Characteristics of the interaction of a laser pulse with a molecular medium are analyzed theoretically in the case when vibrational relaxation takes place in the ground and excited electronic states. The diffusion approximation is used to describe the relaxation transitions. The same approximation is employed in an analysis of the establishment of the limiting steady-state energy of a pulse in a molecular laser amplifier with linear nonresonance losses.
Characteristics of the interaction of a laser pulse with a molecular medium are analyzed theoretically in the case when vibrational relaxation takes place in the ground and excited electronic states. The diffusion approximation is used to describe the relaxation transitions. The same approximation is employed in an analysis of the establishment of the limiting steady-state energy of a pulse in a molecular laser amplifier with linear nonresonance losses.
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.
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, CO, and HF molecular amplifiers for both the electrically and chemically driven systems.
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.
Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.
Two qualitatively different approaches to the dynamics of vibrational wave packets in the presence of medium-induced relaxation, with taking into account relaxation memory effects and without taking them into account (Makovian approximation) were compared for a molecular system with one vibrational degree of freedom (the Morse oscillator) in a medium. The time evolution of the populations of levels, mean system energy, and response of “pumping-probing” experiments were calculated. It was found that, as distinct from the Markovian approximation, the approach including memory effects can predict the evolution of a molecular system satisfying the detailed equilibrium principle. The two approaches specified also predict the existence of a qualitative difference of phase characteristics in the behavior of the system at short times.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.