Holographic Spectroscopy Diffraction from Laser-Induced Gratings

Holographic

Spectroscopy Diffraction from Laser-Induced Gratings X. R. Zhu, D. J. McGraw1, and J. M. Harris Department of Chemistry University of Utah Salt Lake City, UT 84112

The introduction of lasers into spectroscopic instrumentation has produced outstanding gains in detection compared w i t h conventional light sources. These improvements arise not only from t h e h i g h e r optical power output of the laser but also from the unique coherence properties of laser radiation. A new class of sensitive spectroscopic techniques h a s been developed in which heat produced by nonradiative decay of excited species p e r t u r b s t h e optical path within the sample. Differences in the optical properties of photoproducts can also perturb the optical path. The spatial coherence of a laser beam probing the sample makes it possible to observe extremely small perturbations in optical path, a n d thus very weakly absorbing samples can be detected. The spatial intensity distribution of excitation determines what form the perturbation of the optical path will take within the sample. By splitting the excitation laser beam and recombining the two beams within a sample, one can generate an excitation interference pattern that pro'Present address: Department of Physics, Uni versity of New Mexico, Albuquerque, NM 87131

duces a transmission grating or hologram within the sample. The grating can be detected by measuring the diffraction of a probe laser beam. Absorption measurements by this diffraction method are spatially resolved in the sample, and thus a signal on a nearly z e r o - i n t e n s i t y background can be produced. Diffraction from l a s e r - i n d u c e d gratings is termed transient holography or holographic spectroscopy, because the laser-induced grating is an elementary hologram produced by interference between coherent reference and object waves (i). In other words, information about the absorption of radiation, relaxation of excited states, and diffusion of photoproducts is holographically encoded within the sample through interfere n c e of t h e i n c i d e n t e x c i t a t i o n beams. Laser-induced holographic methodology is well developed for measuring physical properties (it has been used to determine t r a n s p o r t rates for heat and photoconductivity) as well as for generating and detecting high-frequency acoustic waves (1-3.. For analytical chemistry applications, holographic spectroscopy is a relatively new technique with several unique attributes for measuring weak absorption, the decay of excited states, and the diffusion of photolabeled products. The technique can be used to make high-sensitivity, lowbackground absorption measurements by taking advantage of spatial

710 A · ANALYTICAL CHEMISTRY, VOL. 64, NO. 14, JULY 15, 1992

selectivity within the sample. It also offers the ability to observe nonlinear excitation processes with high-power lasers, free from background caused by linear absorption. By time-resolving t h e diffraction signal one can study the kinetics and energetics of photoinitiated reactions in liquids on a s u b n a n o s e c o n d t i m e scale a n d transport properties of the sample on much longer time scales.

Principles L a s e r - i n d u c e d gratings. An interference pattern used to create laserinduced gratings is shown as a moiré pattern in Figure l a . Two coherent laser beams derived from the same laser cross at an angle 29 e and have intensities 7a and Ib. The resulting intensity / of the interference pattern χ is given by /(*) = I0 [l + 15 cos (2rcr/rf)]

(1)

where I0 = L + L is the total inten sity of the two excitation beams, (3 is the pattern contrast and is equal to 2(IJb)1/2/I0 (and depends on the rela tive intensities in the two beams), and d is the fringe spacing of the in terference pattern. The size of d de pends on the excitation wavelength X and the crossing half angle 9 e , as illustrated by the Bragg equation d = XJ2 sin 6 e

(2)

Equation 2 indicates that the spacing can be varied by simply adjusting the angle between t h e two excitation beams. For instance, when Xe = 532 0003-2700/92/0364-710A/$03.00/0 © 1992 American Chemical Society

INSTRUMENTATION

nm, d = 0.2 μπι for 9 e = 90°, whereas d = 30 μπι for 0 e = 0.5°. Optical excitation of molecules by the interference pattern initially cre ates a periodic spatial distribution of excited s t a t e s . T h a t d i s t r i b u t i o n comprises a population grating, b e cause the optical properties (e.g., re fractive index and absorption coeffi cient) of t h e s e excited s t a t e s a r e generally different from those of their corresponding ground states. The excited states may decay via a photochemical reaction to yield prod ucts in a spatial pattern similar to that of the initial excitation. These products, along with the de pleted starting compounds, produce a hologram or chemical concentration grating from a modulation of the op tical properties due to chemical com position changes. This concentration grating decays a t a slow rate deter mined by the stability of the photo products or t h e i r m a s s diffusion across t h e g r a t i n g s p a c i n g . T h e excited-state decay also creates a thermal grating because of the tem perature rise from nonradiative r e laxation. This t h e r m a l p a t t e r n causes a density change because of thermal expansion of the sample ma trix, which changes the refractive in dex of the matrix. The thermal grat ing decays with a fast time constant (typically microseconds) characteris tic of thermal diffusion across t h e grating spacing. Diffraction from v o l u m e grat ings. The gratings formed in a sam

ple from excitation with crossed laser beams can be monitored by diffrac tion of a third probe beam intersect ing the excitation volume in the sam ple, as shown in Figure lb. Diffracted probe radiation is measured by a de tector that is not directly illuminated by any laser beam, and thus a lowbackground signal is produced. The angular sensitivity of diffraction de pends on whether the grating is thick (Bragg diffraction) or thin ( R a m a n Nath diffraction) (1, 4, 5). Characteristic diffraction from a thin grating, where t h e grating thickness L is comparable to or less than the fringe spacing, is multipleorder for a probe beam incident a t any angle. Such behavior is familiar to spectroscopists using monochromators with thin diffraction gratings based on surface reflection. For volume holograms, where t h e grating thickness typically is much greater t h a n the fringe spacing, t h e diffraction efficiency is significant

only when t h e probe radiation is incident a t the Bragg angle, θ ρ = ΘΒ, defined relative to the bisector of the two excitation beams. The angle ΘΒ for the incident probe beam depends on the grating fringe spacing and the probe wavelength λ ρ , according to the Bragg equation rearranged as ΘΒ = sin" 1 (Xp/2d)

(3)

In addition, t h e diffracted probe beam radiation propagates predomi nantly at an angle - Θ Β away from the bisector of excitation beams with negligible contributions in the other d i r e c t i o n s . D e v i a t i o n s from t h e Bragg angle result in a rapid d e crease in diffraction efficiency, and no diffraction is observed at higher order Bragg angles (6, 7), as shown in F i g u r e 2. Most e x p e r i m e n t s d e scribed in this paper are under simi larly thick Bragg grating conditions. The angular sensitivity of diffrac tion from volume gratings can be un derstood by considering a thick grat-

(a)

ιX

r zd

2Θ

t

Mirror 1 Sample

(b) Beamsplitter

Excitation beam

θβ

Mirror 2

'»?

Diffracted probe

Probe beam

Detector

Figure 1. Example of an interference pattern and instrumentation for holographic spectroscopy. (a) Interference created by two mutually coherent (same frequency, fixed phase delay) laser beams at wavelength λ„ crossing at a full angle of 2θβ produce interference fringes (shown as a moiré pattern) along the x-axis spaced by a distance d. (b) The interference pattern is generated by splitting the excitation beam and crossing the two beams in the sample. Diffraction within the sample is probed using a third laser beam at wavelength λρ incident at the Bragg angle, θρ = ΘΒ = είη _1 (λ ρ /2(ί); λρ > λ β because in this case θ„ > θβ. ANALYTICAL CHEMISTRY, VOL. 64, NO. 14, JULY 15, 1992 · 711 A

INSTRUMENTATION ing as a compilation of many thin gratings stacked together. Each thin grating gives multiple-order diffrac tion, a n d diffracted beams of t h e same order from different thin grat ings interfere with each other. Only at the Bragg angle do first-order dif fracted beams from t h i n g r a t i n g s constructively interfere with each other and give a maximum signal. For other diffraction orders, the dif fracted beams from different t h i n gratings destructively interfere and no diffracted radiation is observed. The angular dependence for probe diffraction is indeed centered at the Bragg angle (Figure 2). However, the intensity distribution is not a sharp, Dirac delta but r a t h e r a Gaussian function (parabolic on the logarith mic intensity scale) with a nonzero angular width. This angular uncer tainty for the Bragg condition is at tributable to finite spot sizes of the excitation and probe beams, which impose an uncertainty on the spatial frequency of t h e g r a t i n g (7). The Bragg condition is thus less restric tive for finite volume gratings read by a focused probe laser beam than for ideal gratings formed and read by plane waves of infinite extent. The combined interference and dif fraction effects can be described as four-wave mixing in the language of nonlinear optics (1, 7). Diffraction of the probe beam is viewed as interac tion of the three input waves through the third-order susceptibility or non linear polarizability of the sample. In this instance, the Bragg condition corresponds to phase matching for coherent light scattering. The process is called degenerate four-wave mix ing if the frequencies (wavelengths) of the three incident waves and the diffracted wave are the same. In this article the nonlinear optics description will not be used, because the grating approach allows u s to separate the grating formation and decay processes from diffraction or read-out; this separation is appropri ate in t h e s e experiments because grating formation and probing are not generally coincident in time. The grating approach benefits from the well-developed diffraction theory for volume holograms. Most spectroscopists are familiar with diffraction and can readily understand this a p proach. The diffraction efficiency η of a weakly absorbing, thick grating at the Bragg incidence angle, under the weak diffraction limit, is given by η = (jtL/Xp cos ΘΒ)2 χ (ΔΗ* + Ak%) (4) where L is the grating thickness and

Δ« ρ and Akp are the peak-to-null dif ferences of the real and imaginary parts, respectively, of the refractive index at the probe wavelength, which give rise to diffraction ( 10 us). The interference pattern t h a t gen erates the holographic grating in the sample relies on the unique temporal and spatial coherence properties of laser radiation. Spatial coherence of the radiation relates to having pla nar incident wavefronts, as shown in Figure l a , that generate planar in terference fringes of constant spac ing. A TEM 0 0 -mode laser beam (with G a u s s i a n i n t e n s i t y profile a n d spherical phase fronts) from a stable laser resonator can be focused to a waist where the wavefronts become planar and satisfy this requirement. For a laser with poor spatial coher ence, such as a nitrogen laser, the ± 1-order diffracted beams from a holographic grating can be used as the two spatially coherent excitation beams (13). Producing a grating also requires temporally coherent radia tion so that the two beams can inter fere with each other over a signifi cant distance. Temporal coherence derives from a narrow spectral band width. For Δν = 0.5 c m - 1 , the coher ence length is l/Δν = 2 cm, which in dicates that the path difference for the two beams between the beam splitter and the sample must be < 2 cm to generate interference at the sample. An étalon can be added to the laser cavity to improve a broadband laser's temporal coherence. Typically, the excitation beam is focused to deliver high-power density and create strong diffraction, but the spot size of the excitation beams should be large enough so that there are at least 10 interference fringes in the grating. Relationships between spot size, beam divergence, crossing angle, fringe spacing, and grating length indicate that 10 fringes in the grating are needed to ensure that the fringes are plane parallel so that diffraction from various regions of the volume grating interferes constructively at the Bragg angle (9). Tighter focusing leads to curvature of the phase fronts of the laser beam

within the excitation volume and r e sults in nonplanar fringes that reduce diffraction intensity (9, 14). The two excitation beams must also cross at their waists to create uniformly spaced interference fringes (14). To maximize the diffraction signal for a given excitation power, the fringe (pattern) contrast β should be close to unity—a result that can be realized with two laser beams of equal power and spot size. To achieve spatial overlap of one probe and two excitation beams, all three beams can be crossed through a pinhole with a diameter about the size of the excitation and probe beam diameters (12, 14). Diffracted radia tion can be aligned onto the detector by using a reference sample, such as a dye solution with significant ab sorption a t t h e e x c i t a t i o n w a v e length, which will give intense dif fracted radiation that can be visually observed. With a visible beam, spa tial isolation of the diffracted light and detector alignment are straight forward. Applications D e t e c t i o n of w e a k a b s o r p t i o n in small volumes. Diffraction from a thermal grating or hologram is an extremely sensitive method for mea suring weak optical absorption in liq uids (14-17). Two important features of using the thermal grating for this purpose can be seen in Figure l b . First, the diffraction signal is ob served on a z e r o - i n t e n s i t y back ground, and shot-noise-limited de tection can be achieved (14, 15, 17). Second, detection takes place only in the small volume where the two exci tation beams and the probe beam in tersect; light absorption outside this volume does not contribute to the dif fraction signal. Therefore, detection is spatially selective, which could be useful when cell window contamina tion is a problem. In addition, when d e t e c t i n g s a m p l e s e l u t i n g from small-volume flow channels, a large detection cell could be used because the continuity of the sample zone ex iting the flow channel need only be maintained for 5 0 - 1 0 0 μπι beyond t h e point w h e r e t h e l a s e r b e a m s would intersect. Diffraction theory for volume grat ings predicts t h a t tighter focusing of t h e e x c i t a t i o n b e a m s produces a greater diffraction signal for given sample absorptivity and laser pulse energy, so that there are only a few fringes in the grating. This predic tion has been verified experimentally (14); low-concentration a b s o r b e r s were detected in nanoliter volumes

with higher sensitivity than was pos sible by measuring the same concen tration samples in larger volumes. Figure 3 shows how photothermal diffraction can be used to detect weak optical absorption in a 7.6 -nM solution of azulene in CC1 4 with a decadic absorptivity of 1.5 x 10~ 6 c m - 1 (17). The absorbance detection limit -i4min is 4 χ 10~ 7 c m - 1 and corre sponds to 0.5 fg or about 5 million azulene molecules in a 3.3-nL detec tion zone, which is defined by the volume of t h e i n t e r s e c t i n g l a s e r beams. Similar detection capabilities have been demonstrated by Miller and co-workers (16) for measuring very weak vibrational overtone tran sitions in pure solvents. The transient signal in Figure 3 also i l l u s t r a t e s t h e a d v a n t a g e of time-resolving the slowly decaying thermal diffraction signal. Interfer ing Raman scatter from the solvent (or fluorescence from impurities at the probe wavelength) can easily be avoided a few microseconds after the excitation pulse; in this region, de tection is limited only by shot noise from scattered and diffracted probe beam radiation. With low-background m e a s u r e ment of diffracted radiation, detec tion limits are inversely related to the square of the excitation intensity until saturation of the optical transi tion or photolysis of the absorber oc curs. The latter is not a serious prob lem because the average laser power is small (typically 10 mW) and may be reduced further by decreasing the pulse repetition rate. Excitation saturation during the laser pulse is a more serious prob-

, Blank

£-ο ·! c

Azulene

s

ο to

aS 6

«=.5b 9 0

25 50 75 100 Time (μβ)

Figure 3. Thermal grating diffraction transients of 7.6 nM azulene in CCI4. Also shown is a blank response from CCI4, where the intensity spike coincident with excitation is from Raman scatter. Note that increasing intensity is downward. (Adapted with permission from Reference 17.)

ANALYTICAL CHEMISTRY, VOL. 64, NO. 14, JULY 15, 1992 · 713 A

INSTRUMENTATION lem; it limits the heat t h a t can be produced by a molecule during the excitation pulse. For azulene, there is no evidence of saturation in the ex citation power dependence of diffrac tion for pulse energies up to 0.2 m J (17,18). This result is reasonable, be cause the small molar absorptivity of azulene a t the 5 3 2 - n m excitation wavelength (200 L mol" 1 cm" 1 ) leads to an excitation rate keYL of 1.4 χ 10 9 s" 1 at the highest laser power. This excitation rate is much slower than the decay rate of the lowest excited singlet state, which has a 2-ps life time (19). Interestingly, this lack of satura tion in azulene allows an average of 90 photoexcitations of each molecule d u r i n g the 7 0 - n s excitation laser pulse. For molecules with higher mo lar absorptivity or nanosecond excit ed-state lifetimes, the excitation rate could easily exceed the decay rate and saturation would limit sensitiv ity. Excitation saturation generally sets the sensitivity limit of all pulsed laser detection methods based on light absorption. Unlike photolumi nescence methods, when detection is based on nonradiative relaxation of excited states, some saturation can be avoided by adding quencher to the sample, thereby increasing the nonradiative decay rate. While satura tion limits sensitivity for detecting weak absorption, diffraction from volume thermal gratings created by saturated absorption has unique p r o p e r t i e s t h a t yield a powerful method for studying nonradiative, excited-state decay processes. Non l i n e a r optical a b s o r p t i o n c r e a t e s higher order spatial frequencies in a grating that can be selectively moni tored free of interference from linear absorption contributions. Nonlinear absorption and a n harmonic thermal gratings. Exci t a t i o n s a t u r a t i o n p h e n o m e n a are generally difficult to investigate, as illustrated in the upper-right quad rant of Figure 4. Deviations from a linear response must exceed the pro portional noise in t h e e x c i t a t i o n source, which can be significant with pulsed lasers. Under strong satura tion conditions, the energy deposited in the sample (? abs becomes indepen dent of the excitation intensity and nothing can be learned about the un derlying excitation or relaxation ki netics. Laser-induced gratings are unique ly suited for studying nonlinear opti cal excitation of molecules under sat urated absorption conditions. By ex citing the sample with a sinusoidal interference p a t t e r n (lower r i g h t

Sinusoidal

Grating

°a te Linear Saturated

Distorted

Intensity Interference pattern

Figure 4. Effect of saturated optical absorption on a laser-induced grating. The sample is excited with a sinusoidal interference pattern in the χ-axis (lower right quadrant). When the energy deposited in the sample Q abs depends linearly on excitation intensity (dashed line), then the spatial variation of the refractive index is a pure sine wave. With excitation under saturated absorption conditions, the resulting grating is distorted from a sinusoidal shape.

quadrant of Figure 4), a whole range of excitation intensities exists simul taneously in the sample. If the en ergy deposited in the sample depends l i n e a r l y on e x c i t a t i o n i n t e n s i t y (dashed line), the spatial variations of the temperature and refractive in dex modulation are proportional to intensity and contain only the funda mental spatial frequency of the inci dent interference pattern. With exci tation u n d e r s a t u r a t e d absorption conditions, however, the absorbed energy is a nonlinear function of in tensity and the resulting t h e r m a l grating is distorted from a purely si nusoidal shape (upper left quadrant of Figure 4). From the distortion of a nonlinear sample response, a thermal grating generated under s a t u r a t i o n condi tions contains higher order harmon ics of the fundamental spatial fre quency of the excitation interference pattern. This behavior is analogous to t h e s a t u r a t e d , a n h a r m o n i c r e sponse of an audio amplifier to a strong single-frequency tone, which produces audible overtones (higher order harmonics) from signal clip ping. Unlike the distortion of an am plifier in the time domain, the an h a r m o n i c r e s p o n s e of a t h e r m a l


g r a t i n g is in the s p a t i a l domain, which is ideal for the study of nonlinearity because each spatial frequency can be selectively probed by diffrac tion at its corresponding Bragg an gle. Recall that volume gratings in the Bragg limit produce only a single diffracted order for each spatial fre quency present in the index or ampli tude modulation (Figure 2). Thus the series of m- order grating components arising from s a t u r a t e d absorption can be detected by diffraction at a se ries of Bragg angles given by 0Bw! = sin" 1 (mXp/2d), as illustrated in Fig ure 5. Diffraction at higher Bragg angles is characteristic only of non linear excitation processes in the sample, and this higher order diffrac tion can be angularly resolved from diffraction caused by linear excita tion processes. Diffraction at the Bragg angles for higher order thermal gratings, there fore, provides a low background mea surement of nonlinear excitation pro cesses in the sample (6, 7, 18, 20-23). An example of thermal diffraction in the presence of saturated absorption is shown in Figure 6, where excita tion of iodine at 532 nm produces a series of diffracted orders. This re sponse can be compared with that for

azulene in Figure 2, where the ab sence of saturation leads to a single diffracted order. As discussed earlier, azulene is ex tremely difficult to saturate because of its small molar absorptivity at 532 nm and its rapid excited-state decay rate. When azulene serves as a linear absorption reference, the second- and third-order diffraction observed from the iodine can therefore be credibly interpreted as arising from nonlinear absorption. To study the nonlinear absorption mechanism of iodine responsible for the results in Figure 6, the excitation intensity dependence of diffraction from each m- order harmonic grating has been measured (18). Saturated absorption in electronic transitions of molecules in liquids is caused by long-lived excited s t a t e s ("kinetic bottlenecks") and photochemical re actions. The saturation of iodine in hydrocarbons was caused primarily by photodissociation, the yield of which could be estimated from the intensity dependence of higher order diffraction (18, 23). Photodissociation quantum yields as small as 1% could be detected. In CC1 4 , iodine exhibited both photodissociation and a kinetic bottleneck in the longer lived A' ex cited state (18, 23). Nonlinear optical absorption phe nomena, which can be selectively de tected and studied by diffraction from anharmonic thermal gratings, are not limited to saturated absorp tion but can be extended to m u l tiphoton excitation (6, 7, 17). Multiphoton fluorescence spectroscopy can detect short-wavelength emis sion t h a t indicates a h i g h - e n e r g y state was populated by multiphoton excitation. Photothermal m e a s u r e ments cannot distinguish between one-photon and multiphoton absorp tion phenomena based on the excit ed-state quantum energy; one must rely on measurements of the power dependence of the signal (24) in which one-photon absorption by the solvent or impurities represents an interference. Diffraction from anharmonic ther mal gratings, on the other hand, can be used to detect higher order excita tion processes free of background from one-photon absorption, which is analogous to the detection of satu rated absorption discussed earlier. Unlike saturated one-photon absorp tion, however, the a m p l i t u d e s of «ί-order diffraction that arise from «-photon excitation can be predicted by a simple Fourier series t h a t can be used to identify the highest order excitation process in t h e sample.

Δη

Fourier components

m=1

m=2 ΘΒ3

m=3

0Bm = sin-'(mX p /2d)

Figure 5. Probing gratings distorted by nonlinear excitation. An enharmonic grating can be represented as a series of m-order Fourier components (left). Diffraction from these components can be independently measured by varying the probe laser beam through a series of incident Bragg angles (right).

5000

1000 S

500

I 100 Ι 50

f.1 °

5 1.0 0.5 Θ

0.1 0

20

Θ

Β1

40

Β2

60 80 Probe angle (mrad)

ΘΒ3

100

120

Figure 6. Diffraction intensity versus incident probe angle for thermal grating. Sample is 9.4 μΜ solution of U in CCI4. (Adapted with permission from Reference 18.)

Taking the «th power of the excita tion to predict the form of the depos ited heat Qaba(#) Γ(χ)

=/2 [1 + β cos (2jtt/d)]n

(5)

and expanding the result as a Fou rier series in x, one finds that the highest m- order diffraction observed for «-photon excitation is m = η (7). The quantitative capabilities of an h a r m o n i c t h e r m a l g r a t i n g s for

«-photon absorption measurements are notable. Using a dilute one-pho ton absorber as a calibration stan dard, it is possible to measure twophoton absorption cross sections of aromatic compounds with 10% un certainty (7, 17). Diffraction from anharmonic t h e r m a l gratings can be used to detect very weak two-photon absorption phenomena. The fraction of the laser energy deposited into the


INSTRUMENTATION

40 r Azulene •

"m S

30-

£•

g •2-

c D) 0) C

Bromine

ο É 10-

M Time (ris)

Figure 7. Thermal grating diffraction transients. Transients observed for a solution of 51 μΜ Br2 in CCI4 (squares) and solution of 11 μΜ azulene in CCI4 (dotted line). Azulene excited states decay in a few picoseconds, providing an instrument response function to fit the bromine signal to a biexponential decay (5.8 and 25 ns) model (solid line).

sample by two-photon absorption need only be = 10~ 7 to produce a de tectable signal; with a high concen tration of sample molecules, twophoton cross sections as small as 1(T 56 cm 4 s could be detected (17). Three-photon absorption cross sec tions for benzene and chlorobenzene (which arise from further pumping or "up-pumping" of the two-photon ex cited B 2 u state) have also been mea sured with about 20% uncertainty by probing diffraction at the third-order Bragg incidence (7). The same approach has been ex tended to two-step absorption pro cesses composed of sequential, onephoton t r a n s i t i o n s . T h i s form of excited-state up-pumping is common in high-power, pulsed-laser excita tion of molecules. It can lead to sig nificant upper excited-state popula tions and photoionization in solution (the latter process has been used for sensitive detection [25-27]). Despite its potential value for ion ization detection and its fundamen tal role in pulsed-laser photochemis t r y , e x c i t e d - s t a t e u p - p u m p i n g is very difficult to study because inter mediate upper states are generally very short-lived and nonfluorescent. By measuring photothermal diffrac tion intensities at several Bragg or ders as a function of excitation inten sity, a sensitive method for studying this nonlinear optical absorption has

been demonstrated. Studies of photoisomerization and sequential, twostep absorption have been conducted for cyanine dyes (20, 22) and β-caro tene (21). Some of the most interesting re sults were found for two tricarbocyanine dyes, diethyloxatricarbocyanine iodide (DOTCI) and hexamethylindotricarbocyanine iodide (HITCI), which are used as saturable absorb ers in mode-locked lasers. For both of these dyes, an anomalous dip was observed in the intensity dependence of the second-order diffraction effi ciency (22). This behavior could be a t t r i b u t e d to diffraction from two second-order thermal gratings 180° out of phase. Up-pumping of the ex cited-singlet state leads to a secondorder grating t h a t is in phase with the excitation intensity modulation; saturation of ground-state absorp tion generates a second-order ther mal grating that is out of phase with the excitation modulation. At a par ticular average level of excitation, the amplitudes of these two gratings cancel each other, leading to a dip in the diffraction efficiency. The inter ference between these two secondorder gratings is very sensitive to the saturation and up-pumping parame ters and can be used to differentiate between kinetic models. Time-resolved thermal grat i n g s for p h o t o i n i t i a t e d p r o c e s s e s .


We have shown that diffraction from anharmonic thermal gratings can be used to study photophysical pro cesses. An a l t e r n a t i v e method for studying the kinetics of these pro cesses is to resolve the time-depen dent temperature rise in the sample following photoexcitation. Such timeresolved photothermal methods can yield not only the enthalpy stored by excited states and/or photochemical products after pulsed excitation but also the rate at which h e a t is re leased to the environment from ex c i t e d - s t a t e r e l a x a t i o n a n d photo chemical reactions. When combined with yields of formation of interme diate states or photoproducts, excit ed-state enthalpies or bond energies, along with the rate constants for re actions and excited-state decay (2833), can be determined. The time resolution of most photothermal methods (i.e., thermal lens, beam deflection, and photoacoustic spectroscopies) is limited by the time r e q u i r e d for a t h e r m a l l y d r i v e n acoustic wave to carry the density change beyond the excitation region. The excitation zone is defined by the laser beam spot size, leading to a typical rise time of a few hundred nanoseconds (32, 33). Unlike these photothermal meth ods, the rise time of diffraction from a thermal grating is limited only by the time required for t h e acoustic wave to traverse one period of the fringe pattern. If the excitation pulse is faster t h a n this period, an interfer ence is observed in the diffraction signal as two counter-propagating acoustic density waves beat against the stationary thermal grating in the sample. A clever means of eliminat ing this interference is to make the sound wave period comparable to or shorter than the excitation pulse du ration (by varying the angle between excitation beams and t h u s adjusting the fringe spacing) (11, 12). Figure 7 shows an example of us ing time-resolved diffraction from a thermal grating to observe the tem perature rise from a nanosecond ex c i t e d - s t a t e decay in bromine. The signal from a rapidly decaying stan dard, azulene—which has an excit ed-state lifetime of only a few pico seconds and no other intermediate long-lived s t a t e s (18, 19)—is also shown for comparison. The excitation fringe spacing, d = 7.1 μπι, corre sponds to a 7.7-ns period for sound propagation in CC1 4 , which is short compared with the excitation pulse duration of 14 ns. As a result, acoustic oscillations are not observed in the diffraction

signals and the grating amplitude rises to a flat plateau within the ex citation pulse duration. The rise of the diffraction signal from bromine in Figure 7 clearly shows a delay compared with the i n s t r u m e n t limited response of azulene. The fi nite rate of heat production by bro mine could be a t t r i b u t e d to two excited states that are populated by 532-nm excitation (34). One decay component, which has a lifetime of 5.8 ns, was previously identified by flash photolysis (35). The other decay component, which has a lifetime of = 2 5 ns, was confirmed by t i m e resolved n e a r - I R fluorescence and assigned to a low-lying A' excited state. The value of the A' state en ergy from gas-phase measurements was used to estimate the quantum yield of the A' state formation from the relative diffraction amplitudes of the decaying components (34). Several examples of applying pho tothermal diffraction to fast nanosec ond calorimetry of photophysical pro cesses have been published. Zimmt and co-workers have estimated ener gies of the twisted excited singlet state of tetraphenylethylene and its decay rate constants in various sol vents (36, 37). The solvent polarity dependence of the energy and the de cay rate provides evidence for the zwitterionic character of this excited state. Quantum yields and submicrosecond lifetimes of triplet states of aro matic molecules have been measured (38). Our group has used the timeresolved thermal grating technique to follow the energetics and diffu sion-controlled kinetics of recombi nation of dissociated halogens (39, 40). Following escape of radicals from their initial solvent cage on a pico second time scale after photoexcita tion, the nongeminate rate of recom bination can be determined from the finite rise time of the photothermal diffraction signal from the secondorder exothermic reaction. Because the response time of a thermal-phase grating is limited by solvent expansion to the acoustic transit time over the fringe spacing, the fastest rise time is obtained for the smallest fringe spacing (i.e., d = λ β /2), which can be achieved with counterpropagating excitation beam g e o m e t r y . For e x c i t a t i o n w a v e lengths in the near-UV range, this geometry leads to a 100-ps rise time in liquids and a potential time reso lution of nearly 10 ps. Miller and co-workers (11, 41) ob served the occurrence of vibrational energy relaxation from a heme por

phyrin ring to a surrounding protein backbone < 20 ps after photoexcita tion of the porphyrin ring. In thermal grating experiments, the density changes detected are generally driven by an increase in the sample temperature. As shown by Miller and co-workers (41, 42), however, density changes can also be created by opti cally induced differences in molecu lar volume or configuration. Their re sults demonstrate that the tertiary structure of proteins changes on an extremely fast time scale. Whereas the acoustic transit time limits the rise t i m e of a t h e r m a l g r a t i n g , t h e r m a l conductivity be tween fringes defines the decay time of the temperature rise, thus limiting the persistence of a thermal grating to typically tens of microseconds. Al though thermal conductivity imposes a restriction on the slowest rate of heat deposition that can be studied, the decay rate of the thermal grating provides a n a c c u r a t e m e t h o d for measuring thermal diffusion rates in condensed-phase materials (43), in cluding anisotropic materials such as liquid crystals (44). Thermal diffusivity of the medium is determined from the dependence of the decay rate of diffraction on the grating spacing. Measurement of mass diffusion coefficients. Molecular diffusion in condensed-phase media is not only fundamentally interesting but also practically important for determin ing the stability of materials and re sponse time of chemical devices for controlled-release or sensing appli cations. Electrochemical methods are widely used for measuring diffusion coefficients of redox-active species in conductive media, b u t it is much more difficult to measure diffusion of molecules in nonpolar solvents and materials. Common techniques in volve t h e t r a n s p o r t of molecules across macroscopic distances, which requires very long times for observ ing changes in optical density, radio activity, or solution concentration. Holographic methods provide a con venient approach for d e t e r m i n i n g molecular diffusion coefficients be cause the measurement scale is con trollable at microscopic distances. The principle of this approach is to expose photochromic t r a c e r mole cules (dissolved in the medium being studied) to an excitation interference pattern. A periodic concentration of photolabeled molecules is generated and acts as an amplitude or phase grating (45, 46). The efficiency of dif fraction decreases with time, as the p a t t e r n of l a b e l e d m o l e c u l e s is washed out by diffusion. Molecules in

which the photochemically induced changes in optical properties are long-lived—such as azo dyes, where the photoisomer lives more than sev eral seconds (47)—are commonly used for these measurements, so that the decay of diffraction relates only to mass transport of the molecules and not to the recovery of its initial optical properties. An example of using holographic methods to measure mass diffusion is shown in Figure 8, where azobenzene is photoisomerized by 532-nm excitation in a solution of octanol. The spike observed at the beginning of the time-resolved signal in Figure 8a arises from diffraction from a thermal grating and decays in < 100 \is. Decay of diffraction on a millisec ond time scale can be attributed to mass transport of the photolabeled azobenzene molecules. The phenome non is verified in the excitation angle dependence of diffraction decay rate shown in Figure 8b. The time con stant for diffusion across a fringe de pends on the square of the fringe spacing and inversely on the diffu sion coefficient D according to τ = d2/4n2D

(6)

whereas the fringe spacing is con trolled by the excitation crossing an gle according to Equation 2. Because the diffraction efficiency depends on

.•ë·

(a) 80

| ' § 60 .2 2 40

1 | 20 δ

ο 0 ( .

4

8

12

16

Time (με)

300

240

J? 180

^ 120 60 η

0

2

4 6 8 sin2 θ Χ10 4

10

Figure 8. Laser-induced grating measurement of molecular diffusion. (a) Decay of diffraction intensity from 3.3 mM azobenzene in octanol, θ β = 23 mrad. (b) Decay rate of the grating amplitude (inverse of twice the decay time of diffraction) versus sin 2 θβ, fit to Equation 7 to estimate the diffusion coefficient D of the probe molecule.


INSTRUMENTATION the square of the grating amplitude (see Equation 4), the time constant for the decay of diffraction is half the time constant for the diffusional de cay of the grating amplitude. Substi tuting Equation 2 into Equation 6 gives the dependence of the decay rate of the grating amplitude on the excitation beam crossing angle l/T = Z ) ( 4 7 t A e ) 2 s i n 2 9 e

(7)

Equation 7 predicts a linear depen dence of l/τ on sin 2 θ β with a zero in tercept, which is found for the data plotted in Figure 8b. From the slope, the diffusion coefficient D for the probe molecule in the octanol solvent is 4.5 (± 0.2) χ 1(T 6 cm 2 s" 1 . The t r a n s i e n t holography tech nique has been widely used to mea sure molecular diffusion coefficients in liquid crystals as well as in poly m e r solutions a n d m e l t s (45, 46, 48-52). The principal advantage of laser-induced grating over classical tracer methods is that the distance scale for measuring diffusion is con trolled by the fringe spacing (in the 0.2-100-μπι range). Whereas the rel ative range of variation is large, the actual distance scale is several or ders of magnitude shorter than that used in classical tracer methods. The scale has a profound effect on the measurement time, which changes with the square of diffusion distance. Diffusion coefficients as small as 10~ 14 cm 2 /s, too small to be measured by classical methods, can be mea sured in only a few hours by the ho lographic grating technique. Laser-induced holographic meth ods for studying molecular transport have been extended to measuring mi gration rates of ions in electric fields (53, 54). In these experiments, photochromically labeled species migrate in an electric field aligned perpendic ular to fringes in the grating. Migra tion of the photolabeled pattern of molecules produces a t i m e - d e p e n dent phase shift in the diffracted ra diation. When combined with a sta tionary reference wave, the intensity is modulated at a frequency related to the electrophoretic mobility of the sample molecules (53). Alternatively, a second cell without an electric field can be used as a ref erence to yield modulated diffraction of a single probe beam (54). Recently, laser-induced grating methods for measuring diffusion coefficients were applied to absorbed molecules at vac uum-solid interfaces. A pulsed-laser interference pattern is used to desorb molecules from the surface; decay of this pattern is measured by linear diffraction (55) or by diffracted sec

(19) Heritage, J. P.; Penzhofer, A. Chem. Phys. LeU. 1976, 44, 76. (20) Zhu, X. R.; Harris, J. M. Chem. Phys. 1988 124 321 Summary (21) Zhu, X. R.'; Harris, J. M. /. Phys. Chem. 1989, 93, 75. Holographic spectroscopy, based on (22) Zhu, X. R.; Harris, J. M. Chem. Phys. diffraction from laser-induced grat 1990, 142, 301. ings, provides a unique low-back (23) Zhu, X. R.; Harris, J. M. /. Opt. Soc. ground approach for measuring the Am. Β 1990, 7, 796. absorption of radiation, relaxation of (24) Kliger, D. S. Accts. Chem. Res. 1980, 13, 129. excited states, and transport of pho(25) Voigtman, E.; Jurgensen, Α.; Winetoproducts within a sample. For all of fordner, J. D. Anal. Chem. 1981, 53, these applications, sample excitation 1921. by two interfering beams of incident (26) Yamada, S.; Hino, Α.; Kano, K.; Ogawa, T. Anal. Chem. 1983, 55, 1914. laser radiation encodes the absorbed (27) Yamada, S.; Sato, N.; Kawazumi, H.; optical energy, released heat, and Ogawa, T. Anal. Chem. 1987, 59, 2719. photoproducts in a periodic spatial (28) Fuke, K.; Ueda, M.; Itoh, M. Chem. pattern. Diffraction of a probe laser Phys. LeU. 1980, 76, 372. beam by this pattern (reading the ho (29) Rothberg, L. J.; Simon, J. D.; Berstein, M.; Peters, K. S. /. Am. Chem. Soc. logram) provides a low-background 1983, 105, 3464. detection technique for measuring (30) Redmond, R. W.; Heihoff, K.; weak optical absorption, nonlinear Braslavsky, S. E.; Truscott, T. G. Photoabsorption (including saturation and chem. Photobiol. 1987, 45, 209. (31) Terazima, M.; Azumi, T. Chem. Phys. multiphoton effects), fast nonradiaLett. 1987, 141, 237. tive relaxation of excited states, and (32) Isak, S. J.; Komorowski, S. J.; Merthe diffusion of heat and photoprod row, C. N.; Poston, P. E.; Eyring, E. M. ucts through the sample. These tech Appl. Spectrosc. 1989, 43, 419. niques t a k e full advantage of the (33) Poston, P. E.; Harris, J. M. /. Am. Chem. Soc. 1990, 112, 644. unique spatial and temporal coher (34) Zhu, X. R.; Harris, J. M., submitted ence properties of laser radiation. for publication in / Phys. Chem. (35) Abul-Haj, N. A; Kelley, D. F. Chem. Phys. Lett. 1985, 119, 182. (36) Zimmt, M. B. Chem. Phys. Lett. 1989, This work was supported in part by the Na 160, 564. tional Science Foundation under grants (37) Morais, J.; Ma, J.; Zimmt, Μ. Β. /. CHE85-06667 and CHE90-10309. Phys. Chem. 1991, 95, 3885. (38) Terazima, M.; Hirota, N. / Chem. Phys. 1991, 95, 6490. References (39) Zhu, X. R.; Harris, J. M. Chem. Phys. 1991, 157, 409. (1) Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Gratings; Spring- (40) Zhu, X. R.; Harris, J. M. Chem. Phys. Lett. 1991, 186, 183. er-Verlag: Berlin, 1986. (41) Genberg, L.; Richard, L.; McLendon, (2) IEEE J. Quantum Electron.; Eichler, R.; Miller, R.J.D. Science 1991, 125, H. J., Ed.; 1986, 22 (special issue on dy 1051. namic gratings and four-wave mixing). (3) Fayer, M. D. Annu. Rev. Phys. Chem. (42) Miller, R.J.D. Ann. Rev. Phys. Chem. 1991, 42, 581. 1982 33 63 (43) Eichler, H.; Salje, G.; Stahl, H. / (4) Moharam, M. G.; Young, L. Appl. Opt. Appl. Phys. 1973, 44, 5383. 1978, 11, 1757. (44) Urbach, W.; Hervet, H.; Rondelez, F. (5) Gaylord, T. K.; Moharam, M. G. Appl. Mol. Cryst. Liq. Cryst. 1978, 46, 209. Opt. 1981, 20, 3271. (6) McGraw, D. J.; Harris, J. M. Opt. Lett. (45) Hervet, H.; Urbach, W.; Rondelez, F. /. Chem. Phys. 1978, 68, 2725. 1985, 10, 140. (7) McGraw, D. J.; Harris, J. M. Phys. Rev. (46) Hervet, H.; Léger, L.; Rondelez, F. Phys. Rev. 1979, 42, 1681. A 1986, 34, 4829. (47) Photochromism, Techniques of Chemistry (8) Kogelnik, H. Bell. Syst. Tech. J. 1969, Vol. Ill; Brown, G. H., Ed.; Wiley48, 2909. Interscience: New York, 1971. (9) Siegman, A. E./. Opt. Soc. Am. 1977, 4, (48) Wesson, J. H.; Takezoe, H.; Yu, H.; 545. Chen, S. P. /. Appl. Phys. 1982, 53, 6513. (10) Nelson, Κ. Α.; Casalegno, R.; Miller, R.J.D.; Fayer, M. D. /. Chem. Phys. 1982, (49) Rhee, K. W.; Gabriel, D. A; Johnson, C. S.J. Phys. Chem. 1984, 88, 4010. 77, 1144. (11) Genberg, L.; Bao, Q.; Gracewski, S.; (50) Antonietti, M.; Coutandin, J.; GrutMiller, R.J.D. Chem. Phys. 1989, 131, 81. ter, R.; Sillescu, H. Macromolecules 1984, (12) Miller, R.J.D. In Time Resolved Spec 17, 798. troscopy; Clark, R.J.H; Hester, R. E., (51) Zhang, J.; Wang, C. H.; Ehlich, D. Eds.; Wiley: New York, 1990; Chapter 1. Macromolecules 1986, 19, 1390. (13) Bor, Z. Opt. Commun. 1981, 39, 383. (52) Lee, J. Α.; Lodge, T. P. / Phys. Chem. (14) Pelletier, M. J.; Harris, J. M. Anal. 1987, 91, 5546. Chem. 1983, 55, 1537. (53) Rhee, K. W.; Shibata, J.; Barish, Α.; (15) Pelletier, M. J.; Thorsheim, H. R.; Gabriel, D.; Johnson, C. S./. Phys. Chem. Harris, J. M. Anal. Chem. 1982, 54, 239. 1984, 88, 3944. (16) Miller, R. J.D.; Rose, T. S.; Pierre, (54) Kim, H.; Chang, T.; Yu, H. / Phys. M.; Fayer, M. D. Chem. Phys. 1982, 72, Chem. 1984, 88, 3949. 371. (55) Zhu, X. D.; Lee, Α.; Wong, A. Appl. (17) McGraw, D. J.; Harris, J. M. / Opt. Phys. A 1991, 52, 317. Soc. Am. 51985,2, 1471. (56) Zhu, X. D.; Rasing, T.; Shen, Y. R. (18) McGraw, D. J.; Michaelson, J. W.; Phys. Rev. Lett. 1988, 61, 2883. Harris, J. M. /. Chem. Phys. 1987, 86, (57) Zhu, X. D.; Shen, Y. R. Opt. Lett. 2536. 1989, 14, 503. ond harmonic generation to provide surface selectivity (56, 57).


Reproducible Quality

Is Your Assurance of Reproducible Results X. R. Zhu is a postdoctoral research asso ciate at the University of Utah, where he received his Ph.D. in chemical physics in 1989. His graduate research focused on anharmonic grating diffraction for study ing nonlinear optical absorption and dy namic light scattering of polymer solu tions; his current research concerns timeresolved holographic methods for measuring fast photophysics and molecu lar transport at liquid-solid interfaces.

W i t h W h e a t o n 0.1 mL Autosampler Vials Quality Is O n e M o r e Variable That You Don't H a v e to W o r r y About. Wheaton 0.1 mL Plastic Vial with Glass Inner Cone — the economy of plastic and the security of borosilicate glass. ^ ^ — « ^ Wheaton 0.1 mL Polypropylene 0.1 mL Vial — good chemical resistance in a lightweight economical vial. Specify Wheaton...Because not all Autosampler Vials are alike. For product information and a list of the Wheaton distributors nearest you contact 1 -609-825-1100 or FAX 1 -609-825-1368.

WHEATON Manufacturers Since 1888

1000 Ν 10TH STREET MILLVILLE NJ 08332-2092 USA

D. J. McGraw is assistant professor of physics at the University of New Mexico. He received his Ph.D. in physics from the University of Utah in 1986 and was a postdoctoral associate at Stanford. His re search interests include laser-induced gratings, optics metrology, and ultrafast laser spectroscopy. His current research focuses on parametric mode locking that combines pulse generation and frequency upconversion in cw lasers.

J. M. Harris received his Ph.D. in analyt ical chemistry from Purdue University in 1976, after which he joined the chemistry faculty at the University of Utah. Harris has been an Alfred P. Sloan Research Fel low and a recipient of the Coblentz Award in molecular spectroscopy and the ACS Division of Analytical Chemistry Award in Chemical Instrumentation. His re search interests include the application of lasers to analytical chemistry, photother mal spectroscopy, and molecular structure and kinetics at liquid-solid interfaces.

WHEATON CIRCLE 120 FOR DEMONSTRATION

CIRCLE 121 FOR LITERATURE


Holographic Spectroscopy Diffraction from Laser-Induced Gratings

Recommend Documents