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ANALYSIS OF LASER-INDUCED GRATING (LIG) SELF-DIFFRACTION IN AN INDUCED
ABSORBING MEDIUM
C. Weber, R. Renner, C. Klingshirn
To cite this version:
C. Weber, R. Renner, C. Klingshirn. ANALYSIS OF LASER-INDUCED GRATING (LIG) SELF-
DIFFRACTION IN AN INDUCED ABSORBING MEDIUM. Journal de Physique Colloques, 1988,
49 (C2), pp.C2-271-C2-274. �10.1051/jphyscol:1988264�. �jpa-00227681�
JOURNAL DE PHYSIQUE
Colloque C 2 , SupplBment au n06, Tome 49, juin 1988
ANALYSIS OF LASER-INDUCED GRATING (LIG) SELF-DIFFRACTION I N AN INDUCED ABSORBING MEDIUM
C. WEBER, R. RENNER and C. KLINGSHIRN
Department of Physics, University Kaiserslautern, Erwin Schrddinger Strasse 46, 0-67050 Kaiserslautern, F.R.G.
Abstract - We investigate the dynamics of Laser-Induced Gratings (LIG) in a medium showing optical bistability due to increasing absorption (e.g.CdS). Fast switching processes occur in selfdiffraction both in the diffracted and transmitted beams.
Introduction
-
In recent years LIG have proved to offer a powerful possibility to obtain information about elec- tronic excitations and quasiparticles, their interactions and propagation specific for a given material [I]. The material parameters gained by this technique are important for the understanding of the optical nonlinearities which have possible application, such as optical bistability or opto-electronics. In the present contribution we investigate the dynamics of a system showing the nonlinearity of photoinduced absorption under LIG excitation [2]. The experi- mental realisation is obtained in CdS where plasma induced effects lead to a red shift of absorption and to optical bistability [3].In a theoretical analysis, the influence of the ratio lD/A (lD=diffusionlength, A=grating constant) on the density dis- tribution, the switching of absorption and the time dependence of diffracted orders outside the grating are studied, as the dynamics of the system depend strongly on transversal and longitudinal transport of carriers inside the popu- lation density grating. Using nanosecond excitation pulses, time resolved measurements of the diffracted orders show drastic pulse shortening (200ps) with respect to the excitation pulses (4ns), which is explained in terms of a successive dynamic increase of switched volumes in each grating cell during the course of excitation. In the last chapter we investigate the diffraction phenomena when the two pump laser beams are of different intensities. In this case the second pump beam serves as a weak probe beam which monitores the switching action of the bistable device, excited by the other strong beam similar to a one beam excitation.
Time resolved measurements and comparison with our theoretical model
-
A sinusoidally modulated intensity oattern is achieved bv the interference of two coherent laser beams I,.Ih of eaual freauency, which impinge sym- metrically on the c r y k plane at an angle of 28. The photon energy ZGjusted so that the crystal shows the nonli- nearity of photoinduced absorption [4]. Via absorption the intensity pattern is transformed into a corresponding density modulation of electron-hole pairs (N). The density dependent change of the optical properties leads to self- interaction of the light beams inside the periodically modulated medium with grating comstant A (A=lr/ksin8; k=wavevector inside the medium). The diffracted orders arising from the grating reflect the transport properties of the photoexcited carriers which build up the population grating and of course the nonlinearity of the optical properties.
Concerning our theoretical approach which has been outlined in 151 we choose the characteristics of an induced absorber with a smoothed step-like function a(N) (a is the absorption coefficient) which shows close relation to the experimental data. The dispersive changes are assumed to depend linearly on the carrier density at the photon energy of interest. To compute the temporal evolution of the diffracted orders the model takes into account the wave propagation of the various diffracted orders inside the nonlinear medium, the rate equation for the generation, diffusion and recombination of the photoexcited carriers and the outlined quantitative description of the optical nonlinearity.
With a diffusion length of the electron-hole plasma (EHP) of 5pm [6] the theoretical computations are in good agreement with the experimental recordings. Fig.1 shows the theoretical result for the parameters listed in Fig.1 (T is the typical lifetime of the EHP [7], d is the thickness of the crystal); the two pump beams are of equal intensity (b=Ib). In Figla the incoming pump laser pulse is plotted; the rise time of the pulse is taken from experimental recordings. The other insets show the temporal evolution of the first I, and second I, diffracted orders and the ratio of the transmitted intensity and the incident intensity The zero order I, shows clearly the characteristics of optical bistability of an induced absorber. The occurence of the switching process of I, and I, is strongly correlated to the switching process of the crystal and the duration of the peaks is in the order of the lifetime of the carriers and the switch-up time of the grating, respectively. Switch-up means in this context switching to high absorption.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988264
JOURNAL DE PHYSIQUE
. Calculated temporal evolution
t (ns)
of transmitted orders (parameters are listed in upper inset)
In the case of a reduced diffusionlength (e.g. lD=.55pm) the temporal evolution of the transmitted orders shows a different behaviour : the switching process becomes smeared out and the diffracted orders appear during the whole course of excitation.
Fig.2 shows the corresponding experimental findings. We used an eximer-laser pumped dye laser to excite the cry- stal. These measurements have been made with a single shot technique by a streak camera system, which allows us to detect the incident beam and the diffracted orders simultaneously.
Fig.2
-
Single shot recording of incident and transmitted beams in a LIG selfdiffraction arrangment for A=llpm.In agreement with our theoretical model, diffracted orders appear for 200ps, which is in the order of the lifetime of the carriers. The diffracted orders I,,I, show strong pulse shortening and are restricted to the switch-up time of the crystal. The underlying dynamics of the carrier system are shortly mentioned :
At the beginning of the pump pulse, the sinusoidally modulated generation rate produces a population density pat- tern which results in a switch-up of the absorption coefficient only in the regions of maximum excitation, as soon as the critical density is reached there. The increase of absorption leads, via an increased generation rate and diffu-
sion into the direction of the concentration gradient, both to a lateral and a longitudinal increase of the switched volumes. The spatial and temporal expansion of these areas is therefore determined by the pumprate (ad) and the tramport properties of the carriers (characterized by ID). Therefore the temporal dependence of the diffracted orders are strongly influenced by the ratio ID/A.
Fig.3
-
Absorption coefficient a(x,z) in a grating cell for L ~ = 5 p m (other parameters as in Fig.1).Figure 3 documents the dynamical increase of the switched volumes in one of the grating cells at t=500ps and t=625ps during the switching process. The lateral dimension equals one grating period A; the pump laser beam is assumed to impinge onto the crystal from behind.
Fig.4
-
Comparison of experimental (upper) and theoretical (lower) findings: hysteresis loops in the time free re- presentation of first diffracted order I, versus pump pulse $,.At t=500ps the short term build up of a well pronounced absorption grating is shown, which causes a profound contribution to the diffracted orders. Due to the comparably long diifusion length ID (compared to the lateral dimension of a grating cell) the density modulation will soon be equalized when a degenerate EHP has been created
C2-274 JOURNAL DE PHYSIQUE
as one can see in Fig.3 at t=625ps, where nearly the whole cell has reached a state with completely switched absorption.
The contribution of the absorption-grating and the corresponding phase-grating to the diffracted intensity therefore decreases rapidly towarcls the end of the switching process.
In Fig.4 we plotted the time free representation of I, versus I, for comparable system parameters and show the agreement of theoretical and experimental findings.
Pump beams with unequal intensities
-
We shortly examine the case when the two pump laser beams have dif- ferent intensities : Ib=3.10-31a.
Fig.5 shows the corresponding absorption coefficient at t=5OOps and t=625ps. We plotted only one half of a grating period on the x-axis. The situation is very similar to a one beam excitation con- dition as the interference modulation of the two beams-
and therefore the influence of Ib-
is small.In this case the weaker pump beam acts as a probe beam. The f i t diffracted order monitors the switching action of the bistable device, excited by the other stronger beam similar to a one beam excitation. Comparable to the tem- poral behaviour of the diffracted orders under excitation conditions where I,=Ib, I, answers the switching process with a simultaneous short pulse. The maximum first order grating efficiency computed with the same parameters as in Fig.1 is still in the range of .I%.
lb=3.10-' l a
t = 500 ps a 1x.z)
Fig.5 - Absorption coefficient a(x,z) for Ib=3.10-3.I, (shown is one half of a grating cell, other parameters as in Fig.3). The transversal modulation is small.
References
[l] J.P.Eichler, P. Gunter, D.W. Pohl: Laser-induced Gratings. Springer Series in Optical Sciences, Vol. 50 (Springer, Berlin, Heidelberg 1986)
H. Saito, E.O. Gobel: Phys. Rev. B 31, 2360 (1984)
[2] H. Kalt, R. Renner and C. Klingshirn: IEEE J. QE. 22, 1312 (1986)
[3] M. Wegener, C. Klingshirn, S.W. Koch and L. Banyai' Semicond. Science and Technology 1, 366 (1986) and the literature cited therein.
[4] K. Bohnert, F. Fidorra and C. Klingshirn, Z. Physik B 57, 263 (1984) and H.E. Swoboda, F.A. Majumder, V.G. Lyssenko, C. Klingshirn, L. Banyai:
to be published in Z. Physik B (1988)
[5] C. Weber, U. Becker, R. Renner and C. Klingshirn: Appl. Phys. B 45, (1988) in press and C. Weber, U. Becker, R. Renner and C. Klingshirn: submitted to 2. Physik B
[6] F.A. Majumder, H.E. Swoboda, K. Kempf and C. Klingshirn: Phys. Rev. B 32, 2407 (1985) [7] Yoshida, H. Saito, S. Shinoya: J. Phys. Soc. Jpn 50, 881 (1980)
