Light scattering by dielectric bodies in the Born approximation

Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with sharp boundaries. The Green's function for a two-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for a scattered field of two parallel cylinders. The polar diagram is shown to agree with the numerical calculation by the known methods of discrete dipoles and boundary elements.

Figure 1

Domains of integration ${\mathcal{D}}^{+}$ and ${\mathcal{D}}^{-}$ for Eq. (3). The boundary of ${\mathcal{D}}^{-}$ consists of $\gamma =\partial {\mathcal{D}}^{+}$ (solid line) and the external infinitely remote contour $\mathrm{\Gamma }$ (dashed line). Arrows indicate external normals $\mathbf{n}$ to $\partial {\mathcal{D}}^{-}$.

Figure 2

Scheme of $p$-wave scattering by two parallel cylinders. The dielectric permittivity and the radius are indicated in the first (left) and second (right) cylinders. The external infinitely remote contour $\mathrm{\Gamma }$ is not shown.

Figure 3

Polar diagram of scattering by a pair of equal dielectric cylinders at $a=b=0.1\mu \mathrm{m}, {\varepsilon }_p=\varepsilon =2.25$, and $R=0.3\mu \mathrm{m}$ at incidence angle $\alpha =-\pi /4$, wavelength $\lambda =1.5\mu \mathrm{m}$, and distance between the observation point and the center of the first cylinder $r=2\lambda$. First Born approximation (dotted line), second Born approximation (dashed line), and BEM (solid line).

Figure 4

Polar diagram of the scattered field with the same parameters as in Fig. 3: third Born approximation (dotted line), BEM (solid line), and DDA (dashed line). Inset: Magnifcation of the area of the main plot indicated by the box.

Figure 5

Right: Cross section of an infinite cylinder in homogeneous space. The green circle indicates the observation point $\mathbf{r}=(x,y)$. Left: $p$ polarization.