Two-Dimensional Nonlinear Fabry-Perot Interferometer: An Unconventional Computing Substrate for Maze Exploration and Logic Gate Operation

Introduction

Nonlinear optical phenomena have been notable because of its fundamental interest and applications such as all-optical switching (Quintero-Torres, 1995), optical logic gates (Sharfin, 1986), and so on. Especially optical bistability in nonlinear Fabry-Perot interferometer has been studied both experimentally and theoretically as a basis to control light by light (Migus, 1985; Marino, 2007; Ono, 2001; Khoo, 1983; Kreuzer, 1994; Cheung, 1983; Wang, 2001; Quintero-Torres, 1995; Sharfin, 1986). Fabry-Perot interferometer is an optical device consisting of two parallel mirrors with high reflectivity (Figure 1a) in which the injected light is reflected many times between the mirrors. When the round-trip optical length equals to an integral multiple of the light wavelength, the multiply reflected lights interferes constructively and transmittance of the interferometer becomes high because of interference. If the wavelength does not satisfy the condition above, transmittance is low. Therefore, the transmission presents a resonance property as a function of wavelength (Figure 1b). A nonlinear Fabry-Perot interferometer utilizes refractive index change of the medium between the mirrors. This change can be induced by light through third-order nonlinear optical process or heat through temperature dependence of refractive index. Assume that a Fabry-Perot interferometer is off-resonant at the wavelength of incident laser light as shown by the dashed thick line in Figure 1b. When the incident light intensity is increased from zero, small fraction of the incident light enters in the interferometer and the intensity in the interferometer increases almost proportional to the incident light intensity. At certain intensity of incident light, positive feedback starts: increase of light intensity in the interferometer causes change in refractive index and resonance shift, resulting in further increase of intensity in the interferometer. This turns the device to a resonant state or “ON” state with high transmission. When decreasing the incident light intensity, the “ON” state is kept down to a considerably weak light intensity, since large fraction of light enters to the interferometer. Thus hysteresis and bistability is realized.