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Soviet Journal of Quantum Electronics

Six-photon resonance parametric up-conversion in a nonmonochromatic pump field

N. A. Iskanderov, Vladimir A. Kudryashov, I. N. Matveev, A N Chernyshev

Published Oct 31, 1981• 0 citations
Publisher

Abstract

Six-photon parametric up-conversion under conditions of two-, three-, and four-photon resonance of a constant nonmonochromatic pump field is analyzed allowing for population migration, transient response of the medium, Stark shift of the levels, and width of the frequency spectrum of the the pump field. It is found that in the steady-state conversion regime, the maximum average conversion efficiency in the four-photon resonance case differs only negligibly from the maximum conversion efficiency in a monochromatic field, whereas in the two-photon and three-photon resonance cases it is higher than the maximum efficiency in a monochromatic pump field. An analysis is made of the influence of optically induced relaxation on the average conversion efficiency under conditions of pulsed excitation of two-, three-, and four-photon resonances.

DOI
10.1070/qe1981v011n10abeh008494

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Six-photon parametric up-conversion under conditions of two-, three-, and four-photon resonance of a constant nonmonochromatic pump field is analyzed allowing for population migration, transient response of the medium, Stark shift of the levels, and width of the frequency spectrum of the the pump field. It is found that in the steady-state conversion regime, the maximum average conversion efficiency in the four-photon resonance case differs only negligibly from the maximum conversion efficiency in a monochromatic field, whereas in the two-photon and three-photon resonance cases it is higher than the maximum efficiency in a monochromatic pump field. An analysis is made of the influence of optically induced relaxation on the average conversion efficiency under conditions of pulsed excitation of two-, three-, and four-photon resonances.
Four-photon parametric up-conversion of a weak infrared signal under conditions of two-photon resonance of a constant nonmonochromatic pump field is analyzed allowing for population migration, transient response of the medium, Stark shift of the levels, and width of the pump frequency spectrum. It is found that under steady-state conversion conditions in a nonmonochromatic pump field, it is possible to achieve an average conversion efficiency differing only negligibly from the maximum conversion efficiency in a monochromatic pump field. An analysis is made of the influence of optically induced relaxation on the average conversion efficiency in the transient regime. Numerical estimates are made of the transition parameters for an alkali metal vapor in a frequency-degenerate pump field exciting a two-photon transition.
A theoretical analysis is made of the process of parametric up-conversion of the frequency of an infrared signal involving two-photon resonance of a pump field whose spectrum is considerably wider than the widths of the atomic transition lines. It is shown that the maximum steady-state efficiency of conversion in a wideband field is only slightly different from the maximum efficiency of conversion in a regular and monochromatic field. A dynamic improvement in the conversion efficiency is possible under transient interaction conditions.
Four-wave parametric amplification is discussed when the incident pump frequency is close to a two-photon resonant transition in the material. Expressions for the amplification factor are obtained both under steady-state and pulsed excitation and also for a nonmonochromatic pump. For ultrashort-pulse excitation an ’’energy theorem’’ is derived and discussed. In steady state, expressions for optimum frequency and intensity are obtained. The amplification factor under broad-band excitation decreases with increasing pump linewidth.
A study is made of the evolution of ultrashort pulses of interrogation and generated fields, traveling across a medium after a pump pulse under two-photon resonance conditions. It is shown that, in spite of the absence of overlap of the pulses in space and time, the generated wave becomes phase-locked. The area theorem is obtained for the process in question. It is found that at large distances the second pulse should give rise to a subpulse of the interrogation field and a proportional subpulse whose area tends to zero or to 2π. This conclusion about the formation of subpulses and their limiting areas applies also in the two-photon interaction case. A report is given of an estimate of the threshold intensities of an interrogation pulse in cesium and sodium vapors. The maximum conversion efficiency is found as a function of the pump energy, parameters of the investigated medium, and frequencies of the interacting fields. It is shown that an overall conversion efficiency close to 100% can be obtained when the intensities of the pump and interrogation fields are within the capabilities of the currently available lasers.
A theoretical analysis is made of a four-wave parametric interaction accompanied by reversal of the signal wavefront in a thin layer of a two-level medium as a result of a two-photon resonance of opposite waves of randomly modulated pumping. An allowance is made for the inertia of the interaction, saturation of the transition involved in the interaction, Stark shift of the levels, and width of the pump spectrum. A study is made of the influence of random modulation of the pump waves on the average value and relative variance of the intensity of the reversed wave. It is shown that the relative amplitude of the intensity fluctuations of the reversed wave is minimal when the maximum average intensity is reached.