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Annual Meeting Optical Society of America

Theory of optical phase conjugation in coupled ion pairs

Juan Francisco Lam

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Coupled ion pairs in solids have played an important role in the development of new solid-state lasers. The long-range interaction among two or more ions provides a channel for the inversion of population, leading to the discovery of new emission lines. Because of the relatively large optical cross sections, coupled ion pairs may provide new media for the implementation of a solid-state phase conjugate mirror. We present a theory of optical phase conjugation via four-wave mixing in such novel materials. For a model ion-doped solid-state system, the calculations give the following conclusions. First, the spectral linewidth is proportional to the square root of the intensity of the radiation field in an inhomogenously broadened material for fixed ion density. Second, the linewidth decreases with increasing ion density for the fixed intensity level. And last, the saturation intensity also decreases with increasing ion density for the fixed optical intensity. The behavior of the linewidth and the saturation intensity are attributed to the strong interaction among two nearest-neighbor ion pairs, which leads to the generation of additional energy dumping pathways.

DOI
10.1364/oam.1988.fb1

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Coupled ion pairs in solids have played an important role in the development of new solid-state lasers. The long-range interaction among two or more ions provides a channel for the inversion of population, leading to the discovery of new emission lines. Because of the relatively large optical cross sections, coupled ion pairs may provide new media for the implementation of a solid-state phase conjugate mirror. We present a theory of optical phase conjugation via four-wave mixing in such novel materials. For a model ion-doped solid-state system, the calculations give the following conclusions. First, the spectral linewidth is proportional to the square root of the intensity of the radiation field in an inhomogenously broadened material for fixed ion density. Second, the linewidth decreases with increasing ion density for the fixed intensity level. And last, the saturation intensity also decreases with increasing ion density for the fixed optical intensity. The behavior of the linewidth and the saturation intensity are attributed to the strong interaction among two nearest-neighbor ion pairs, which leads to the generation of additional energy dumping pathways.
Abstract : A study of novel nonlinear optical processes is presented, along with comparison with available experimental data. Five key areas were investigated using novel theoretical approaches. Analysis of phase conjugate optics of rare earth doped solids predicts inhomogenous saturation behavior, pair quenching effects and concentration dependent filtering property, in agreement with experiments. Theory of millimeter wave phase conjugation and novel modulation techniques for communication purposes in semiconductor superlattices are described. The physics of self-pumped phase conjugation in resonant systems are quantified, and the demonstration of a self-pumped phase conjugate mirror at diode laser wavelengths is achieved. A theoretical model, based on the Davydov Hamiltonian, gives absorption lineshapes in agreement with experiments, and predicts the onset of bistability and energy transfer in two-beam coupling. An analysis of the role of multiple longitudinal phonon coupling to Wannier excitions yields Fano-like profiles in four-wave mixing spectroscopy.
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].
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
A new class of laser is reported in which inversion is due to pair-mediated upconversion, quite distinct from conventional sequential one-photon or multiphoton excitation mechanisms. Upconversion of radiation is standardly accomplished by multiphoton processes relying on linear or nonlinear susceptibilities of individual atoms. However, more efficient upconversion can occur by cooperative multiatom processes involving simultaneous transitions on two or more atoms. Cooperative pair pumping in 5% Er:LiYF4 produces laser action from upconverted energy states following pumping at 1.54 µm with a flashlamp-pumped Er:glass laser on the ground to the 4/13/2 transition. Two neighboring 4/13/2 ions decay cooperatively to yield one 4/9/2 ion (which relaxes quickly to 4/11/2), competing effectively with spontaneous emission because of strong interatom coupling and long 4/13/2 lifetime. The upconversion pair process is shown for the first time to be so effective in Er:YLF that this mechanism alone can invert the 4/11/2 state with respect to lower states, generating long delays proportional to inverse pump energy in the onset of lasing.
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.