Abstract
AbstractWith a view to application to millimeter wave integrated circuits, we analyze theoretically resonance characteristics of a whispering gallery mode (W.G. mode) propagating along a circumference of an elliptical dielectric cylinder. A wave equation is derived in an elliptic coordinate system and an eigenvalue equation includes Mathieu functions with a large order is obtained. Since this eigenvalue equation is an infinite dimensional determinant, we introduce a new technique to solve the eigenvalue equation. In this determinant, we pay our attention to diagonal elements that affect mainly resonance order. By means of this approach, it becomes possible to estimate a number of approximate terms of the eigenvalue equation to keep an accuracy of a resonance frequency constant even if an eccentricity of the ellipse is increased, namely the ellipse is flatter. It is also possible to find numerically the resonance frequency and electric field distribution of the W.G. mode for the elliptical cylinders with various eccentricity.
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More From: Electronics and Communications in Japan (Part II: Electronics)
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