## Abstract

The discrete-dipole approximation is applied to vector diffraction analysis in a system with large-numerical-aperture (NA) optics and subwavelength targets. Distributions of light diffracted by subwavelength dielectric targets are calculated in a solid angle that corresponds to a NA of 0.9, and their dependence on incident polarization, target shape, and target size is studied. Electric field distributions inside the target are also shown. Basic features of the vector diffraction are clearly demonstrated. This technique facilitates understanding of the vectorial effects in systems that are expected to be applied in the future to optical data storage.

© 2001 Optical Society of America

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### Equations (10)

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(1)
$${P}_{j}={\alpha}_{j}\left({E}_{\mathrm{inc},j}-\sum _{k\ne j}{A}_{\mathit{jk}}{P}_{k}\right),$$
(2)
$${E}_{\mathrm{inc},j}={E}_{0}exp(i\mathbf{k}\xb7{\mathbf{r}}_{j}-i\omega t),$$
(3)
$${A}_{\mathit{jk}}=\frac{1}{4\pi {\u220a}_{0}}\frac{exp({\mathit{ikr}}_{\mathit{jk}})}{{r}_{\mathit{jk}}}\left[{k}^{2}({\stackrel{\u02c6}{r}}_{\mathit{jk}}{\stackrel{\u02c6}{r}}_{\mathit{jk}}-{1}_{3})+\frac{{\mathit{ikr}}_{\mathit{jk}}-1}{r_{\mathit{jk}}{}^{2}}(3{\stackrel{\u02c6}{r}}_{\mathit{jk}}{\stackrel{\u02c6}{r}}_{\mathit{jk}}-{1}_{3})\right]\hspace{0.5em}\hspace{0.5em}(j\ne k),$$
(4)
$$\alpha _{j}{}^{\mathrm{CM}}=3{d}^{3}{\u220a}_{0}\frac{{\u220a}_{j}-{\u220a}_{0}}{{\u220a}_{j}+2{\u220a}_{0}},$$
(5)
$$\alpha _{j}{}^{\mathrm{LDR}}=\frac{\alpha _{j}{}^{\mathrm{CM}}}{1+(\alpha _{j}{}^{\mathrm{CM}}/{d}^{3})[({b}_{1}+n_{j}{}^{2}{b}_{2}+n_{j}{}^{2}{b}_{3}S)(\mathit{kd}{)}^{2}-(2/3)i(\mathit{kd}{)}^{3}]},\hspace{1em}\hspace{1em}S=\sum _{j=1}^{3}({\stackrel{\u02c6}{a}}_{j}\stackrel{\u02c6}{e}_{j}{}^{2}),$$
(6)
$$\sum _{k=1}^{N}{A}_{\mathit{jk}}{P}_{k}={E}_{\mathrm{inc},j},$$
(7)
$${e}_{\mathrm{local}}\equiv \frac{|A\times P-{E}_{\mathrm{inc}}|}{|{E}_{\mathrm{inc}}|}\u2a7d5\times {10}^{-5},$$
(8)
$${E}_{\mathrm{far}}(\mathbf{r})=\frac{1}{4\pi {\u220a}_{0}}\frac{{k}^{2}exp(\mathit{ikr})}{r}\sum _{j=1}^{N}exp(-\stackrel{\u02c6}{\mathit{ikr}}\xb7{\mathbf{r}}_{j})\times (\stackrel{\u02c6}{r}\stackrel{\u02c6}{r}-{1}_{3}){P}_{j},$$
(9)
$${E}_{j}={P}_{j}/{\alpha}_{j}.$$
(10)
$${e}_{\mathrm{far}}\equiv \frac{\iint |{E}_{\mathrm{far}}-{E}_{\mathrm{ref}}{|}^{2}\mathrm{d}\alpha \mathrm{d}\beta}{\iint |{E}_{\mathrm{ref}}{|}^{2}\mathrm{d}\alpha \mathrm{d}\beta},$$