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Physical Review A

Propagation and superposition of light pulses in a dye medium

S. L. Chin, Andrzej Zardecki

Published Apr 1, 1976• 3 citations
Publisher

Abstract

We have developed a self-consistent description, based on the semiclassical radiation theory of the propagation of a light pulse in a dye medium. The multilevel nature of the energy bands of a dye molecule and the solvent cage effect in a solution are taken into account. In the case of light pulses whose duration is much shorter than the solvent-solute relaxation time but much longer than the time of atomic phase memory, the latter being of the order of ${10}^{\ensuremath{-}12}$ sec for dyes, we solve the coupled system of equations for the field and the medium by the perturbation procedure. The hole-burning effect is incorporated into the solution in a natural manner. This is especially clear in the direct transition approximation where all the intermediate transitions are neglected. A recent idea of pulse superposition, consisting in storing the energy of a pulse in the form of population inversion followed by stimulated emission triggered by another pulse, is further discussed. Contrary to the orginal model developed by one of us (S.L.C.), we show that no cw pumping is required. The feasibility of the pulse superposition is supported by some experimental results obtained by sending a train of 10-psec pulses through a glycerine solution of oxazine 1 perchlorate.

DOI
10.1103/physreva.13.1528

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A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.

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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.

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The nonlinear absorption of intense laser light is used to obtain information about the times required for spectral cross relaxation (${T}_{3}$) and collisional dephasing (${T}_{2}$) in organic-dye solutions. The steady-state transmission experiment of Huff and DeShazer indicates that ${T}_{2}$ is in the range 0.1-1 psec for cryptocyanine-methanol, while ${T}_{3}$ is in the range 1-10 psec. For DDI-glycerin (1, 1\ensuremath{'}-diethyl-2, 2\ensuremath{'}-dicarbocyanine-iodide-glycerin), measurements of ultrashort-pulse transmission as a function of incident energy and optical polarization suggest a value ${T}_{2}=0.4\ifmmode\pm\else\textpm\fi{}0.2$ psec for that system. These results are based on a new set of rate equations for absorption by inhomogeneously broadened organic-dye solutions. The equations display the effects of spectral cross relaxation and are not limited to light intensities less than those at which coherent interaction effects become important. For the case of ultrashort incident pulses, the equations are extended to account for excited-state absorption, the dependence of absorption on optical polarization, and the existence of a multiplicity of interacting excited states.

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Pulse propagation in the amplifier of a high-power iodine laser

H. Saito, Taro Uchiyama, Tomoo Fujioka

Pulse propagations in an amplifier in the case of the photodissociation iodine laser are investigated with the use of semiclassical treatments, especially when the input pulse fed into the amplifier has a width comparable to or shorter than the transverse relaxation time of the amplifier medium. In our semiclassical equations for pulse propagation in an iodine amplifier, the populations of all hyperfine levels [2P1/2(F= 3, 2),2P3/2(F = 4, 3, 2, 1)], the polarizations of optically allowed transitions (\DeltaF = 0, \pm 1), and the Doppler detuning effects were taken into consideration. Based on the numerical integrations of the semiclassical equations, the propagated pulse shape and the population distributions of the hyperfine levels are discussed. From our calculations, it has been made clear that bandwidth limitations of pulses in the range of pulsewidths of 0.1 ns and below can be avoided by making use of the nonlinear amplification that results from the coherent interaction between the propagated pulse field and the amplifier medium.

IEEE Journal of Quantum Electronics•Apr 1, 1978•13 citations
We have developed a self-consistent description, based on the semiclassical radiation theory of the propagation of a light pulse in a dye medium. The multilevel nature of the energy bands of a dye molecule and the solvent cage effect in a solution are taken into account. In the case of light pulses whose duration is much shorter than the solvent-solute relaxation time but much longer than the time of atomic phase memory, the latter being of the order of 10\ensuremath−12{10}^{\ensuremath{-}12}10\ensuremath−12 sec for dyes, we solve the coupled system of equations for the field and the medium by the perturbation procedure. The hole-burning effect is incorporated into the solution in a natural manner. This is especially clear in the direct transition approximation where all the intermediate transitions are neglected. A recent idea of pulse superposition, consisting in storing the energy of a pulse in the form of population inversion followed by stimulated emission triggered by another pulse, is further discussed. Contrary to the orginal model developed by one of us (S.L.C.), we show that no cw pumping is required. The feasibility of the pulse superposition is supported by some experimental results obtained by sending a train of 10-psec pulses through a glycerine solution of oxazine 1 perchlorate.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.
The problem of a light pulse propagating in a nonlinear laser medium is investigated. The electromagnetic field is treated classically and the active medium consists of thermally moving atoms which have two electronic states with independent decay constants ${\ensuremath{\gamma}}_{a}$ and ${\ensuremath{\gamma}}_{b}$ in addition to the decay constant ${\ensuremath{\gamma}}_{\mathrm{ab}}$ describing the phase memory. The self-consistency requirement that the field sustained by the polarized medium be equal to the field inducing the polarization leads to coupled equations of motion for the density matrix, and equations of propagation for the electromagnetic field. Although the theory is developed for a Doppler-broadened gaseous medium, it may also be applied to a solid medium with inhomogeneous broadening. A unified treatment is given encompassing a wide range of pulse durations from cw signals to psec pulses. Continuous pumping is allowed, as well as any amount of detuning of the carrier frequency of the pulse from the atomic resonance frequency. The three independent decay constants ${\ensuremath{\gamma}}_{a}$, ${\ensuremath{\gamma}}_{b}$, and ${\ensuremath{\gamma}}_{\mathrm{ab}}$ provide greater flexibility than that obtained by using 1T1\frac{1}{{T}_{1}}T1​1​ and 1T2\frac{1}{{T}_{2}}T2​1​. The equations are solved analytically in a few specialized cases and numerically in the general case. Flow charts for accomplishing the numerical integration are given. Among the special problems considered is the apparent paradox of pulses propagating faster than the velocity of light under circumstances described by Basov et al. It is shown that this contradiction with relativity arises from the use of an unphysical initial condition.
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.
The nonlinear absorption of intense laser light is used to obtain information about the times required for spectral cross relaxation (T3{T}_{3}T3​) and collisional dephasing (T2{T}_{2}T2​) in organic-dye solutions. The steady-state transmission experiment of Huff and DeShazer indicates that T2{T}_{2}T2​ is in the range 0.1-1 psec for cryptocyanine-methanol, while T3{T}_{3}T3​ is in the range 1-10 psec. For DDI-glycerin (1, 1\ensuremath{'}-diethyl-2, 2\ensuremath{'}-dicarbocyanine-iodide-glycerin), measurements of ultrashort-pulse transmission as a function of incident energy and optical polarization suggest a value ${T}_{2}=0.4\ifmmode\pm\else\textpm\fi{}0.2$ psec for that system. These results are based on a new set of rate equations for absorption by inhomogeneously broadened organic-dye solutions. The equations display the effects of spectral cross relaxation and are not limited to light intensities less than those at which coherent interaction effects become important. For the case of ultrashort incident pulses, the equations are extended to account for excited-state absorption, the dependence of absorption on optical polarization, and the existence of a multiplicity of interacting excited states.
Pulse propagations in an amplifier in the case of the photodissociation iodine laser are investigated with the use of semiclassical treatments, especially when the input pulse fed into the amplifier has a width comparable to or shorter than the transverse relaxation time of the amplifier medium. In our semiclassical equations for pulse propagation in an iodine amplifier, the populations of all hyperfine levels [2P1/2(F= 3, 2),2P3/2(F = 4, 3, 2, 1)], the polarizations of optically allowed transitions (\DeltaF = 0, \pm 1), and the Doppler detuning effects were taken into consideration. Based on the numerical integrations of the semiclassical equations, the propagated pulse shape and the population distributions of the hyperfine levels are discussed. From our calculations, it has been made clear that bandwidth limitations of pulses in the range of pulsewidths of 0.1 ns and below can be avoided by making use of the nonlinear amplification that results from the coherent interaction between the propagated pulse field and the amplifier medium.