Ying-Nan Chiu, "General Orientation Dependence of Rayleigh and Raman Scattering and Scattering by Linear Molecules in Arbitrary Electronic States*," J. Opt. Soc. Am. 60, 607-620 (1970)
Modern angular-momentum techniques are used to study a few refined aspects of the conventional Raman effect—aspects not easily accessible in the old days of Placzek, who used mainly direction cosines and circular coordinates. The intensity at an arbitrary direction of observation (specified by three instead of one Euler angles, ϕs,θs,ψs), of scattering by random molecular systems, has been derived. In the limit of ϕs=ψs=0, θs=π/2−Θs=Φs, it reduces to that of Placzek. The intensity of the Rayleigh and Raman scattering by uniformly oriented molecules (in solid matrices or in molecular crystals) has also been derived. It is illustrated for oriented molecules with cylindrical symmetry. The Raman scattering by rotating linear molecules in arbitrary electronic states has been investigated. The general formulas derived are usable also in electronic Raman effects.
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Angular functions for observation of Raman-scattered light with arbitrary polarization and propagation directions. Case I: incident light X polarized.a–c
Σm{(Dm−11∓Dm11)[C2(11j; m, −1, m−1)+C2(11j; m, 1, m+1)]−[(Dm−11∓Dm11)*(Dm−2, −11∓Dm−2,11)C(11j; m, −1, m−1)×C(11j; m −2, 1, m −1)+c.c]}
For use in Eqs. (17a) and (17b). Incident light is propagated along Z. Upper sign is for IX′X(kZ′kZ), lower sign is for IY′X(kZ′kZ) (see Fig. 2).
The subscript s in φs, θs, ψs,.Θs, Φs have been omitted for brevity.
In I⊥(obs||), the parallel sign means that the observation direction lies on the plane made by the incident polarization and propagation directions. The perpendicular sign means that the polarization of the observed scattered light is perpendicular to this plane (see Fig. 1).
Table II
Angular functions for observation of Raman-scattered light with arbitrary polarization and propagation directions. Case II: incident light Y polarized.a,b
Σm{(Dm−11∓Dm11)2[C2(11j; m, −1, m−1)+C2(11j; m, 1, m+1)]+[(Dm−11∓ Dm11)*(Dm−2, −11∓Dm−2,11)C(11j; m, –1, m−1)×C(11j; m−2, 1, m−1)+c.c.]}
For use in Eqs. (18a) and (18b). Incident light is propagated along Z. Upper sign is for IX′Y(kZ′kZ), lower sign is for IY′Y(kZ′kZ), (see Fig. 2).
The subscripts s in φs, θs, ψs, Θs, and Φs, have been omitted for brevity.
In I||(obs ⊥), the perpendicular sign means that the observation direction lies on the plane perpendicular to the incident polarization direction. The parallel sign means that the polarization of the observed scattered light is parallel to the incident polarization (see Fig. 1).
Tables (2)
Table I
Angular functions for observation of Raman-scattered light with arbitrary polarization and propagation directions. Case I: incident light X polarized.a–c
Σm{(Dm−11∓Dm11)[C2(11j; m, −1, m−1)+C2(11j; m, 1, m+1)]−[(Dm−11∓Dm11)*(Dm−2, −11∓Dm−2,11)C(11j; m, −1, m−1)×C(11j; m −2, 1, m −1)+c.c]}
For use in Eqs. (17a) and (17b). Incident light is propagated along Z. Upper sign is for IX′X(kZ′kZ), lower sign is for IY′X(kZ′kZ) (see Fig. 2).
The subscript s in φs, θs, ψs,.Θs, Φs have been omitted for brevity.
In I⊥(obs||), the parallel sign means that the observation direction lies on the plane made by the incident polarization and propagation directions. The perpendicular sign means that the polarization of the observed scattered light is perpendicular to this plane (see Fig. 1).
Table II
Angular functions for observation of Raman-scattered light with arbitrary polarization and propagation directions. Case II: incident light Y polarized.a,b
Σm{(Dm−11∓Dm11)2[C2(11j; m, −1, m−1)+C2(11j; m, 1, m+1)]+[(Dm−11∓ Dm11)*(Dm−2, −11∓Dm−2,11)C(11j; m, –1, m−1)×C(11j; m−2, 1, m−1)+c.c.]}
For use in Eqs. (18a) and (18b). Incident light is propagated along Z. Upper sign is for IX′Y(kZ′kZ), lower sign is for IY′Y(kZ′kZ), (see Fig. 2).
The subscripts s in φs, θs, ψs, Θs, and Φs, have been omitted for brevity.
In I||(obs ⊥), the perpendicular sign means that the observation direction lies on the plane perpendicular to the incident polarization direction. The parallel sign means that the polarization of the observed scattered light is parallel to the incident polarization (see Fig. 1).