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Nonlinear index of ruby via nondegenerate two-wave mixing

C. L. Adler, N. M. Lawandy

Published May 21, 1990• 0 citations
OpenAlex

Abstract

Two-waving mixing is a process in which the interference of two waves in a medium with a third-order susceptibility modulates the index of refraction of the medium, causing energy exchange between the two beams. The effect has been used to study the resonance enhanced nonlinear index of refraction in pink ruby.1,2 In Ref. 1, the sign of the real part of the nonlinear index was shown to be the same on both sides of line center at 488 and 580 nm. This is contrary to a prediction one would make using a two-level model for the nonlinear index of refraction. We present the results from a series of experiments aimed at determining the origin of the nonlinear index of refraction in ruby.

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arXiv:2006.00363•Journal of Physics B Atomic Molecular and Optical Physics•Jan 29, 2021•4 citations
Two-waving mixing is a process in which the interference of two waves in a medium with a third-order susceptibility modulates the index of refraction of the medium, causing energy exchange between the two beams. The effect has been used to study the resonance enhanced nonlinear index of refraction in pink ruby.1,2 In Ref. 1, the sign of the real part of the nonlinear index was shown to be the same on both sides of line center at 488 and 580 nm. This is contrary to a prediction one would make using a two-level model for the nonlinear index of refraction. We present the results from a series of experiments aimed at determining the origin of the nonlinear index of refraction in ruby.
The ratio of the imaginary to the real part of the complex nonlinear refractive index has been measured by two-wave mixing in acridine orange doped fluorophosphate glass, fluorescein doped boric acid glass, and ruby at argon-ion wavelengths. A new and simple two-wave mixing measurement is described in which one of the beams contributing to a stationary interference pattern in the nonlinear absorber is subject to a phase transient. This results in a variation of the energy coupling between the beams from which the phase of the nonlinear index and also the sign of its real and imaginary parts can be determined. A simple theory based on homogeneously broadened absorption agrees with the phase of the nonlinear index in acridine, but not in fluorescein where excited state absorption is determined to be greater than absorption from the ground state. These results are compared with new nondegenerate two-wave mixing measurements in which the contribution from the phase and absorption gratings can be determined independently.1 Comparison of results from the two approaches enables the contribution of excited state absorption to the two-wave mixing to be qualified.
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].
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.
Abstract We report experimental and theoretical results of two symmetrical signals of degenerate four-wave mixing generated in rubidium vapor. Both nonlinear signals are induced by two almost copropagating laser beams, with k ⃗ a and k ⃗ b wave-vectors, and detected simultaneously in the 2 k ⃗ a − k ⃗ b and 2 k ⃗ b − k ⃗ a directions. In each direction, we observe a single peak when the two beams are tuned on the closed transition 85 Rb 5 S 1/2 ( F = 3) → 5 P 3/2 ( F = 4). The excitation spectra reveal a small frequency separation between the two peaks, which is explained when propagation effects are taken into account. Furthermore, our theoretical analysis shows that a correct description of the frequency position of each peak is achieved with a variable refractive index for both lasers, in which the scanning laser experiences an anomalous window in the refractive index near resonance.