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In this paper, a classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics. Based on the Bohr–Sommerfeld model of a hydrogen-like atom in the adiabatic approximation, the computational formulas of the linear and nonlinear parameters and the damping coefficient of the quantized oscillator are derived and further expressed in terms of microphysical quantities, such as electronic charge and mass, Bohr radius, and effective quantum number. In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field. A new relationship is proposed to determine the transition eigenfrequency according to the peak frequency and full width at half maximum of an absorption spectrum. Our theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of two kinds of organic molecules turn out to be in good agreement with the experimental ones. These results suggest that our advancement in the quantization of the Lorentz oscillator is likely successful to make it available for use in the quantitative description of atomic or molecular 1PA and 2PA processes. Generally, the improved Lorentz oscillator may also be more suitable for approximating both linear and nonlinear properties of many dielectric or optoelectronic materials due to its relative simplicity.

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An approach is proposed to analyze the two- and three-photon absorption process using the open-aperture Z-scan technique. The normalized transmittance equations of one pulse energy presented here can be used to investigate the effect of different temporal profiles of excitation laser pulses on the nonlinear absorption coefficients (NACs). The numerical simulations show that our method is well in accordance with the usual Z-scan in determination of two- and three-photon absorption coefficients in 0.6-1.0 ranges of nonlinear energy transmittance for the typical pulse models, such as Gaussian, sech2, Lorentz, and asymmetric sech2 models. Our results suggest that the introduced parameter in relation to the pulse envelope in the approach may become a candidate for the parameters taking account of the NAC deviation from the pulse profiles of the probe laser.

The spectroscopic properties of a new chlorophyll derivate photosensitizer (CDP) are studied under the excitation wavelengths at 800 and 400 nm using femtosecond pulses from a Ti: sapphire laser. The damaging effect of CDP on the BEL-7402 cancer cells is also investigated upon two-photon illumination at 800 nm. The normalized fluorescence spectra of CDP in tetrahydrofuran (THF) show that two-photon and one-photon spectra have the same distributions and the same emission bands (675 nm). The lifetimes of two-and one-photon induced fluorescence of this molecule are of the order of 5.0 ns. By comparing the data it is shown that there is some difference between the two lifetimes, but the difference is less than one nanosecond. The two-photon absorption cross section of the molecule is also measured at 800 nm and estimated as about V ƍ 2 § 31.5×10 50 cm 4 ·s·photon 1 . The results of two-photon photodynamic therapy (TPPDT) tests show that CDP can kill all of the tested cancer cells according to the usual Eosine assessment. Our results indicate that the two-photon-induced photophysical, photochemical and photosensitizing processes of CDP may be basically similar to those of one-photon excitation. These behaviors of the sample suggest that one may find other possible methods to estimate some photosensitizers' effects in details such as their distribution in cells and the reactive targets of the sub-cellular parts of some tumor cells via two-photon excitation techniques. photosensitizer, chlorophyll derivate, two-photon fluorescence, two-photon absorption cross-section, TPPDT, BEL-7402 cell