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crosstalk ratio of both output waveguides can be as small as a Ϫ23 dB, while the measured propagation loss of a straight-channel waveguide is kept within the range of 1.1-1.25 dB/cm. Without using electrically controllable couplers to serve as 3-dB splitters or combiners, the total device length can be reduced to 18 mm. The switching voltage-length product is 8.5 V-cm for the TM-polarized light at 1.32 m. Using the properties of high optical-damage resistance in the Zn-diffused LiNbO 3 waveguide, fast modulation and high-power-operation integrated devices will be of great interest in the near future.

SUMMARYIn this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very e cient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning e ect on the resonant frequency and half-power bandwidth are also presented.

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