Optical bistability in semiconductor periodic structures

IEEF JOURNAL OF OUANTUM ELECTRONICS. VOL 27. NO 5. MAY 1991

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Optical Bistability in Semiconductor Periodic Structures J . He and Michael Cada, Member, IEEE

Abstract-We report on a theoretical demonstration of optical bistability in periodic layered media, particularly in longperiod GaAs-AIAs superlattices. The proposed structure consists of a periodic multilayer system, as opposed to previously demonstrated nonlinear bistable devices which employed Fabry-Perot etalons. The optical resonance effect which is essential for bistable devices is, in our case, induced by a refractive index modulation. The nonlinear active medium is distributed in the whole structure rather than placed between the two mirrors of a Fabry-Perot cavity. It is shown by a complete calculation of wave propagation in the periodic nonlinear medium that a multiple valued feature appears in the structure's nonlinear reflectivity spectrum. The input/output characteristics of the structure exhibit bistable hysteresis similar to that of a nonlinear Fabry-Perot etalon. Both the reflection and the transmission modes a r e analyzed. The intensity threshold for bistability is shown to be a s low a s 9 kW/cmz for a 30-period GaAs-AIAs superlattice of a thickness of about 4 pm. The characteristics of this type of device a r e discussed and compared to thosc based on Fabry-Perot etalons.

I . INTRODUCTION PTICAL nonlinearity and bistability in semiconductors have received increasing interest because of their potential applications for optical logic and all-optical signal processing [ l ] , [ 2 ] . It is known that semiconductors such as GaAs or multiple quantum wells (MQW) of GaAs-GaAlAs exhibit large optical nonljnearities in the vicinity of bandgap because of resonance enhancement. Many nonlinear bistable devices with low switching powers have been demonstrated [3]-[9] using the resonant nonlinearity. All of these devices demonstrated so far include a Fabry-Perot etalon which consists of either externally deposited dielectric mirrors or monolithic integrated Bragg reflectors. The nonlinear active media such as GaAs or MQW are placed between the two mirrors of the Fabry-Perot etalon. In this paper, we report on our: theoretical demonstration of a similar bistable function of a different structure which only consists of a periodic multilayer system. This structure is similar to a single Bragg reflector. However, the operating wavelength is chosen to be at the reflectivity

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Manuscript received May 2 2 , 1990: revised November 2. 1990. The work of M . Cada was supported by the Natural Science and Engineering Research Council (NSERC) of Canada. The authors are with the Department o t Electrical Engineering. Technical University of Nova Scotia. Halitax. N . S . . Canada B3J 2x4. IEEE Log Number 9144638.

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Fig. I. Average energy density in a 30-period GaAs-AIAs superlattice ( d , = 576 A , d 2 = 704 A ) in ratio with that of an incident beam in the air (a) and reflectivity at normal incidence (b) as a function of wavelength in the vicinity of the optical stopband.

minimum of the medium in the vicinity of its optical stopband rather than inside the stopband for which the structure would act as a Bragg reflector. In 1979, Winful et al. [lo] first demonstrated the optical bistability of periodic media in the form of a distributed feedback structure (DFB) in integrated optics. However, the bistability in such a structure has not been extensively studied, and no experiment has been done using this type of structure until very recently [ l l ] . Also, recently, it has been shown that, for a light wave propagating in a periodic layered medium, there exists an optical resonance effect when the light wavelength is in the vicinity of the optical stopband [ 121. When the resonance occurs, the light intensity in the medium is strongly increased and the intensity of the reflected beam is minimal (Fig. 1 ) . The reflectivity spectrum exhibits a sharp negative peak in the vicinity of the stopband if the thickness

0018-9197/9110500-1182$01 00

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1991 IEEE

HE AND CADA: OPTICAL BISTABILITY IN SEMICONDUCTOR PERIODIC STRUCTURES

of the structure (or the number of periods) is sufficiently large [12]. For a light wavelength corresponding to the resonance peak, a small variation of the refractive index will cause a large variation in the reflectivity, and also in the light intensity inside the medium. If the periodic layered medium includes at least one nonlinear material such as GaAs whose refractive index is dependent on the light intensity, the optical feedback mechanism for bistable operation can be established. The intensity variation of the light field in the nonlinear medium causes a refractive index variation, and this refractive index variation induces, in turn, a light intensity variation through the optical interference effect. With this feedback mechanism, the reflected or transmitted intensity can exhibit differential gain or hysteresis in its response to the incident intensity. Such behavior is very similar to that of nonlinear Fabry-Perot etalons, and it can be employed in an optical transistor, a differential amplifier, bistable devices, optical memory, etc.

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which is perpendicular to the layers. Layers are supposed to be extending to infinity in both the x and y directions. Assuming that the thicknesses of the two different kinds of layers are, respectively, d , (GaAs) and d2 (AlAs), the period is then D = d , d2. The refractive index n ( z ) , its imaginary part K ( z ) , and the nonlinear coefficient n ‘ ( z ) can, respectively, be written as

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where n l , n2 are, respectively, linear refractive indexes of medium 1 (GaAs) and medium 2 (AIAs), and no is the average refractive index with no = (1 - X ) n , + X n 2 and X = d 2 / D . K , , K ~and , K~ are corresponding imaginary parts of the refractive indexes, and n ; , n;, and n;l are corresponding nonlinear coefficients. f ( z ) is a periodic function given by

11. THEORETICAL MODEL

In order to demonstrate the existence of optical differential gain and hysteresis in a nonlinear periodic structure, we analyzed the optical wave propagation in the medium by using the coupled-mode method. We used the parameters of long-period GaAs-AIAs superlattices for the calculation since they can be fabricated with high quality using current crystal growth technology such as molecular beam epitaxy or metalorganic chemical-vapor deposition. The general results can be extended to other periodic structures in different material systems. As was discussed above, optical nonlinear devices require two mechanisms: an intensity-dependent refractive index change, and an optical resonance effect. GaAs has a high nonlinearity for light wavelengths close to its band edge. However, optical absorption is also high in this region, which reduces the optical resonance effect. There exists, therefore, a tradeoff between the nonlinearity and the absorption for choosing an operating wavelength. According to the measurements [ 131, the absorption decreases sharply just below the bandgap ( E , = 1.42 eV), while the nonlinear coefficient remains sufficiently high (about 2 X lop7cm2/W) for photon energy around 1.4 eV. Hence, we designed our device structure so that it operates at 1.4 eV, which corresponds to a light wavelength of about 885 nm. Near the electronic band edge, the GaAs nonlinearity is saturable. If we write the nonlinear refractive index change as A n = n ’ l ( l is the light intensity), the nonlinear coefficient n’ will decrease with increasing intensity. On the other hand, the absorption of GaAs is also saturable. The saturation of absorption increases the optical intensity in the resonant structure, which in turn compensates for decreases of the nonlinear coefficient. Therefore, for reasons of simplicity, we neglect the saturations of both nonlinearity and absorption in this paper. Consider a light wave propagating in the z direction

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