## Abstract

It is demonstrated that the occurence of backscattered polarization patterns relates to the conservation of angular momentum of light. Using the geometrical phase formalism in the spin space, we develop a model where the helicity-maintaining and the helicity-flipping multiple-scattering processes can be accounted for. The model explains practically all the symmetries present in the spatially resolved Mueller matrices.

© 2008 Optical Society of America

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### Equations (15)

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(1)
$${\mathbf{E}}_{i}={E}_{L}\widehat{L}+{E}_{R}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left(i\delta \right)\widehat{R},$$
(2)
$${E}_{s}={E}_{L}{A}_{L}(r,\varphi )\mathrm{exp}\left[i{\psi}_{L}(r,\varphi )\right]\mathrm{exp}(-i2\varphi )\widehat{L}$$
(3)
$$+{E}_{R}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left(i\delta \right){A}_{R}(r,\varphi )\mathrm{exp}\left[i{\psi}_{R}(r,\varphi )\right]\mathrm{exp}\left(i2\varphi \right)\widehat{R},$$
(4)
$$I=\u27e8{\left[{E}_{L}{A}_{L}(r,\varphi )\right]}^{2}+{\left[{E}_{R}{A}_{R}(r,\varphi )\right]}^{2}\u27e9,$$
(5)
$$Q=\u27e82\phantom{\rule{0.2em}{0ex}}\mathrm{Re}\left[{E}_{L}{E}_{R}{A}_{L}(r,\varphi ){A}_{R}(r,\varphi )\mathrm{exp}[i{\psi}_{L}(r,\varphi )-i{\psi}_{R}(r,\varphi )-i\delta ]\mathrm{exp}(-i4\varphi )\right]\u27e9,$$
(6)
$$U=-\u27e82\phantom{\rule{0.2em}{0ex}}\mathrm{Im}\left[{E}_{L}{E}_{R}{A}_{L}(r,\varphi ){A}_{R}(r,\varphi )\mathrm{exp}[i{\psi}_{L}(r,\varphi )-i{\psi}_{R}(r,\varphi )-i\delta ]\mathrm{exp}(-i4\varphi )\right]\u27e9,$$
(7)
$$V=\u27e8{\left[{E}_{L}{A}_{L}(r,\varphi )\right]}^{2}-{\left[{E}_{R}{A}_{R}(r,\varphi )\right]}^{2}\u27e9.$$
(8)
$$I=({E}_{L}^{2}+{E}_{R}^{2}){A}^{2}\left(r\right),$$
(9)
$$Q=\u27e82\phantom{\rule{0.2em}{0ex}}\mathrm{Re}\left[{E}_{L}{E}_{R}{A}^{2}\left(r\right)\mathrm{exp}(-i4\varphi )\right]\u27e9=2{E}_{L}{E}_{R}{A}^{2}\left(r\right)\mathrm{cos}(4\varphi +\delta ),$$
(10)
$$U=-\u27e82\phantom{\rule{0.2em}{0ex}}\mathrm{Im}\left[{E}_{L}{E}_{R}{A}^{2}\left(r\right)\mathrm{exp}(-i4\varphi )\right]\u27e9=2{E}_{L}{E}_{R}{A}^{2}\left(r\right)\mathrm{sin}(4\varphi +\delta ),$$
(11)
$$V=({E}_{L}^{2}-{E}_{R}^{2}){A}^{2}\left(r\right).$$
(12)
$$\left(\begin{array}{cc}\hfill {E}_{L}^{\left(s\right)}\hfill & \hfill (r,\varphi )\hfill \\ \hfill {E}_{R}^{\left(s\right)}\hfill & \hfill (r,\varphi )\hfill \end{array}\right)=\sqrt{\u27e8{A}^{2}\left(r\right)\u27e9}\left[\begin{array}{cc}\hfill a\left(r\right)\mathrm{exp}(-i2\varphi )\hfill & \hfill (1-a\left(r\right))\hfill \\ \hfill (1-a\left(r\right))\hfill & \hfill a\left(r\right)\mathrm{exp}\left(i2\varphi \right)\hfill \end{array}\right]\left(\begin{array}{c}\hfill {E}_{L}^{\left(i\right)}\hfill \\ \hfill {E}_{R}^{\left(i\right)},\hfill \end{array}\right)$$
(13)
$$a=1-\frac{b-\sqrt{b-{b}^{2}}}{2b-1}.$$
(14)
$$p\left(\Omega \right)=\frac{\mathrm{exp}(-{k}^{2}\u22152)}{2\pi}+\frac{k\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(\Omega \right)}{\sqrt{2\pi}}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}[-\frac{{k}^{2}\phantom{\rule{0.2em}{0ex}}{\mathrm{sin}}^{2}\left(\Omega \right)}{2}]\Phi \left[k\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(\Omega \right)\right],$$
(15)
$$\Phi \left(z\right)=\frac{1}{\sqrt{2\pi}}{\int}_{-\infty}^{z}\mathrm{exp}(-\frac{{y}^{2}}{2})\mathrm{d}y.$$