Polarizability tensor ($p_i^{\mathrm{induced}}={\sum }_j{\alpha }_{ij}{E}_j$)

The linear response relating an induced electric dipole moment to an applied electric field. In ordinary nonresonant Raman spectroscopy, changes in its symmetric components during a normal mode determine activity. These components transform like $x^2,y^2,z^2,xy,xz,yz$.

A slender high-permittivity particle responds mainly along its axis $\mathbf{u}$, giving $\mathbf{\alpha }\simeq {\alpha }_{\parallel }\mathbf{u}{\mathbf{u}}^{\mathsf{T}}$. Far-field projection into an observation plane leaves one real polarization direction. Every nonzero output is therefore linearly polarized in this leading approximation, even for circular or unpolarized input.