## Abstract

A theoretical and numerical investigation is devised for resonant light scattering of an off-axis normally incident Gaussian beam by two parallel nonabsorbing cylinders based on the related beam theory developed in J. Opt. Soc. Am. A **14**, 640 (1997). By varying the half-beam width, we show that the multireflection process between the two scatterers can be minimized. Moreover, the study is an attempt to understand the underlying physics present in the process of resonance excitation by evanescent wave coupling.

© 2002 Optical Society of America

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### Equations (27)

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(1)
$${\mathbf{E}}_{z}={E}_{0}exp\{-{w}_{0}^{-2}[(y-{y}_{0}{)}^{2}+(z-{z}_{0}{)}^{2}]\}exp[{\mathit{ik}}_{x}(x-{x}_{0})]{\stackrel{\u02c6}{u}}_{z},$$
(2)
$${\mathbf{E}}_{\mathrm{inc}}={E}_{x}{\stackrel{\u02c6}{u}}_{x}+{E}_{z}{\stackrel{\u02c6}{u}}_{z}.$$
(3)
$${\psi}_{i}^{j}={\int}_{-\infty}^{+\infty}\mathrm{d}{k}_{z}\sum _{\mathit{in}=-\infty}^{\infty}{F}_{n}^{j}{A}_{n}^{j}({k}_{z}){Z}_{n}(\rho ({k}_{i}^{2}-{k}_{z}^{2}{)}^{1/2})exp(\mathit{in}\varphi )exp({\mathit{ik}}_{z}z),$$
(4)
$${A}_{n}(h)\approx \frac{1}{4\pi {s}^{2}(1-{h}^{2})}exp\left(-\frac{{h}^{2}}{4{s}^{2}}\right){\int}_{-\infty}^{+\infty}\mathrm{d}{h}_{y}\times exp\left[-\left(\frac{{h}_{y}^{2}}{4{s}^{2}}+{\mathit{qh}}_{y}\right)\right],$$
(5)
$${A}_{n}(h)\approx \frac{1}{2{\pi}^{1/2}s(1-{h}^{2}{)}^{1/2}}\times exp\left\{-{s}^{2}{\left[{k}_{0}{y}_{0}+\frac{n}{(1-{h}^{2}{)}^{1/2}}\right]}^{2}-\frac{{h}^{2}}{4{s}^{2}}\right\}.$$
(6)
$${n}_{max}=-{k}_{0}{y}_{0}(1-{h}^{2}{)}^{1/2}-\frac{h(1-{h}^{2}{)}^{1/2}}{2{s}^{2}}.$$
(7)
$${A}_{{n}_{max}}(h)=\frac{1}{2{\pi}^{1/2}s(1-{h}^{2})}.$$
(8)
$${A}_{n}(h)\approx \frac{{A}_{{n}_{max}}(h)}{2}=\frac{1}{4{\pi}^{1/2}s(1-{h}^{2})}.$$
(9)
$${n}_{\mathrm{bl}}={n}_{\mathrm{nor}}-\frac{h}{2{s}^{2}},$$
(10)
$$h=2{s}^{2}({n}_{\mathrm{nor}}-{n}_{\mathrm{bl}}).$$
(11)
$$\mathbf{S}=\frac{1}{2}[({E}_{z}{H}_{y}^{*}){\stackrel{\u02c6}{u}}_{x}+({E}_{z}{H}_{x}^{*}-{E}_{x}{H}_{z}^{*}){\stackrel{\u02c6}{u}}_{y}+({E}_{x}{H}_{y}^{*}){\stackrel{\u02c6}{u}}_{z}].$$
(12)
$${E}_{z}{H}_{y}^{*}=\frac{{F}^{2}{E}_{0}^{2}}{\omega}\left[-\frac{2i\delta ({k}_{x})}{{\mu}_{0}{w}_{0}^{2}}+\frac{i4(z-{z}_{0}{)}^{2}\delta ({k}_{x})}{{\mu}_{0}{w}_{0}^{4}}-\frac{{k}_{x}exp(-{\mathit{ik}}_{x}x)}{{\mu}_{0}}\right]exp({\mathit{ik}}_{x}x),$$
(13)
$${E}_{z}{H}_{x}^{*}=\frac{{F}^{2}{E}_{0}^{2}}{\omega}\left[-\frac{i(y-{y}_{0})}{{\mu}_{0}{w}_{0}^{2}}\right],$$
(14)
$${E}_{x}{H}_{z}^{*}=\frac{{F}^{2}{E}_{0}^{2}}{\omega}\left[-\frac{8i(z-{z}_{0}{)}^{2}(y-{y}_{0})}{{\mu}_{0}{w}_{0}^{6}}\right]exp(-{\mathit{ik}}_{x}x),$$
(15)
$${E}_{x}{H}_{y}^{*}=\frac{{F}^{2}{E}_{0}^{2}}{\omega}\delta ({k}_{x})(z-{z}_{0})\times \left[-\frac{4i\delta ({k}_{x})}{{\mu}_{0}{w}_{0}^{4}}+\frac{8i(z-{z}_{0}{)}^{2}\delta ({k}_{x})}{{\mu}_{0}{w}_{0}^{6}}-\frac{{k}_{x}exp(-{\mathit{ik}}_{x}x)}{{w}_{0}^{2}{\mu}_{0}}\right],$$
(16)
$${\mathbf{S}}_{{w}_{0}\to \infty}=\frac{1}{2}({E}_{z}{H}_{y}^{*}){\stackrel{\u02c6}{u}}_{x}=\frac{{k}_{0}{E}_{0}^{2}}{2\omega {\mu}_{0}}{\stackrel{\u02c6}{u}}_{x},$$
(17)
$${E}_{\mathrm{total},z}={E}_{\mathrm{inc},z}+{E}_{\mathrm{scatt}\hspace{0.5em}\mathrm{pump},z}+{E}_{\mathrm{scatt}\hspace{0.5em}\mathrm{probe},z}.$$
(18)
$${H}_{l}({\rho}_{2}{\tilde{k}}_{0})exp(\mathit{il}{\varphi}_{2})=\sum _{q=-\infty}^{\infty}{Z}_{q-l}(d{\tilde{k}}_{0}){Y}_{q}({\rho}_{1}{\tilde{k}}_{0})exp(\mathit{iq}{\varphi}_{1}),$$
(19)
$$\sum _{k=-\infty}^{\infty}\left[{\delta}_{n,k}-{T}_{n}^{{O}_{2}}\sum _{q=-\infty}^{\infty}{i}^{(k-n)}{T}_{q}^{{O}_{1}}{H}_{k-n}^{(1)}(d{\tilde{k}}_{0})\times {H}_{q-n}^{(1)}(d{\tilde{k}}_{0})\right]{A}_{k,{O}_{2}}^{s,\mu}$$
(20)
$$={T}_{n}^{{O}_{2}}{A}_{n,{O}_{2}}^{\mu}+{T}_{n}^{{O}_{2}}\sum _{q=-\infty}^{\infty}{i}^{q-n}{T}_{q}^{{O}_{1}}{A}_{q,{O}_{1}}^{\mu}{H}_{q-n}^{(1)}(d{\tilde{k}}_{0})$$
(21)
$$\times exp[{\mathit{ik}}_{0}h({z}_{1}-{z}_{2})],$$
(22)
$${T}_{n}^{{O}_{i}}=2{\mathit{iD}}_{i}^{1}{\left\{{u}_{i}^{2}\pi [{H}_{n}({u}_{i}){]}^{2}\left[{D}_{i}^{1}{D}_{i}^{2}-(\mathit{nh}{)}^{2}\times {\left(\frac{1}{{u}_{i}^{2}}-\frac{1}{{v}_{i}^{2}}\right)}^{2}\right]\right\}}^{-1}-\frac{{J}_{n}({u}_{i})}{{H}_{n}({u}_{i})},$$
(23)
$${D}_{i}^{1(2)}=\frac{{H}_{n}^{\prime}({u}_{i})}{{u}_{i}{H}_{n}({u}_{i})}-\frac{{\mu}_{i}}{{\mu}_{0}}\left(\frac{{\u220a}_{i}}{{\u220a}_{0}}\right)\frac{{J}_{n}^{\prime}({v}_{i})}{{v}_{i}{J}_{n}({v}_{i})},$$
(24)
$$\mathrm{\Delta}y\sim a{\left(\frac{2\pi}{\beta}\right)}^{2/3}.$$
(25)
$$|{A}_{n}^{s,\mu}(\beta ){|}^{2}\approx C\frac{({\mathrm{\Gamma}}_{n}^{\mu}{)}^{2}}{(\beta -{\beta}_{n}^{\mu}{)}^{2}+({\mathrm{\Gamma}}_{n}^{\mu}{)}^{2}}+\tilde{P}(\beta ),$$
(26)
$${S}_{i}^{z}(\rho )=\frac{1}{2\pi {S}_{\mathrm{inc}}}{\int}_{0}^{2\pi}\mathrm{d}\varphi |{E}_{i}^{z}{|}^{2},$$
(27)
$$\mathrm{\Delta}{N}_{\mathrm{probe}}=-\mathrm{\Delta}a\frac{{N}_{\mathrm{probe}}}{a}.$$