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THEORETICAL ANALYSIS OF TRANSVERSE AND CROSSTALK EFFECTS IN THERMOOPTIC
ABSORPTIVE BISTABILITY
J. Oberle, J.-Y. Bigot, A. Daunois
To cite this version:
J. Oberle, J.-Y. Bigot, A. Daunois. THEORETICAL ANALYSIS OF TRANSVERSE AND
CROSSTALK EFFECTS IN THERMOOPTIC ABSORPTIVE BISTABILITY. Journal de Physique
Colloques, 1988, 49 (C2), pp.C2-439-C2-442. �10.1051/jphyscol:19882104�. �jpa-00227614�
JOURNAL DE PHYSIQUE
Colloque C 2 , Supplement au n06, Tome 49, juin 1988
THEORETICAL ANALYSIS OF TRANSVERSE AND CROSSTALK EFFECTS IN THERMOOPTIC ABSORPTIVE BISTABILITY
J. OBERLE, J.-Y. BIGOT and A. DAUNOIS
Institut de Physique et Chimie des Materiaux de Strasbourg, Unite Mixte 380046, CNRS
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ULP-
EHICS, Groupe dlOptique Nonlineaire et d'Optoelectronique, 5, Rue de l'Universit6, F-67084 Strasbourg Cedex, FranceR6sum6
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On analyse l'influence de la propagation transverse et longitudi- nale de la chaleur sur les propriktks de commutation d'un bistable thermo- optique absorptif soumis A une excitation laser continue et adresse par une impulsion de courte dude. Les effets de diaphonie optique entre deux pixels adjacents sont discutes.Abstract
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We study the influence of the transverse and longitudinal pro- pagation of heat on the switching dynamics of a thermooptic absorptive bistable device monitored by a cw laser beam and adressed by an external pulse of short duration. Crosstalk effects between two adjacent pixels are discussed.1
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INTRODUCTIONThe realization of arrays of bistable pixels, working in parallel, requires the control of transverse effects like the diffraction of light and the diffusion of the carriers which are responsible of the optical nonlinearity. Among the diffe- rent systems which have been investigated theoretically /I/, it appears that the diffusion is very important for the transverse coupling. Here, we analyze the dynamics of a thermooptic bistable device in longitudinal and transverse space directions when one of its pixels is adressed by an external pulse of short duration. We show that the energy dissipation through diffusion is not only important for the crosstalk between neighbouring pixels but also gives rise to a complex space time switching behavior of each bistable element.
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THEORETICAL MODELWe consider a semiconductor, which absorption near the band to band transition fulfills the Urbach rule. It has been shown in various semiconductors /2/ that such a device is optically bistable, with a clockwise hysteretic cycle in'the transmitted versus incident intensity curve, the nonlinear mechanism being an increase of absorption due to the increase of temperature induced by the laser.
The system is prepared near its up-down switching threshold with a cw beam and a short pulsed laser beam is used to induce the switching. In these conditions, it has been shown experimentally that, for dispersive interference filters /3/ and absorptive CdS platelets / 4 / , the switching dynamics is governed by the pulse characteristics and by the position of the holding point. Our purpose is to see how the propagation of heat in the sample influences the longitudinal and transverse intensity profile of the cw beam.
The evolution of the system is reasonably described by the macroscopic set of equations :
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19882104
C2-440 JOURNAL DE PHYSIQUE
(Eo
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%oli bw, 0 a, (T) = wco exp [ - 2c0 tanh(-
2kb T ) 1 SWL 0
k indexes the two beams (k = c : cw beam, k = p : pulsed beam). T is the tempe- rature of the medfium of conductivity A , heat capacity C and density p. P,, and &, are the power densities and electric field amplitudes of the two beams
02
energies %wk and n,, ot; are their refractive index and coefficient of absorption (Anc is the nonlinear part of the refractive index which, in the case of strong absorption, plays a minor role)
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The parameters in Eq. (3) are the ones usually used in the Urbach model of absorption. To obtain the complete spatio-temporal variation of the device, Eqs. (1)-(3) have been solved numerically with a 5 t h order centered difference predictor corrector algorithm. The boundary condi- tions for the electric fields are given by the continuity equation :cnC
and q U r f a r e the incident field amplitudes outside and inside the nonlinear medium.It has been found that considering the temperature convection at the interfaces is identical to consider an abrupt change of temperature between the sample and the surrounding air.
The model is applied to CdS platelets where the static bistable behavior and switching dynamics have been extensively studied experimentally /4/. The polari- zation vectors of the two laser beams are assumed to be parallel to the c axis.
The following values of the parameters are used : h = 20 W/K/M, p C = 1.58 lo6 ws/IC/m3, a m = 8 10" m-' , c0= 2.22, Eo = 2.6275 eV, %wLO = 24 meV, hwc= 2.41 eV, bwp = 4.025 eV, nc = 2.6, np = 2.4, a = 3.6 10' m-'
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The value of hwc corresponds to theP514.5 nm emission line of a cw Argon laser and kwp to the 308 nm UV emission of an excimer laser.
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NUMERICAL R E S U mFig. 1 shows the space-time switching behavior of the cw laser beam when it has been first prepared near its up-down switching threshold and then adressed by a pulse of 15 ns duration (FWHM). The two laser beams have the same Gaussian transverse profile of intensity, the diameter of the spot being of 55 p m - The temporal profile of the address pulse is also Gaussian. The incident power corresponding to the up-down threshold is of 3 mW in the center of the spot. In Fig 1-a), a slight decrease of intensity occurs in the center part of the beam which reaches an intermediate level ( W 0.5 mW), where it stays during the whole temporal scale displayed in the figure (60 ns). This decrease is more pronounced (as seen in fig. 1-b) when the incoming pulse power is higher (1 kW in 1-b) instead of 0.5 kW in 1-a)).
Figure 1 : Space-time behavior of Figure 2 : Space-time switching down the cw beam addressed by a of the cw beam (a) and corresponding pulse of 0.5 kW (a) and 1 kW (b) diffusion of the temperature (b)
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Themaximum power. address pulse has 1 kW maximum power.
It is worth to notice that the center part of the cw beam in fig. 1-b) increases after about 40 ns, giving rise to a hole structure. This is due to the strong gradient of temperature near the center of the spot which contributes to cool down the material after a certain time. This does not mean that the device will not switch. In fact, after about 1 ps, the power of the cw beam decreases slowly down to the low transmitting level. This is seen in fig. 2-a) which represents the dynamics for the same parameters than in fig. 1-b), but on a much longer temporal scale. Simultaneously, the temperature diffuses and its transverse profile becomes flat as seen in fig. 2-b) (notice that for a convenient under- standing of the temperature increase during the switching process, the time axis is reversed in fig. 2-b)).
By increasing the input pulsed beam, it is possible to stabilize the device on the low transmitting level just after the pulse. In this case however, there is a high loss of energy through diffusion. This loss shows up by an increase of temperature much beyond the spot diameter, up to the total diffusion length which could not be reached with our transverse space grid but, which can be estimated to about 300 pm with rough calculations. This diffusion length is the minimum separation to prevent crosstalk between adjacent bistable elements. One should notice, however, that the crosstalk occurs in a temporal range which is of the order of the thermal relaxation time (millisecond), no interferences appearing during the first microsecond, even for light spots separated by 110 pm as shown in fig. 3. In this figure, the address pulse has been send on one of the two spots.
JOURNAL DE PHYSIQUE
Figure 3 : Dynamics of two adjacent cw light spots, before the occurence of crosstalk for one address pulse of maximum power 0.5 kW: a) cw intensity profile, b) corresponding temperature profile.
In conclusion, we have shown that an induced absorption bistable device displays a complex switching behavior when the transverse diffusion is important. It appears that, during the switching process, there is a temporal range where the bistable element may come back near its initial transmitting level and then, relax down to the low transmitting one. To compete with this energy loss through diffusion, one may increase the address pulse power which, however, requires a good heat sinking of the device to prevent its overheating and to minimize crosstalk.
Acknowledgments : The computing facilities have been attributed by the "Conseil Scientifique du Centre de Calcul Vectoriel pour la Recherche" (FRANCE).
REFERENCES
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(Springer Verlag 1986), p. 193
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Daunois, A., Bigot, J-Y., Leonelli, R. and Smith, S . D . , Opt. Commun. 62 (1987) 360
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