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One-dimensional Nonlinear Photonic Crystal Structure for All-optical Signal Processing

Mei Yuan-yuan

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Considering a one-dimensional photonic crystal covering nonlinear medium layer,the transfer matrix algorithm for one-dimensional inhomogeneous medium was applied to found the theoretical analysis model for the electromagnetic wave propagations.The plane electromagnetic waves solutions were obtained.And numerical realization method was also given out.The investigations show that the method simulated exactly the behavior of electromagnetic wave propagating in 1-D nonlinear medium.And optical bistable switching of 1-D photonic crystal with nonlinear medium layer covering can be shown validly and concisely.

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Considering a one-dimensional photonic crystal covering nonlinear medium layer,the transfer matrix algorithm for one-dimensional inhomogeneous medium was applied to found the theoretical analysis model for the electromagnetic wave propagations.The plane electromagnetic waves solutions were obtained.And numerical realization method was also given out.The investigations show that the method simulated exactly the behavior of electromagnetic wave propagating in 1-D nonlinear medium.And optical bistable switching of 1-D photonic crystal with nonlinear medium layer covering can be shown validly and concisely.
We study the optical bistable properties in one-dimensional photonic crystal with symmetric structure (AB)N(D)M(BA)N, where A is high refractive index medium, B is low refractive index medium, D is defect layer, N is the number of layer periods at the left and right of the defect layer. M determines the thickness of the defect layer with Kerr medium. First, we analyze mechanisms producing bistability by the structure consisted of a nonlinear layer sandwiched between Bragg reflectors. Then by using the transfer matrix method, we calculate numerically the threshold value of the bistability switching in one-dimensional photonic crystals with structure (AB)N(D)M(BA)N. The investigations show that the number of layer periods (N) and the thickness of the defect layer (M) influence the threshold value of the bistability switching. We confirm the parameter of the bistability switching to produce the lower threshold value.
In this paper, a one-dimensional photonic crystal composed of two defect layers with optical gain is considered. We place a nonlinear layer between two defect layers. Using the modified transfer matrix method, the effect of increasing the optical gain on the bistablity threshold is studied in both normal and oblique incidences. Our calculations show that the threshold of bistability decreases with increasing the optical gain. However, increasing the optical gain above a particular value leads to the enhancement of bistability threshold.
The transfer matrix, which represents the dispersive medium's layer, can be rigorously obtained by using Lorentz model and considering boundary conditions. The detailed investigation on polaritons in a symmetric photonic crystal with absorptive type of dispersive medium's layer is presented by adjusting parameters of the dispersive medium's layer. It's found that the absorptive type of dispersive cavity and reinforced dispersive cavity may demonstrate similar properties in normal modes coupling, the homogeneous broadening effect, and the detuning effect. But there exists evident differences in transmitted intensity and frequency shift. Finally, the optical bistability in one-dimensional symmetric photonic crystal both with absorptive type of dispersive medium's layer and with Kerr nonlinear layer is also investigated. It's found that optical bistability threshold of the photonic crystal with dispersive medium layer is a little lower than that of structure without dispersive medium laver.
The one-dimensional mirror structure photonic crystals,and when the quantum wave equation of photon was applied to one-dimensional photonic crystals were studied by quantum theory method. it could be obtained the quantum transfer matrix,the quantum transmissivity and the quantum reflectivity.The effects of the defect layer number,absorbing and active medium on the quantum transmission properties was studied,which can help to design optical filter,amplifier and attenuator. When the defect layer is inserted,the defect model appears sharp peak. With the addition of defect layer number,the number of defect model increases,and the optic filter of multiple channel can be designed. When adding absorbing medium in the defect layer,the defect model intensity becomes weaken. when adding active medium in the defect layer,the defect model intensity becomes enhanced,so the optic amplifier and attenuator can be designed.
The optical transfer matrix theory is used to research the transmission characteristics of an one-dimensional photonic crystal.If the defect layer is nonlinear medium which is saturatedly absorbed,the optical bistable properties are studied based on the sensitivity change of incident light transmittivity of nonlinear medium.And the analytical formula related to the input-output of the light intensity is deduced.When the saturated absorption is above a certain value,the optical bistablity will appear in the system.Finally the change law of the incident light threshold value of the optical bistablity is studied.