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Applied Physics Letters

Optical phase conjugation with frequency up-conversion via high-order, nondegenerate multiwave mixing

M. Ducloy

Published Jun 1, 1985• 27 citations
Publisher

Abstract

One proposes a new way of getting optical phase conjugation, associated to frequency conversion (namely, frequency doubling, frequency multiplication or mixing), within a broad angular field of view. This technique is based on nondegenerate, higher order multiwave mixing in a phase-matched backward configuration. Applications to wave front reversal, spatial or temporal information processing with frequency up-conversion are outlined.

DOI
10.1063/1.95797

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Nondegenerate four-wave mixing (FWM) has been used for wavelength conversion of optical information.1 In such experiments, two beams F-P (frequency ω1) intersect in a nonlinear medium with a small crossing angle θ (≈ 10 mrad), while a third beam B {frequency ω2) is nearly counterpro- pagating to F [Fig. 1(a)]. This can be viewed as real-time holography with frequency conversion.1 However, the physics differ considerably when the medium is transparent at frequency ω1, as there is no optically induced grating. This occurs when FWM is based on resonant two-photon, ω1 + ω2, absorption (frequencies ω1 and ω2 being resonant with a cascade three-level system and ω1 coupling unpopulated excited states). One interesting feature is that the two-photon coherence is nearly Doppler-free and does not depend much on the θ angle.

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Phase conjugate optics : on the theory, observation, and utilization of temporallly-reversed wavefronts as generated via nonlinear optical parametric interactions

David M. Pepper

This thesis describes theoretical and experimental aspects as well as potential applications in the field of coherent optics known as Phase Conjugate Optics (PCO). By utilizing nonlinear optical techniques, real-time or wavefront reversal of an arbitrary incident electromagnetic field can be realized. The nonlinear optical interaction gives rise to what is referred to as the phase conjugate (of the incident monochromatic wave) by performing the operation of complex conjugation upon the incident wave's complex spatial amplitude in real time. This conjugate wave, which is also designated as being a wavefront, has the property of exactly retracing the path of the incident field. The ability of the conjugate wave to correct for inhomogeneous linear and nonlinear (intensity-dependent) aberrations as well as polarization distortions is proved. In particular, the theory of a degenerate four-wave nonlinear optical interaction as providing for the conjugator is presented. The effects of linear and nonlinear losses upon this interaction are discussed. The quantum mechanical origin of the third order nonlinear optical susceptibility responsible for the four-wave mixing process is analyzed for both single and two-photon allowed transitions in an atomic (or molecular) system. The analogies of four-wave mixing with that of real-time holography are discussed. The theory of conjugation via four-wave mixing in optical waveguides is presented. Several of the above characteristics of conjugate fields are verified experimentally where conjugate fields via degenerate four-wave mixing were observed both in the bulk and in waveguide geometries, using carbon disulfide as the nonlinear medium. Amplified time-reversed wavefront generation as well as a mirrorless optical parametric mode of oscillation have been observed, both in agreement with theoretical predictions. Potential applications of PCO are discussed in three different regimes: spatial-frequency, temporal-frequency, and spatial/temporal frequency domains. In the first category, the ability of PCO to correct for image modal dispersion in optical waveguides as well as the use of PCO to perform real-time coherent image processing and nonlinear microscopy is discussed. Temporal-frequency domain applications of PCO to be analyzed include the use of a nearly degenerate four-wave mixing process as a narrowband, wide field-of-view optical filter, capable of an amplified bandpass. The ability of a PCO interaction to renarrow (transform limited) optical pulses which have been temporally spread due to propagation through (group velocity) dispersive channels is analyzed. A potential application of PCO in the field of nonlinear laser spectroscopy is presented. Specifically, the scattering of a probe photon off a two-photon coherent state (created in a three-level atomic system) is shown to yield a conjugate replica. This conjugate replica is capable of providing sub-Doppler width resolution of the two-photon resonance. Further, in the transient regime, the optical free-induction decay of the conjugate wave is capable of yielding detailed spectral features of the three-level system such as the anharmonic contribution to a (nearly) harmonic potential. This technique, performed in the time domain, is known as [alpha]-beat spectroscopy. Finally, a detailed theoretical and experimental study is presented of a laser resonator in which one (or both) of the mirror(s) comprising the optical cavity is replaced by a conjugate mirror (PCM). This novel resonator, which is termed a conjugate resonator (PCR), combines many of the spatial- and temporal-frequency aspects of PCO interactions discussed above. The stability criterion, transverse and longitudinal mode spectra, and the PCR output energy, as well as the frequency locking features of the laser modes to the PCM are discussed.

•Mar 1, 1980•2 citations
One proposes a new way of getting optical phase conjugation, associated to frequency conversion (namely, frequency doubling, frequency multiplication or mixing), within a broad angular field of view. This technique is based on nondegenerate, higher order multiwave mixing in a phase-matched backward configuration. Applications to wave front reversal, spatial or temporal information processing with frequency up-conversion are outlined.
Nondegenerate four-wave mixing (FWM) has been used for wavelength conversion of optical information.1 In such experiments, two beams F-P (frequency ω1) intersect in a nonlinear medium with a small crossing angle θ (≈ 10 mrad), while a third beam B {frequency ω2) is nearly counterpro- pagating to F [Fig. 1(a)]. This can be viewed as real-time holography with frequency conversion.1 However, the physics differ considerably when the medium is transparent at frequency ω1, as there is no optically induced grating. This occurs when FWM is based on resonant two-photon, ω1 + ω2, absorption (frequencies ω1 and ω2 being resonant with a cascade three-level system and ω1 coupling unpopulated excited states). One interesting feature is that the two-photon coherence is nearly Doppler-free and does not depend much on the θ angle.
Four wave mixing, a third-order optical parametric process, is the nonlinear optical process in which four waves interact with each other through the third-order optical nonlinearity. In this process, three waves form a nonlinear polarization at the frequency of the fourth wave. An important application of degenerate four wave mixing is the generation of phase conjugate wave or simply the phase conjugation. The phase conjugate wave has the same wavefront as the incident wave; however, it propagates backward. The phase conjugation is equivalent to the time reversal. Straightforward application of the time reversal is the correction of phase aberration. Suppose that, the incident wave propagates in the nonuniform medium, such as a laser amplifier, where the temperature is fluctuated by intense pumping. Then, the incident wave suffers severe phase aberration during the propagation and the transmitted wave is then reflected by the phase conjugate mirror and goes back into the same nonuniform medium.
The imaging properties of wave-front reversal with nonlinear probe dependence and large frequency conversion are investigated. A calculation is made of the field generated by an arbitrary probe field distribution. It is found that a phase-matching problem, similar to that in nondegenerate four-wave mixing, limits the spatial resolution. Lensless imaging is shown to be impossible because of the nonlinearity of the process. The use of the process as a frequency-converting mirror in a conventional imaging system is studied with diffraction theory. Aberrations in such a system cannot be compensated by a phase-conjugate mirror with large frequency conversion.
This thesis describes theoretical and experimental aspects as well as potential applications in the field of coherent optics known as Phase Conjugate Optics (PCO). By utilizing nonlinear optical techniques, real-time or wavefront reversal of an arbitrary incident electromagnetic field can be realized. The nonlinear optical interaction gives rise to what is referred to as the phase conjugate (of the incident monochromatic wave) by performing the operation of complex conjugation upon the incident wave's complex spatial amplitude in real time. This conjugate wave, which is also designated as being a wavefront, has the property of exactly retracing the path of the incident field. The ability of the conjugate wave to correct for inhomogeneous linear and nonlinear (intensity-dependent) aberrations as well as polarization distortions is proved. In particular, the theory of a degenerate four-wave nonlinear optical interaction as providing for the conjugator is presented. The effects of linear and nonlinear losses upon this interaction are discussed. The quantum mechanical origin of the third order nonlinear optical susceptibility responsible for the four-wave mixing process is analyzed for both single and two-photon allowed transitions in an atomic (or molecular) system. The analogies of four-wave mixing with that of real-time holography are discussed. The theory of conjugation via four-wave mixing in optical waveguides is presented. Several of the above characteristics of conjugate fields are verified experimentally where conjugate fields via degenerate four-wave mixing were observed both in the bulk and in waveguide geometries, using carbon disulfide as the nonlinear medium. Amplified time-reversed wavefront generation as well as a mirrorless optical parametric mode of oscillation have been observed, both in agreement with theoretical predictions. Potential applications of PCO are discussed in three different regimes: spatial-frequency, temporal-frequency, and spatial/temporal frequency domains. In the first category, the ability of PCO to correct for image modal dispersion in optical waveguides as well as the use of PCO to perform real-time coherent image processing and nonlinear microscopy is discussed. Temporal-frequency domain applications of PCO to be analyzed include the use of a nearly degenerate four-wave mixing process as a narrowband, wide field-of-view optical filter, capable of an amplified bandpass. The ability of a PCO interaction to renarrow (transform limited) optical pulses which have been temporally spread due to propagation through (group velocity) dispersive channels is analyzed. A potential application of PCO in the field of nonlinear laser spectroscopy is presented. Specifically, the scattering of a probe photon off a two-photon coherent state (created in a three-level atomic system) is shown to yield a conjugate replica. This conjugate replica is capable of providing sub-Doppler width resolution of the two-photon resonance. Further, in the transient regime, the optical free-induction decay of the conjugate wave is capable of yielding detailed spectral features of the three-level system such as the anharmonic contribution to a (nearly) harmonic potential. This technique, performed in the time domain, is known as [alpha]-beat spectroscopy. Finally, a detailed theoretical and experimental study is presented of a laser resonator in which one (or both) of the mirror(s) comprising the optical cavity is replaced by a conjugate mirror (PCM). This novel resonator, which is termed a conjugate resonator (PCR), combines many of the spatial- and temporal-frequency aspects of PCO interactions discussed above. The stability criterion, transverse and longitudinal mode spectra, and the PCR output energy, as well as the frequency locking features of the laser modes to the PCM are discussed.