## Abstract

The mode characteristics of a three-dimensional (3D) microdisk with a vertical refractive index distribution of ${n}_{2}\u22153.4\u2215{n}_{2}$ are investigated by the *S*-matrix method and 3D finite-difference time-domain (FDTD) technique. For the microdisk with a thickness of $0.2\text{\hspace{0.17em}}\mu \mathrm{m}$ and a radius of $1\text{\hspace{0.17em}}\mu \mathrm{m}$, the mode wavelengths and quality factors for the ${\mathrm{HE}}_{7,1}$ mode obtained by 3D FDTD simulation and the *S*-matrix method are in good agreement as ${n}_{2}$ increases from 1.0 to 2.6. But the *Q* factor obtained by the 3D FDTD rapidly decreases from $1.12\times {10}^{4}$ to 379 as ${n}_{2}$ increases from 2.65 to 2.8 owing to the vertical radiation losses, which cannot be predicted by the proposed *S*-matrix method. The comparisons also show that quality factors obtained from the analytical solution of two-dimensional microdisks under the effective index approximation are five to seven times smaller than those of the 3D FDTD as ${n}_{2}=1$ and $R=1\text{\hspace{0.17em}}\mu \mathrm{m}$.

© 2006 Optical Society of America

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