354 OPTICS LETTERS / Vol. 27, No. 5 / March 1, 2002

Photochromic polymers for the optical homodyne detection ofultrasonic surface displacements

Ulrich Gubler, Daniel Wright, and W. E. Moerner

Department of Chemistry, Stanford University, Stanford, California 94305-5080

Marvin B. Klein

Lasson Technologies, 6059 Bristol Parkway, Culver City, California 90230

Received August 23, 2001

We present a novel scheme with which to detect small ultrasonic surface displacements by use of a pho-tochromic polymer instead of a photorefractive material as an adaptive beam combiner in a two-wave mixinggeometry. Poly(methyl methacrylate) is doped with a derivative of zinc tetrabenzoporphyrin that possessesa long-lived triplet state that can be efficiently populated in a reversible manner. The resulting dynamichologram consists of local absorption and refractive-index gratings, which can process speckled beams ref lectedfrom rough surfaces. We believe that this is the first use of a local nonlinear medium for adaptive homodynedetection of ultrasonic surface displacements. © 2002 Optical Society of America

OCIS codes: 090.2880, 090.7330, 120.4290, 160.4330, 160.5470.

Nondestructive inspection with ultrasonic waves iswidely used in industry. The standard technique,which uses ultrasonic transducers, is mature andprovides high sensitivity for small surface displace-ments. However, transducers need direct contactwith the workpiece, making the transducer techniqueimpractical for such applications as inspection athigh temperatures or in hazardous environments. Aremote technique is more desirable in these cases andalso permits faster scanning over uneven surfaces.

A technique that fulf ills these requirements islaser-based ultrasonics. Ultrasonic waves in theworkpiece are launched by a short, intense laserpulse and then monitored after passage through thesample by a second laser beam, which detects thesurface displacement as a phase modulation. Forthe detection system, which has to convert the phasemodulation into a detectable intensity modulation,various designs have been proposed.1 Homodyneadaptive interferometry that uses the photorefractiveor the photo-emf effect is of special interest, as thetransient hologram in such a material can adapt toslow movements of the workpiece and thus is sen-sitive only to fast ultrasonic transients. No activestabilization of optical path lengths is required as forconventional interferometers, and the system also canprocess speckled beams from rough surfaces.

The novel technique presented here is similar in ex-perimental design to the standard two-wave mixingscheme of photorefractive materials2 – 4 but is consid-erably different in the physical origin of the effect. Inphotorefractive materials the refractive-index gratingis formed by diffusion and drift of electronic chargesand is spatially shifted with respect to the intensitygrating. This spatial shift of the index grating is un-desirable, as linear detection is optimized for an un-shifted grating.

In our new scheme, a photochromic materialwith transient saturable absorption is used as theadaptive beam combiner. The optical response de-

0146-9592/02/050354-03$15.00/0

pends only on the change of the optical propertiesbetween two molecular states; hence the effect ispurely local. Energy exchange between the beamsin the two-wave mixing geometry is not possiblefor the photochromic system as for photorefrac-tive materials. Such exchange is, however, notnecessary for the detection of fast phase modu-lation, as we show here.

For our demonstration of adaptive optical interfer-ometry by the photochromic effect we chose the mole-cule meso-tetra(p-tolyl)-Zn-tetrabenzoporphyrin (TZT;see Fig. 1). We mixed 0.5-wt. % TZT into a toluenesolution of poly(methyl methacrylate) (PMMA) andcast f ilms of l � 45 mm thickness sandwiched betweentwo glass slides. The triplet state of TZT is efficientlypopulated (triplet yield, 0.88; Fig. 1) and relativelylong lived ��40 ms�; therefore, moderate laser powersefficiently populate the triplet state, yielding light-induced changes in optical properties at the pumpingwavelength.

The triplet population can be treated as saturableabsorption �a�:

Fig. 1. Molecular structure and energy-level diagram ofTZT. The triplet state T1 can be eff iciently populated,as the rate k12 for the intersystem crossing is larger thanthe rate k10 of the spontaneous decay of singlet state S1to ground state S0. The triplet lifetime tT � k20

21 deter-mines the recovery time of the system, s is the absorptioncross section, and F is the photon f lux.

© 2002 Optical Society of America

March 1, 2002 / Vol. 27, No. 5 / OPTICS LETTERS 355

a�I � � Ntots1

1 1 I�Isat,

Isat � hnk20�k10 1 k12�

k12s, (1)

where Ntot denotes the density of TZT molecules, s

is the absorption cross section of TZT at the incidentlaser frequency n of intensity I , Isat is the saturationintensity parameter (200 mW�cm2 at l � 647 nm), andh is Planck’s constant.

The change in absorption has to be accompaniedby a change in refractive index n because of theKramers–Kronig relations. A set of equations simi-lar to those for saturable absorption can be derived:

n�I � � Ntotk1

1 1 I�Isat1 nPMMA ,

k�v� �cp

PZ `

0

s�v 0�v02 2 v2 dv0, (2)

where k�v� is the Kramers–Kronig transform of thecross section s�v� and P denotes the Cauchy principalvalue of the integral. The material parameter k�v�does not depend on the incident intensity and is a func-tion of the molecular spectrum only. It can be inter-preted as the contribution of a single molecule to n�v�.

Knowing the change of the absorption over a suff i-ciently broad wavelength range, one can calculate themaximum change in refractive index, as depicted inFig. 2. The wavelength for the experiments describedbelow is chosen in the onset of the absorption peakat 647 nm, as the change in refractive index is mostprominent in this region and can reach as much as sev-eral times 1023 for complete depopulation of the groundstate. The absorption from the lowest triplet state5 isnear 500 nm and can be neglected.

The intensity grating in the two-wave mixing experi-ment will create a population grating and consequentlyalso absorption and refractive-index gratings. Follow-ing a derivation for two-wave mixing that is analogousto that for photorefractive materials6 and assuming amuch smaller intensity of the signal beam than the ref-erence beam �IS ,, Iref �, we f ind the signal that resultsfrom a small ultrasonic perturbation of the phase w�t�of the signal beam:

IS�l� � IS�0�exp�2al� �exp�22g0l�

1 2 exp�2g0l�sin�g00l�w�t�� , (3)

g0 � Ntots1

�1 1 Iref�Isat�Iref�Isat

4, (4)

g00 � Ntotk1

�1 1 Iref�Isat�2pIref�Isat

l, (5)

a�Iref� � Ntots1

1 1 Iref�Isat. (6)

As there is no phase shift between the intensity grat-ing and the refractive-index grating, there is no am-plification term as in photorefractive materials.6 Fordetection of w�t�, the term sin�g00l� that stems from the

refractive-index grating has to be different from zero.The size of the effect scales with the ratio of the refer-ence to the saturation intensity.

To compare the sensitivity of the photochromic poly-mer with an ideal interferometer, we calculate the sig-nal-to-noise ratio �S�N� of Eq. (3) in the shot-noise limitwith the ultrasonic phase replaced by surface displace-ment d�t�, using w�t� � �4p�l�d�t�. Again, followingearlier derivations for photorefractive materials,7

S�N �

∑2hPS�0�hnDf

∏1�2 4p

lexp�2al�2�sin�g00l�drms , (7)

where h denotes the quantum efficiency of the detec-tor, Df the bandwidth of the detection system, anddrms the root-mean-square amplitude of the ultrasonicsurface displacement. The S�N depends only on aver-age absorption a and coupling coefficient g00 from thelocal refractive-index grating. The relatively strongabsorption grating cannot contribute to the homodynedetection. Equation (7) has to be compared with

�S�N�ideal �

∑2hPS�0�hnDf

∏1�2 4p

ldrms (8)

of an ideal interferometric detection system.4,6 Thesurface displacement for unity SNR ratio at powerPS � 1 W and an extrapolated bandwidth Df � 1 Hzis called noise-equivalent surface displacement, whichis a f igure of merit for the sensitivity of the ultrasonicdetection system and can be expressed for the pho-tochromic system relative to an ideal interferometerdrms � Fdrms

ideal with the relative sensitivity

F �exp�al�2�sin�g00l�

. (9)

Equation (9) illustrates the critical trade-off of pho-tochromics: One must work near an absorption to ob-tain large index changes, but excessive loss reducessensitivity.

To measure the relative sensitivity F of our pho-tochromic material in a two-wave mixing geometry,we simulated the ultrasonic surface displacement withan electro-optic phase modulator in one of the beams(Fig. 3, inset). The two beams overlap at an exter-nal angle of 30± in the photochromic film, and thesignal beam is detected by a fast photodiode (NewFocus 1801; 125-MHz bandwidth; quantum eff iciency,

Fig. 2. Absorption spectra of the TZT–PMMA film andthe possible refractive-index change if the absorption iscompletely bleached. The arrow at l � 647 nm indicatesthe wavelength of the laser measurements.

356 OPTICS LETTERS / Vol. 27, No. 5 / March 1, 2002

Fig. 3. Frequency response of the photochromic detectionsystem for several intensities I . The response at high fre-quencies is f lat and rolls off near 10 Hz. The frequency ofthe phase modulation is simulated by an electro-optic (EO)phase modulator (inset).

Fig. 4. Measurement of ultrasonic surface displacementwith the photochromic polymer. The surface displace-ment is created with a pulse-driven transducer mountedupon the back side of a mirror (inset).

h � 91.2%). The signal is analyzed on an electronicspectrum analyzer (HP 8591A) with a bandwidth of10 kHz about the modulation frequency of the elec-tro-optic phase modulator (100 kHz). The intensityratio of the two beams was 1:60; the strong beam hada peak intensity of 1 W�cm2. Evaluating Eq. (9) withthe experimental parameters (a � 30 cm21 and g 00 �5 cm21), we can expect a relative sensitivity F � 50.

In our experiment the S�N grows linearly with theamplitude of the surface displacement, in agreementwith Eq. (7). If the measurement is extrapolated toa S�N of 1 the noise-equivalent surface displacementis drms � 2.3 3 1026 nm �W�Hz�1�2. The ideal homo-dyne limit with our photodetector is drms

ideal � 2.16 31028 nm �W�Hz�1�2, which results in the relative sen-sitivity F � 100 for our photochromic system, in agree-ment with the estimate above.

When the modulation frequency of the phasemodulator is varied, we can determine the high-passcharacteristic by recording the roll-off of the sensitivityto small frequencies. Figure 3 displays the detectorsignal versus the modulation frequency for various

intensities. For all intensities the high-frequencyresponse is f lat, as expected. Compensation band-widths (3 dB) of �10 Hz are reached, which is whatcould be expected for the 40-ms triplet lifetime ofthe TZT molecule. For applications, compensationbandwidths in the kilohertz range are desired,1 whichcan be achieved by choice of a molecule with a shortertriplet lifetime and faster population dynamics.

For a direct proof of principle using photochromicpolymers as a part of a laser-based ultrasound de-tection system we generated an ultrasonic wave ofa few nanometers’ amplitude upon a mirror by apulsed transducer mounted upon the back side of thismirror (Fig. 4, inset). The detection bandwidth waslimited by the oscilloscope to 20 MHz, and the ratioof the beam powers was 1:50, with a peak intensityof 500 mW�cm2 for the stronger beam. The ultra-sonic wave can be clearly seen on the oscilloscopetrace (Fig. 4), and several repeatable features of theultrasonic surface displacement can be distinguished.The peaks of the compression waves had a spacingof �2 ms, with contributions from shear and Lambwaves between them.

In conclusion, we have demonstrated detection ofsmall phase modulation by dynamic holography ina photochromic polymer, which can be used, for ex-ample, as an adaptive beam combiner in the homodynedetection of laser-based ultrasound. Compensationbandwidths of the order of 10 Hz were obtainedwith a simple, low-cost material. The sensitivity isroughly 2 orders of magnitude less than from thatfor the ideal homodyne interferometer, owing to thesmall index modulation achieved per absorbed photon.These specif ications are not yet satisfactory for a realapplication; however, for a f irst proof of principle theperformance is promising. To improve the sensitivity,optical transitions with different shapes, such as withsteeper long-wavelength edges, should be considered.Paths to improve both speed and sensitivity by meansof organic synthesis are open and will lead this noveltype of detection scheme closer to competing withother detection techniques.

This study was supported in part by U.S. Air ForceOffice of Scientif ic Research grant F49620-00-1-0038.W. E. Moerner’s e-mail address is moerner@stanford.edu.

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