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Annual Meeting Optical Society of America

Approach to nonlinear optical balance

James J. Wynne

Published Jan 1, 1987• 0 citations
Publisher

Abstract

In the presence of resonant multiphoton excitation, experimental observations of photoionization, fluorescence, and amplified spontaneous emission have shown suppression of these effects.1 There is a common mechanism tying these phenomena together. All these processes involve the coherent nonlinear coupling of two or more optical waves via a dissipative nonlinear optical medium. Independent of initial conditions, as these waves propagate through the nonlinear medium, they develop amplitudes and relative phases that minimize the dissipative losses. The condition of minimum loss is one in which the excitation of the nonlinear medium is reduced due to the waves being in a state of nonlinear optical balance. This balance is stabilized by the dissipation. Other combinations of amplitude and phase are more lossy and rapidly damped out.

DOI
10.1364/oam.1987.tud13

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In the presence of resonant multiphoton excitation, experimental observations of photoionization, fluorescence, and amplified spontaneous emission have shown suppression of these effects.1 There is a common mechanism tying these phenomena together. All these processes involve the coherent nonlinear coupling of two or more optical waves via a dissipative nonlinear optical medium. Independent of initial conditions, as these waves propagate through the nonlinear medium, they develop amplitudes and relative phases that minimize the dissipative losses. The condition of minimum loss is one in which the excitation of the nonlinear medium is reduced due to the waves being in a state of nonlinear optical balance. This balance is stabilized by the dissipation. Other combinations of amplitude and phase are more lossy and rapidly damped out.
Suppression of photoionization, fluorescence, amplified spontaneous emission, and nonlinear optical conversion have all been reported in the presence of resonant multiphoton excitation.1 At first glance, the nonlinear phenomena manifesting this suppression and the order of the nonlinear processes appear to be quite distinct. In some cases, this suppression has been shown to result from a destructive interference (alternatively, a competition) between alternative excitation pathways to the resonant intermediate state.2
As a succession of two pulses propagates through a medium which exhibits a resonance (single or multiphoton), the resonant parts of the susceptibility will depend on the relative phase of the two pulses, provided the delay between the pulses is shorter than the phase relaxation time of the interaction. As a result of this "coherent interaction", the reradiation of the sample (the fluorescence, the absorption and the generation of harmonics) will be a periodic function of the phase difference and delay between the two pulses of the sequence 1. The study of these coherent effects is important, because one expect to find conditions under which the maximum harmonic conversion to much shorter wavelengths can be greatly enhanced 2. The presence of the multiphoton resonance enhances the nonlinear susceptibility responsible for the harmonic generation, but reduces also the maximum achievable conversion efficiency because of resonant losses (depletion of the fundamental by multiphoton absorption). The latter effect can be eliminated by a judicious choice of the pulse sequencing and phasing. In addition to demonstrating, for the first time, coherent interaction enhancement in harmonic generation, the data of third harmonic versus relative phase of the pulse sequences enable us to measure the phase angle of the third order susceptibility (hence the contribution of the continuum relative to that of the resonance).
When a strong near-resonant laser beam propagates through an atomic vapor, it can simultaneously induce several different nonlinear optical processes. In certain restricted conditions, these processes evolve independently of one another, but in general these processes compete. We have observed competition1 between four-wave mixing2 (FWM) and amplified spontaneous emission3 (ASE) and have presented an explanation for this phenomenon based on the solution of the coupled-amplitude equations of nonlinear optics. We extend our previous work by presenting a more detailed theoretical explanation of this effect and evidence that competition of this sort occurs quite generally in nonlinear optical systems.
Introduction We have already encountered situations in which light of one frequency falling on an atomic system gives rise to light of different frequencies (cf. Section 15.6). The atom may here be considered to play the role of a (noisy) nonlinear transducer for the incident field. Even stronger nonlinear effects arise when one is dealing with a large number of atoms, or a nonlinear medium . Under these circumstances it is sometimes permissible to ignore the atomic structure and to treat the medium as a continuum, as in Maxwell's electromagnetic theory. The subject of the interaction of the incident field with the nonlinear medium is usually known as nonlinear optics. The subject had its beginnings in an experiment in which a strong beam of red light (wavelength 6943 Å) from a ruby laser was allowed to fall on a quartz crystal, and a faint beam of blue light at a wavelength of 3472 Å, the first harmonic of the red, was produced (Franken, Hill, Peters and Weinreich, 1961). The development of the subject of nonlinear optics into a mature field is due largely to the work of Bloembergen and his collaborators. In the following we shall consider only a few simple illustrative examples of phenomena in nonlinear optics. More topics and more detail can be found in the books by Bloembergen and others (Bloembergen, 1965; Yariv, 1967, Chap. 21; Shen, 1984; Schubert and Wilhelmi, 1986; Butcher and Cotter, 1990; Boyd, 1992).
Competition between amplified spontaneous emission (ASE) and the four-wave-mixing (FWM) process has been observed under conditions of two-photon resonant excitation of the sodium 3d level. The nature of the competition is that the FWM process is able to prevent the occurrence of ASE, even though the gain of the ASE process calculated in the absence of competition effects is much larger than that of FWM. The ASE is suppressed because the fields generated by the FWM process create a new excitation pathway connecting the ground and 3d levels, and under quite general conditions this pathway interferes destructively with that due solely to the applied laser field. These effects are modeled theoretically by solving perturbatively the density-matrix equations of the atomic system, thereby determining the population in the upper level and the nonlinear polarization of the medium. The coupling between the various optical fields due to the nonlinear polarization is described by coupled amplitude equations. The solution to these equations predicts that when the wave-vector mismatch is not too large the fields evolve spatially to reach steady-state values, and that the population excited to the 3d level by the total steady-state optical field is much smaller than that due to the incident laser field alone. We have observed experimentally the suppression of ASE by FWM and have observed that this suppression does not occur when the medium is excited with counterpropagating beams that cannot efficiently excite the FWM process. In addition, we have conducted a series of experiments that shows that the degree of suppression of ASE depends on the intensity and focusing characteristics of the incident laser as expected on the basis of our theoretical model.
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].