Interaction of Hermite–Gaussian Beams with a Macroscopic Atomic Target

A theoretical analysis is presented on the photoexcitation of a macroscopic atomic target by a Hermite–Gaussian (HG) beam within the framework of density matrix theory. Special emphasis is paid to the influence of the incoming HG mode on the population of an excited state and the emitted fluorescence radiation. In particular, a general expression for the alignment parameter of the excited state is derived, which depends on the beam parameters of the HG mode. Although the developed theory can be applied to any atomic system, here the electric dipole transition $3s{}^2{S}_{1/2}\to 3p{}^2{P}_{3/2}$ in neutral sodium atoms is investigated when driven by three ${\mathrm{HG}}_{10}$, ${\mathrm{HG}}_{01,}$ and ${\mathrm{HG}}_{11}$ modes. For this optical (valence-shell) excitation, it is demonstrated that the population of the excited state is sensitive to the beam waist and the mode index of the HG beam. Furthermore, the influence of beam parameters on the angular distribution and linear polarization of the emitted fluorescence radiation is discussed.