On the effects of permanent molecular dipoles in the simultaneous absorption of two photons: full generalized rotating wave approximation versus analytical results

Three-Photon Spectroscopy of Porphyrins

Recent advances in laser technology have made three-photon (3P) microscopy a real possibility, raising interest in the phenomenon of 3P absorption (3PA). Understanding 3PA of organic chromophores is especially important in view of those imaging applications that rely on exogenous probes, whose optical properties can be manipulated and optimized. Here, we present measurements and theoretical analysis of the degenerate 3PA spectra of several phosphorescent metalloporphyrins, which are used in the construction of biological oxygen probes. The effective 3PA cross sections (σ⁽³⁾) of these porphyrins near 1700 nm, a new promising biological optical window, were found to be on the order of 1000 GM3 (1 GM3 = 10^-83 cm⁶ s²), therefore being among the highest values reported to date for organic chromophores. To interpret our data, we developed a qualitative four-state model specific for porphyrins and used it in conjunction with quantitative analysis based on the time-dependent density functional theory (TDDFT)/a posteriori Tamm-Dancoff approximation (ATDA)/sum-over-states (SOS) formalism. The analysis revealed that B (Soret) state plays a key role in the enhancement of 3PA of porphyrins in the Q band region, while the low-lying two-photon (2P)-allowed gerade states interfere negatively and diminish the 3PA strength. This study features the first systematic examination of 3PA properties of porphyrins, suggesting ways to improve their performance and optimize them for imaging and other biomedical applications.

Bloch-Siegert effects in two-photon excitations: Fixed laser-molecule configurations versus orientational averaging

The two-level rotating wave approximation for two-photon excitations in dipolar molecules is modified to include the effects of the Bloch-Siegert shift in the two-photon resonance energy. The resulting analytical results are used to establish a criterion for when Bloch-Siegert effects are important and the relevance of these effects are compared for fixed laser-molecule configurations versus orientationally averaged results. Two-level model molecules, with parallel permanent and transition dipoles, are used in this work and the effects of Bloch-Siegert shifts are discussed for resonance profiles, time-dependent populations of the excited state, and time-averaged excitation rates. Bloch-Siegert shifts can have pronounced effects on resonance energies and the shape of resonance profiles and, for example, on the magnitudes and the temporal locations of the maxima in the temporal evolution of the time-dependent properties of the system.

One- and two-photon absorption in solution: the effects of a passive auxiliary beam

The efficiencies of one- and two-photon absorption by chromophores in solution may be significantly modified by a sufficiently intense beam of off-resonant light. A molecular analysis based on quantum electrodynamics (QED) fully accounts for this phenomenon of laser-modified absorption. A time-dependent perturbation-theory treatment describes the process in terms of stimulated forward Rayleigh-scattering of the auxiliary beam occurring simultaneously with the absorption interaction(s). Our formulation accommodates media modifications to the basic character of light-matter interactions, taking into account the refractive and dispersive properties of a solution-phase environment. This introduces the bulk refractive index of the solvent directly into the QED framework. The measurable electronic response of molecules freely rotating in solution is defined by an average of all orientations. We explicitly derive fixed-orientation and rotationally averaged calculations for the Fermi-rule rate of laser-modified one- and two-photon absorption. For a given beam polarization geometry, the solution-phase molecular response is expressible as a set of natural invariant scalars. These results reveal details of the dependence on the beam polarisations and on the rotationally averaged molecular response: we illustrate the breadth of variation available via geometric manipulation of beam polarization, and raise new possibilities for quantum weak measurements of laser states.