Scattering of scalar light fields from collections of particles

Using the angular spectrum representation of fields and the first Born approximation we develop a theory of scattering of scalar waves with any spectral composition and any correlation properties from collections of particles which have either deterministic or random distributions of the index of refraction and locations. An example illustrating the far-field intensity and the far-field spectral degree of coherence produced on scattering of a model field from collections of several particles with Gaussian potentials is considered.

Figure 1

Notation relating to the scattering of two correlated plane waves from a collection of particles.

Figure 2

(Color online) The coordinates of the particles (a) $(0,0,1m)$; (b) $(0,3\times {10}^{-7}m,1m)$, $(0,-3\times {10}^{-7}m,1m)$; (c) $(0,0,1m)$, $(0,3\times {10}^{-7}m,1m)$, $(0,-3\times {10}^{-7}m,1m)$, $(3\times {10}^{-7}m,0,1m)$, $(-3\times {10}^{-7}m,0,1m)$; (d) $(0,0,1m)$, $(0,3\times {10}^{-7}m,1m)$, $(0,-3\times {10}^{-7}m,1m)$, $(3\times {10}^{-7}m,0,1m)$, $(-3\times {10}^{-7}m,0,1m)$, $(0,0,1+3\times {10}^{-7}m)$, $(0,3\times {10}^{-7}m,1+3\times {10}^{-7}m)$, $(0,-3\times {10}^{-7}m,1+3\times {10}^{-7}m)$, $(3\times {10}^{-7}m,0,1+3\times {10}^{-7}m)$, $(-3\times {10}^{-7}m,0,1+3\times {10}^{-7}m)$.

Figure 3

Contours of the spectral density of the far field produced by scattering of two correlated plane waves on particles with Gaussian potential. The parameters $\sigma$ and $\Delta$ are kept fixed: $k\sigma =1$, $k\Delta =1$, (a) one particle; (b) two particles; (c) five particles; (d) ten particles.

Figure 4

Contours of the spectral density of the far field produced by scattering of two correlated plane waves on two particles with Gaussian potential. The parameter $\Delta$ is kept fixed: $k\Delta =1$, (a) $k\sigma =3$, (b) $k\sigma =1.5$, (c) $k\sigma =0.9$, (d) $k\sigma =0.5$.

Figure 5

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on two particles with Gaussian potential. The parameter $\sigma$ is kept fixed: $k\sigma =1$, (a) one particle, $k\Delta =10$; (b) one particle, $k\Delta =0.1$; (c) two particles, $k\Delta =10$; (d) two particles, $k\Delta =0.1$.

Figure 6

(Color online) Modulus of the spectral degree of coherence of the far field as a function of ${\theta }_d={\theta }_2-{\theta }_1$, where ${\theta }_1=0$, produced by scattering of two correlated plane waves, (a) on different number of particles ($k\sigma =1$, $k\Delta =1$); (b) on five particles, for different $\sigma$ values $(k\Delta =1)$; (c) on five particles, for different $\Delta$ values $(k\sigma =1)$.