Holographic spectroscopy. Diffraction from laser-induced gratings

Holographic Spectroscopy D i ffraction from

Laser-Induced Gratings X. R. Zhu, D. J. McGraw’, and J. M. Harris Department of Chemistry University of Utah Salt Lake City, UT 841 12

The introduction of lasers into spectroscopic instrumentation has produced outstanding gains in detection compared with conventional light sources. These improvements arise not only from the higher optical power output of the laser but also from the unique coherence properties of laser radiation. A new class of sensitive spectroscopic techniques has been developed in which heat produced by nonradiative decay of excited species perturbs the 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, and 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 prolPresent address: Department of Physics, University of New Mexico, Albuquerque, NM 87131

710 A

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 a r e spatially resolved in the sample, and thus a signal on a nearly zero-intensity background can be produced. Diffraction from laser-induced gratings is termed transient holography or holographic spectroscopy, be cause the laser-induced grating is an elementary hologram produced by interference between coherent reference and object waves (1). In other words, information about the absorption of radiation, relaxation of excited states, and diffusion of photoproducts is holographically encoded within the sample through interfer ence of t h e incident excitation beams. Laser -induced holographic methodology is well developed for measuring physical properties (it has been used to determine transport 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, low background absorption measure ments by taking advantage of spatial

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 the diffraction signal one can study the kinetics and energetics of photoinitiated reactions in liquids on a subnanosecond time scale and transport properties of the sample on much longer time scales. Principles Laser-inducedgratings. An interference pattern used to create laser induced gratings is shown as a moir6 pattern in Figure la. Two coherent laser beams derived from the same laser cross a t an angle 28, and have intensities I, and Ib. The resulting intensity I of the interference pattern x is given by I(%)= 10 [ l + p cos (2” (1) where Io = I, + Ib is the total intensity of the two excitation beams, p is the pattern contrast and is equal to 2(1a1b)1’2/1,-, (and depends on the relative intensities in the two beams), and d is the fringe spacing of the interference pattern. The size of d depends on the excitation wavelength A, and the crossing half angle e,, as illustrated by the Bragg equation d = h,/2 sin 8, (2) Equation 2 indicates that the spacing can be varied by simply adjusting the angle between the two excitation beams. For instance, when A, = 532 0003-2700/92/0364-71OA/$03.00/0 0 1992 American Chemical Society

nm, d = 0.2 pm for 8, = go", whereas d = 30 vm for 8, = 0.5". Optical excitation of molecules by the interference pattern initially creates a periodic spatial distribution of excited states. That distribution comprises a population grating, be cause the optical properties (e.g., refractive index and absorption coefficient) of these excited states are generally different from those of their corresponding ground states. The excited states may decay via a photochemical reaction to yield products in a spatial pattern similar to that of the initial excitation. These products, along with the depleted starting compounds, produce a hologram or chemical concentration grating from a modulation of the optical properties due to chemical com position changes. This concentration grating decays at a slow rate determined by the stability of the photoproducts or their mass diffusion across t h e grating spacing. The excited-state decay also creates a thermal grating because of the temperature rise from nonradiative relaxation. 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 matrix, which changes the refractive index of the matrix. m e thermal P a t ing decays with a fast time constant (typically microseconds) characteristic of thermal diffusion across the grating spacing. Diffractionfrom V O h n e matings. The gratings formed in a sam-

ple from excitation with crossed laser beams can be monitored by diffraction of a third probe beam intersecting the excitation volume in the sample, as shown in Figure lb. Diffracted probe radiation is measured by a detector 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 (RamanNath diffraction) (1,4, 5). Characteristic diffraction from a t h i n grating, where t h e grating thickness L is comparable to or less than the fringe spacing, is multipleorder for a probe beam incident at any angle. Such behavior is familiar to spectroscopists using monochromators with thin diffraction gratings based on surface reflection. For volume holograms, where the grating thickness typically is much greater than the fringe spacing, the diffraction efficiency is significant

only when the probe radiation is incident at the Bragg angle, 8, = OB, defined relative to the bisector of the two excitation beams. The angle 8, for the incident probe beam depends on the grating fringe spacing and the probe wavelength &, according to the Bragg equation rearranged as 8B = sin-' (&/2d) (3) In addition, the diffracted probe beam radiation propagates predominantly at an angle -eB away from the bisector of excitation beams with negligible contributions in the other directions. Deviations from t h e Bragg angle result in a rapid decrease in diffraction efficiency, and no diffraction is observed at higher order Bragg angles (6, 7), as shown in Figure 2. Most experiments described in this paper are under similarly thick Bragg grating conditions. The angular sensitivity of diffraction from volume gratings can be understood by considering a thick grat -

d

Figure 1. Example of an interference pattern and instrumentationfor holographic SPectrosCoPY(a) Interference created by two mutually coherent (same frequency, fixed phase delay) laser beams at wavelength h, crossing at a full angle of 28, produce interference fringes (shown as a moire 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 i'n the sample. Diffraction within the sample is probed using a third laser beam at wavelength I,, incident at the Bragg angle, e, = OB = sin-'(hP/2d); I,, > h, because in this case e, > e.,


711 A

INSTRUMENTATION ing as a compilation of many thin gratings stacked together. Each thin grating gives multiple - order diffraction, and diffracted beams of the same order from different thin gratings interfere with each other. Only at the Bragg angle do first-order diffracted beams from thin gratings constructively interfere with each other and give a maximum signal. For other diffraction orders, the diffracted beams from different thin 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 rather a Gaussian function (parabolic on the logarithmic intensity scale) with a nonzero angular width. This angular uncertainty for the Bragg condition is attributable to finite spot sizes of the excitation and probe beams, which impose an uncertainty on the spatial frequency of the grating (7). The Bragg condition is thus less restrictive 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 diffraction effects can be described as four-wave mixing in the language of nonlinear optics (1,7). Diffraction of the probe beam is viewed as interaction 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 us to separate the grating formation and decay processes from diffraction or read-out; this separation is appropriate in these 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 approach. The diffraction efficiency q of a weakly absorbing, thick grating a t the Bragg incidence angle, under the weak diffraction limit, is given by

q = (d/& COS e,)2 x (Ani + ~ k i ) (4) where L is the grating thickness and 712 A

An, and Akp are the peak-to-null differences of the real and imaginary parts, respectively, of the refractive index a t the probe wavelength, which give rise to diffraction (8).The modulation of the imaginary part of the refractive index is related to modulation of the absorption coefficient Act in cm-’ by Akp = Ac&/47c. Note that the diffraction efficiency grows in proportion to the square of the refractive index and absorptivity modulation (because the grating acts on the electric field phase and amplitude, and intensity depends on the square of the scattered electric field). This response produces a quadratic dependence of the diffraction signal on the concentration of absorber in the sample. Equation 4 is obtained for diffraction of plane waves from gratings of finite thickness but infinite area. For Gaussian laser beam-induced grat ings, the grating thickness depends on the spot size, we, of the excitation laser beams, which create the grating and their crossing angle (see Figure l),L = 2wJsin 8,. The diffraction efficiency for gratings induced by Gaussian - shaped laser beams has been derived by Siegman (9).Correction for the beam profile is a constant factor that depends on the ratio of the probe and excitation beam spot sizes and their crossing angles. On the basis of Equation 4, diffraction is expected to arise from changes in the refractive index and the absorption coefficient. Modulation of the absorption coefficient originates from the formation of excited states and/or photochemical products. Spatial variation of the sample absorption produces a n “amplitude grat ing,” because it generates diffraction through absorptive modulation of the probe beam electric field amplitude. Modulation of the refractive index forms a “phase grating” that generates diffraction by modulating the optical path or phase of the probe beam. Phase gratings can originate from several sources. The formation of excited states and/or photochemical products that absorb light also generates a phase grating (in addition to an amplitude grating), the strength of which is related to the absorption coefficient through the Kramers-Kronig transform ( I ) . In liquids, the strongest contribution to phase gratings is generally caused by heating from relaxation of excited states, which leads to large changes in the solvent’s density and refractive index. Diffraction from excited-state or photoproduct population gratings


Figure 2. Demonstrationof the Bragg condition. Diffraction intensity versus incident angle for the probe beam. The thermal grating was generated in a 6.7-pM solution of azulene in CCI, by 532nm pulses from a Nd:YAG laser. Diffraction at the second Bragg incidence angle OB2 is indistinguishable from the noise level. (Adapted with permission from Reference 7.)

and thermal-phase gratings can be distinguished by probing a t different wavelengths (10-12).The population grating can be monitored at a wavelength at or near an absorption band maximum where the spatial modulation of concentration contributes greatest to amplitude and phase gratings. A thermal grating modulates the refractive index through a change i n solvent density. This change can be selectively detected by diffraction of a probe beam with a wavelength that is much longer than any absorption band origin (where diffraction from the population grat ings is negligible). In this article we will focus on the thermal - phase grating and its appli cations in detecting weak optical absorption and in measuring excitedstate decay kinetics. Concentration or population gratings of longer lived photoproducts will be discussed briefly to illustrate their utility in measuring diffusion coefficients of molecules in liquids and solids. Instrumentation Figure l b shows instrumentation requirements for a laser -induced grat ing experiment. Excitation radiation is generated by a pulsed laser (e.g., at 532 nm from a Q-switched, frequencydoubled Nd:YAG laser), and the output is split into two equal-intensity beams recombined in the center of the

sample. Radiation from a continuouswave laser (e.g., at 632.8 nm from a He-Ne laser) is used to probe diffraction from the laser-induced grating. The diffracted beam is angularly resolved, spectrally filtered, and imaged onto a photomultiplier tube. Diffraction signals a r e typically acquired and averaged by use of a transient recorder or a digitizing oscilloscope. Choosing an optical configuration suitable for small crossing angles 8, of the excitation beams creates thicker, higher efficiency thermal gratings with larger fringe spacings and longer thermal decay times (> 10 ps). The interference pattern that generates 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 planar incident wavefronts, as shown in Figure la, that generate planar interference fringes of constant spacing. A TEM,,-mode laser beam (with Gaussian 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 coherence, such as a nitrogen laser, the f l-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 radiation so that the two beams can interfere with each other over a significant distance. Temporal coherence derives from a narrow spectral bandwidth. For Av = 0.5 cm-', the coherence length is l/Av = 2 cm, which indicates that the path difference for the two beams between the beamsplitter and the sample must be < 2 cm to generate interference at the sample. An etalon 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 den sity 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 results in nonplanar fringes that reduce diffraction intensity (9, 14).The two excitation beams must also cross a t their waists to create uniformly spaced interference fringes (14).To maximize the diffraction signal for a given excitation power, the fringe (pattern)contrast p 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 radiation can be aligned onto the detector by using a reference sample, such as a dye solution with significant absorption at t h e excitation wavelength, which will give intense diffracted radiation that can be visually observed. With a visible beam, spatial isolation of the diffracted light and detector alignment are straightforward. Applications Detection of weak absorption in small volumes. Diffraction from a thermal grating or hologram is an extremely sensitive method for measuring weak optical absorption in liquids (14-17).Two important features of using the thermal grating for this purpose can be seen in Figure lb. First, the diffraction signal is observed on a zero-intensity background, and shot-noise-limited detection can be achieved (14,15, 17). Second, detection takes place only in the small volume where the two excitation beams and the probe beam intersect; light absorption outside this volume does not contribute to the diffraction signal. Therefore, detection is spatially selective, which could be useful when cell window contamination is a problem. In addition, when detecting samples eluting from small-volume flow channels, a large detection cell could be used because the continuity of the sample zone exiting the flow channel need only be maintained for 50- 100 pm beyond the point where the laser bea would intersect. Diffraction theory for volume ings predicts that tighter focusi the excitation beams produces greater diffraction signal for given sample absorptivity and laser pulse energy, so that there are only a few fringes in the grating. This prediction has been verified experimentally (14);low-concentration absorbers were detected in nanoliter volumes

with higher sensitivity than was possible by measuring the same concentration 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, with a decadic absorptivity of 1.5 x cm-' (17). The absorbance detection cm-' and correlimit Aminis 4 x sponds to 0.5 fg or about 5 million azulene molecules in a 3.3-nL detection zone, which is defined by the volume of t h e intersecting laser beams. Similar detection capabilities have been demonstrated by Miller and co-workers (16)for measuring very weak vibrational overtone transitions in pure solvents. The transient signal in Figure 3 also illustrates the advantage 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, detection is limited only by shot noise from scattered and diffracted probe beam radiation. With low-background measurement of diffracted radiation, detection limits are inversely related to the square of the excitation intensity until saturation of the optical transition or photolysis of the absorber ocnot a serious probverage 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.....

I

Figure 3.Thermal grating diffraction transients of 7.6 nM azulene in CCI,. 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.)


713 A

INS7RUMEN7ATION lem; it limits the heat that can be produced by a molecule during the excitation pulse. For azulene, there is no evidence of saturation in the excitation power dependence of diffraction for pulse energies up to 0.2 mJ ( I 7,18).This result is reasonable, because the small molar absorptivity of azulene at the 532-nm excitation wavelength (200 L mol-' cm-l) leads to an excitation rate k,, of 1.4 x lo9 s-' a t 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 lifetime (19). Interestingly, this lack of saturation in azulene allows an average of 90 photoexcitations of each molecule during the 70-ns excitation laser pulse. For molecules with higher molar absorptivity or nanosecond excit ed-state lifetimes, the excitation rate could easily exceed the decay rate and saturation would limit sensitivity. 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 saturation limits sensitivity for detecting weak absorption, diffraction from volume thermal gratings created by saturated absorption has unique properties t h a t yield a powerful method for studying nonradiative, excited-state decay processes. Nonlinear optical absorption creates higher order spatial frequencies in a grating that can be selectively monitored free of interference from linear absorption contributions. Nonlinear absorption and anharmonic thermal gratings. Excitation saturation phenomena are generally difficult to investigate, as illustrated in the upper-right quadrant of Figure 4. Deviations from a linear response must exceed the proportional noise in the excitation source, which can be significant with pulsed lasers. Under strong saturation conditions, the energy deposited in the sample QabS becomes independent of the excitation intensity and nothing can be learned about the underlying excitation or relaxation kinetics. Laser-induced gratings are uniquely suited for studying nonlinear optical excitation of molecules under sat urated absorption conditions. By exciting the sample with a sinusoidal interference pattern (lower right 714 A

Figure 4. Effect of saturated optical absorption on a laser-induced graring. The sample is excited with a sinusoidal interference pattern in the x-axis (lower right quadrant). When the energy deposited in the sample C?, 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 simultaneously in the sample. If the energy deposited in the sample depends linearly on excitation intensity (dashed line), the spatial variations of the temperature and refractive index modulation are proportional t o intensity and contain only the fundamental spatial frequency of the incident interference pattern. With excitation under saturated absorption conditions, however, the absorbed energy is a nonlinear function of intensity and the resulting thermal grating is distorted from a purely sinusoidal shape (upper left quadrant of Figure 4). From the distortion of a nonlinear sample response, a thermal grating generated under saturation conditions contains higher order harmonics of the fundamental spatial frequency of the excitation interference pattern. This behavior is analogous to the saturated, anharmonic response of a n audio amplifier to a strong single -frequency tone, which produces audible overtones (higher order harmonics) from signal clipping. Unlike the distortion of an amplifier in the time domain, the anharmonic response of a thermal

ANALYTICAL CHEMISTRY, VOL. Ei4, NO. 14, JULY 15, 1992

grating is in the spatial domain, which is ideal for the study of nonlinearity because each spatial frequency can be selectively probed by diffraction at its corresponding Bragg angle. Recall that volume gratings in the Bragg limit produce only a single diffracted order for each spatial frequency present in the index or amplitude modulation (Figure 2). Thus the series of m-order grating components arising from saturated absorption can be detected by diffraction at a series of Bragg angles given by €IBm = sin-' (m%/2d), as illustrated in Figure 5. Diffraction at higher Bragg angles is characteristic only of nonlinear excitation processes in the sample, and this higher order diffraction can be angularly resolved from diffraction caused by linear excitation processes. Diffraction at the Bragg angles for higher order thermal gratings, therefore, provides a low background measurement of nonlinear excitation processes 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 excitation of iodine at 532 nm produces a series of diffracted orders. This response can be compared with that for

azulene in Figure 2, where the absence of saturation leads to a single diffracted order. As discussed earlier, azulene is extremely 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 states (“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 CCl,, iodine exhibited both photodissociation and a kinetic bottleneck in the longer lived A’ excited state (18,23). Nonlinear optical absorption phenomena, which can be selectively de tected and studied by diffraction from anharmonic thermal gratings, are not limited to saturated absorption but can be extended to multiphoton excitation (6, 7, 17). Multiphoton fluorescence spectroscopy can detect short - wavelength emis sion that indicates a high-energy state was populated by multiphoton excitation. Photothermal measure ments cannot distinguish between one-photon and multiphoton absorption phenomena based on the excited-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 excitation processes free of background from one-photon absorption, which is analogous to the detection of saturated absorption discussed earlier. Unlike saturated one-photon absorption, however, the amplitudes of m-order diffraction that arise from n-photon excitation can be predicted by a simple Fourier series that can be used to identifjr the highest order excitation process in the sample.

Figure 5. Probing gratings distorted by nonlinear excitation. An anharmonic 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).

Figure 6. Diffraction intensity versus incident probe angle for thermal grating. Sample is 9.4 pM solution of I, in CCI,. (Adaptedwith permission from Reference 18.)

Taking the nth power of the excitation to predict the form of the deposited heat Qa&)

:=’

’”(’) r1 p ‘Os (2”a1” (5) and expanding the result as a Fourier series in x, one finds that the highest m-order diffraction observed for n-photon excitation is m = n (7). The quantitative capabilities of anharmonic t h e r m a l g r a t i n g s for +

n-photon absorption measurements are notable. Using a dilute one-photon absorber as a calibration standard, it is possible to measure twophoton absorption cross sections of komatic compounds with 10% uncertainty (7, 17). Diffraction from anharmonic thermal gratings can be used to detect very weak two-photon absorption phenomena. The fraction of the laser energy deposited into the


715 A

INSTRUMENTATION ,

Figure 7. Thermal grating diffraction transients. Transients observed for a solution of 51 pM Br, in CCI, (squares) and solution of 11 pM azulene in CCI, (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 = low7to produce a detectable signal; with a high concentration of sample molecules, twophoton cross sections as small as cm4s 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 excited B,, state) have also been measured with about 20% uncertainty by probing diffraction at the third-order Bragg incidence (7). The same approach has been extended to two-step absorption processes composed of sequential, onephoton transitions. This form of excited-state up-pumping is common in high-power, pulsed-laser excitation of molecules. It can lead to significant upper excited-state populations and photoionization in solution (the latter process has been used for sensitive detection [25-271). Despite its potential value for ionization detection and its fundamental role in pulsed-laser photochemistry, excited-state up-pumping is very difficult to study because intermediate upper states are generally very short-lived and nonfluorescent. By measuring photothermal diffractim intensities at several Bragg orders as a function of excitation intensity, a sensitive method for studying this nonlinear optical absorption has 716 A

been demonstrated. Studies of photoisomerization and sequential, two step absorption have been conducted for cyanine dyes (20,22) and p-carotene (21). Some of the most interesting results were found for two tricarbocyanine dyes, diethyloxatricarbocyanine iodide (DOTCI) and hexamethylindotricarbocyanine iodide (HITCI), which are used as saturable absorbers in mode-locked lasers. For both of these dyes, an anomalous dip was observed in the intensity dependence of the second-order diffraction efficiency (22). This behavior could be attributed to diffraction from two second-order thermal gratings 180" out of phase. Up-pumping of the excited-singlet state leads to a secondorder grating that is in phase with the excitation intensity modulation; saturation of ground - state absorption generates a second-order thermal grating that is out of phase with the excitation modulation. At a particular average level of excitation, the amplitudes of these two gratings cancel each other, leading to a dip in the diffraction efficiency. The interference 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 gratings for photoinitiated processes.


We have shown that diffraction from anharmonic thermal gratings can be used to study photophysical processes. An alternative method for studying the kinetics of these processes is to resolve the time-dependent temperature rise in the sample following photoexcitation. Such time resolved photothermal methods can yield not only the enthalpy stored by excited states and/or photochemical products after pulsed excitation but also the rate a t which heat is released to the environment from excited-state relaxation and photochemical reactions. When combined with yields of formation of intermediate states or photoproducts, excit ed - state enthalpies or bond energies, along with the rate constants for reactions and excited- state decay (2833), can be determined. "he time resolution of most photothermal methods (i.e., thermal lens, beam deflection, and photoacoustic spectroscopies) is limited by the time required for a thermally driven 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 (32,331. Unlike these photothermal methods, the rise time of diffraction from a thermal grating is limited only by the time required for the acoustic wave to traverse one period of the fringe pattern. If the excitation pulse is faster than this period, an interference 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 eliminating this interference is to make the sound wave period comparable to or shorter than the excitation pulse duration (by varying the angle between excitation beams and thus adjusting the fringe spacing) (11,12). Figure 7 shows an example of using time-resolved diffraction from a thermal grating to observe the temperature rise from a nanosecond excited-state decay in bromine. The signal from a rapidly decaying standard, azulene-which has an excited-state lifetime of only a few picoseconds and no other intermediate long-lived states (18,19)-is also shown for comparison. The excitation fringe spacing, d = 7.1 l m , corresponds to a 7.7-ns period for sound propagation in CCl,, 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 excitation pulse duration. The rise of the diffraction signal from bromine in Figure 7 clearly shows a delay compared with t h e i n s t r u m e n t limited response of azulene. The finite rate of heat production by bromine could be attributed 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 =25 ns, was confirmed by timeresolved near-IR fluorescence and assigned to a low-lying A' excited state. The value of the A' state energy 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 photothermal diffraction to fast nanosecond calorimetry of photophysical processes have been published. Zimmt and co-workers have estimated energies of the twisted excited singlet state of tetraphenylethylene and its decay rate constants in various solvents (36, 37). The solvent polarity dependence of the energy and the decay rate provides evidence for the zwitterionic character of this excited state. Quantum yields and submicrosecond lifetimes of triplet states of aromatic molecules have been measured (38). Our group has used the timeresolved thermal grating technique to follow the energetics and diffusion - controlled kinetics of recombi nation of dissociated halogens (39, 40). Following escape of radicals from their initial solvent cage on a picosecond time scale after photoexcitation, the nongeminate rate of recombination 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 = he/2), which can be achieved with counterpropagating excitation beam geometry. For excitation wavelengths in the n e a r - W range, this geometry leads to a 100-ps rise time in liquids and a potential time resolution of nearly 10 ps. Miller and co-workers (11,41) observed the occurrence of vibrational energy relaxation from a heme por-

phyrin ring to a surrounding protein backbone c 20 ps after photoexcitation of the porphyrin ring. In thermal grating experiments, the density changes detected a r e 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 optically induced differences in molecu lar volume or configuration. Their results demonstrate that the tertiary structure of proteins changes on an extremely fast time scale. Whereas the acoustic transit time limits the rise time of a thermal grating, thermal conductivity between fringes defines the decay time of the temperature rise, thus limiting the persistence of a thermal grating to typically tens of microseconds. Although 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 accurate method for measuring thermal diffusion rates in condensed-phase materials (43), including 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 determining the stability of materials and response 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, but it is much more difficult to measure diffusion of molecules in nonpolar solvents and materials. Common techniques involve t h e transport of molecules across macroscopic distances, which requires very long times for observing changes in optical density, radioactivity, or solution concentration. Holographic methods provide a convenient approach for determining molecular diffusion coefficients because the measurement scale is controllable at microscopic distances. The principle of this approach is to expose photochromic tracer 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 diffraction decreases with time, as the p a t t e r n of labeled molecules 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 several 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 c 100 ps. Decay of diffraction on a millisecond 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 constant for diffusion across a fringe depends on the square of the fringe spacing and inversely on the diffusion coefficient D according to

z = d2/4n2D whereas the fringe spacing is controlled by the excitation crossing angle according to Equation 2. Because the diffraction efficiency depends on

6

Figure 8. Laser-induced grating measurement of molecular diffusion. (a) Decay of diffraction intensity from 3.3 mM azobenzene in octanol, 8, = 23 mrad. (b) Decay rate of the grating amplitude (inverse of twice the decay time of diffraction) versus sin2 e, fit to Equation 7 to estimate the diffusion coefficient D of the probe molecule.


717 A

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 decay of the grating amplitude. Substituting Equation 2 into Equation 6 gives the dependence of the decay rate of the grating amplitude on the excitation beam crossing angle

l l r = D (4nlh J' sin2 8, (7) Equation 7 predicts a linear depenwith a zero indence of 11.5on sin' 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) x cm2 s-'. The transient holography technique has been widely used to measure molecular diffusion coefficients in liquid crystals as well as in polymer solutions and melts (45, 46, 48-52). The principal advantage of laser-induced grating over classical tracer methods is that the distance scale for measuring diffusion is controlled by the fringe spacing (in the 0.2-100-pm range). Whereas the relative range of variation is large, the actual distance scale is several orders 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 a s small as cm'ls, too small to be measured by classical methods, can be measured in only a few hours by the holographic grating technique. Laser-induced holographic methods for studying molecular transport have been extended to measuring migration rates of ions in electric fields (53, 54). In these experiments, photochromically labeled species migrate in an electric field aligned perpendicular to fringes in the grating. Migration of the photolabeled pattern of molecules produces a time-dependent phase shift in the diffracted radiation. When combined with a stationary 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 reference 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 vacuum-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 sec718 A

ond harmonic generation to provide surface selectivity (56, 57). Summary Holographic spectroscopy, based on diffraction from laser-induced grat ings, provides a unique low-background approach for measuring the absorption of radiation, relaxation of excited states, and transport of photoproducts within a sample. For all of these applications, sample excitation by two interfering beams of incident laser radiation encodes the absorbed optical energy, released heat, and photoproducts in a periodic spatial pattern. Diffraction of a probe laser beam by this pattern (reading the hologram) provides a low - background detection technique for measuring weak optical absorption, nonlinear absorption (including saturation and multiphoton effects), fast nonradiative relaxation of excited states, and the diffusion of heat and photoproducts through the sample. These techniques take full advantage of the unique spatial and temporal coherence properties of laser radiation. This work was supported in part by the National Science Foundation u n d e r g r a n t s

CHE85-06667and CHE90-10309.

References (1) Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Gratings; Springer-Verlag: Berlin, 1986. (2) IEEE J. Quantum Electron.; Eichler, H. J., Ed.; 1986,22 (special issue on dynamic gratings and four-wave mixing). (3) Fayer, M. D. Annu. Rev. Phys. Chem. 1982,33,63. (4) Moharam, M. G.; Young, L. Apgl. Opt. 1978.11. - , 1757. (5) Gaylord, T. K.; Moharam, M. G. Appl. Opt. 1981,20,3271. (6) McGraw, D. J.; Harris, J. M. Opt. Left. 1985,10,140. (7 McGraw, D. J.; Harris, J . M. Phys. Rev. A 1986.34.4829. ( 8 ) Kogelnik, H. Bell. Syst. Tech. J. 1969, 48,2909. (9) Siegman, A. E.J. Opt. SOC.Am. 1977,4, - 1

~

(19) Heritage, J. P.; Penzhofer, A. Chem. Phvs. Left. 1976.44.76. ( 2 0 j Zhu, X. R.; Harris, J. M. Chem. Phys.

1988. 124. ~~, 321. ~

- 7

~

(21) Zhu, X. R.; Harris, J. M. J. Phys. Chem. 1989,93,75. (22) Zhu, X. R.; Harris, J. M. Chem. Phys. 1990,142,301. (23) Zhu. X. R.: Harris.' J . M. I. OOt. SOC. Am. B isgo, 7, 796. (24) Kliger, D. S. Accts. Chem. Res. 1980, 13,129. (25) Voigtman, E.; Jurgensen, A,; Wine-

" .

fordner, J. D. Anal. Chem. 1981, 53,

1921. (26) Yamada, S.; Hino, A , ; Kano, K.; Ogawa, T. Anal. Chem. 1983,55,1914. (27) Yamada, S.; Sato, N.; Kawazumi, H.; Ogawa, T. Anal. Chem. 1987,59,2719. (28) Fuke, K.; Ueda, M.; Itoh, M. Chem. Phys. Lett. 1980,76,372. (29) Rothberg, L. J.; Simon, J. D.; Ber-

stein, M.; Peters, K. S. J. Am. Chem. SOC.

1983,105,3464. ( 3 0 ) Redmond, R. W.; Heihoff, K.;

Braslavsky, S. E.; Truscott, T. G. Photochem. Photobiol. 1987,45,209. (31) Terazima, M.; Azumi, T. Chem. Phys. Lett. 1987,141,237. (32) Isak, S. J.; Komorowski, S. J.; Merrow, C. N.; Poston, P. E.; Eyring, E. M. Appl. Spectrosc. 1989,43,419. (33) Poston, P. E.; Harris, J. M. 1. Am. Chem. SOC.1990,112,644. (34) Zhu, X. R.; Harris, J. M., submitted for publication in J. Phys. Chem. (35) Abul-Haj, N. A.; Kelley, D. F. Chem. Phys. Lett. 1985,119,182. (36) Zimmt, M. B. Chem. Phys. Lett. 1989, 160,564. (37) Morais, J.; Ma, J.; Zimmt, M. B. J. Phys. Chem. 1991,95,3885. (38) Terazima, M.; Hirota. N. I. Chem. Phvs. 1991.95.6490 (39f Zhu, X: R.: Harris, J . M. Chem. Phys. 1991,157,409. (40) Zhu, X. R.; Harris, J. M. Chem. Phys. Lett. 1991,186,183. (41) Genbere. L.: Richard. L.:, McLendon, R.; Mil1ery'R.J.D. Science 1991, 125, .n..

IUDI.

(42) Miller, R.J.D. Ann. Rev. Phys. Chem. 1991,42,581. (43) Eichler, H.; Salje, G.; Stahl, H. J. Appl. Phys. 1973,44,5383. (44) Urbach. W.: Hervet. H.: Rondelez.' F. Mol. CrJst. Liq. Cyst. 1978,46,209. (45) Hervet, H.; Urbach, W.; Rondelez, F. J. Chem. Phys. 1978,68,2725. (46) Hervet, H.; Leger, L.; Rondelez, F. Phys. Rev. 1979,42,1681. (47) Photochromism, Techniques of Chemistry

Vol. III; Brown, G. H., Ed.; WileyInterscience: New York. 1971.

545

(17) McGraw, D. J.; Harris, J. M. J. Opt. SOC.Am. B 1985,2,1471. (18) McGraw, D. J.; Michaelson, J. W.;

Harris, J. M. J. Chem. Phys. 1987,86, 2536.

ANALYTICAL CHEMISTRY, VOL. 64, NO. 14, JULY 15, 1992

K. W.; Gabriel, D. A,; Johnson, iys. Chem. 1984,88,4010. (50) Antonietti, M.; Coutandin, J.; Grutter, R.; Sillescu, H. Macromolecules 1984, 17,798. (51) Zhang, J.; Wang, C. H.; Ehlich, D. Macromolecules 1986,19,1390. (52) Lee, J. A.; Lodge, T. P. J. Phys. Chem. 1987,91,5546. (53) Rhee, K. W.; Shibata, J.; Barish, A,; Gabriel, D.; Johnson, C. S. J Phys. Chem. 1984,88,3944. (54) Kim, H.; Chang, T.; Yu, H. J. Phys. Chem. 1984,88,3949. (55) Zhu, X. D.; Lee, A.; Wong, A. Appl. Phys. A 1991,52, 317. (56) Zhu, X. D.; Rasing, T.; Shen, Y. R. Phys. Rev. Lett. 1988,61,2883. (57) Zhu, X. D.; Shen, Y. R. Opt. Lett. 1989,14,503.

I s Your Assurake of

X. R. Zhu is a postdoctoral research associate at the University of Utah, where he received his Ph.D. in chemical physics in 1989. His graduate research focused on anharmonic grating difiaction for studying nonlinear optical absorption and dynamic light scattering of polymer solutions; his current research concerns timeresolved holographic methods f o r measuring fast photophysics and molecular transport at liquid-solid inte$aces.

With Wheaton 0.1 mL Autosampler Vials Quality Is One More Variable That You Don’t Have to Worry 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 - 6 0 9 - 8 2 5 - 1 1 0 0 or FAX 1 - 6 0 9 - 8 2 5 - 1 368.

rL A

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

J M.Harris received his Ph.D. in analytical chemistry fiom Purdue University in 1976, after which he joined the chemistry faculty at the University of Utah. Harris has been an Alfied P. Sloan Research Fellow and a recipient of the CoblentzAward in molecular spectroscopy and the ACS Division of Analytical Chemistry Award in Chemical Instrumentation. His research interests include the application of lasers to analytical chemistry, photothermal spectroscopy, and molecular structure and kinetics at liquid-solid inte@iaces.

Manufacturers Since 1888

1000 N 1OTH STREET MlLLVlLLE NJ 08332-2092 USA

A

A A

c C l h u I lku FOR DEMONSTRATION

CIRCLE 121 FOR LITERATURE

ANALYTICAL CHEMISTRY, VOL. 64, NO. 14, JULY 15, 1992

719 A

Holographic spectroscopy. Diffraction from laser-induced gratings

Recommend Documents