Spectral holeburning and holography VI: Photon echoes from cw spectrally programmed holograms in a Pr3+:Y2SiO5 crystal

1 October 1995

OPTICS COMMUNICATIONS Optics Communications 120 ( 1995) 103-l 11

EISEWIER

F&l length article

Spectral holeburning and holography VI: Photon echoes from cw spectrally programmed holograms in a Pr3+ : Y,Si05 crystal Stefan B. Altner, Stefan Bernet., Alois Rem, Eric S. ~aniloff, Urs P. Wild

Felix R. Graf,

Physical Chemistry Laboratory, Swiss Federal institute of Technology. ETH-Zentrum, CH-8092 Zurich. Switzerland

Received 6 February 1995; revision received 24 April 1995

Abstract Spectral programming of stimulated photon echoes is presented. The preparation pulses - pulse #l and #2 of the three pulses of the echo sequence-are substituted by writing a frequency dependent modulation into the inhomogenously broadened absorption line of a persistent spectral holeburning material. A holographic setup is used, and arbitrarily predefined echo signals can be generated. Linear response theory is applied to calculate the required modulation of both the intensity of the write beam and the holographic spatial phase as a function of optical frequency. Experimental results are shown using a Pr” : Y$iO, crystal at cryogenic temperatures.

1. Introduction

During recent years considerable interest has developed in new methods of high density optical data storage and processing. Materials which exhibit persistent spectral holeburning (PSHB) have shown a poi:ential to be of use in future concepts of ul~~igh data si:orage density [ I,21 and information processing [ 3-611. The very high frequency selectivity provided by these materials has been exploited both, in the frequency and the time domain [ 7-111. While frequency domain techniques have the advantage of using low light intensities, and therefore allow for the use of large spatial areas for parallel info~ation storage and processing, they presently lack speed for data transmission and processing. Photon-echo related techniques on the other hand have been shown to be capable of high speed recording and recalling of large amounts of data. 0030-401g/95/$09.50 0 1995 Elsevier Science B.V. All &hts reserved ~~D~OO30-4018(95)00347-9

Holography has proven to be a key technique for optical data storage in the spatial domain due to its property of being a background free method. The combination of holography and PSHB in the frequency domain [ 12-141 and the time domain [9,15,16] has been investigated. A non-collinear scheme of a photonecho experiment can be considered a realization of the combination of spatial holography and time domain techniques. In analogy to spatial holograms where a grating in real-space can diffract light, i.e. changes the propagation direction of the light, time domain holography describes the process of an incoming light pulse being “diffracted” in time off a frequency grating that is present in the sample in the form of a frequency dependent ~ansmittance modulation. The time domain diffraction then consists of a change in the temporal profile of the pulse. The three-pulse stimulated photonecho experiment can be considered to be a time domain

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holographic experiment where the first two pulses write a frequency dependent population grating [ 17,18 1. This grating determines the temporal shape of the echo that is produced when a third pulse hits the sample. In order to combine the advantages of frequency domain techniques with the properties of spatial and time domain holography, we propose and demonstrate an experimental scheme where spatial and frequency gratings are written simultaneously into a PSHB active sample. This is accomplished by using a tunable cw laser and controlling its intensity as well as the spatial phase of the hologram as a function of frequency [ 19231. Similar experiments have been performed by Sonajalg et al. [ 241, who studied time responses of PSHB filters in a non-holographic setup, by Mitsunaga et al. [ 111, who programmed arbitrary time domain patterns still using a non-holographic setup, and Schwoerer et al. [ 26,271, who synthesized sub-picosecond pulse shapes in a two-beam setup by using dyedoped polymers as a PSHB active material. Our goal is to program a PSHB material in such a way that it generates arbitrary predefined pulses and pulse-trains as “echoes” to an incoming pulse [28]. We use linear filter theory to calculate the necessary amplitude- and spatial phase functions that have to be written into the sample as a function of the optical frequency. We give experimental results obtained with a Pr3+ doped YZSi05 crystal.

2. Theory 2. I. General According to linear filter theory [ 291 the temporal response P,,,(t) to an excitation signal for a passive system is given by the convolution of the impulse response T(t) of the system and the excitation signal Pi”(t): P0~,(t) = T(t)

@pin(r>

.

Taking the Fourier transform and rearranging leads to

F( u)

E”,( v>

= -

pin(

u, ’

(1)

the terms

(2)

where the quantities are now functions of frequency and for clarity are marked with a ‘ -‘. The “spectral

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transfer function” F(V) is a complex function that can be written as the product of an amplitude A ( Y) = 1F( Y) 1 and a phase function rp( V) : QV)=A”(Y)exp[-icp(v)].

(3)

In order to obtain an arbitrary output (echo) signal from the system as a response to an arbitrary input signal Pi,(t), the system must have sufficiently high frequency selectivity as well as the property that both amplitude and phase can be controlled separately in an arbitrary fashion.

Potit

2.2. Optical realization with a single-beam plane wave setup

Identifying Pi”(t) with the electric field of a laser pulse and T(t) with the time response of a highly frequency selective spectral holeburning material, the optical realization of the above considerations is straightforward [ 301. The PSHB material must be programmed such that it reveals the proper spectral transfer function F( Y) when illuminated with an incoming optical field. This can be done by a frequency selective illumination of the sample resulting in afrequency (and in a holographic setup spatially) dependent concentration modulation of the photo-active species. By virtue of absorption and refraction the spectral (and spatial) shape of an incoming optical field Pi,(t) is modified leading to the desired outgoing pulse pattern P,,,(t) . f(v) can be programmed into a PSHB sample of thickness d using a single plane wave write beam. One obtains a spatially invariant frequency dependent concentration modulation of the photo-active species as shown in Fig. la (left side). The corresponding spectral transfer function has the form ?‘(v)=exp[

-inl(y)d]

,

(4)

with n(v) =n’( V) -in”(v) denoting the complex index of refraction consisting of a refractive part n’( Y) and an absorptive part n”( u) . Due to the fact that n’( V) and n”( V) are linked by the Kramer+Kronig relations a pure time shift of an incoming pulse cannot be programmed using this arrangement since that requires the spectral transfer function to be a pure linear phase shift as a function of the frequency [ 301. Nevertheless all desired echo patterns can be obtained with the restriction that the readout pulse cannot be suppressed. In fact this has been

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b)

0.8

0.6

Fig. 1. Concentration modulations of the photo-active species (left sides) and corresponding time responses (right sides) for different experimental schemes. (a) Plane wave setup: modulation only along the frequency axis; read-out pulse (full line pulses) and echo pulse (dashed line pulses) are visible. (b) Holographic setup, no phase control: modulation along the frequency axis ndthe spatial dimension (the diffraction orders are labeled 1.0, and - 1); read-out and echo pulses an: visible along all axes, (c) Holographic setup, linear phase modulation as function of the optical frequency; read-out pulse, echo and conjugated echo are separated,

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shown by Mitsunaga [ 1 l] and is depicted in Fig. la (right side). It is worth noting that a pure amplitude modulation would lead to a non-causal response. The refractive index change connected with any change of the absorption in a dielectric medium assures the causal properties of the response [ 3 1 I. 2.3. Optical realization with a two-beam holographic setup In this case T( V) originates from a spatially dependent concentration modulation in the form of a sinusoidal grating that has been burned into the thin PSHB sample. Using a holographic setup consisting of an “object” and a “reference” beam, the interference pattern creates a transmittance of the form [ 321 f= exp

-i[ri,

+ An^cos(K*x+

cp)]

(5) fia( V) and Afi( V) denote the complex index of refraction with fir,(v) as the average over the whole sample area and its spatial modulation amplitude Ari( v), respectively. cp( V) is the spatial phase of the grating which is varied by 27r when one of the two beam paths is lengthened by one wavelength. Furthermore, K = 21r/_4 is the grating vector resulting from a grating with a fringe spacing of A = h/2 sin( p/2) with pbeing the angle between the two beams. With the assumption of low modulation depth it has been shown in Ref. [20] that the resulting spectral transmission function consists of three parts describing the optical waves propagating into the directions k,, k,-K,andk,+K If0 = exp

f,,

=&Ati

p_, =f,,Ati

- ifi

2Ird h cos( P/2) 1 ’ rd

e-irp= pAse-&,

A cos( P/2) rd ?co@/2)

+ip=~A$e+iv_

e

(6)

fob,I’&,Aii, cpare all functions of frequency. First one could consider an experiment in which the spatial phase cp(V) is kept constant and the frequency modulation is achieved by burning a frequency dependent concentration modulation into the sample. The

resulting frequency and spatial concentration grating (due to the holographic setup) is shown in Fig. 1b (left side). The responses of such an experiment are depicted in Fig. lb (right side). The difference to the collinear plane wave setup lies in the fact that now three beams can be monitored (transmission and the two diffracted beams), whereas the temporal shape is the same for all three beams. Note, that the read-out pulse is present in all three signal patterns. In order to manipulate the signals in the time dimension as well, the additional degree of freedom coming from the spatial phase, cp( v), is exploited. In conjunction with the refractive index change induced by the absorption changes this spatial phase allows for the adjustment of phase matching conditions in the different diffraction orders. Considering for example the “ + 1” direction (see Eq. (6) ), the requirement of having independent control over amplitude (via Ari( V) ) and phase (via rp( V) ) is fulfilled and arbitrary P,,(t) cm be produced by arbitrary Pi,(t). Fig. 1~ (left side) shows the concentration modulation leading to a spectral transfer function with a linear phase shift in frequency. This produces signals as sketched in Fig. lc (right side). In the “ + 1” direction constructive interference leads to the desired (time delayed) echo whereas in the transmission only the reference pulse appears and in the “ - 1’ ’ direction the time reversed conjugated beam would appear if there had not been the refractive index that suppresses this non-causal echo [ 25,271. The task now is to find an instruction which we call the “sweep function” S(V) that defines how to modulate the concentration of the absorbers as a function of frequency and spatial location. Three sources contribute to S(V): the spectral shape of the excitation pulse (or more generally of the excitation pulse pattern), the spectral shape of the desired pulse pattern, and the response of the material. The “sweep function” S(V) must be chosen such that, when convolved with the spectral transfer function of a hole burnt at a single frequency y$@( v), it leads to the desired spectral transfer function of Eq. (2)) i.e. f( V) = Tyf’e(

V) @,s”(V) .

(7)

Since the phase rp( V) is defined relative to an arbitrary phase IJ+,at frequency v,, it is, in the case of a single frequency hologram, set to zero and only the diffraction resulting from both the amplitude grating

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and the refractive index grating enters ?yfle( V) . They are, as mentioned above, related by the KramersKronig relations which are mathematically equivalent to the Hilbert transform I? [ 33 ] : fyf’e(

y) =P,IA~(~)

+ii?[h~(u)~

1.

(8)

p is a factor as defined in Eq. (6) which contains material constants and dimensions as well as optical parameters such as angles between the holographic beams. An’ ( u) = G( An”) and An”( V) denote the modulation of the refractive and the absorptive index. Due to their fixed relation, one can derive fyf”( Y) by measuring the absorption hole pattern only. Using Eqs. (2)) (7), and ( 8) together with the properties of Fourier transforms (P), inverse transforms (P - ’ ), and convolutions, an equation linking the “sweep function’ ’ with the excitation pulse, the desired echo pulse, and the spectral shape of an absorption hole in the PSHB material, is obtained: S(v)=Ia(v)(exp[-ill

The calculated “sweep function” s( V) can be used directly to write the desired spectral transfer function into the holeburning material. The absolute due of the “sweep function” corresponds to the light i ntensity, and the phase to the spatial hologram phase. Both can be adjusted during exposure as a function af the optical frequency. A few features of Eq. (9) are worth noting. First, a restriction imposed by this equation is, that the factor I’,,,( u) lPi,( u), representing the ratio of the echo pulse spectrum to the reference pulse spectrum, remains finite. Therefore the spectrum of the excitation pulse must already contain all frequency compo:nents required by the desired pulse echo since our system is considered to be linear and no new frequencies are created, Second, for an experimentally realizable “sweep function”, the term fi -‘(T’{ A#‘( u) + i&[ A$‘( V) ] ) ) describing the time response of a single frequency hologram must not approach zero. Therefore, the design of an appropriate “sweep function” is not possible for echo pulse-trains, which have a time delay larger than the FID time of a single frequency hologram (i.e. the inverse of the programmed frequency resolution of the sample). Furthermore, com-

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plicated hole structures as for example in our P2 + : Y,Si05 sample [ 341 may lead to additional time intervals within the response decay time, where the response approaches zero. Thus at these intervals no photon-echo intensity can be expected. Within these limitations, Eq. (9) can be used to find a “sweep function” for any frequency selective sample material, which allows an arbitrarily predefined pulse-train to be programmed as a response to a given excitation pulse.

3. Experimental The experimental setup is illustrated in Fig. 2. The experiments are performed using a Coherent 899-29 Autoscan dye laser, with sulforhodamin B as the dye, pumped by a Coherent Innova 200 argon ion laser. The laser linewidth is approximately 1.5 MHz. The intensity is controlled by an EOD LA3 10 intensity stabilizer. Its external modulation input is used to adjust the light intensity during burning as a function of the light frequency via an IOTECH 488/4 digital-to-analog converter (DAC). The beam passes through an acousto-optic modulator ( AOM, Brimrose TEM- lOO30), which is used, by means of a Stanford DG 535 pulse generator, to produce pulses during read-out with a minimum of 15 ns FWHM. The beam is slightly expanded by a telescope and split by a 50/50beamsplitter cube to obtain reference and object beams. An electro-optic phase shifter (EO-PS, Gsanger LMO 202 PHAS-IR) is placed in the path of the object beam.

BS

linear

diode Fig. 2. Experimental setup. STAB1 = intensity stabilizer, AOM = acousto-optic modulator, BS = beamsplitter, EO-PS = electro-optic phase shifter, SH = shutter, HOL = photomultiplier for holographic signal, TRM = photomultiplier for transmission signal. For experimental details see text.

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Both beams recombine on the sample where they form an interference pattern which is recorded as a hologram. Application of a voltage to the EO-PS changes the optical path length of the object beam (half wave voltage = 280 V) and thus alters the spatial phase of the interference grating on the sample. An increase of half a wavelength shifts the spatial phase by - rr per definition. Because the range of the EO-PS is limited by the maximal applicable voltage, a sawtooth-like modulo (27r) phase control was used to get an unlimited and fast phase control. The use of the EO-PS instead of a mirror, mounted on a piezoelectric transducer, as in earlier experiments [ 4,14,20,21], increases linearity and speed as well as the repeatability enormously. The phase of the interference grating was detected by deflecting the two interfering beams with a beamsplitter cube to a diode array. The signal of the diode array is monitored on an oscilloscope. The holograms representing the desired transfer function are recorded by continuously scanning the laser frequency over a range of several holewidths, while simultaneously adjusting the light intensity and the hologram phase as a function of the frequency. This recording technique, leading to frequency and phase swept (FPS) holograms [ 221, causes hologram erasure in a conventional, non-frequency selective recording material. If a holeburning sample is used as a recording material this recording technique creates novel diffraction properties, such as enhanced diffraction efficiency, non-destructive holographic read-out, and spectral line narrowing and crosstalk minimization of the holographic signal [ 22,231. For read-out the object beam is blocked and the reference beam is attenuated. Two photomultipliers detect the transmitted and the diffracted light intensity. Their signals are fed into a Stanford SR-400 gated photon counter or into a Stanford SR-430 Multichannel scaler with 5 ns binwidth. All experimental components such as laser, stabilizer, DAC, shutters, photon counter are controlled by a SUN Spare station via a GPIB interface. The sample consists of a cylindrically shaped (length: 4 mm; diameter: 8 mm) P?’ doped Y2Si05 crystal with excellent optical quality. The concentration of the Pr3+ ions is 0.1 vol %. An Oxford MD10 bath cryostat was used to cool the crystal to 1.7 K. The optical transition used in the experiment is the 3H4-1D2 transition, for which two zero-phonon lines are observed because of two inequivalent yttrium sites that

are replaced by the P?’ [ 341. The experiments described in this paper were performed using site 2. Its absorption is centered at 607.933 nm, with an inhomogeneous width of 10 GHz and an absorption of OD 0.6. The mechanism of spectral holeburning consists of a redistribution of population within the three ground-state (3H4) hypertine levels. Because the homogenous linewidth of the P?’ ions in this type of crystal is smaller by orders of magnitude than the spectral width of the laser, the observable holes are laserlinewidth limited. As described in Ref. [35], a complicated hole pattern is observed when exposing the sample to light of a single wavelength. This results from the hyperfine structure that is buried within the inhomogenous broadening of the line. A typical hole/ antihole pattern is shown in Fig. 3. With a burning time of 1 s the intensity used for exposure is 500 yW/cm’.

4. Results and discussion Fig. 3 shows the transmission and the diffraction efficiency of a single frequency hologram in the Pr3 + : Y,Si05 sample measured by first burning a single

Holographic -

40

- 20

signal

Frequency %fset [MHz]

J - 20

20

40

20

I 40

L

Frequency &et

[MHz]

Fig. 3. Diffracted and transmitted signals from a hologram, recorded with cw light at a single frequency position. (a) Experimentally obtained traces, (b) simulated traces. The spectra are limited by tbe laser resolution of l-2 MHz. Due to the holeburning mechanism of the redistribution of population in the hyperfme levels, a complicated hologram and transmission pattern is observed.

S.B. Altner et al. /Optics

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0

‘s

200

T

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600

Communications 120 (1995) 103-111

A

800

/

Time delay [ns]

Fig. 4. Experimental and theoretical time response (FID) of a single frequency hologram to an Gaussian excitation pulse with 60 ns FWHh4. The first signal is the excitation pulse, measured in transmission, whereas the echo is monitored in the + 1 diffractior order. The time response acts as an envelope for the signal intensities which can be expected in pulse shaping experiments. Therefore the time range accessible for pulse shaping experiments is limited to approximately 500 ns delay. The theoretical pulse echo from the single

frequency hologram structure of Fig. 3 is plotted in the lower graph and fits the experimental result. frequency

hologram

in the inhomogenous

band, and then scanning

range of the hole structure. Sideholes

absorption hole shape, the free induction decay (RD) shows a modulated structure with a second small maximum at 450 ns delay. Programming of pulse echoes with a time delay where the FID approaches zero is not possible. Using this result, a sample calculation for the “sweep function” of a 100 ns delayed pulse echo as a response to a Gaussian excitation pulse with 15 ns FWHM has been performed. For the FF’S hologram a sweep range of 80 MHz is sufficient, because it covers the frequency spectra of the excitation and echo pulses. The amplitude and phase of the corresponding “sweep function”, calculated from Eq. (9) is plotted in Fig. 5. Note, that in the case of a purely Lorentzian absorption hole shape, without side- and antiholes, the phase would be a linear function of the frequency with a slope of - 27r per 10 MHz, without any amplitude modulation. The differences are due to the non-Lorentzian hole structure. Experimentally it is observed that the small amplitude modulations can be replaced by a constant amplitude without significantly decreasing the signal quality. Most of the time information of the echo signal lies in the phase function, which is linear with a modulo

absorption

the cw laser over the spectral

(increased Ixansmission) and antiholes (decreased transmission) appear around the central hole peak in the transmission data. In the background free holographic experiment shown below, both types of holes lead to a holographic signal. For calculations it has to be taken into ao:ount that the light diffracted from holes and antiholes is phase shifted by rr. For the simulated transmission and hologram shapes shown below, values of the hyperfine splittings from Ref. [34] have been used in order to generate the hole pattern, assuming a laser linewidth of 1.5 MHz. The same parameters are used for the calculation of the time response and the “sweep functions” in the next figures. Fig. 4 compares the experimentally measured time response of a single frequency hologram to an excitation pulse with 60 ns FWHM to the theoretlcally expected response. In the theoretical calculation, T(t) is determined from the simulated absorption spectrum in Fig. 3 as the Fourier transform of F( V) according to Eq. (8). A Gaussian shape with 60 ns FWHM is assumed for the excitation pulse. Due to the complex

109

,x

1.0

‘E 0.8 -

/-l**/-XPd-d\.

i 0.6 g

2 0.4 g 0.2 x w 0?40

-20 0 20 Frequency offset [MHz]

40

-20

40

1 .o g 0.8

: 0.6 $ 0.4 E 0.2 0.0 - 40

0

20

Fig. 5. Example for a “sweep function” calculated according to Eq. (9) in order to get a 100 ns time delay for the pulse echo afier arrival of an excitation pulse with 15 ns FWHM. The amplitude of the “sweep function”, shown in the upper graph, corresponds in the case of a linear burning kinetics to the intensity of the recording light, adjusted with the intensity modulator. The phase, plotted in the lower graph, corresponds to the hologram phase, adjusted by accurately controlling the electro-optic phase shifter (EO-PS) in the object beam path. The constant-amplitude trace represents an approximate “sweep function” amplitude for the delayed pulse without accounting for complex spectral features of the crystal.

S.B. Almer

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200 Time [ns]

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et al. /Optics

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Fig. 6. Experimentally detected reference pulse (separated upper trace) and pulse echoes for programmed time delays ranging from 80 ns to 375 ns (lower traces). The +oordinates of the individual traces are shifted with respect to each other for better representation.

(2rr) sawtooth modulation (see Section 3). Data files as shown in Fig. 5 are used in our experiment directly as an input for the intensity modulator and the electrooptic phase shifter, controlling the light intensity and the spatial phase of the hologram as a function of the light frequency, respectively. Reading of this hologram at its center frequency with a near-Gaussian reference pulse with 15 ns FWHM should yield an echo pulse with 15 ns FWHM, delayed by 100 ns. Experimental verifications are shown in Fig. 6. Analogous phase “sweep functions” as in Fig. 5 were calculated to create single pulses with time delays ranging from 80 to 375 ns as echoes to a single Gaussian excitation pulse with 15 ns FWHM. The excitation pulse as measured directly from the transmission signal is shown in the separated first trace, defining the staring point for our time domain measurements. Below, traces of the echoes for the programmed pulse delay times, measured in the + 1 diffraction order, are shown. For a better representation the y-coordinates of the individual traces are shifted with respect to each other, but the relative intensities are maintained. The intensity of the pulse echoes at different time delays samples the time response function (FID) of a single frequency hologram, shown in Fig. 4. Good signal-to-noise ratios are obtained for time delays up to 375 ns. Note, that the programming of a 375 ns pulse delay (second trace

120 (1995)

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I1

from the top) corresponds to an optical delay line of 113 m, which would have to be introduced in a holographic accumulated stimulated photon-echo experiment working with delay lines instead of the adjustable phase shifter. Fig. 7 shows the results of a similarexperiment, where pulse sequences, consisting of 5, 3, and 2 pulses with 15 ns FWHM were programmed according to Eq. (9). In contrast to the previous single-echo experiments, now besides the phase also the intensity had to be adjusted properly as a function of the optical frequency. The dashed lines represent the resulting echoes when the “sweep function” is used in a theoretical simulation. The experimentally obtained pulses match these theoretical curves very well and the echo pulses appear exactly at the predetermined time delays, demonstrating that our sample can be programmed with cw light as an arbitrary pulse generator. It must be pointed out that the shown capability of this method as well as of the material was limited by experimental parameters. First, although the homogeneous linewidth of the Pr3+ : Y-$0, sample is in the order of kHz, the laser linewidth of l-2 MHz limits the width of spectral holes. This reduces the FID time, where a pulse echo can be detected with reasonable intensity, to less than 500 ns. On the other hand, the employed AOM was capable of producing pulses with 15 ns FWHM, so that the time range for pulse shaping

100 Time [ns] Fig. 7. Examples of programmed pulse sequences (full lines) and of the theoretically expected pulse-trains (dashed lines). From the bottom to the top of the figure, “sweep functions” were calculated in order to get photon echoes consisting of five pulses at time delays of 60,90, 120, 150, and 180 ns, of three pulses at 50, 100, and I50 ns. and of 2 pulses at 50 and 150 ns, respectively. In all traces the first small pulse is the excitation pulse, visible in the diffracted signal due to scattering.

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experiments extended only over approximatel:y 30 FWHM of the pulse. Better results might be expected by using either a faster AOM for the production of shorter pulses, or a frequency narrowed laser to increase the FID time. Another problem was that the main presumptions of our calculations, linear burning kinetics and a linear superposition of spectrally adjacent holograms, were barely fulfilled. The hologram parts which are burnt later erase the former ones due to the kir etics of the burning process. Also the redistribution of molecules, excited from different hyperline levels, might happen with strongly different time constants, disturbing the assumptions of linear burning. The problem can be partially solved by reducing the burning intensity, and instead repeating the burning sweep a few times.

Acknowledgements Support by the “Swiss Priority Program: Optical Sciences, Applications, and Technology” is gratefully acknowledged. Furthermore we thank Dr. Masaharu Mitsunaga of NIT Basic Research Laboratories, Japan for the gift of the sample.

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science and applications, Topics in current physics, Vol. 44 (Springer, Berlin, 1988). 12 1U.P. Wild, S.E. Bucher and F.A. Burkhalter, Appl. Optics 24 (1985) 1526. [ 3] U.P. Wild, A. Renn, C. De Caro and S. Bernet. Appl. ‘Optics 29 ( 1990) 4329. ]4] U.P. Wild and A. Renn, J. Mol. Electron. 7 (1991) 1. [ 51 G.C. Bjorklund, U.S. Patent No. 4.306,771 (December 1982). [ 6 ] A. Rebane and 0. Ollikainen, Optics Comm. 83 ( 1991) 246. [ 71 W.H. Hesselinkand D.A. Wiersma, Phys. Rev.Lett.43 (1979) 1991. 18 1T.W. Mossberg, Opt. Lett. 7 (1982) 77. [ 91 A. Rebane and R. Kaarli, Chem. Phys. Lett. 101 (1983.1 317. [lo] W.R. Babbitt and T.W. Mossberg, Optics Comm. 65 (1988) 185. [ 11 1M. Mitsunaga, R. Yano and N. Uesugi, Optics L&t. 16 ( 1991) 264.

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