## Abstract

Results are presented of the predictions of Mie’s series solution to the scattering of an electromagnetic plane wave from a dielectric sphere of index 1.333. Cases of size parameters near 200 and 500 are examined in detail in an attempt to understand the mechanism responsible for the backscattering of light. These calculations demonstrate that the backscattering is due mainly to the last few significant terms in the Mie expansion, which can be associated with geometrical rays grazing the droplet surface, or “surface waves.” Sharp periodic spikes in the dependence of the backscattered intensity are shown to be associated with very slightly damped surface waves of both polarizations involving hundreds of circumvolutions. The geometrically computed axial contribution to the backscattered light is shown to be present in the Mie results.

© 1966 Optical Society of America

Full Article |

PDF Article
### Equations (9)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$\begin{array}{c}{I}_{\text{axial}}=\left[R{x}^{2}/2{\left(2-n\right)}^{2}\right]\\ \phantom{\rule{1em}{0ex}}\times \left[\left({n}^{2}-2n+2\right)+n\left(2-n\right)\phantom{\rule{0.2em}{0ex}}\text{cos}4nx\right],\end{array}$$
(2)
$$\begin{array}{l}{I}_{1}\left(90\xb0\right)=0.053{x}^{2}/4\\ {I}_{2}\left(90\xb0\right)=0.003{x}^{2}/4.\end{array}$$
(3)
$$S\left(0\xb0\right)=\alpha \left(1+{A}^{4}+{A}^{8}+{A}^{12}+\dots \right)+B,$$
(4)
$$S\left(0\xb0\right)=\alpha /\left(1-{A}^{4}\right)+B.$$
(5)
$$Q={Q}_{0}+\left(4\alpha /{x}^{2}\right)\phantom{\rule{0.2em}{0ex}}\left(\frac{1-a\phantom{\rule{0.2em}{0ex}}\text{cos}\varphi}{1+{a}^{2}-2a\phantom{\rule{0.2em}{0ex}}\text{cos}\varphi}\right),$$
(6)
$$Q\left(\varphi \right)=\frac{{C}_{1}}{1+{\left(\varphi /g\right)}^{2}}+{C}_{2},$$
(7)
$$S\left(180\xb0\right)=\alpha {A}^{2}/\left(1-{A}^{4}\right)+D,$$
(8)
$$\begin{array}{c}I\left(180\xb0\right)=\frac{{\left(\alpha /g\right)}^{2}}{1+{\left(\varphi /g\right)}^{2}}\\ \phantom{\rule{1em}{0ex}}\times \left[1+\left(2/\alpha \right)\phantom{\rule{0.2em}{0ex}}\left(\pm g\phantom{\rule{0.2em}{0ex}}\text{Re}D+\varphi \phantom{\rule{0.2em}{0ex}}\text{Im}D\right)\right]+{D}^{2}.\end{array}$$
(9)
$$S\left(90\xb0\right)=\delta \left(A+{A}^{3}+{A}^{5}+\dots \right)+E.$$