Spectral manifestation of coherent backscattering
In Section 3.2 we discussed how coherent backscattering affects intensity and polarization phase curves producing there brightness and polarization opposition effects. Recently it has been found that coherent backscattering also manifests itself in spectral data. It affects the depth of the absorption bands and makes it dependent on the phase angle. The physics of this is clear: since coherent backscattering produces brightness opposition effect of different steepness at different absorptions, the steepness of the opposition effect is different within and outside of the absorption bands and, thus, the absorption bands should have different depth and, most likely, shape at different phase angles. This fact was confirmed at observations of Saturn’s satellites. Their spectra have distinct ice absorption bands in the near infrared and these bands do change with phase angle (Fig. 5.6). Although this effect has been studied so far for regolith surfaces it should also exist for any medium whose light scattering is affected by coherent backscattering.
We modeled spectral manifestation of the coherent backscattering using the T-matrix code and presenting the surface of Saturn’s satellites as a large icy aggregate similar to those described in Sections 3 and shown in Fig. 3.4. Fig 5.7 presents the results of our simulations of the ice absorption band at 2.8 ^m at different size of monomers and packing density of the aggregate. One can see that the simulations correctly reproduce the observed tendencies. More so, the variations in the rate of the change of the absorption band depth and shape promise that the study of the spectra at several phase angles can serve as a new remote sensing tool to reveal properties of monomers and their arrangement in aggregates.
Fig. 5.6. Spectrum of Saturn’s icy satellite Rhea at a variety of phase angles.It is clearly seen that the depth of the absorption bands varies with phase angle as it should be in accordance with the coherent backscattering. The red dashed ellipse shows the band whose modeling is presented in Fig. 5.7.
Fig. 5.7. Simulations of the phase angle variations in the spectra of icy aggregates. Different phase angles (PA) are indicated in the left panel. The left panel is for the monomer of radius 1.0 ^m and packing 5%, the middle panel is for the same monomers but different packing, 10%, and the right panel is for the same packing as the middle one but for smaller monomers, r= 0.85 ^m. In all cases the overall size of the aggregate is 14 ^m.
Circular polarization of the light scattered by aggregates
Circular polarization was observed in the light scattered by the dust in comets (Rosenbush et al., 2007) and molecular clouds (Hough et al., 2001). It is well known that circular polarization manifests violation of mirror symmetry in the medium. Van de Hulst (1957) showed (see his Section 5.22) that circular polarization arises when the medium has unequal number of left-handed and right-handed identical but mirror asymmetric particles. This immediately shows that if we consider light scattering by a single aggregate, let say BPCA or BCCA, then even in the case of random orientation of this aggregate its circular polarization does not vanish as the majority of ballistic aggregates are asymmetric (Fig. 5.1). This was repeatedly shown by computer simulations of light scattering by aggregates (Kolokolova et al., 2006; Guirado et al., 2007). However, ensembles of natural aggregates, such as cosmic dust, usually do not have domination of particles of a specific handiness. So, in the case when some ensemble of natural aggregates demonstrates circular polarization, it has another violation of mirror symmetry than that resulted from the asymmetric arrangement of the monomers in the aggregates.
One of the most common violations is alignment of elongated particles (e.g., in magnetic field). This is a very common situation for cosmic dust and numerous papers on alignment of aggregates and their circular polarization have been published (see reviews by Lazarian, 2007; 2009 and reference therein). One more opportunity for mirror asymmetry of aggregates is optical activity of their material. Optical activity is typical for organics of biological origin due to the homochirality of their molecules (i.e. domination of left handed amino acids and right handed sugars). Recently the T-matrix code by Mackowski & Mishchenko (1996) has been updated to allow accounting for the optical activity of the monomer material (Mackowski et al., 2011). Below we show some results of the computer modeling based on this code.
To avoid the influence of mirror asymmetry of the aggregate itself, described above, we performed the calculations for a completely symmetric aggregate like a cube of spheres or 3D-cross. The optical activity was described by a complex parameter p=pr+ipi that demonstrated the difference in the complex refractive index for the light with left-handed and right-handed polarization; here Pr described the circular birefringence of the material and pi described its circular dichroism. The code correctly predicted the equal but opposite sign of the circular polarization in the case of aggregates of the opposite sign of p. The modeling by Kolokolova et al. (2011b) showed that the circular polarization quickly increased with increasing optical activity, size of monomers, and especially size of the aggregate. An interesting result was a strong dependence of the circular polarization on the packing density of the aggregates. Fig. 5.8 shows that the circular polarization is much larger and increases more quickly with the size of aggregate in the case when the aggregate is more compact. This probably demonstrates an increasing influence of the diffuse multiple scattering as the aggregate becomes larger or more compact, and more monomers are involved in the light scattering.
Fig. 5.8. Dependence of absolute values of circular polarization on the size of a 3D-cross aggregate (left) and cubic aggregate (right). The radius of the monomers is 50 nm; the wavelength is 650 nm. The dashed line is for a single monomer; solid lines are for the aggregates of 9, 125, and 343 monomers (thickness of the line increases with the number of monomers). In the simulations we used m=1.55002+i0.0006002 andfi=7.034*10-6-i*0.8692*10-8 which were estimated based on the measured excess of left-handed amino acids in some meteorites (Pizzarello & Cronin, 2000; Pizzarello & Cooper, 2001).
It is evident that diffuse multiple scattering can affect circular polarization because at each consequent scattering on an optically active monomer circular polarization should increase. This effect is opposite to the depolarization of linearly polarized light in a result of multiple scattering. Linear polarization depends on the plane in which the scattering happens, and at multiple scattering this plane changes randomly thereby randomizing the resultant polarization (see Section 3.1). Orientation of the scattering plane does not affect circular polarization, and its formation is determined only by the fact that the light repeatedly interacts with optically-active scatterers. Since the cubic aggregate shown in Fig. 5.8 represents the case of a densely packed aggregate, we expect that its light scattering is also affected by near-field effects. How near-field effects influence circular polarization is a topic of a separate study that still needs to be done.
Conclusions
We have briefly described a progress recently made in the understanding and modeling of a variety of physical effects associated with electromagnetic interaction between constituent scatterers in a complex object such as an inhomogeneous particle or an aggregate of small monomers. Our test objects were aggregates as a common example of natural particles. In the case when such aggregates are made of particles much smaller than wavelength, effective medium theories can be applied to study their light scattering. However, natural, especially cosmic, particles are aggregates of monomers larger than wavelength when observed in the visible spectral range. Their light scattering requires a more sophisticated approach. We showed that with increasing packing density of aggregates interaction of their monomers becomes more complex and involves diffuse multiple scattering, coherent scattering, and, at even larger packing densities, near-field effects. The diffuse multiple scattering simplifies dependencies of intensity and polarization on phase angle reducing the resonant oscillations typical for single scattering by particles of size larger than wavelength. In its turn, coherent scattering complicates the phase curves adding brightness and polarization opposition feature in the backscattering domain. Development of these features becomes even more complex when the packing density increases and near-field effects become not negligible. The near-field effects affect all phase angles, changing value and location of both the polarization minimum and maximum as well as behavior of the intensity. The correct accounting for all these effects is possible by using rigorous solutions of the Maxwell equations for complex objects. In the case of aggregates, such a solution is provided by the superposition T-matrix approach (Mackowski & Mishchenko, 1996). We use this approach to simulate properties of large aggregates. This allows us not only to study all types of interaction separately and find conditions for their realization, but also to interpret the observational data for cosmic dust. The T-matrix modeling provides: (1) explanation of specifics of phase dependencies of intensity and polarization for cometary and other cosmic dust; (2) explanation of spectral dependence of polarization for comets and asteroids and its variations with wavelength; (3) explanation of variations in depth of spectral bands observed for Saturn’s satellites; (4) study of circular polarization of light scattered by objects of biological interest. This modeling also allows us to reveal the characteristics of dust particles in a variety of natural environments thereby validating it as a powerful tool for remote sensing applications.
