## Abstract

Morphology-dependent resonances (MDR's) of polystyrene microspheres were excited by an optical fiber coupler. For optical elimination of the air–cladding interface at the optical fiber coupler surface, the microsphere was immersed in an index-matching oil. MDR's were observed, even though the relative refractive index between the microsphere and the oil was only 1.09. The observed MDR spectra are in good agreement with the generalized Lorenz–Mie theory and the localization principle. The scattering efficiency into each MDR is estimated as a function of the impact parameter by means of generalized Lorenz–Mie theory.

© 1997 Optical Society of America

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### Equations (11)

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(1)
$$b=\left(n+\frac{1}{2}\right)\frac{\mathbf{a}}{x}.$$
(2)
$$B_{n}{}^{m}=\frac{{\mathbf{a}}^{2}}{n(n+1){\psi}_{n}(x)}{\int}_{0}^{4\pi}\mathrm{d}\mathrm{\Omega}{H}_{r}(\mathrm{\Omega}){{Y}_{\mathit{nm}}}^{*}(\mathrm{\Omega}),$$
(3)
$$\frac{\mathrm{d}\u220a}{\mathrm{d}t}=\frac{{\sigma}_{\mathrm{mode}}}{{\sigma}_{\mathrm{total}}}{P}_{i}-\frac{\u220a}{\tau}=\u3008{\sigma}_{\mathrm{mode}}\u3009{P}_{i}-\frac{\u220a}{\tau}={\sigma}_{\mathrm{mode}}\u3008{I}_{i}\u3009-\frac{\u220a}{\tau},$$
(4)
$${\u220a}_{0}=\frac{{\sigma}_{\mathrm{mode}}}{{\sigma}_{\mathrm{total}}}{P}_{i}\tau =\u3008{\sigma}_{\mathrm{mode}}\u3009{P}_{i}\tau ={\sigma}_{\mathrm{mode}}\u3008{I}_{i}\u3009\tau .$$
(5)
$${\sigma}_{\mathit{an}}=\frac{2\pi}{{k}^{2}}|{a}_{n}{|}^{2}(2n+1),$$
(6)
$${\sigma}_{\mathit{bn}}=\frac{2\pi}{{k}^{2}}|{b}_{n}{|}^{2}(2n+1),$$
(7)
$${\sigma}_{\mathrm{total}}=\sum _{n=1}^{\infty}{\sigma}_{\mathit{an}}+{\sigma}_{\mathit{bn}}=\frac{2\pi}{{k}^{2}}\sum _{n=1}^{\infty}(|{a}_{n}{|}^{2}+|{b}_{n}{|}^{2})\times (2n+1)=2\pi {\mathbf{a}}^{2}.$$
(8)
$${\sigma}_{\mathit{an}}=\frac{2\pi}{{k}^{2}}|{a}_{n}{|}^{2}\left[\frac{2n+1}{2n(n+1)}\right]\sum _{m=-n}^{n}|{A}_{n}^{m}{|}^{2}\frac{(n+|m|)!}{(n-|m|)!},$$
(9)
$${\sigma}_{\mathit{bn}}=\frac{2\pi}{{k}^{2}}|{b}_{n}{|}^{2}\left[\frac{2n+1}{2n(n+1)}\right]\sum _{m=-n}^{n}|B_{n}{}^{m}{|}^{2}\frac{(n+|m|)!}{(n-|m|)!},$$
(10)
$${\sigma}_{\mathit{an}}=\frac{2\pi}{{k}^{2}}|{a}_{n}{|}^{2}(2n+1)|A_{n}{}^{\pm 1}|,$$
(11)
$${\sigma}_{\mathit{bn}}=\frac{2\pi}{{k}^{2}}|{b}_{n}{|}^{2}(2n+1)|B_{n}{}^{\pm 1}|.$$