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Optics Express

Energy transfer between incident laser and elastically backscattered waves in nonlinear absorption media

Richard L. Sutherland

Published Jan 1, 2005• 4 citations
Publisher

Abstract

A model of energy transfer by nearly degenerate two-beam coupling in media exhibiting two-photon and excited state absorption is presented and discussed. The two beams include an incident laser, which has a nonlinear time dependent phase, and an elastically backscattered wave derived from the incident laser. Superposition of these two waves creates an index modulation, arising from a spatially modulated, two-photon-created excited-state population, which couples the forward and backward propagating waves. Reflectance of the stimulated wave and transmittance of the incident laser are computed, including the effects of two-photon absorption andexcited state absorption as well as energy transfer between the two beams, and the relevance of the results to experimental measurements is discussed. The backscattered wave has a frequency that is unshifted with respect to that of the incident laser, and the small signal gain is proportional to the square of the incident laser intensity. The different effects due tomultimode and chirped waves are also discussed.

DOI
10.1364/opex.13.009788

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Physical Review A•Sep 1, 1989•26 citations
A model of energy transfer by nearly degenerate two-beam coupling in media exhibiting two-photon and excited state absorption is presented and discussed. The two beams include an incident laser, which has a nonlinear time dependent phase, and an elastically backscattered wave derived from the incident laser. Superposition of these two waves creates an index modulation, arising from a spatially modulated, two-photon-created excited-state population, which couples the forward and backward propagating waves. Reflectance of the stimulated wave and transmittance of the incident laser are computed, including the effects of two-photon absorption andexcited state absorption as well as energy transfer between the two beams, and the relevance of the results to experimental measurements is discussed. The backscattered wave has a frequency that is unshifted with respect to that of the incident laser, and the small signal gain is proportional to the square of the incident laser intensity. The different effects due tomultimode and chirped waves are also discussed.
A systematic study of degenerate two-wave mixing in the stationary regime in thin nonlinear local-response media is presented. The model is based on the coherent interaction of four waves, the two incident beams, and the two main diffracted waves. Analytical results are obtained in all cases investigated under the assumption of weak-beam amplification. It is demonstrated that the energy transfer arises only from the forward degenerate four-wave mixing terms. In particular, the theoretical results show two new features: (1) the gain factor of the interaction is substantially reduced because of the phase change associated with the two-wave mixing terms and (2) a phase mismatch can compensate for this phase change, leading to an appreciable gain enhancement. Moreover, the general case is solved numerically. Particular attention is given to the influence of separate two-wave and forward degenerate four-wave mixing terms. Self-diffraction effects and the gain dependence versus the ratio of the pump-beam intensity to the signal-beam intensity are investigated.
Energy transfer between two laser beams of comparable intensity due to their nonlinear interactions in an atomic vapor was investigated. Strong coupling occurs due to stimulated Rayleigh scattering when the frequencies of the two waves differ by the inverse of the excited-state lifetime. The energy transfer between two nearly equal energy pulses from an alexandrite laser tuned near the 4/sup 2/S/sub 1/2/ to 4/sup 2/P/sub 3/2/ transition of potassium vapor was measured. It was found that as much as 85% of the total incident energy was contained in one of the output beams.>
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
A frequency-unshifted and backward stimulated scattering can be efficiently generated in one-photon-absorption free but two-photon absorbing materials. Using a number of novel two-photon absorbing dye solutions as the scattering media and nanosecond pulsed laser as the pump beams, a highly directional backward stimulated scattering at the exact pump wavelength can be readily observed once the pump intensity is higher than a certain threshold level. The spectral and spatial structures as well as the temporal behavior and optical phase-conjugation property of this new type of backward stimulated scattering have been experimentally studied. This stimulated scattering phenomenon can be explained by using a model of two-photon-excitation enhanced standing-wave Bragg grating initially formed by the strong forward pump beam and much weaker backward Rayleigh scattering beam; the partial reflection of the pump beam from this grating provides an positive feedback to the initial backward Rayleigh scattering beam without suffering linear attenuation influence. Comparing to other known stimulated (Raman, Brillouin, Rayleigh-wing, and Kerr) scattering effects, the stimulated Rayleigh-Bragg scattering exhibits the advantages of no frequency-shift, low pump threshold, and low spectral linewidth requirement.
The solution of the nondegenerate two-wave-mixing problem in an absorptive Kerr medium including the contribution from nonlinear absorption is obtained for the first time to our knowledge. This solution enables us to analyze the influence of nonlinear absorption on the two-wave-mixing gain and account for previously unexplained results reported for ruby and Cr3+:YAlO3. The effect of nonlinear absorption of a pump beam on the gain of a probe beam is shown to be minimized when incident intensities of the interacting beams are equal. The intensity dependence of the two-wave-mixing gain for dispersive (ruby and Cr3+:YAlO3) media and the gain measurements for absorptive (fluorescein-doped glass) media are also in agreement with the new theory.
We show that it is possible to transfer energy efficiently between two laser beams of comparable intensity by means of the near-resonant nonlinear response of an atomic vapor. The coupling is due to stimulated Rayleigh scattering and occurs when the frequency difference between the two beams is approximately the inverse of lifetime of the excited atomic state. We have measured the coupling between two beams from an Alexandrite laser tuned near the 42{4}^{2}42S1/2{S}_{1/2}S1/2​\ensuremath{\rightarrow}42{4}^{2}42P3/2{P}_{3/2}P3/2​ potassium transition and found that one of the transmitted beams can contain up to 85% of the total incident energy.