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Topical Meeting on Optical Bistability (OB)

Composite Logic Gate Element and Multiplexer for Optical Computing and Optical Communication

Joseph W. Haus, C. M. Bowden, Chi C. Sung

Published Jan 1, 1985• 1 citation
Publisher

Abstract

Mirrorless (cavityless) optical bistability (OB), due to temperature-dependent renormalization of the absorption peak of the bound exciton resonance in CdS has been observed and interpreted1 in terms of coupling between the internal field intensity and the temperature in the nonlinear material. It was shown2 that the heat conductivity boundary conditions determine the conditions for bistability of a sample of the material. In fact, we showed earlier that when the boundary conditions at the ends of the sample are such that the heat resistance at the exit end HL = h1/3 where ho is the heat resistance at the entrance face, two hysteresis curves result, one clockwise with increasing input intensity at lower incident fields due to increasing absorption and the other at higher field values due to decreasing absorption which is counter-clockwise, Figures 1a and 1b.

DOI
10.1364/obi.1985.md24

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Nonlinear Optics•Dec 4, 2003•0 citations
Mirrorless (cavityless) optical bistability (OB), due to temperature-dependent renormalization of the absorption peak of the bound exciton resonance in CdS has been observed and interpreted1 in terms of coupling between the internal field intensity and the temperature in the nonlinear material. It was shown2 that the heat conductivity boundary conditions determine the conditions for bistability of a sample of the material. In fact, we showed earlier that when the boundary conditions at the ends of the sample are such that the heat resistance at the exit end HL = h1/3 where ho is the heat resistance at the entrance face, two hysteresis curves result, one clockwise with increasing input intensity at lower incident fields due to increasing absorption and the other at higher field values due to decreasing absorption which is counter-clockwise, Figures 1a and 1b.
Optical bistability in the presence of an optically induced absorption is observed when a thin 13-μm CdS sample is inserted between two mirrors of 90 % reflectivity, in our experiment, a modulated cw laser of ~15-mW peak power is tuned on each side of the free exciton resonance in CdS, and the transmission characteristics are studied. A theoretical calculation including both absorptive and dispersive effects is presented and good agreement is obtained. The absorption coefficient and the index of refraction of the material are connected by Kramers-Kronig relations. Propagation effects are taken into account. Sufficiently long pulses (40 ms) are considered to allow the thermally induced absorption to occur. For detunings above the free exciton resonance, we predict that counterclockwise hysteresis loops will first be observed as the intensity rises; for detunings below the free exciton resonance, only clockwise hysteresis loops are predicted. These predictions were experimentally verified. Power levels of the order of 5–10 mW were sufficient to observe bistability. Cavity effects were also observed.
Optical bistability caused by thermal heating is observed when the CdS crystal is excited near the I2 bound exciton absorption line [1]. Impact ionization of free and bound excitons occurs in the crystal upon its illumination in electric field. The probability of impact ionization depends in a threshold way on exciton and free carrier concentration. At a certain field dependent carrier concentratiοn avalanche occurs, the electric current therewith increases the crystal temperature by 5-20 K [2] which is followed by a red I2 shift. The shift leads to an increase in absorption, carrier density and current. Therefore, feedback results from impact ionization current heating the crystal (Fig. 1).
Mirrorless optical bistability has been established in CdS1 and in multiple quantum well (MQW) GaAs structures2. The mechanism responsible for the bistable behavior in these semiconductors is the coupling between the temperature distribution and the electric field intensity in the sample. In these semiconductors, the mechanism is simple enough that a quantitative analysis should be possible. However, a successful model of bistability in these systems must await a careful experimental analysis of the thermal boundary conditions3. With this caveat we have proceeded with the theoretical development. Steady-state results for CdS and MQW GaAs are presented.
Optical bistability (ob) is investigated in CdS in a wide range of intensities. Under pulsed excitation (total pulse width 20 nsec) we find at 5K for ħωexc ≈ 2.550 eV on the flank of the AΓ5 exciton ob of the induced absorption type for incident intensities of Iexc ≈ 1kW/cm2. The nonlinearity is in this case a collision-broadening of the free exciton resonance [1]. The commutation times τ↓ and τ↑ are about 1 nsec and 5 nsec, respectively. For ħωexc ≈ 2.546 eV we observe absorptive ob due to the formation of an electron-hole plasma [2] for Iexc ≈ 1MW/cm2. Single shot experiments show τ↓ ≲ 500 psec being thus to our knowledge one of the shortest commutation times reported for single beam ob so far. The observed hysteresis loops are compared to model calculations with variable pulse lengths. The comparison indicates true ob in our experiments.
A general discussion of the linear-optical properties of free and bound excitons in direct-gap semiconductors at low temperature is presented. This discussion then specializes to CdS. The nonlinear-optical response of CdS is introduced by first discussing the saturation behavior of bound excitons. A new type of cavityless optical bistability based on induced absorption near the free and bound excitons is described. Finally, fast all-optical switching (<1 nsec) at very low switching energies (<8 pJ) is demonstrated, using the giant nonlinearity associated with bound excitons.
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.