Abstract

The characteristics of whispering-gallery modes (WGMs) in 3-D cylindrical, square, and triangular microcavities with vertical optical confinement of semiconductors are numerically investigated by the finite-difference time-domain (FDTD) technique. For a microcylinder with a vertical refractive index 3.17/3.4/3.17 and a center layer thickness 0.2 $\mu{\hbox {m}}$, $Q$-factors of transverse electric (${\hbox {TE}}$) WGMs around wavelength 1550 nm are smaller than ${\hbox {10}} ^{3}$, as the radius ${R} < 4~\mu{\hbox {m}}$ and reach the orders of ${\hbox {10}} ^{4}$ and ${\hbox {10}} ^{6}$ as $R = 5~{\hbox {and }}~6 ~\mu{\hbox {m}}$, respectively. However, the ${\hbox {Q}}$-factor of transverse magnetic (${\hbox {TM}}$) WGMs at wavelength 1.659 $\mu {\hbox {m}}$ reaches 7.5$\,\times {\hbox {10}} ^{5}$ as $R = 1~\mu{\hbox {m}}$. The mode coupling between the WGMs and vertical radiation modes in the cladding layer results in vertical radiation loss for the WGMs. In the microcylinder, the mode wavelength of ${\hbox {TM}}$ WGM is larger than the cutoff wavelength of the vertical radiation mode with the same mode numbers, so ${\hbox {TM}}$ WGMs cannot couple with the vertical radiation mode and have high $Q$-factor. In contrast, ${\hbox {TE}}$ WGMs can couple with the corresponding vertical radiation mode in the 3-D microcylinder as $R < 5~\mu{\hbox {m}}$. However, the mode wavelength of the ${\hbox {TE}}$ WGM approaches (is larger than) the cutoff wavelength of the corresponding radiation modes at $R = 5~\mu{\hbox {m}}$ (6 $\mu{\hbox {m}}$), so ${\hbox {TE}}$ WGMs have high ${\hbox {Q}}$-factors in such microcylinders too. The results show that a critical lateral size is required for obtaining high $Q$-factor ${\hbox {TE}}$ WGMs in the 3-D microcylinder. For 3-D square and triangular microcavities, we also find that the ${\hbox {Q}}$-factor of ${\hbox {TM}}$ WGM is larger than that of ${\hbox {TE}}$ WGM.

© 2008 IEEE

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