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Science Publishers eBooks

Optical and Quantum Computing

Preecha Yupapin, Chat Teeka, J. Ali

Published May 2, 2012• 0 citations
Publisher

Abstract

The close form of Eq. (8.3) indicates that a ring resonator in the particular case is very similar to a Fabry-Pérot cavity, which has an input and output mirror with a field reflectivity, (1 – k), and a fully reflecting mirror. k is the coupling coefficient, and x = exp(–aL/2) represents a roundtrip loss coefficient, f0 = kLn0 and z kLn ENL in2 2= are the linear and nonlinear phase shifts, k = 2p/l is the wave propagation number in a vacuum, where L and a are a waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the results as shown in Eq. (8.3), similarly, when the output field is connected and input into the other ring resonators.

DOI
10.1201/b11935-10

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The close form of Eq. (8.3) indicates that a ring resonator in the particular case is very similar to a Fabry-Pérot cavity, which has an input and output mirror with a field reflectivity, (1 – k), and a fully reflecting mirror. k is the coupling coefficient, and x = exp(–aL/2) represents a roundtrip loss coefficient, f0 = kLn0 and z kLn ENL in2 2= are the linear and nonlinear phase shifts, k = 2p/l is the wave propagation number in a vacuum, where L and a are a waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the results as shown in Eq. (8.3), similarly, when the output field is connected and input into the other ring resonators.
With the exception of Chapter 1, up to this point we have considered cavityless optical systems. With this chapter, instead, we start focussing on the case that the atomic medium is located in an optical cavity. We describe in detail the case of a unidirectional ring resonator, the boundary condition which characterizes it and the relations between its output fields and the intracavity field (Sections 8.1–8.3). We discuss the transmission of an empty cavity (Section 8.4) and of a cavity that contains a linear medium (Section 8.5). Optical cavities An optical cavity or optical resonator is formed by at least two mirrors, appropriately arranged in such a way that the radiation beam follows a closed path. The beam splitters allow the radiation to escape from the cavity (output) and allow one to inject radiation into the cavity (input). In order to confine the radiation transversally with respect to the direction of propagation, the mirrors are usually spherical (see Fig. 1.2). The case of cavities with spherical mirrors will be described in Part III of this volume. On the other hand, an analytical treatment of the problems is possible only within the plane-wave approximation which we will use in the remainder of Part I and in Part II. In accord with this, we assume here that the mirrors are planar. The two most common types of optical resonator are the Fabry–Perot cavity and the ring cavity . The planar Fabry–Perot cavity consists in two beam splitters in a parallel configuration as shown in Fig. 8.1. Within the cavity there are two counterpropagating fields, E F propagating in the forward direction and E B propagating in the backward direction with respect to the input field E I . Because we have derived the Maxwell–Bloch equations for the unidirectional configuration, in this and the following chapters we focus on the case of a ring cavity, which allows unidirectionality. The Fabry–Perot case will be considered in Chapter 14.
We theoretically propose a method to restore weak pulse signals submerged in noise via stochastic resonance, which is based on the optical bistability induced by the molecule reorientation in a Fabry-Perot cavity with an intracavity nematic liquid-crystal film. The bistable properties of this cavity are analyzed with different reflectance of the mirrors, initial phase shift and initial angle between the phase propagation vector and the director. The cross-correlation coefficient between pure input pulses and output is calculated to quantitatively evaluate the influence of noise intensity on output. The simulation results show a cross-correlation gain of 3.2 and that the buried signal can be recovered effectively by this device. It proves the potential of using this structure to recover noise-hidden pulse signals in an all-optical system.