicaldiagnostics, comm unications, da ta storage and m any other applications. A vital aspectof this modest miniaturization (from a few metres to tens of cm) will be that of adram atic cost reduction-making state-of-the-art picosecond an d femtosecond lasersviable for O E M applications. It is hoped that this will spur a n explosion of technologicalinnovations to complement the revolution in scientific research that is being driven bythe ready availability of a -IO6 improvement in temporal resolution and the concomit-ant increase in peak optical power. The physics of compactjlow-cost lasers, however,does not differ significantly from that of their larger ancestors and most of this articlewill deal with the so called large-frame lasers.In the space available, it is not possible to provide a complete record of the progressmade in ultrashort pulse generation, or even to provide a comprehensive list of refer-ences. This review is inevitably drawn from a personal perspective and will concentrateon developments an d ideas which have been imp ortan t to the authors work and under-standing of the field. Th e central aim is to explain the state-of-the-art of ultrafast lasers,to show how this has evolved and to project current trends to the near future, Thisreview is not intended to answer specialized questions but to provide a basic andhopefully intuitive introduction to an important, and relatively mature, research fieldwhich is increasingly being adopted by non-specialists as a means to understand ultrafastprocesses in many diverse branches of science and technology. Written by an experi-mentalist, this article includes only such mathem atics as is necessary for the understand-ing of the basic tools of the trade. There are many excellent works covering theoreticalaspects of every topic included in this review and some of these have been referencedfor the benefit of those who wish to study a particular topic in detail. There are alsomany excellent text books which give a more thorough introduction to the basic topicscovered here. References [1-4] are a personal selection.The discussion here will be limited to ultrashort pulse generation from continuouswave (cw) mode-locked lasers, with particular reference to dye lasers and vibronicsolid-state lasers, since these are the most important for ultrashort pulse generation.


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172 P M W FrenchSemiconductor lasers and fibre lasers will be mentioned in passing. Most ultrafast lasersare predominantly homogeneously broadened and no account here will be taken ofinhomogeneous broadening or of the physics particular to specific laser gain media.Space constraints also preclude the possibility of discussing the wealth of ultrafastdiagnostic an d time-resolved spectroscop ic techniques which have been developed. Som eattentio n will be paid, how ever, to the stand ard ultrafast diagnostics of sffG autocorrela-tion an d streak cam eras since they a re essential to any ultrafast laboratoty. The firstsection of this article introduces the essential issues of ultrashort pulse generation andsome of the laser media which have been employed to this end. The second section isa historical overview of the evolution of ultrafast lasers. This assumes some knowledgeof the field and a newcomer may be well advised to first read sections 3 and 4 whichdiscuss the basic principles in more depth. Section 3 discusses the various techniquesfor mode-locking lasers and is intended to be comprehensible to a reader with anelementary knowledge of laser physics. Section 4 deals with the roles of gro up velocitydispersion an d self-phase mod ulation which are crucial to the generation of femtosecondpulses. Finally, section S discusses the most common techniques for measuring ultra-short pulses.1.2. Issues it1 ultrashort pulse generationF or the users of u ltrashort pulses, the first issue is to find a suitable laser which providesradia tion at the w avelength of interest. In the past this has mainly confined the applica-tions to those spectral regions covered by laser dyes which may be excited by argonion lasers, krypton ion lasers an d the fundamental outp ut of the N d : YAG laser and itsharmo nics. W hile this provided broad and relatively conven ient coverage for the visiblespectrum, the infra-red was less accessible due to the scarcity of suitable dyes and thedifficulties associated with the toxicity and poor photochemical stability of those dyesthat did exist. In the near infra-red, tunable ultrashort pulses could be obtained fromcryogenic colour-centre lasers bu t this was not considered a convenient option by manyresearchers who relied on the Nd-doped solid-state lasers at 1.06 p m and 1.3p m , Therecent development of broadly tunable, vibronic solid-state media which operate atroom temperature has transformed ultrafast laser physics, providing unprecedentedspectral coverage and the last decade has seen tremendous advances in the technology.These media will be briefly discussed in section 1.3.Having established that a suitable laser exists, the next step is to generate theultrashort pulses by mode-locking. The many techniques for mode-locking lasers arereviewed i n section 3. Essentially they require some form of amplilude modulationapplied to the laser radiation which has a period equal to the cavity round trip time.This modulation may be derived externally, as in the case of active mode-locking, ori t may be derived passively from the radiation itself via a n intensity-dependent lossmechanism. T here are alternative app roaches to ultrashor t pulse generation using gain-switching in which femtosecond pulses may be generated by pumping a cascade of shortcavity lasers with ever shorter pump pulses e.g. .[SI.This works well with dye laserswhich can exploit uv excimer pump lasers and achieve broad spectral coverage. Ingeneral, however, most users prefer cw lasers for their experiments which generallyproduce shorter and cleaner pulses because the pulse shaping takes place over many100s to 1000s of round trips. Indeed, passively mode-locked cw lasers offer one of thehighest peak-to-background ratios of any ultrafast signal that can be synthesized. Theprecise mode-locking technique employed wil l depend on the characteristics of the laser


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The generution of ultrashort laser pulses 173media. the desired pulse duration and practical considerations such as cost, the stabilityand pulse quality requirements and the need for synchronization to other signals.Requirements for pulse durations vary with application :many electronic detectionsystems are limited to temporal resolutions of tens of ps while pump/probe measure-ments can exploit pulses shorter than 1Ofs. In general, it is not significantly easier togenerate picosecond pulses than femtosecond pulses if high temporal and amplitudestability is required. A picosecond laser is not simply a bad femtosecond laser and, infact, a conventional actively mode-locked solid-state laser would probably have ahigher com pone nt cost th an a state-of-the-art Ti : sapph ire laser generating 20 fs pulses.Once the desired pulse duration and wavelength have been determined, the first consid-eration is the bandwidth of the system. By the uncertainty principle, an ultrashort pulsein the time domain must have a correspondingly broad spectrum in the frequencydomain. It is therefore necessary to establish that the gain medium has a sufficientlybroad linewidth to amplify the ultrashort pulses a nd that the othe r com pone nts (mirrors,mod ula tor s etc) ar e sufficiently broa db an d in their reflection/transmission responses totransmit the pulses without filtering the pulse spectrum. In particular, if the laser is tobe spectrally tuned using an element such as a prism or a birefringent (Lyot) filter,then this filter must have a sufficiently broad pass-band. Note that where picosecondpulses are required, it is often necessary to restrict the bandwidth of the laser in orderto discriminate against noise. This is the case when a relatively weak mode-lockingtechnique such as synchronous pumping is employed.To generate pulses much shorter t han a picosecond, it is necessary to take accountof group velocity dispersion (cvD)-the phenomenon which causes different frequencycom pon ents t o travel a t different speeds, thereby broadening the pulses as they circulatein the laser cavity (see section 4). T h e spectral width of the pulses is inversely propor-tional to the temporal duration and so as pulses become shorter, they become moresusceptible to CVD. For picosecond lasers, CVD is usually neglected although it isoptimized in the latest picosecond Ti :sapphire lasers which pennit the pulse durationto be continuously adjusted up to -100 ps. Clearly excessive CVD will prevent thegeneration of short pulses and so it should be minimized. This is usually achieved byincluding components in the laser cavity which provide adjustable CVD of the oppositesign to the laser medium and other components. Thus the net cavity round-trip CV Dexperienced by the pulse may be arbitrarily set to zero or some optimum value.A further property of ultrashort pulses is that they tend to exhibit high peak powers.Typically th e average power from a c w laser is not greatly reduced by the mode-lockingprocess. M os t lasers deliver -100 mW average out put power, *an order of magnitude,although there are obviously exceptions. With an output coupler of a few YO, ne canestimate average intracavity power levels of -1-100 W. There is no fundamental reasonwhy mode-locking should dramatically reduce the average power from the laseralthough the insertion loss of the components required to achieve mode-locking willusually entail some penalty. Suppose that the laser is mode-locked such that it generatespulses of 1 ps duration at a pulse repetition rate of 100MHz-corresponding to a 10 nscavity round -trip time. Th e intracavity pulse energy will therefore be -10 nJ-I pJ andthe peak pow ers will be IO kW-l M W . For most lasers, cavity radiation is focused toa beam waist of tens of p m i n the gain medium in order to achieve a sufficiently highpopulation inversion. Thus peak intensities reach levels of 1O8-1Oi0 W cm-* in a beamof 100p m d iameter. At such high intensities, which are actually quite modest estimates,the refractive index of the intracavity media can become non-linear and this gives riseto se@+liu.w modulation (SPM) due to the optical Kerr effect. SPM causes the pulse


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174 P M Mi Frenchspectrum to broaden which can increase the loss at any spectral filter in the laser. Itcan also, together with GVD, cause the pulses to either broaden or compress and i t cancause the laser to become unstable. This interaction is discussed in section 4. In practice,to generate femtosecond pulses, first GVD must be reduced so that u ltrashort pulses canpropagate in the laser cavity. Secondly, the interaction of SPM and GVD must be explo-ited in such a way a s to obtain shorter, stable pulses. The ab ility to control this inter-action determines how short a pulse can be generated.The optical Kerr effect may a lso be exploited to achieve mode-locking. Either temp o-ral SPM or self-focusing may be used to generate an intensity-dependent loss for theintracavity rad iation which results in powerful pulse shap ing. This technique is possiblewhen the intracavity power levels are high enough to access the non-linear refractiveindex of the laser medium. The development of high average power ultrafast solid-statelasers has dem onstrated the potential of this approach. Its major drawback is that itdoes require high intensities to work and this means that lasers mode-locked in thismanner are often not scr-starting, i.e. they do not become modelocked as soon asthey are switched on. The physics underlying the self-starting of lasers is not yet fullyunderstood and the self-starting issue remains one of the most serious impediments tothe widespread development of ultrafast lasers. In practice, many laser systems use a'conventiona l' self-starting mode-locking technique to generate picosecond pulses andthen use the optica l Kerr effect to com press the pulses to the femtosecond regime. Thefinal dura tion is then determined by the interaction of SPM and C V D .The discussion of applications of ultrashort pulses is beyond the scope of this articlebut I will make a few observations in this section. First, the most important scientificapplication of ultrashort pulses is time-resolved spectroscopy. Widely tunable fem to-second lasers permit time-resolved studies of many physical, chemical and biologicalprocesses. Pulses of a few femtoseconds duration enable molecular dynamics to beresolved. Femtochemistry in particular is growing into a huge field and there appearsto be a real chance of directly controlling chemical reactions using appropriate ultrafastoptical signals. Solid-state physics can be studied with sufficient resolution to resolveelectron dynam ics in semiconductors and there is much current investigation of ultrafastlight-matter interactions. I t is now possible to generate pulses shorter than the homo-geneous dephasing times of many systems and coherent phenomena are routinelystudied. In particle accelerators, femtosecond pulses are being used in photo-injectorsto generate extremely short bursts of electrons. Potential real-world applications of highlime resolution include ultrahigh bit-rate optical signal processing and com munications,high speed electronics and time-gated imaging through turbid media which may findwidespread medical application. The ability to coherently extract large amounts ofstored energy from laser amplifiers in a very short time using femtosecond oscillatorsand amplifiers has produ ced relatively com pact (table-to p) laser systems delivering peakpowers in the tens of TW range. These have been applied to m ultiphoton and atom icphysics experim ents and have been used to generate extremely bright bursts of x-rays,At more modest levels, powerful ultrashort pulses have been used to study a widevariety of non-linear optical effects. Th e list of applications is vast and the number ofusers of ultrafast laser technology is increasing rapidly. This article is intended toillustrate some of the physics underlying the technology and will perhaps assist thegrowth of the ultrafast community.1.3. Ulmfusr laser media1.3.I . Fi\.ed-wauclengfh lasers. The first laser to be mode-locked was the helium-neonlaser [6] but the extremely narrow gain-linewidth only perm itted the generation of ns


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The generation of ultrashort laser pulses 175pulses. Mode-locking achieved picosecond pulse dura tions in a number of broaderlinewidth fixed-wavelength laser media including the ruby laser at 694 nm, the argonion laser at 514 nm, the krypton ion laser at 647 nm, Nd:doped Y A G and glass lasersat 1.064 p m and E r:doped glass at 1.55 pm . The electronic transitions in N d : u a c andruby are homogeneously broadened due to collisions of the ions with the crystal latticephon ons. G as lasers exhibit electronic transitions which are predominantly inhomogene-ously broadened due to Doppler broadening. The Nd :glas s and Er:glass lasers, whichexhibit the broadest gain linewidth of the common fixed-wavelength lasers and haveyielded the shortest pulses, are predom inantly inhomogeneously broadened due to localinhomogeneities in the glass host. The fixed-wavelength solid-state lasers tend to haverelatively long upper state lifetimes ( p s to ms) and low gain cross sections. This leadsto a high energy storage cap acity, mak ing them useful a s laser amplifiers and efficientlaser oscillators, but it also means that they are difficult to saturate and this has animpact on the mode-locking techniques which may be applied Lo them. It also meansthat they have a s trong tendency to Q-switch when there is a saturable absorber in thecavity.No ble ion gas lasers have a linewidth sufficient to supp ort pulses of -50 ps dura tionbu t typically deliver pulses >IO0 ps when actively mode-locked. They are useful aspum p sources for synchronously mode-locked dye lasers and, like other fixed-wave-length lasers, more often provide the c w laser pump source for tunable ultrafast lasers.I n its own right, however, the arc-lamp-pumped N ~ : Y A Gs one of the most widelyused ultrafast lasers, typically delivering -100 ps pulses with of the order of tens of Waverage outp ut po wer. In recent years i t has been partly supplanted by N ~ : Y L Fhichgenerates pulses of -30 ps duration with comparable power levels. Semiconductordiode-pumped N d : doped lasers have now generated rather shorter pulses and haveprovided the first all-solid-state, com pact ultrafast lasers. Diod e-pum ped Nd :YAG andN d : V L F lasers have generated pulses as short as 8.5 ps [7] and 6 ps [SI respectivelyusing the technique of Kerr lens mode-locking. An arc-lamp-pumped N d: Y L F laser hasgenerated pulses as short as 2.3 ps [9]. Laser-pumped and diode-pumped Nd:glasslasers have generated subpicosecond pulses in many configurations and the shortestpulses of -32 fs were obtained from a krypton ion laser-pumped Nd:glass fibre laser[IO]. E r: glass fibre lasers have received considerable attention as can didates for ultrafastoptical telecommunications sources and diode-pumped erbium fibre lasers have gener-ated pulses as sho rt as -100 fs [1 I ] .1.3.2. Dye lasers. Th e first tunable u ltrafast lasers were c w dye lasers and the passivelymode-locked dye laser held the record for the shortest pulses for many years. Theshortest pulses ever generated, of 6 fs duration, were obtained from a fibre-opticallycompressed dye laser [12]. Since its demonstration in 1966 by Sorokin and Lankard[131, the dye laser has been one of the m ost versatile and most widely employed lasersources. Organic dyes are laser media whose absorption bands in the ultraviole t, visibleor near infrared spectrum result from the presence ofconju gated bonds in the molecularstructure with associated delocalized x-electrons. Laser transitions occur between themanifold of vibrational (and rotational) energy levels associated with the electronicenergy levels. This type of laser action is described as vibronic (or vibrational-elec-tronic). The ground state singlet electronic level (So) is separated from the singlet andtriplet excited levels (SI, T I ) by IO 000-30 000 cm-I. There are vibrational and rota-tional levels associated with each electronic level which are separated by -1000cm-'and -10 cm-' respectively. Interaction with the solvent of the dye produces collisionaland electrostatic perturbations that homogeneously broaden these levels resulting in


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I16 P M M Frenchelectronic levels which are essentially continua of states. I t is the range of possibletransitions hetween these continua that provide th e broad absorption and emissionhands of laser dyes. Much work has been done selecting an d engineering dye moleculesto shift the central transition frequency from the ultraviolet to the near infra-red. Toda ythe broad emission bands of organic laser dyes provide spectral coverage from -320[I41 to -1800 nm [ 1 5 ] . All laser dyes tend to have high gain cross sections and shortupper state lifetimes (-11s). They are the most easily saturable laser media and thishas dominated the development of the mode-locking techniques with which they haveproduced ultrafast lasers.At first glance, their high gain cross sections, large homogeneously broadened line-widths and cost effectiveness made dyes almost the ideal ultrafast laser medium. Unfor-tunately they have a limited lifetime due to photochemical degradation, a re inconvenientto handle and are often toxic and carcinogenic. There are problems associated withtriplet-quenching in which the long-lived triplet state traps excited molecules and soinhibits laser ac tion. This is avoided in c w lasers by flowing the dye solution rapidlythrough the pumped active volume in a jet stream and sometimes by the addition ofchemical triplet-quench ing agents such a s COT (cycloctatetraene) or oxygen to thedye solution. For many applications dye lasers are being replaced by broadly tunablevibronic solid-state lasers such as titanium-doped sapphire but there remain manyultrafast dy e lasers in operation and they provide useful coverage of the visible spectrumwhere there are no broadly tunable solid-state lasers. Although the first mode-lockeddye lasers were flashlamp pumped [16], it was the c w dye laser which became thestandard laboratory ultrafast laser and on which much of femtosecond laser physicswas learned. Th e tuning range o f c w dye lasers is limited by the available pump sources.Argon ion lasers are able to provide c w pum p radiation from wavelengths as short as275 nm and the various emission lines of krypton and argon ion lasers provide pumppower a t wavelengths up to -800 nm, as indicated in table I . Nd :YAG lasers provide

Tab lc 1. Common pum p sources for cw asersAvailableAvailable Pump PumpPump pump power wavelength power

P ump laser wavelength ( n m ) ( W ) (nm) W )Argon ion laser 476-514 25 472.7 1.2528.7 2 465.8 0.75

514.5 10 457.9 I.4501.7496.5488.0476.5

1.5 454.5 I .92.5 351,1-385.8 38 333.6-363.8 72 .8 275.4-305.5 0.6Krypton ion laser 752.2-799.3 I6647.1-676.4 4 .6

520.8-568.2 3.6Laser diodes -670 - 10

-980 - 3(1GaAlP)(InGaAs)

Nd:vhc aser I064 22and harmonics 532 3

468.0-530.9 1.5406.7422.6 1 .3337.5-365.4 2

-800-900 -10(GaAIAs)( InGdAsP)355 2266 I

- 480 -.I


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The generation of ultraslzorr laser pulses 177useful pum p power at 1.064 pin and I .3 pin although there are not many infra-red dyeswhich are sufficiently srnble for c w operation . Reference [I71 provides a comprehensivelisting of laser dyes, their properties and references on previous work. The physics ofdyes an d dye lasers are discussed further in [IS] and [191.1.3 .3. Tunable solid-stnte lasers. The Ti: sapphire laser has become almost synonym ouswith femtosecond laser technology and it, together with other room-temperature vib-ronic laser media, looks set to replace ultrafast dye lasers in almost all applications.Table 1 gives a list of potential pum p sources for c w vibronic solid-state lasers. Suchlasers offer all the convenience of so lid-state laser media, they have long (-,us) lifetimesand gain linewidths which exceed those of dyes by almost an order of magnitude. Thebroad absorption/emission linewidths arise as a consequence of the strong couplingbetween the vibrational energy states o f the host crystals and the electronic energystates of the active ions-hence the label vibronic solid-state lasers. This strong coup-ling between vibrational and electronic energy states depends critically on the preciseinteraction between the active ion and host crystal fields. Vibronic lasers are usuallytransition earth meld1 ions, such as Ti3, C r and Cr4+doped into suitable hosts. Thetransition metal ions are appropriate since their electronic structure is that of argonwith the valence electrons filling the 3d shell outside the inert 3s2, 3p6 configuration.Thus these electrons are exposed and can interact strongly with the host crystal field.In contrast, the fixed-wavelength lasers tend to be rare earth ions (e.g. Nd?, Er3+ etc)with the valence electrons filling the 4f shell inside the 5s2, 5p6 shells. In this case, theelectrons responsible for the laser transition are shielded from the host crystal field bythe inert gas structure. Consequen tly there is no significant interaction and the transi-tions tend to be narrow. N ote that the transition metal ions do not always form vibroniclasers in crystals. Cr+:sapphire is ruby, a narrow linewidth, fixed wavelength lasermedium, while c r : L i s ~ ~ rovides a vibronic tunable laser. The difference arisesbecause the local crystal field in LisnF is stronger than in sapphire, Even in ruby,however, the absorption bands are broad as a consequence of the coupling betweenvibra tional and electronic energy states. The physics of solid-state lasers is discussed atlength in [20-221.Ti:sapphire was first lased in 1982 by Moulton and subsequently characterized [23]as a promising tunable laser medium with an upper state lifetime of 3 ps and one ofthe highest gain cross sections of any solid-state laser. It tunes from -680-1 130 iim-the widest percentage tunability of any laser. With improvements in the crystal quality,argon-ion laser-pumped cw. Ti: sapphire lasers deliver several W of average outputpower and have generated pulses as short as -10 fs. The design of such lasers is rathersimilar to cw ye lasers with the dye jet stream being replaced by the T i:sapph ire laserrod and the folding angle at the focusing mirrors being adjusted to compensate forastigmatism e.g. [24]. Typically th e pump and laser radiation are focused to


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178 P M M Fwiichcrystals are promising materials which tune over the region -750-1000 nm and whichhave absorption bands suitable for pumping with diode lasers at 670 nm and withcotiventional flashlamps and perhaps arc lamps. They have an upper state lifetime-7Ops and so are well suited as laser amplifiers and low threshold diode-pumpedoscillators. Pulses as short as 33 fs have been generated from an argon-ion pumpedCr3 + LisAF laser [25] and already the first diode-pum ped femtosecond Cr : LisAFlasers have been demonstrated [25]. In thenear infra-red, Cr: Forsterite and Cr4t :YAGprovide coverage from 1.13-1.37pm and 1.35-1.58pm respectively. Kerr lens mode-locking has yielded pulses as short as 25 f s from Cr4t :Forsterite [27] and pulses asshort as 70 fs have been generated from Y A G lasers (281. These Cr 4t: doped lasersare readily pumped by c w N d :YAG lasers a t 1.06 pm and may be directly diode-pumpedinto the same absorption band e.g. using pump laser diodes at 980 nm. Their upperstate lifetimes and gain cross sections are comparable lo Ti:sapphire and so one canexpect similar performance from thecw lasers. Up to now, the crysta l quality is inferiorto Ti :sapphire and there are problems with thermal lensing and excited stale absorption.Nevertheless, these lasers can deliver -1 W average output power for -10 W pump

C+*:ForstterIte-H-SH err-

SH C=F8H n:sapphire--r I1W 400 GOO 800 TOO0 1200 1400 1600 1800

Wavelength (nm)Figure 1. Tuning range of roomtemperature c w vibronic solid-state lasers.

power. Figure I shows the tuning range of just four room-temperature c w vibronicsolid-state lasers. It will be seen that with second harmonic generation, most of thevisible and near infra-red spectrum is covered up to -1.6 pm . There is still a small gaparound 600 nm which is, ironically, where (ultrafa st) c w dye lasers perform best. It islikely that this region will be covered in the near future, perhaps by Pr+-doped lasers.There are a number of other tunable vibronic lasers which operate at cryogenictemperatures. These include divalent transition metal lasers such as N iM g0 andC O :M gF2 and alkali-halide colour centre lasers. The practical difficultieso f workingat 77 K have precluded the widespread application of these lasers but they have beendemon strated as c w mode-locked systems. The former transition metal lasers can bepumped at 1.3 pm by a N d :u n c laser and tune from -1.6-1.73 pm and 1.62-2.1 p mrespectively. They have been actively mode-locked to yield pulses o f tens of ps 1291.Colour-centre lasers provide spectral coverage form -800 nm to -3 pm and mayoperate either c w or pulsed. The energy levelsof hese media a re associated with defectsin alkali-halide crystals. These are vacancies in the crystals which may be filled by e itherelectrons or small alkali ion impurities. Some common co lour-centre active media areNaC I, Na F, NaCl:OH -, KCI:Li, KC I:Na and KCI:TI. Reference [30] provides auseful review of colour-cen tre lasers. They have received a considerab le am oun t ofatten tion as ultrafast lasers and the NaC1:OH- and K CI:TI lasers in particular have


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The generation of ultrashort laser pulses 1I9been used to generate femtosecond lasers tunable through the telecommunicationswin-dow around 1.5Spm e.g. [31]. The upper-state lifetimes and gain cross sections ofcolour-centre lasers vary considerably from values which are similar to dyes (tens ofns) to parameters which are more like transition metal lasers (e.g. 1.6 p s for KC1:TI).As well as requiring cryogenic operating temperatures, c w colour-centre lasers alsosuffer from photo-degradation and these practical inconveniences mean that they willbe replaced by either vibronic room-temperature solid-state lasers or optical parametricoscillators.1.3.4. Semiconductor lasers. Semiconductor lasers exhibit linewidths of the order of-1Onm and generated pulses as short as a few 100 fs duration. They are clearly astrong candidate for com pact ultrafast laser sources and will almost certainly find real-world applications a s such. Ultrafast sem iconductor laser physics is a huge field in itselfand semiconductor lasers are outside the scope of this article although they will bementioned in passing. Their upper state lifetime and gain cross sections are comparableto those of dyes and so gain (and absorption) saturation plays a strong role in theirmode-locking. In general, although i t is possible to genera te -600 fs pulses from monol-ithic semiconductor structures e.g. [32], femtosecond pulse generation requires the sem-iconductor amplifier to be used in an external cavity. One reason fo r this is that theyexhibit high non-linearity when interacting with ultrashort pulses and attempts at gener-ating u ltrashort pulses by directly mode-locking semiconductor lasers are usually com-plicated by unwanted phase modulation which arises from the carrier dynamics of gainswitching and depletion. External cavities permit the incorporation of approp riate chirpcompensation devices. They also permit the cavity length to be extended such that anexternal K F drive signal may be synchronously applied for active mode-locking. Theshortest pulses to be directly generated from an actively mode-locked semiconductorlaser are 580 fs [33]. External compensation of the frequency modulation has generatedpulses as short as 200 fs [34] from a hybridly mode-locked semiconductor laser whichwas externally amplified and compressed with an appropriate dispersive delay line.Reference [34] gives a review of ultrashort pulse generation from semiconductor lasers.In practice the degree of complexity required to generate clean ultrashort pulsesfrom semiconductor lasers makes them no more simple than a diode-pumped solid-state laser. It is very difficult to simultaneously optimize all the parameters of semicon-ductor diode lasers. Although diode lasers and diode arrays can deliver tens or evenhundreds of watts of average output power, it is not generally possible to achieve ahigh quality spatial and temporal profile at the same time. One reasonably successfultechnique to achieve good beam quality is to use the tapered amplifier geometry in amaster oscillator-power amplifier ( M O P A ) scheme which can prov ide high outpu t powersin a diffraction-limited beam [35]. A n all-semiconductor device can be constructed byinjection-locking the power amplifier with a low power, diffraction-limited ultrafastdiode laser. An alternative scheme, which can provide com parable ou tput powers, betterbeam qu dity and rather shorter pulses for a s imilar level of complexity, is to use diodelasers or diode ar rays to pump a m ode-locked (vibronic) solid-state laser. This approachis being applied to C r: LisAF, as discussed in the previous section. I t has already beenapplied to Nd : YAG and Nd : Y L F lasers for p icosecond pulse generation and to N d: glassand Er:glass fibre lasers for both picosecond and femtosecond operation. Table Iindicates the wavelengths a t which high power diode laser pum p sources are ava ilable.The rapid development of new vibronic solid-state media and ingenious pumpingschemes make this app roach extremely promising.


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I80 P rM W French2. I-listorical overview2. I . I n / r o d ~ i c t i o ~ iThe first laser to be mode-locked was a helium-neon laser in 1964 [36]. Nanosecondpulses were generated using an infracavity loss modulator and this was explained asactive mode-locking. Subsequen tly many new mode-locking techniques have been dem-onstrated and pulse durations have been reduced to the the -10 fs regime. There aremany excellent reviews of m ode-locking which cover the historical development in moredepth than I shall attempt here. In particular, Smith has provided a useful review ofthe early research on mode-locking from a 1970 perspective [37], New has describedthe development until 1983 [38] and Krausz e / a1 have summarized the importantadvances of the last decade [39], It is not possible to reference here all the significantpapers in this field or to acknowledge all the contributions to its development. This isa personal overview and I have cited those papers which have come to my attention,trying particularly to include those related to significant developmentsi n the field.Over three decades, the development of ultrafast lasers has been described in termsof three generations [39]which have been closely related to the breakthroughs in thelaser media and appropriate pumping schemes. The first generation of mode-lockedlasers were mostly lam p-pum ped solid-state lasers, dye lasers o r gas lasers. They weremode-locked using generic active or passive techniques to generate pulses of tens ofpicoseconds dura tion. Active modulation techniques alone were shown to be unable tomode-lock the whole of the available gain linewidths and the pulse durations achievedby passive mode-locking were limited to the recovery time of the resonni?/saturableabsorbers. Furtherm ore, the fact that the flashlamp pump pulses were limited to a few100{is duration nieant that there were only a limited number of cavity round-trips onwhich the mode-locking mechanism could act on the pulses. This issue was addressedfor the second generation of ultrafast lasers which was engendered by the dem onst rationof the c w dye laser [40]. This quickly led to the c w m ode-locked dye laser [4 l whichcould also take advantage of the strong gain/absorption saturation of dyes to achievemore powerful pulse compression than was hitherto possible. Essentially, by using twoseparate mechanisms to shape th e leading and trailing edges of the pulses, they achieveddura tions sho rter than the recovery times of the resonant non-linearities they exploited.The resulting lasers generated subpicosecond pulses and it was then necessary to takegrou p velocity dispersion (G V D ) nto accoun t. This led to a greatly improved under-standing of the interactioii of G V D and non-linear frequency chirp and resulted i n thegeneration of sub-30 fs pulses whose duration was limited by the gain linewidths ofthe dyes. Extracavity pulse compression yielded sub-10 fs pulse durations. The thirdgeneration was ushered in by the demo nstration of the soliton laser [42] which showedthat ~ z o ~ z - r e s o ~ u n ~ode-locking techniques based on the optical Kerr effect could beused to produce femtosecond pulses. A parallel and equally important developmentwas the emergence of 'Ti:sapphire as a broadly tunable vibron ic solid-state laser mediumwhich did not exhibit strong gain saturation under cw pumping. This laser requiredthe non-resonant m ode-locking techniques and prompted the intensive research whichhas produced widely tunable ultrafast lasers generating sub-100 fs pulses over a broadspectral range. One is templed to say that the development of mode-locking techniquesis almost at an end since we have the means to mode-lock almost any laser medium,given sufficient intracavity power. Certainly a major part of ultrafast laser developmentin the near future will be to develop new broadband gain media and apply existing


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The generation of ultrashort laser pulse's 181mode-locking techniques. J envisage the fourth generation of ultrafast lasers to becompact practical devices appropriate to rea-world applications. These lasers willalmost certainly be diode-pumped and they will be versatile in terms o f pulse repetitionrate and energy. With the help of non-linear frequency shifting techniques such asharmonic generation and optical parametric amplification, they will provide a broadspectral coverage. Finally, they will hopefully be designed to be robust and low-costsuch that they will become standard instrumentation in laboratories and applicationssites.

2.2. First generation: picosecond lmemAfter the experimental observation of the mode-locking of the He-N e laser, theoreticaldescriptions of mode-locking were published e.g. [43,44]. FM modulation was used tomode-lock a He-Ne I451 soon after and active mode-locking techniques were appliedto argon ion [46] and ruby [47] lasers. In 1965, th e use of a fast saturable absorberdye to passively mode-lock a laser was demonstrated with ruby [48] an d was quicklyapplied to Nd :glass lasers [49] whose inhomogeneously broadened linewidth couldpotentially support subpicosecond pulses. Unfortunately, the poor thermal propertiesof the glass host precluded c w operation (cf the arc-lamp-pumped N ~ : Y A Gaser) formost ultrafast experiments and investigations were limited to @switched, mode-lockedpulse trains of uncertain reproducibility at 1.06pm . A great improvement in tunabilitycame with the invention of the dye laser which had a huge impact of ultrafast laserdevelopment. W hile still opera ting in pulsed mode, the spectral coverage of such lasersmeant t ha t they became significantly m or e useful research tools which in tu m increasedthe motivation to improve ultrafast laser technology. Flashlamp pumped dye laserswere passively mode-locked using fast satu rable absorber dyes [50] in 1969an d yieldedpulses a s short a s 6 ps [51]. Subsequent investigations of new laser am plifier/saturableab so rber com binations extended the tunability of ultrafast Rashlamp pumped dye lasersfrom the blue to the near infra-red [38, 21. T he demonstration of m ode-locking bysynchronous pumping o f a dye laser [53-55) using a frequency-doubled Nd :glass lasermore or less completed the range of mode-locking techniques available to the firstgeneration of ultrafast lasers.The technique o f passive mode-locking was especially successful an d this possibilityto generate such short pulses prompted the invention of new techniques for ultrashortpulse measurement such as second ha rm oni c autocorrelation [56] (which is discussedin section 5 ) and two-photon fluorescence (TPF) [57]. The minimum pulse durationachievable with a fast saturable ab sor ber is limited to its absorption recovery time [ 5 8 ]for which the lower limit is -10 ps (e.g. for the Kod ak dyes A9740 or ,49860). Initiallythere were many over-optimistic interpretations of pulse width measurements fromsolid-state lasers due to the fact that noise bu rsts give similar TPF traces to pulses withcomparable spectral widths. Understanding the correct contrast ratios fo r TPF profilesof mode-locked pulses [59] led to more consistent experimental reports and usually thepulse durations were rather longer than the minimum possible values determined bythe gain linewidth and the saturable absorption recovery times. Streak cameras werealso employed to measure pulsewidths and to follow the dynamics of ultrafast laserse.g. [60]. On e problem with passive mode-locking was that the sat ura ble absorber dyealso Q-switched the lasers and terminated laser action before a steady-state could beestablished, even for cw umping. A second problem was that the high pulse energies


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182 P M M French(and correspondingly high intensities) produced strong non-linear self-phase modula-tion of the pulses which, together with GVD, led to spectral and temporal broadening.I t was shown that for passively m ode-locked flashlamp pumped lasers, the mode-lockingwas non-determ inistic with the pulses growing from stochastic fluctuations i n the cavityradiation e.g. [61,62]. To p e rf o m reasonably reproducible experiments with pulses ofcon stan t energy, it was necessary io switch a single pulse out of the evolving Q-switchedmode-locked pulse train, either by cavity dum ping the laser durin g the evolution of thepulse train e.g. [63], or by selecting and switching out a pulse from the laser output[64]. A relatively recent alternative approach to the operation of pulsed ultrafast lasershas been to include a negative feedback device in the cavity which functions like aninverse saturable absorber (i.e. the loss increases with intensity). Th is frustrates the Q-switch and prolongs the mode-locked pulse train for the duration of the pum p excitatione.g. [65], thus providing many more cavity round-trips for the mode-locking processto act on the pulses and achieving durations close to the minimum possible.Active mode-locking via am plitude or frequency mo dulation was applied to pulse-pumped and c w lasers. In particular, lhe actively mode-locked N d : u n o laser [66]received much attention since the possibility of c w pumping (using lungsten filamentlamps and arc lamps) furnished a relatively efficient laser with high average power,delivering pulses of -30 ps estimated dura tion [67 ]. A theoretical descriplion of activemode-locking using A M and FM, together wilh an experimental investigation of theNd:uno laser was published in the seminal papers by Kuizenga and Siegman [68]which predicted the achievable pulse duration in an actively mode-locked laser as afunction of the m odulation and laser param eters. Their model worked reasonably wellfor the narrow linewidth gain media such as N ~ : Y A Gu! was less successful withbroadband gain media. Experimentally, i t proved difficult to generate pulses muchshorter than -100 ps with arc-lamp-pumped N d : u n c lasers and this became a standardcommercial ultrafast laser. Recently actively mode-locked N ~ : Y L Fasers of a verysimilar design have generated pulses of -30 ps due to the broader gain linewidth.Du ring the early research on mode-locking, the phenomenon of spontaneous mode-locking or self-mode-lockingwas observed in He-N e lasers [69] and discussed in termsof the non-linear behaviour of the laser medium. It was also observed in ruby [70],Nd:glass [71], argon ion [72] and other lasers. Self-locking was analysed in terms offrequency pulling of combination tones (beat frequencies) of oscillating modes to othermode frequencies e.g. 1731or in the time dom ain in terms of efficient interaction o f so-called n-pu lses with the population inversion [74]. Spon taneous mode-locking did no tprove a reliable approach for the generation of ultrashort pulses and was more or lessabandoned in favour of actively or passively mode-locked c w lasers but the ideas areonce again important in the effort lo understand the start-up of the third generationfemtosecond solid-state lasers which are o ften described as self-mode-locked.The role of non-linear frequency chirp was also studied in first generation ultrafastlasers as a means to passive FM mode-locking [75, 761 and as a source o f instabilitye.g. [77]. Researchers used the time-bandwidth product (see section 3) as a means ofassessing the quality o f the mode-locking and, particularly for solid-state lasers, oftenmeasured values far in excessof he theoretical minimum. To explain this, some authorsconsidered linear frequency chirp arising from dispersion in the laser medium e.g.[78,79], but for the case of passively mode-locked Nd:g lass lasers, i t became clear itwas due to non-linear self-phase modulation (SPM) arising from the optical Kerr effect[so, 811. Techniques for compressing chirped optical pulses da te back to the interfero-meter proposed by Gires and Tournois in 1964 [82] and compression of pulses after


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The generation of ultrashort laser pulses 183active phase modulation were proposed [83] and demonstrated [84]. In 1968 Treacydemonstrated tha t pulses from a passively mode-locked Nd:glass laser could be com-pressed by an appropria te dispersive delay line [U].He proposed the use of diffractiongratings [86] nd this, combined with the use of a non-linear medium (CS2) to chirppulses for exlracavify compression [87], essentially laid the foundations for the srM/GVD pulse compressor which was demonstrated to compress 20ps pulses from aNd:glass laser to -2 ps [SS]. One further idea to exploit the optical Kerr effect was touse self-focusing for pulse com pression [89], thereby anticipating the inventionof Kerrlens mode-locking and todays state-of-the-art femtosecond lasers.2.3. Second generation: femtosecond dye lasersThe development of the cw dye laser was an important breakthrough for ultrafastlasers since it provided a tunable broadband laser in which the various pulse-shapingtechniques of both active and passive mode-locking could act on the circulating pulseswith cumulative effect until a steady-state was reached. As well as greatly increasingthe effectiveness of the mode-locking techniques, the c w mode-locked laser was also areproducible source of high quality pulses which were reasonably straightforward tocharacterize and to apply to ultrafast measurements. c w colour centre laser also pro -vided much improved performance through passive mode-locking with fast semi-conductor saturable absorbers whose recovery times were subpicosecond e.g. [90].Semiconductor lasers were also passively mode-locked using fast semiconductor satu -rable absorbers to generate pulses of 1.6 ps duration [9l] . The pulses from such laserswere observed to be chirped and subsequent compression yielded durations of 0.83 ps[92]. Actively ]node-locked semiconductor lasers generated pulses as short a s 580 fs 1931.Most of the research effort directed towards femtosecond pulse generation, however,concentrated on mode-locking c w dye lasers which prov ided the first w idespreadultrafast laser technology. The two m ost powerful approaches were synchronous pump-ing and passive mode-locking with a slow saturable absorber (see section 3) . The sametechniques were also applied to colour-centre lasers an d semiconductor lasers with lesssuccess but it was from these systems that the techniques for the third generation offemtosecond solid-state lasers evolved. As well as the general references already cited,[94] provides an excellent review of femtosecond dye lasers.Th e first c w mode-locked dye laser was domonstrated in 1972 by Ippen el a1 [95].This was a Rhodamine 6G dye laser mode-locked with a cell of the saturable absorberdye, DODCI, in the cavity. Pulses as short as 1.5 ps were generated which was surprisingsince the recovery time of the absorber was several hundred picoseconds. A theory toexplain this result, and anom alously short pulses obtained from passively mode-lockedflashlam p-pumped dye layers, was presented by New [96,97] who explained how thecombined action of saturable absorption and saturable gain could generate muchshorter pulses than the recovery times of either the gain or absorption. R apid progresswas made experimentally with the introduction of free-flowing dye jet streams, ratherthan flow cells [98], and the first subpicosecond pulses were generated by Shank andIppen using a mixture of amplifier and absorber dye flowing in a single jet stream [99].This laser also included an acousto-optic cavity-dumper and thereby produced pulsesof 60.5 ps duration with -4 kW peak power. I n a later experiment with separateamplifier and absorber dye jets, the same authors used a diffraction grating pair tocompress chirped output pulses to 300 fs [1001. At this time, Haus published a theoryof mode-locking with a slow saturable absorber which built on the work of New and


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I84 P M W Frenchderived a closed form so lution fo r the pulse shape which was shown to be a hyperbolicsecant [ l o l l . The experimental dye laser was further refined to incorporate collidingpulse mode-locking (CPM). In the first implementation, the saturable absorber wasflowed through a cell contacted onto the end mirror of the cavity such that the retro-reflecting pulses set up a standing wave in the absorber and the coherent addition ofthe interfering light fields saturated the absorption more efficiently. Pulses of 300 fswere obtained directly from the laser [IO21 which were a factor of two shorter thanobtained without this effect. The next advance was to construct a laser with no intracav-ity bandwidth limiting elements such as prisms and pulses of 200 fs were generatedusing only the dielectric coatings of the mirrors to control the laser wavelength [103].This approach was combined with the colliding pulse geometry in a linear and a ringconfigura tion a nd generated sub-100 fs pulses for the first time directly from the laseroscillator [104]. This landmark experiment prompted much research on CPM ring dyelasers and significantly shorter pulses (e.g. 55 fs [IOS]) were obtained from a ring laserwith carefully (but empirically) selected mirrors. The CPM mechanism was studied indetail e.g. [IO61 but eventually proved to be essentially unnecessary once the crucialrole of frequency chirp and GVD was elucidated. One interesting variation of the CPMtechnique was to use an anti-resonant ring configuration [IO71 which h a d been previ-ously demonstrated with passively mode-locked solid-state lasers [ lox].It was the systematic optimization of the intracavity frequency chirping mechanismtha t led to the state-of-the-art CPM dye lasers and ultimately to the femtosecond solid-state lasers of today. Dietel et a/ log , 1101 showed that the pulses from a CFM dyelaser exhibited a negative chirp and demonstrated that they could minimize the pulseduration by changing the intracavity glass-path in the laser. The glass-path was intro-duced by a prism which was located such that the cavity focusing optics reduced itstendency to limit the available bandwidth [ l I] . Time-dependent saturation of thesaturable absorption was proposed as a source of non-linear chirp [70] leading to pulsecompression with the GVD of the prism glass [1121. Formation of frequency chirp insaturable absorbers received considerable attention, e.g. [ I 131 and the optimization ofcph i lasers was shown to be sensitive to the precise detuning from the absorber resonancei.e. to the laser wavelength. The next important stepwas the proposal and demonstrationof using prism pairs to provide adjustable intracavity GVD [ I 141. Initially this did notimprove the pulse duration because the optimum GVD had already been achieved bymirror selection. Th e GVD contribution from dielectric mirrors was explicitly modelled[11 , 1161 an d this completed the basis on which to optimize GVD in femtosecond lasers.Martinez et a / [1171 pointed out that soliton shaping in such lasers, could lead to thegeneration of shorter pulses in a manner analogous to compression in optical fibres.Subsequent more sophisticated theoretical models considered the interaction of GVDwith frequency chirp arising from both SPM due to the Kerr effect and the time-depen-dent saturation ofthea bso rptio n [ I 18, 1191. In 1985 Valdmaniset a / [ 1 2 0 ]demonstrateda c rM ring dye laser which generated pulses as short as 27 fs . This laser was designedto maximize the positive frequency chirp due to SPM in the dye jets and minimize thenegative contribution due to absorption saturation [1211. This work prcmpted muchmore investigation of the pulse shaping mechanisms in C P M dye lasers (see sections 3and 4) a lthough significantly shorter pulses were not reliably generated since the du ra-tions were already limited by the linewidths of the amplifier and absorber dyes. Salinet a/ 11221 observed high order soliton propagation in a CPM dye laser and proposedthis as a compression mechanism and a perturbed non-linear SchrBdinger equation( NLSE) as a model o f the laser. Haus and Silberberg [I231 predicted that soliton shaping


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The generation of ullrashorf laser pulses 185would decrease the achievable pulse du ra tio n only by a factor of two before instabilitiesset in. They suggested that the shortest pulses would be obtained for zero intracavityCVD and external linear compression but Avramopoulos et a1 [124], showed theoreti-cally and experimentally that the dye laser, with its stro ng spectral filter, due to thefinite linewidths of the gain, absorption and cavity optics, was unstable for zero GVDand produced the shortest pulses for net negative GVD. These pulses were transforin-limited (i.e. chirp free). This work also indicated that the higher order soliton com-pression was not app rop riat e for such a system and that the NL S E could only be usedto describe the laser when the spectral width of the pulses was much less than that ofthe effective filter.Most o f the development of femtosecond dye lasers was undertaken using the CPMring laser based on the design of 11211 using Rhodamine 6GjDODCl as the saturableamplifier/absorber dyes. Th e same techniques were eventually successfully applied t oother amplifier/absorber dye combinations (e.g. [1251 and references therein) providingspectral coverage with -100 fs pulse generation from the blue [I261 to the near infra-red [127]. It was observed, however, that not all combinations of gain and absorberdyes would result in passive mode-locking, even though they fulfilled the criteria setout by New [96, 971. Empirical selection of successful saturable absorbers based onsystematic lifetime measurements (e.g. [128]) confirmed the hypothesis that a shortlifetime was required for the absorber to initiate mode-locking e.g. [125]. This wassupported by a theoretical model of New and Rea [129]. Alternative techniques forproviding adjustable GVD were employed including Gires-Toumois interferometers[ I 301 which offered the possibility of compen sating for higher order G V D [I311 althoughthis did not result in the generation of shorter pulses [132], suggesting that this wasnot an issue for the relatively narrow spectral widths imposed by the dye media. Analternative technique for adjusting the cavity CVD was to employ dielectric mirrorcoatings off-resonance by using an appropriate non-resonant wavelength [I331 or byvarying the angle of incidence [1341.1974 1991. it was no t until 1985 [1351 th at altem ative amplifier/absorber dye com bina-tions were used to generate fs pulses a t wavelengths outside the -590-640 nm range ofRh od am i ne ~ G / D O D CI .his lack of tunability was largely met by c w m ode-lockeddye lasers synchronously pumped by mode-locked ion lasers or frequency-doubledNd : Y A G lasers. The first demonstrations of synchronous pumping using Q-switchedmode-locked solid-state lasers [53-551 generated pulses of >IO ps duration . Improvedpulse compression was achieved by using a c w pu m p source which provided manymo re cavity round-trips for the pulses to be compressed and the first experiments yieldedpulses o f 2.8 ps duration [1361. The technique was quickly extended to other laser dyesproviding broad spectral coverage from the blue (pumped with a mode-locked argonion laser in the u v [1371) to the near infra-red (pumped with a mode-locked krypton ionlaser 11381 or with a mode-locked N ~ : Y A Gaser [1391) and this app roach subsequentlybecame the principal commercial ult raf as t laser system. Any c w laser which can beexcited by a mode-locked c w laser can obviously be s y n ch ro n o u sl y p u ~ ~ ~ p e ~ ,f the pulseenergy of the slave laser is sufficient to saturate the gain, then the laser will becomesynchronously mode-locked. In practice this means that all laser dyes which could bepumped by the c w mode-locked ion lasers or N ~ : Y A Gasers were available for c wmode-locking. T he technique has also been applied to co lour-centre lasers e.g. [140, 1411where the higher saturation flux mak es the pulse shaping less effective but still achievesdurations of a few ps. Subpicosecond operation was first demonstrated by Heritage

Although the passively mode-locked femtosecond dye laser was demonstrated in ,


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I86 P M I+ Frenchand Jain [I421 who used 5 ps pulses from a synchronously pumped Rhodamine 6Glaser to synchronously pump a Rhodam ine B laser. The pulse duration obtained withsynchronous mode-locking was shown theoretically 11431 and experim entally[144, 1451to decrease with the square root of the duration of the pump pulses, to increase withthe square root of the intracavity bandwidth 11431 and to decrease with synchronouspum p power [146, 1471. Th is prom pted several researchers to synchronously pump dyelasers with fibre-optically compressed pulses from mode-locked Nd :YAG lasers, therebyobtaining pulses of 0 0 0 s duration e.g. [148, 1491.The p rincipal disadvantages of synchronous pumping were associated with the needto maintain an accurate match (within a few microns) between the lengths of the pumpan d slave lasers (see section 3). This was observed experimentally [150, 1511 and wasin agreem ent with various theoretical models e.g. [152-1541, Subsequently i t was pro-posed that the slave laser cavity should be slightly longer than the pum p laser to accountfor the fact that the pulse experienced a forward time-shift upon amplification [1551.Experimental [144, 1561 studies revealed that for longer slave cavity lengths, singlepulse trains were obtained but for shorter cavities, satellite pulses were also observed.Theoretical studies indicated that the precise cavity mismatch at which the shortestpulses were obtained depended on the pulse dura tion an d the bandw idth of the spectralfilter in the cavity [117, 1571 but generally the slave laser cavity needed to be longerthan the pump cavity to elimina te the formation of satellites, but this condition did notcorrespond to the shortest pulsewidth measurements. Th e role of stochastic spontaneousemission in the synchronously mode-locked laser was shown by Catherall and New[1571to introduce random fluctuations in the pulse trains which could not be eliminatedaltho ugh they would not be directly observed in time-averaged autocorrelation measure-ments [I581 (bu t usually would p roduce the expon ential sloping wings often observed inearly subpicosecond synchronously mode-locked lasers). Precisely matching the cavitieswould cause the slave pulse to lose synchronism with the pum p pulses because of theforward time-shift in the amplifier and therefore would impair the mode-locking. Onthe other ha nd, lengthening the slave cavity to acco mm odate this time-shift would causethe broadband noise fluctuations, which arise from spontaneous em ission, to circulatea t a dilferent repetition rate to the slave pulses and cause random substructure to appearon the pulse trains. This conflict and the corresponding instabilities could be grea tlyameliorated by reducing the width of the cavity spectral filter to limit the bandwidthof the noise fluctuations and tbe pulses to the picosecond regime i.e. closer to thatof the pump pulses 11591. This approach was adopted in the standard commercialsynchronously mode-locked dye lasers and in many ultrafast applications laboratories.An alternative approach was to pump a dye laser with compressed pulses of a few psor even subpicosecond duration [148, 149, 160, 1611 and obta in near transform-lim itedfemtosecond pulses. Recently a technique has been proposed [1621 and demonstrated[1631 to reduce the deleterious effects of spontaneous emission by feeding back a smallpart of the laser output to act a s a coherent seed which swam ps the noise backgroundbut which do es not affect the pulse-shaping dynamics. This has resulted in stable pulsetrains of transform -limited pulses.A compromise between passive mode-locking and synchronous pumping, calledhybrid mode-locking was also developed for ultrafast dye lasers. Essentially the per-formance was a reflection of this compromise: the selection of appropriate saturableabsorber combinations was less restricted than for pure passive mode-locking but therequirement for accurate matching of the cavity lengths was retained. The saturableabsorber tended to suppress the noise background, reduce the wings of the pulses and


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The generation of ul1r.ashor.t laser pulses I87relieve the problems caused by the forward time-shift in the amplifier by offsetting i tagainst a backward time-shift in the absorber, The precise mode of operation dependedon the amplifier/absorber dyes used and on the pumping conditions. The earliesthybridly mode-locked laser was demonstrated by Shank and Ippen in 1974 and gener-ated pulses of 0.5-1 ps from a laser in which Rhodamine 6G and DODC~were flowedi n a single jet stream [1641. Similar schemes utilizing a composite gain/absorber mediumwere domonstrated to provide spectral coverage i n the visible from 535 nm to 61 1 nme.g. [165, 1661 and in the near infra-red from 750 to 850 nm e.g. [167, 1681. Typicallythese lasers employed much weaker saturable absorber concentrations than the passivelymode-locked lasers and generated pulse of several 100 fs duration. Pulse shapes tendedto resemble Lorentzian profiles with sloping wings, indicative of fluctuations in pulseprofile or duration. A composite dye jet hybridly mode-locked laser yielded pulses asshort as 70 fs [1691 but this result was not reproduced by other workers and i t mayperhaps have been due to a fortuitous optimization of intracavity GVD. Hybridly mode-locked dye lasers with separate absorber and amplifier dye jets were also developed andcolliding-pulse-ring [1701 and anti-resonant-ring [171) laser cavities were employed toenhance the pulse shortening, resulting in the generation of pulses as short as 85 fs[1721. The incorporation of intracavity prism pairs led to shorter pulses of durationscomparable to the contemporary passively mode-locked lasers e.g. [173,1741althoughthe sloping wings of the autocorrelatiou traces and the excess time-bandwidth productsindicated that the pulse trains were not of the same quality. Linear dispersion-compen-sated cavities were found to generate similar duration pulses to the CPM configuration.This approach was useful for several infra-red amplifier/absorber dye combinationswhich would not work in pure passively mode-locked lasers e.g. [175, 1761 and refer-ences therein. Chesnoy and Fini [I771 published a simple scheme to lock the cavitylength of the dye laser to its optimum value which many researchers found of practicalvalue. A n alternative scheme based on the strength of a second hannonic signal [I781was also proposed and most workers reported a sub-micron sensitivity of the pulseduration to the cavity length of the dye laser. The ultimate hybridly mode-locked dyelasers generated close to transform-limited pulses of less than 30fs duration e.g.[179, I 801and the cavity designs were very similar to their purely passively mode-lockedcounterparts. I n general, hybridly mode-locked dye lasers were experimentally morecomplex than purely passively mode-locked dye lasers and often gave inferior perform-ance but found useful application in the near infra-red spectral region where the lifetimesof the amplifier/absorber dyes precluded passive mode-locking. Today this spectralregion is directly covered by femtosecond Ti :sapphire lasers.A n important development to femtosecond dye lasers was the fibre-optic pulsecompressor (see section 4). Reference [1811 provides a useful introduction to this topicand [I821 provides a tutorial overview offibre-optic compression. Following the propo-sal to compress pulses with chirp generated using SP M arising from the optical Kerreffect [87], experiments with a liquid CS2-filled fibre domonstrated that a linear chirpcould be obtained at power levels below the threshold for self-focusingor self-trapping[183]. The development of very low loss, single-mode optical fibres [I841 provided amore convenient non-linear medium for S P M [1851 and compression experiments werecarried out using negatively dispersive delay lines (near-resonant sodium vapour) toachieve 1 .1 ps duration [186]. Shank et al [I871 combined sphi in the silica fibre withnegative GVD from the diffraction grating pair of Treacy [86] to compress 90 fs to 30 fsand so invented the fibre-grating compressor. It was shown theoretically that the positiveGVD of the fibre in the visible spectral region served to make the chirp from the SPM


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188 P M W Frenchrelatively linear and so large compression factors were achievable [1881. Th e techniquewas applied to the output of a synchronously mode-locked picosecond dye laser andyielded tunable pulses of -450 fs duration 11891. This system was later refined and thecompressed pulses were again compressed in a second fibre-grating stage to producetunable pulses of 90 f s duration [1901. A useful analysis of achievable fibre-optic pulsecompression was published by Tomlinson et a/ [I911 which suggested shorter pulsescould be obtained with higher peak powers and shorter fibre lengths. The techniquewas successfully applied to amplified passively mode-locked CPM dye lasers to yieldpulses of 16 fs at IOHz repetition rate [I921 and 12 fs a t 500 Hz 11931. At the sametime, the c w mode-locked Nd :YAG laser was compressed by several groups to providepulses as short as 1.8 ps with peak powers of -3.4 kW 11941. A @switched mode-locked Nd : Y A G laser was compressed to -3 ps at 500Hz epetition rate yielding peakpowers as high as 1.5 M W 11951. The largest compression factor ever achieved wasobtained with a 1.3 p m N d :u ,\ c laser which was compressed first from 90 ps to I .5psusing a fibre-grating com pressor with positively dispersive fibre and then to 33 fs usingsoliton compression i n a fibre with negative GVD 196].As described above, compressed cw mode-locked Nd:Yac lasers were used tosynchronously pum p dye lasers to obtain tunable fem tosecond pulses, e.g. [148, 1491.An alternative approach to generate widely tunable femtosecond pulses was to improveon the experiment of [I901 an d to include an am plifier between the two fibre-gratingcompressors. This yielded tunable pulses as short as 16 f s a t a repetition rate o f 200 Hz[ I 971. The principal disadvantages associated with this scheme were the fact that thefibre-optic com pressor tended to produce pulses with some of the energy in a pedestaland the experimental ditliculties associated with optimizing the fibre-grating com-pressors for fluctuating input signals from the synchronously mode-locked dye laser.Yet ano ther scheme for obtaining tunab le femtosecond pulses was to use the relativelyhigh quality amplified, compressed pulses from a passively mode-locked CPM laser togenerate a femtosecond white-light continuum (e.g. [198]) and either employ thisdirectly as a probe signal or select the desired spectral com ponen t an d am plifyit furtherto the required energy [199]. This was a complex experimental system but providedsignificant wavelength flexibility.The development of the copper vapour laser-pumped dye amplifier permitted thefibre-grating compression of 40 fs pulses from a CPM ring dye laser to 8 fs at a repetitionrate of 5 kHz [200]. The transform-lim ited dura tion of the associated spectrum was 6 fsand in a subsequent experiment using a fibre-grating com pressor which also incorpor-ated a prism sequence which permitted i t to compensate for both second and thirdorder phase variations, the 6 fs pulse duration was achieved [201]. These transform-limited pulses, of only three optical cycles, remain the shortest generated to date. Theexperimental inconvenience of working with dye lasers, however, is leading to theirreplacenien l in most ultrafast laser app lications by femtosecond solid-state laser systems.

2.4. Thirdgeneration: ferntosecoridsolid-state lasersAlthough they have not produced significantly shorter pulses than the second genera-tion cw femtosecond dye lasers, femtosecond solid-state lasers have transformedultrafast laser physics-particularly in terms of convenience and applica tion. As dis-cussed earlier, the two crucial elements to this revolution were the exploitation of theoptical Kerr effect as an effectively nstantaneous non-resonant saturable absorber andthe development of ultra-broadband vibronic laser media such as Ti :sapphire. With


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The geiieration of ultrasliort laser pulses 189these elements and with the experience of optimizing intracavity GVD gained from cwfemtosecond dye lasers, sub-100 fs generation has become routine. The much greaterconvenience and tunability of femtosecond solid-state lasers have had a huge impacto n ultrafast science an d a re far m ore significant developments th an a further reductionit! the pulse du rati on . While the second generation of femtosecond lasers were generallynot commercially available and required several man-years of experience to operatethem routinely, the commercial femtosecond Ti: sapp hire lasers are certainly state-of-the-art and usually provide superior performance, in terms of power and tunability,compared to home-built systems. Comm ercial lasers typically provide pulses with du ra -tions limited to -100 fs bu t most researchers d o no t require the sub-20 fs pulses achiev-able from specially optimized systems. The ease of use and high power available fromcommercial systems is leading to their increasingly widespread applications in physics,engineering, chemistry, biology and other disciplines. Reference [39] provides anexcellent review of the developm ent of fem tosecond solid-state lasers an d [202] providesa snapshot of the current state-of-the-art. Of course progress has continued in thedevelopment of other ultrafast lasers including dye lasers and semiconductor lasers (see[203] fo r a recent review), femtosecond solid-state lasers have dominated the field andthis section will concentrate on their development.The potential of the optical Kerr effect to simulate a saturable absorber withoutcompromising the tunability o f a laser was demonstrated by Dahlstrom [204] who usedthe optical Kerr effect to induce an intensity-dependent polarization rotation of theintracavity light. The presence of intracavity polarizers translates this to an intensity-dependent loss which can provide passive mode-locking and/or Q-switching in anmanner similar to a real saturable absorber. Earlier, Comley er a/ [205] had reportedpassively mode-locking a ruby laser using an intracav ity optical Kerr cell without explic-itly considering intensity-dependent loss. As mentioned earlier, a n alternative approachto simulate satur able abs orptio n with the optical Ker r effect by using self-focusing wasproposed by Lariontsev and Serkin [ 8 9 ] . Initially, strong non-linearity based on theorientation dynamics of anis otrop ic niolecular liquids was used to provide the opticalKerr effect. Unfortuna tely, this non-linear response, and therefore tha t of any simulatedsaturable absorption, was temporally limited to the molecular orientation relaxationtime which was typically greater than a few picoseconds and this in turn limited theminimum achievable pulse durations. The difficulties in exploiting the relatively weakresponse of faster electronic non-linearities and the impressive successes achieved byfemtosecond c w passively mode-locked dye lasers resulted in little atte ntio n subse-quently being paid to these non-resonant app roac hes to passive mode-locking.The breakthrough in non-resonant mode-locking which triggered the renaissance inultrafast solid-state lasers was the demonstration of the soliton laser in 1984 byMollenauer and Stolen [206]. This was a synchronously-pumped colour centre laserwhich achieved -100 fold pulse compression to 210 fs by exploiting the optical Kerreffect induced in a single mode silica fibre which was located in a coupled resonantcavity. It washighly significant that the practically instantaneous electronic noii-lin-earity of the glass could be accessed by the power levels available in a c w laser due tothe lon g interaction length of the fibre geometry. This experiment p rom pted much workby other researchers to understand this surprising result and Lo apply the technique tooth er laser media. Figure 2 illustrates schematically how todays solid-state femtosecondlasers evolved f rom the soliton laser (i.e. an actively mode-locked laser with a resonantnon-linear external cavity that exhibited anomalous CVD and therefore pulse com-pression, as indicated in figure 2 1 ~ ) ) . nitially, the fibre in the external cavity was


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190 P M W Frencli

Figure 2. Schematic ofevolution offemlosecond solid-state lasers.

required to compress the picosecond pulses generated by the actively mode-lockedeolourcentre laser, due to the soliton shaping effect of SP M and anomalous GVD. The eom-pressed pulses were then re-injected back into the main laser cavity and this 'seeding'with shorter pulses resulted in enhanced mode-locking. It was observed that th e lengthof the external cavity needed to be interferometrically stable and an elegant activestabilization feedback loop was developed for this purpose [207].At first this approach to mode-locking seemed restricted in scope since the laserwas required to opera te at wavelengths for which the fibre was anomalously dispersive.Several groups constructed theoretical models of this system and Blow and Woodpredicted from num erical simulations [208] that soliton shaping (i.e. pulse compression)was not necessary in the optical fibre for this successful enhancement of the mode-locking using a non-linear external cavity. This was confirmed experimentally usingfibre whieli did not exhibit anomalous dispersion [209-21 I ] . Using a non-/incur intcr-fero~~zelcre.g. a non-linear external resonan t cavity) to achieve compression had beenproposed in 1986 by Piche an d Ouellefte [212] and passive mode-locking with a coupiednon-linear Michaelson interferometer was demonstrated using a CO2 laser [213]. In1989, Mark et a1 [214] applied a non-linear interferometer model to a synchronouslypumped colour centre laser with a non-linear external resonator and produced a simple


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The generation of ultrashort laser pulses 191and convincing description of the pulse compression/enhanced mode-locking mechan-ism which was described as Additive Pulse Mode-Locking or APM. Since anomalousGVD was no longer an issue for A P M , the generic picture of the mode-locked laserbecame that of figure 2(6). This immediately suggested that the technique could beapplied to a wide range of laser media covering the visible and near infra-red spectralregions. It was applied to Ti:sapphire [215], using an intracavity acousto-optic modul-ator to initially actively mode-lock theTi:sapphire laser, and directly generated femtose-cond pulses from this laser medium for the first time. Almost simultaneously,Goodberlet et ai [216] generated chirped pulses of 1.4 ps duration from a similar laserand demonstrated that the active mode-locking of the Ti:sapphire laser was not neces-sary since the mode-locking was sustained once the modulator was switched off. Thisconfirmed that APM was truly a passive mode-locking mechanism. Thus the typical APMlaser with a non-linear coupled cavity evolved to the stage indicated in figure 2(c) andwas quicly adapted to other laser systems including diode-pumped [217] and lamp-pumped [218] N ~ : Y A Gasers, a krypton ion laser-pumped Nd:glass laser [219], lamp-pumped [220] and diode-pumped [221] N ~ : Y L Fasers and a Cr:Forsterite laser [222].The pulses generated were sub-100 fs or close to the limits imposed by the linewidthsof the gain media.The principle disadvantage of APM is the need to maintain the cavity lengths tointerferometric stability. This issue was elegantly side-stepped in an experiment to pass-ively mode-lock a N ~ : Y A Gaser [223] using a non-linear Sagnac interferometer (oranti-resonant ring), rather than a coupled cavity (i.e. a Fabry-Perot interferometer).Such a configuration has the advantage that, since the pulses to be interferometricallycombined propagate around the same path in the Sagnac interferometer (albeit inopposite directions), then any fluctuations in cavity length will be experienced equallyby both arms of the interferometer and will not affect the coherent addition. An all-fibre embodiment of a non-linear Sagnac interferometer, the Non-linear Optical LoopMirror, or NOLM, had previously been proposed 1.2241 as an element with an intensity-dependent reflectivity. This approach was subsequently applied to fibre lasers in whicha Sagnac interferometer containing a length of fibre and a Nd:glass fibre amplifier wasused to achieve pulse compression [225] and mode-locking [226], yielding pulses of125 fs duration. The non-linear Sagnac interferometer incorporating the amplifier wastermed a Non-linear Amplifying Loop Mirror, or N A L M . Following the proposal toincorporate a non-linear Sagnac interferometer i n a unidirectional ring laser [227], thisrealization of APM was applied to Er:glass fibre lasers, resulting in the Figure of 8Laser or FSL [228]. Pulses of a few 100fs duration were obtained by several researchgroups, e.g. [229-2311 and this type of laser was the subject of intensive research whichwas particularly directed towards understanding the source of instabilities associatedwith soliton-like pulse propagation that were observed as the pulse duration approachedits minimum value e.g. [232]. By carefully optimizing the GVD of mode-locked fibrelasers, sub-100 fs pulses can be obtained, e.g. [233]. This topic is discussed in greaterdepth in sections 3.3.3.2 and 4.4.4.An alternative implementation of A PM in fibre lasers was to use non-linear polariza-tion rotation, induced by the optical Kerr effect. Essentially the scheme proposed byDahlstrom [204] can be implemented using a length of optical fibre to replace the Kerrcell. This was proposed by Stolen e / a1 [234] as an intensity discriminator to removelow level pedestals from intense fibre-optically compressed pulses. Mode-locking bynon-linear polarization rotation may be considered as A P M in which the two polarizationstates of the fibre correspond to the excitations of an equivalent Mach-Zehnder fibre


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192 P M W fieitchinterferometer [235,236]. The technique was applied to a dispersion-compensatedNd:gla ss fibre laser and achieved pulse duration s as short as 70 Is [237]. Subsequentlyi t was applicd to Er:glass fibre lasers to yield picosecond [238] and femtosecond e.g.[239,240] pulses. These femtosecond Er:glass fibre lasers suffered from the same soli-ton in stabilities as their Sagnac interferometer counterparts a nd , after careful optimiza-tion of the GVD, yielded pulses as short as 77 fs 12411 from a laser whose net GVD wasslightly positive and so would no t su pport so liton propaga tion. The shortest pulses yetobtained from a fibre laser were of 32 fs duration, obtained from an Nd fibre laser,mode-locked using mM /polarization rotation [242].The essential experimental feature of A P M is that it exploits optical fibre to providethe Kerr non-linearity i n a geometry which provides a large interaction length. Asdiscussed in section 3.3.3.2, this produces significant non-linear phase shifts for rela-tively low intracavity power, perm itting self-starting, but the interferometric natu re ofthe A m mechanism makes the laser operation sensitire to perturbations e.g. arisingfrom environmental changes. While the Sagnac interferometer is insensitive to changesi n cavity length since the interferometer arm s share the sam e physical path , the polariza-tion state of the light in the oplical fibre is sensitive to environmental perturbations.Any change in polarization sta te will effect the coherent addition of the signals in theinterferometer an d so degrade the A PM laser performance. It is therefore desirable todesign a femtosecond laser which does not requ ire an optical fibre or active stabilizationof the cavity length. One approach, initially demonstrated with Ti:sapph ire and desig-nated resonant passive mode-locking, or R P M , was to replace the fibre in the resonantexternal cavity with a multiple-quantum well (M Q W ) aturable ab sorber [243]. Thislaser was found to adjust its operating wavelength to accommodate any relative changein cavity length 12441 and so was stable to interferometrk fluctuations-at the cost offluctuations in the laser wavelength. The use of a real saturable absorber compromisedthe tunability o f this mode-locking scheme but this was somewhat alleviated by thedemonstration of broadban d bulk semiconductor absorbers in lieu of the MQW absor-bers [245]. TypicaUy RPhf generated pulses of a few picoseconds duration. The pulsedura tion is limited by the absorption recovery dynam ics of the saturab le absorber andby any etalon formed by the difference n the lengths of the main and external cavities.The latter issue may be avoided by using the M Q W semiconductor in the main lasercavity as a fast saturable absorber to genera te pulses of less than -200 fs dura tione.g. 12461. A n elegant refinement of the RPM technique was to construct a compositemonolithic structure comprising a partially transmissive main laser cavity mirror, thesaturable absorber and a high reflector which was spaced to provide the optimuminterferometric condition for the addition of the radiation from the saturable absorbercavity and the main cavity. Th is device, which thus avoids all issues of cavity lengthstabilization, was described as an anti-resonant Fabry-Perot saturable absorber, orA-FPSA, and i t has been successfully applied to mode-lock several laser media e.g. 12471an d to initiate mode-locking based on the optical Kerr effect e.g. [248]. R P M , includingthe A -F P S A , is reviewed in [249].

The intensive investigation of A PM lasers, particularly Ti :sapphire, led to severalsurprising observations. I n particular, it was shown that passive mode-locking of aTi:sapphire laser could be obtained, even without a fibre or other non-linear elementin the external cavity 12501. I t was observed that moving one of the mirrors in the laseror the linear external cavity was necessary to achieve mode-locking and that there wasno need to match or to stabili7,e the cavity lengths. Figure 2(d) llustrates this movingmirror mode-locking. Typically pulses as short as a few ps were generated and the


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The generation of ultrashort laser pulses 193technique was shown to be applicable to Nd:glass fibre lasers [251]. Subsequently itwas demonstrated tha t the external cavity w as not necessary and simply moving themirror of a cw (Ti:sapphire) laser at speeds of a few mm s- was sufficient to producemode-locking [252]. This situation is represented in figure 2(e). The mode-lockingmechanism was no t explained until very recently but the techniqu? is reminiscent of anexperiment by Smith who used a moving mirror to mode-lock a HeNe laser in 1967[253]. Sargsjan er a/ [254] showed that the coupled linear cavity could increase thefrequency shift imparted by the moving mirror due to the Doppler effect, although thisfrequency shift would still be much less than the longitudinal mode spacing. Cutler[255] showed empirically that the action ,of the moving mirror would be to prevent theestablishment of c w laser action by the Doppler shifting of the laser modes ou t of thegain linewidth. He also observed in numerical simulations that the presence of non-linearity in the cavity with a moving mirror could lead to mode-locking. Wu et a1 [256]explained how th e combined action of SPM with a finite gain linewidth would tend topull the laser frequency towards the centre of t

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