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Soviet Journal of Quantum Electronics

Deformation of the space–time structure of a laser pulse as a result of two-photon absorption

J. Badziak

Published Feb 28, 1982• 0 citations
Publisher

Abstract

Paraxial equations for the intensity and eikonal of a light wave, and also a kinetic equation for the difference between the level populations are used to analyze deformation of the space–time structure of a laser pulse occurring in a medium exhibiting two-photon absorption under noncoherent interaction conditions. The analysis is made using time and space compression functions, and the results of a numerical solution of two-dimensional equations for the propagation of radiation. A determination is made of the principal laws governing the changes in the time and space distributions of the intensity of radiation under quasisteady and transient interaction conditions, and also in the case of a small signal. It is shown that two-photon absorption results in a significant inhomogeneity of the space–time structure of a pulse. The results are given of experimental investigations of changes in the time, space, and energy characteristics of a neodymium laser pulse undergoing two-photon absorption in gallium arsenide.

DOI
10.1070/qe1982v012n02abeh005462

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Paraxial equations for the intensity and eikonal of a light wave, and also a kinetic equation for the difference between the level populations are used to analyze deformation of the space–time structure of a laser pulse occurring in a medium exhibiting two-photon absorption under noncoherent interaction conditions. The analysis is made using time and space compression functions, and the results of a numerical solution of two-dimensional equations for the propagation of radiation. A determination is made of the principal laws governing the changes in the time and space distributions of the intensity of radiation under quasisteady and transient interaction conditions, and also in the case of a small signal. It is shown that two-photon absorption results in a significant inhomogeneity of the space–time structure of a pulse. The results are given of experimental investigations of changes in the time, space, and energy characteristics of a neodymium laser pulse undergoing two-photon absorption in gallium arsenide.
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In this paper, the propagation of nanosecond laser pulses in various media with reverse saturable absorption is studied by numerical methods. Numerical simulation of the propagation of nanosecond laser pulses in a three-level medium with reverse saturable absorption was carried out using the classical transport equation for the case of incoherent nonlinear interaction of radiation with the medium described by the proposed three-level model. The degree of pulse deformation in such media is estimated. It is shown that with an increase in intensity, the pulse begins to deform, the pulse front shortens, the trailing edge becomes longer, the asymmetry coefficient increases. An additional maximum begins to form during a trailing edge with a further increase in intensity. As the additional maximum increases, the asymmetry coefficient monotonously decreases to negative values.
An image-converter streak camera with picosecond time resolution was used in a study of the kinetics of formation of pulses in a traveling-wave laser in which molecular dye solutions were subjected to two-photon optical pumping. An analytic expression was obtained for the lasing threshold of a nonresonator traveling-wave laser in the case of pulsed (τp τe) and quasicontinuous (τp > τe) pumping. Satisfactory agreement was obtained between the calculated and experimental lasing threshold. The kinetics of the compression of output pulses, determined as a function of the pump radiation intensity, was described by rate equations. At pumping rates up to 10 times the threshold a qualitative agreement between the experimental and calculated results was obtained employing a two-band energy model of the dye with a short (compared with the duration of the pump pulses τp) vibrational relaxation time τe. At rates of excitation well above the threshold the kinetics of compression and delay changed, and the output pulses were split into two components, which was interpreted (in the specific case of rhodamine 6G) using a four-band energy scheme. A practical conclusion of this investigation was in the form of recommendations on the use of the proposed approach as a simple method for generating high-intensity single picosecond superradiance pulses of duration τsr with frequency up-con version and a compression coefficient τp/τsr ~ 10.
The interaction between the laser pulse with a small-area and a three-level atomic system is investigated.The formation and characterization of the shaped laser pulse are analyzed and the two-photon transition is studied with the shaped laser pulse.The influence of the relaxation of the excited state and the length of the shaping medium on the two-photon absorption is discussed.Based on the dispersion theory the oscillation of the transient twophoton transition is explained.The result indicates that the transition probability of two-photon absorption evolves regularly with the several values of parameters such as the length of medium(l),relaxation time(t2) and bandwidth(Δω).Meanwhile the transition probability appears in the transient oscillation.
The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency ω0 and that of combination of ω0 and the trigger-field frequency ω1(2ω0 + ω1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable.
We study the evolution in time and in one space coordinate of picosecond laser pulses interacting with a nonlinear medium modeled by three quantum states. This is done by solving numerically the equation of evolution of the density matrix elements together with the Maxwell equation. The nonperturbative treatment of the density matrix allows us to understand the contribution of the different optical transitions and populations to the pulse deformation during its propagation. We apply the model to CuCl where the quantum levels are the fundamental, the excitonic, and the biexcitonic states. Near the two-photon resonance, the pulse is strongly altered and the excitonic and biexcitonic levels show a population inversion. A modulation of the amplitude and a superbroadening of the phase occur during the propagation.