Far-infrared and Raman vibrational transitions of a solid sphere: Selection rules

Spherical Growth and Surface-Quasifree Vibrations of Si Nanocrystallites in Er-Doped Si Nanostructures

“…Their eigenfrequencies are characterized by two quantum numbers of l and n. The spheroidal mode of l 0 is purely radial with spherical symmetry. It produces totally polarized spectra and thus can easily be observed in the low-frequency Raman spectra according to the section rules [26]. Currently, these Raman peaks should be from the contribution of a spheroidal mode with l 0 and n 0.…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…For m ± 1 it follows in the described setup (normal incidence, n F P = 1) 91) or in the frequency domain 92) with ν being the velocity of light in vacuum.…”

“…Such modes don't cause inelastic light scattering, only spheroidal modes, where the displacement is also (or fully) radial, contribute to the light scattering spectrum. [52,92,93] By chosing only the spheroidal modes out of the simulated eigenmodes, those with higher l are easily obtained from the FEM results. Checking the displacement and the deformation in the intersecting planes as in Fig.…”

“…[83] Due to selection rules only two distinct vibration eigenmodes contribute to the RS of spherical particles with diameter (d) much smaller than the wavelength of the probing light (d ≪ λ). [92] For bigger spheres with d ∼ λ, Brillouin light scattering (BLS) in the GHz-range becomes the technique of choice. [32,45,46] Due to the consideration of higher-order terms in the electric multipole expansion and of retardation effects, [52,93] BLS can resolve a multitude of eigenmodes.…”

Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

“…However, it does not correlate to whether the mode is SPH L or SPH T except at high enough η. URS is an interesting quantity because it is the one we have to monitor for the surface deformation mechanism except for ℓ = 0 modes. Group theoretical arguments 7 show that only SPH modes with ℓ=0 and ℓ=2 are Raman active. This assumes that the nanoparticle is perfectly spherical in shape and spherically symmetric in all of its properties.…”