Scattering matrix orientation-averaged

All the essential ingredients for calculating the average scattering matrix for a randomly oriented anisotropic dipole are now at hand. From the relations (5.50), after a good bit of algebra, we obtain... 

Thus, the orientation-averaged scattering cross-section for macroscopically isotropic and mirror-symmetric media is proportional to the sum of the squares of the absolute values of the transition matrix in the particle coordinate system. The same result holds true for an ensemble of randomly oriented particles illuminated by a linearly polarized plane wave. 

Despite the derivation of simple analytical formulas, the above analysis shows that the orientation-averaged extinction and scattering cross-sections for macroscopically isotropic and mirror-symmetric media do not depend on the polarization state of the incident wave. The orientation-averaged extinction and scattering cross-sections are invariant with respect to rotations and translations of the coordinate system and using these properties, Mishchenko et al. [169] have derived several invariants of the transition matrix. 

For macroscopically isotropic media, the orientation-averaged scattering matrix has sixteen nonzero elements (cf. (1.113)) but only ten of them are independent. For macroscopically isotropic and mirror-symmetric media, the orientation-averaged scattering matrix has a block-diagonal structure (cf. (1.114)), so that only eight elements are nonzero and only six of them are independent. In this case we determine the six quantities Sei3 9) ),... 

The Fortran code SCSMTM for computing the T-matrix of a sphere cluster and the orientation-averaged scattering matrix and optical cross-... 

N.G. Khlebtsov, Orientational averaging of light-scattering observables in the T-matrix approach, Appl. Opt. 31, 5359 (1992)... 

Figure 14. Extinction and scattering spectra for ballistic RF aggregates with different conjugate numbers N = 1-100. All data are averaged over random orientations (T-matrix method) without statistical averaging. Parameters of conjugates are the shell thickness and refractive index s = 2.5 nm, =1.40, respectively, the gold core diameter <7 =15 nm (a,b) and 60 nm (c,d).

It must be remembered that, when examining or describing the effects of fibre additions, changes in SFRC properties are always expressed in terms of average fibre content. It is implicitly assumed that the fibres are uniformly distributed throughout the matrix, and, moreover, that they are randomly oriented. Unfortunately, neither assumption is likely to be correct after the SFRC has been placed and compacted by vibration [23], and this leads not only to a considerable amount of scatter in the test data, but also to a considerable variability in measured values due to the direction of loading (in relation to the direction of casting). 

In this section we review the general properties of the transition matrix such as imitarity and symmetry and discuss anafjdical procedures for averaging scattering characteristics over particle orientations. These procedures... 

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