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Physical Review A

Influence of Vibrational, Rotational, and Reorientational Relaxation on Pulse Amplification in Molecular Amplifiers

F. A. Hopf, C. K. Rhodes

Published Aug 1, 1973• 29 citations
Publisher

Abstract

Short-pulse amplification in gaseous molecular amplifiers is complicated by many aspects of atomic and molecular interactions. Among these are the various vibrational, rotational, and reorientational relaxational processes which influence the coupling of the energy stored in the molecular radiators to the electromagnetic field. The properties of plane-wave pulse amplification, especially in the saturated regime, are examined numerically in order to quantitatively determine the detailed effects of these relaxational phenomena. As expected, the results for saturated amplification show that the amount of extracted energy decreases significantly when the rotational relaxation time is sufficiently long in comparison to the pulse width. We also observe the development of pulse-shape variations which are a direct result of the collisional phenomena and differ qualitatively from the results obtained for amplifying media without an energy reservior. There is a tendency for the pulse lengths to increase owing to the energy transfer, in contrast to the strong narrowing effects which occur in the absence of the collisional processes. The influence of reorientational collisions is found to be small, accounting for less than a 20% effect on the over-all conclusions. Finally, we present results concerning the development of an asymptotic pulse shape in high-gain amplifiers. In this case, the pulse shape clearly exhibits the competition between the stimulated rate, which scales with the optical flux, and the collisional rates which are determined by the particle density. Calculations of this nature may be applied directly to C${\mathrm{O}}_{2}$, CO, and HF molecular amplifiers for both the electrically and chemically driven systems.

DOI
10.1103/physreva.8.912

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Short-pulse amplification in gaseous molecular amplifiers is complicated by many aspects of atomic and molecular interactions. Among these are the various vibrational, rotational, and reorientational relaxational processes which influence the coupling of the energy stored in the molecular radiators to the electromagnetic field. The properties of plane-wave pulse amplification, especially in the saturated regime, are examined numerically in order to quantitatively determine the detailed effects of these relaxational phenomena. As expected, the results for saturated amplification show that the amount of extracted energy decreases significantly when the rotational relaxation time is sufficiently long in comparison to the pulse width. We also observe the development of pulse-shape variations which are a direct result of the collisional phenomena and differ qualitatively from the results obtained for amplifying media without an energy reservior. There is a tendency for the pulse lengths to increase owing to the energy transfer, in contrast to the strong narrowing effects which occur in the absence of the collisional processes. The influence of reorientational collisions is found to be small, accounting for less than a 20% effect on the over-all conclusions. Finally, we present results concerning the development of an asymptotic pulse shape in high-gain amplifiers. In this case, the pulse shape clearly exhibits the competition between the stimulated rate, which scales with the optical flux, and the collisional rates which are determined by the particle density. Calculations of this nature may be applied directly to CO2{\mathrm{O}}_{2}O2​, CO, and HF molecular amplifiers for both the electrically and chemically driven systems.
The results are given of a theoretical investigation of the interaction of a laser pulse with a molecular medium. Allowance for the vibrational relaxation processes is made within the diffusion approximation framework which makes it possible to describe relaxation as the diffusion of particles in continuous electron energy bands. A simultaneous solution is obtained of the diffusion equations for the medium and the equations for the radiation field in the special cases of slow and fast vibrational relaxation. It is shown that the fast relaxation, which prevents gain saturation, increases the signal energy compared with the case of slow relaxation in an amplifying medium and reduces this energy compared with such relaxation in an absorbing medium. Expressions are obtained for the functions which describe the distributions of the band particles established by the investigated signal. The analysis made shows that the diffusion model can be applied to the interaction between laser pulses and molecular media.
Coherent amplifications of short pulse XeCl lasers are theoretically studied using multi-level Maxwell-Bloch equations including real vibrational-rotational structures of a gain spectrum of XeCl. The model can successfully predict coherent effects such as the quantum beat caused by spectrum overlaptions of several vibrational-rotational transitions involved in the short pulse laser spectrum. Saturation of amplified energy caused by formation of a 2 π-pulse-like pulse. Since a pulse area necessary for the production of a 2π-pulse-like pulse which depletes all the upper state populations accessible to the laser spectrum depends on the laser pulse width, an effective saturation energy is a function of the laser pulse width. When absorption in the amplifier media is not negligible to the small-signal gain, an effective u-pulse-like pulse is generated instead of a 2π-pulse-like pulse. The laser pulse width is shortened by the π or 2π-pulse-like pulse formation, and even shorter pulses than the linear limitation defined by the gain spectrum width can be generated if the amplified pulse intensity becomes very strong.
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.
Using semiclassical radiation theory, a formalism similar to that used by Lamb in his Theory of an Optical Maser is developed for studying the amplification of vector traveling waves in a laser-type medium. The effect of the medium on the waves is given in terms of space (or time) dependent field amplitudes and phases and a nonlinear index of refraction. With particular emphasis on typical gaseous media, the effects of Doppler broadening are treated in detail for arbitrary ratios of natural to Doppler linewidths. Polarization and propagation vectors in various directions are considered, and the nonlinear effects are found to make an isotropic medium effectively anisotropic. Lowest order nonlinear effects (due to a polarization cubic in the field amplitudes) are studied extensively, and the frequency dependence of several of these processes is presented in graphical form. In particular, the introduction of fields at new frequencies and polarization effects are considered. The characteristics of these nonlinear processes peculiar to Doppler broadened lines are discussed, and the processes are interpreted in terms of saturation and coherent modulation of the population inversion density. Strong nonlinear effects are considered in a more approximate way and are found to consist of saturation of the various linear and nonlinear processes previously considered. These strong nonlinear effects should occur at low enough intensities to be easily observed in practice on a CW basis. With the present formalism, the analytical results of Gordon, White and Rigden regarding gain saturation in laser amplifiers are obtained, and the extension is made to include frequencies away from line center and the effects of multiple spectral components. Again, the introduction of fields at new frequencies is considered in detail. These results are also discussed in terms of saturation and coherent modulation of the populations and hole burning.
Wave-mechanical phenomena such as resonance and interference, in both light and matter, are central to the principles of quantum coherent control over molecular processes. Focusing on the dynamical aspects, this dissertation is a compilation of studies on the interaction physics involving wave packets in molecules, the driving light field, and the underlying coherence and control. In each work, we will demonstrate interesting correlations between the properties of a carefully designed excitation light field and desirable outcomes of the molecules quantum dynamics. We will analyze the dynamical effect of a Feshbach resonance in the adiabatic Raman photoassociation for ultracold diatomic molecule formation from ultracold atoms. A narrow resonance is shown to be able to increase the effective number of collisions, in an ultracold atomic gas, that are available for photoassociation. This results in an optimal resonance width much smaller than the atomic collision energy bandwidth, due to the balance between the effective collision rate and single-collision transfer probability. Next, we demonstrate the linear molecular response to high-intensity, broadband, shaped optical fields. We show that this originates from interferences based on intra-pulse Raman excitations, and thus response linearity is not unique to the first-order perturbative limit and can not be used to infer the strength of the field. In the last study, we simulate the stochastic vibrational wave packet and dissociation-flux dynamics in a molecule excited by light with temporal and spectral incoherent properties. Between this case and that using a coherent pulse with the same spectral profile, we compare the vibrational wave functions and the loss of electronic and vibrational coherence, and demonstrate the qualitative difference between coherently and incoherently driven dynamics in molecules.