Fiber-optic multiple-wavelength filter based on one-dimensional photonic bandgap structures with defects

In this paper, a theoretical analysis is given of an optical fiber multiple-wavelength tunable filter based on a one-dimensional (1-D) photonic bandgap (PBG) structure with four defects. To understand the positioning of the modes in the bandgap, a previous analysis of structures with one and two defects is performed. By adequate parameterization, it will be possible to control the central wavelengths of the various filters of the device. Parameters responsible for this effect are the contrast of refractive indexes of high- and low-index layers, the optical thickness of the defects, and the number of layers stacked among the defects related to those stacked at the extremes. In addition to this, the finesse of the filters can be controlled by the adequate addition of layers among defects. As a result, a simple 1-D PBG structure with defects will permit designing almost any multiple-wavelength filter, with immediate application in the treatment of wavelength-division-multiplexed (WDM) signals. The possibility of the tunability of this device can be introduced if materials are included whose refractive index changes with some parameter, such as temperature, voltage, or strain. As an example, liquid crystals change their refractive index with an applied voltage, leading to a shift of the central wavelengths of the filters.