Two-photon excited fluorescence spectroscopy

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Abstract
The intensities of two‐photon excited fluorescence (TPEF) experiments are derived by the density matrix formalism for a symmetric top molecule. Although we only consider systems under collision‐free conditions and unpolarized ground state, this treatment can be extended to incorporate collisional relaxation processes and polarized ground state. The two‐photon excitation and the fluorescence detection operators are resolved into their irreducible tensor components. For an identical‐frequency two‐photon absorption, the two‐photon excitation operator can be decomposed into a scalar and a quadrupole part. The scalar operator only prepares the population of the excited state density matrix ρe. The quadrupole operator can prepare ρe into monopole through hexadecapole polarizations. In addition to these two sources, a mixed term which combines the scalar and the quadrupole operator can propare ρe into a quadrupole polarization for the Q rotational branch of ΔK=0 two‐photon transitions for linearly polarized light. In two‐photon absorption experiments which only detect the population of ρe, the mixed term cannot be probed. Since the fluorescence detection operator detects the population, orientation and alignment of ρe, the fluorescence intensities in irreducible tensor operator representation can be put into a condensed form that clearly describes all the polarization and angular momentum dependences.