Eigenmode Analysis of Whispering Gallery Modes of Pillbox-Type Optical Resonators Utilizing the FE-BPM Formulation

Ryuichi KOYA
Osami WADA
Ryuji KOGA

IEICE TRANSACTIONS on Electronics   Vol.E78-C    No.11    pp.1638-1645
Publication Date: 1995/11/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
optical integrated circuit,  whispering gallery mode,  optical resonators,  eigenmode analysis,  

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To evaluate the radial eigenmode field distributions and the resonance wavelengths of axially symmetric pillbox resonator, a numerical method is described which is based on the FE-BPM expression in cylindrical coordinates. Under the weakly guiding approximation, we solve Fresnel equation and can get a fairly accurate result. By using effective index method, 3-D pillbox guiding structure is reduced to 2-D one which is then used for the analysis. One advantage of this method is that it is applicable for the axially symmetric optical waveguides with arbitrary index distribution. The validity of this method is checked by comparing the results of this method with those of the analytical ones. This method is applied for the evaluation of the coupling properties of a coupled structure consisting of a pillbox resonator and a curved waveguide placed outside the pillbox. This coupled structure has a good prospect to be used as optical wavelength filter. By varying the separation distance between the pillbox and the outer curved waveguide, the power transfer due to coupling is determined near the resonance wavelength 0.9 µm.