Method of Designing a Corrugated Optical Waveguide Filter

Abstract

The method of designing a corrugated optical waveguide filter is proposed to yield an arbitrary spectral profile of the reflection coefiicient. It gives the functional dependence of the corrugation depth on distance along the wave propagation direction. The basis of the theory of the method is a combination of the effective index approach and the Fourier transformation technique. It represents the spectral profile of the reflection coefficient approximately to Fourier transformation 0L the spatial profile of the effective reLractive index. Examples are presented to illustrate how to apply the technique.

A Bessel function-based design method of a periodic multireflection optical filter

“…The optical wave propagates in the z direction with a propagation constant of b. If the deviation Dn(z) from the average value of the refractive index is not too large and if the variation Dn(z) depends on a sufficiently large distance L, the electric field reflectivity r(b) of the filter can be described approximately by the following Fourier transform relationship [5,6]:…”

“…There are several ways to compute a more accurate reflection coefficient [8,9]. In this paper, the F matrix with a simple description is used and the filter characteristics are confirmed [5,6].…”

Synthesis of Multilayer and Waveguide Filters for use in Optical Communication Systems

“…Such index variation may be done periodically [2][3][4][5][6][7][8], such as the common Bragg reflectors, or aperiodically [9][10][11][12], which can then be employed by the transfermatrix method to calculate the reflectivity spectrum [13][14][15][16]. On the other hand, the aperiodic-type design helps to reduce the sidelobes, vary the bandwidth and attain output spectrum with multi-bands [14][15][16]. However, a guide to the profile of the spatial index variation that corresponds to the desired output spectrum is essential to approach to the optimum index profile.…”

“…However, a guide to the profile of the spatial index variation that corresponds to the desired output spectrum is essential to approach to the optimum index profile. Some authors determined this guide as inverse Fourier transformation of the reflection coefficient [14,15], however accuracy of this relationship deteriorates dramatically with decreasing the bandwidth. Then careful techniques are required to optimize such approximate guide of index variation so as to fit the reflectivity spectrum calculated by an accurate method (such as the transfer-matrix method) to desired spectrum [14].…”