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Annual Meeting Optical Society of America

Pulse reshaping and coherent sideband generation effects on multiple-photon excitation of polyatomic molecules

Stephen Garner, Cyrus D. Cantrell

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We use a semlclassical, effective-state approach to laser pulse propagation in a gas of polyatomic molecules. Our numerical model of multiple-photon excitation includes quasicontinuum transitions to calculate the effects of coherent propagation on multiple- photon absorption. The molecular model consists of a single ground state and several bands of discrete states, which are successively connected by means of electric-dipole transitions.1 This model correctly simulates some of the major characteristics of multiple- photon absorption, such as power threshold, fluence-dependent absorption, and complete population inversion at large fluences. As the pulse propagates, the Rabi oscillations induced in the lower-level states are encoded onto the pulse and create a series of peaks and troughs similar to those found in pulse propagation in two-level systems.2 Another coherent propagation effect that can change the excitation process is coherent sideband generation. Temporal distortions and the generation of new frequencies result in changes in the population distribution among the states, as well as changes in the total population transferred to the quasicontinuum. The effective increase in total population transfer by propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristics of the pulse.

DOI
10.1364/oam.1990.thn6

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We use a semlclassical, effective-state approach to laser pulse propagation in a gas of polyatomic molecules. Our numerical model of multiple-photon excitation includes quasicontinuum transitions to calculate the effects of coherent propagation on multiple- photon absorption. The molecular model consists of a single ground state and several bands of discrete states, which are successively connected by means of electric-dipole transitions.1 This model correctly simulates some of the major characteristics of multiple- photon absorption, such as power threshold, fluence-dependent absorption, and complete population inversion at large fluences. As the pulse propagates, the Rabi oscillations induced in the lower-level states are encoded onto the pulse and create a series of peaks and troughs similar to those found in pulse propagation in two-level systems.2 Another coherent propagation effect that can change the excitation process is coherent sideband generation. Temporal distortions and the generation of new frequencies result in changes in the population distribution among the states, as well as changes in the total population transferred to the quasicontinuum. The effective increase in total population transfer by propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristics of the pulse.
Using a semiclassical, effective-state approach to laser pulse propagation in a dilute gas of polyatomic molecules, a numerical model of multiphoton excitation which includes quasi- continuum transitions is used to calculate the effects of coherent propagation on multi-photon absorption. The initial laser field is assumed to be a quasimonochromatic Gaussian envelope which is nearly resonant with a portion of the lower vibrational states of the molecule. The molecular model consists of a single ground state and several bands of discrete states which are successively connected via electric dipole transitions. This model correctly mimics some of the major characteristics of multiphoton absorption, such as power threshold, fluence dependent absorption, and complete population inversion at high fluences. The model also allows for the calculation of the polarization induced in the medium by the electric field, and the subsequent influence that the polarization has on the field. As the pulse propagates, the Rabi oscillations induced in the lower level states become encoded onto the pulse, creating a series of peaks and troughs similar to the behavior of pulse propagation in two-level systems. Another coherent propagation effect which can change the excitation process is coherent sideband generation. The temporal distortions and the generation of new frequencies results in changes in the population distribution among the states, as well as changes in the total population transferred to the quasi-continuum. The pulse reshaping occurs while the total fluence of the pulse is decreasing due to energy loss to the quasi-continuum. The effective increase in total population transfer due to propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristic of the pulse. These processes play an important role in any system where the efficient transfer of laser energy to the medium is required, such as laser-induced chemistry and laser isotope separation.
We study a model where two discrete levels are coupled to a band of closely spaced levels forming a quasicontinuum (QC). This model describes how the initial-stage coherence in multiphoton excitation of polyatomic molecules interferes with the recurrent time dynamics due to the QC coupling. The time evolution of the system is solved exactly assuming the QC to be infinite, flat, and uniform; and a detailed investigation of different special cases is carried out. Weak QC excitation is found to exhibit features which are connected to few level dynamics rather than to an irreversible decay, and we study how this modifies the absorption cross section and the Rabi oscillations. The conditions for coherent trapping are discussed.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
Rabi oscillations reflect the existence of a coherent superposition of two molecular eigenstates during the interaction of molecules with a strong, resonant electromagnetic field. This phenomenon is not restricted to two-level systems. We demonstrate its occurrence in a three-level system where the radiation induces a two-photon absorption. The intermediate level is (slightly) detuned from resonance. For a theoretical description the dressed-state picture is adopted. The two-photon excitation is performed either by using one laser, yielding a one-color two-photon process, or by using two counterpropagating, spatially overlapping laser beams, yielding a two-color two-photon process. Rabi oscillations are produced by varying the fluence, i.e., by changing either the laser power or the molecule-laser interaction time. For the one-color case the two-photon transition dipole moment for an SF6{\mathrm{SF}}_{6}SF6​ transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. \textcopyright{} 1996 The American Physical Society.
Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order \ensuremath{\pi} pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon \ensuremath{\pi} pulse driven with near-infrared photons. In other words, a single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.