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Physical Review A

Nonlinear optical pulse propagation in molecular media

Y. B. Band, Raanan Bavli

Published Oct 1, 1987• 28 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.36.3203

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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.
We consider the nonlinear propagation of an intense short pulse of polarized light through a molecular medium with ground- and excited-state absorption, excited-state emission, and fluorescence from the excited state to the ground state and possibly to a lower-lying excited state. We incorporate the effects of saturation, field-induced alignment, and rotational diffusion of the molecules in the medium. Our approach uses a slowly varying envelope approximation for the light propagation and rate equations for the effective parallel and perpendicular (and higher-multipole) population components of the molecular states. The time dependence of the anisotropy of the fluorescence occurring after preparation of the medium by the intense short pulse is determined. We can treat propagation through an optically nonthin medium wherein the intensity of the pulse decreases while propagating through the medium. An example of a 100-ps pulse propagating through a sample of Rhodamine-6G is presented. We compare our method with others used to describe intense-short-pulse propagation in molecular media.
We present a novel approach to molecular spectroscopy with light pulses of arbitrary strength and duration. The key quantity is the frequency-resolved net energy transfer dE/dω which reveals at which frequencies energy is transferred from the field to the molecule (absorption) or from the molecule to the field (stimulated emission). It is shown that dE/dω can be expressed as the Fourier transform of the cross-correlation function of the molecular polarization P(t) and the time derivative of the applied field, dℰ/dt. In this sense, it is formally equivalent to the absorption cross section under weak-field conditions which, as commonly known, can be represented as the Fourier transform of the autocorrelation function S(t). The time-dependent polarization P(t) is determined by exact integration of the time-dependent Schrödinger equation including the light-matter interaction to all orders. It is shown that under weak-field conditions the expression for dE/dω reduces to the well-known cross section formula in the time-dependent picture of spectroscopy, multiplied by the spectral intensity of the light pulse. Therefore, we consider the expression for the frequency-resolved energy transfer, which is valid for arbitrary electric fields, as the natural extension of the absorption cross section in the weak-field limit. Furthermore, dE/dω is shown to be formally equivalent to the change of the spectral intensity, ΔI(ω), of an optical pulse after transmission through a sample, the latter being derived by solving Maxwell’s equations under well-known approximations. The theory is applied to a simple one-dimensional model with two electronic states and the frequency-resolved energy transfer is investigated as a function of the field strength. For sufficiently strong fields, dE/dω exhibits transitions between essentially all vibrational levels in the ground and all states in the excited electronic manifold. The new expression distinguishes between absorption and emission and that is clearly seen in the spectra.
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.
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.
We describe the absorption characteristics of polarized light pulses of short temporal duration in media with a ground state absorption cross section and large excited state absorption cross section. The effects of rotational diffusion, pulse depletion, finite pulse propagation time, and transition dipole moment orientation are properly treated. Significant enhancement of the reverse saturation due to excited state absorption results when the ground and excited state absorption dipole moments are parallel.
We theoretically analyze linear and nonlinear coherent propagation of linearly polarized, plane-wave, resonant single-cycle terahertz pulses through spatially extended rigid-rotor molecular media. Our model incorporates mixed state medium preparation, nonperturbative nonlinearities, saturation, coherence, memory effects, and propagation, but ignores the effects of damping. Explicit solutions are reported in the linear propagation regime. These solutions are the multilevel superposition of linear, single-cycle $0\ensuremath{\pi}$ pulses, and appear as temporal beats in the time domain. For media initially in thermal equilibrium, the pulse and molecular beats are dispersive and broaden temporally with increased propagation distance. In the simplified limit of equal rotational line strength (an idealized situation), the emitted impulses are exact temporal copies of the input pulse. An efficient, scalable computational method for solving the reduced multilevel Maxwell-Bloch equations for molecular media is reported. This method is based on a standard differential method for the propagation equation together with an operator splitting method for the Bloch equations. It invokes neither the slowly varying envelope (SVEA) or rotating wave approximations (RWA), and incorporates a large number of possible energy eigenstates (we solve for 7744 levels). Case studies of nonlinear single-cycle pulse propagation are then provided by means of computer solutions. In the nonlinear regime, we observe strong molecular orientations and suppression of the pulse and orientational revivals predicted by linear theory. For sufficiently strong pulses, coherent bleaching effects lead to increased transmission of the driving pulse, which also bears signs of self-modulation and carrier-shock formation.