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Journal of the Optical Society of America A

Image formation in phase conjugation with large wavelength conversion

Peter Unsbo, Farhad Saeidi, Göran Manneberg

Published Dec 1, 1993• 3 citations
Publisher

Abstract

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.

DOI
10.1364/josaa.10.002532

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Optics Express•Jan 1, 2006•14 citations
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.
We show that one can generate the time-reversed replica of an "input" monochromatic, image-bearing beam by coupling it into a waveguide where it interacts with counterpropagating multimode "pump" waves of the same frequency. The nonlinear electric polarization density that is third order in the propagating electric fields in the guide medium generates the replica by the process of "four-wave mixing." We show also that the input beam can serve simultaneously as its own pump beam. If the frequency ν of the backward pump beam is different from the frequency ω to of the input beam, then the "phase-conjugate" to the input is generated at the entrance plane to the guide, and this radiates a replica of the input field, magnified by\omega/\nu, back along the input beam. The pump power required per resolution element to phase-conjugate a beam in a waveguide is orders-of-magnitude less than for the corresponding process with free (unguided) waves interacting in an infinite medium. Unlike the requirements for free waves, the pump waves do not need to be well aligned or single-mode to produce high fidelity in the replication process. Neither does the guiding structure or enclosed medium have to be precise in dimension or uniformity; the main requirements on the guiding structure being that it not attenuate the waves too heavily. Formulas are derived for the replication efficiency and fidelity in the various guided configurations. We also show how the process can be used: 1) to make a narrowband optical filter with a large acceptance solid angle; 2) to perform image-frequency conversion; 3) to obtain Raman and two-photon spectra of small samples; and 4) to achieve broadband optical amplification. We examine the conditions under which phase conjugation and these applications can be performed at several frequencies simultaneously. Limitations placed by the power-dependence of propagation constants are derived.
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.
The schemes for recording and reading of dynamic holograms in conditions of nondegenerate four- and six-wave mixing in a nonlinear Fabry-Perot interferometer have been analyzed theoretically. It has been demonstrated that there is a possibility for a considerable improvement in the diffraction efficiency and angular selectivity of dynamic gratings in the interferometer compared to the off-cavity interaction. A method for the frequency conversion of coherent images with simultaneous phase conjugation has been realized experimentally.
We demonstrate that the phase conjugation of a beam during nondegenerate four-wave mixing is accompanied by a spatial shift relative to the degenerate conjugate-beam location. Experiments with a photorefractive phase-conjugate mirror reveal that the phase-conjugate beam shifts have a nonmonotonic dependence on the probe's detuning frequency and comprise both lateral displacements of up to 218 mum and angular tilts of up to 34 arc sec. An approximate theory based on spatial dispersion coefficients is in partial agreement with the experimental results.
This work presents theoretical and experimental studies of the processes of light field transformations upon frequency-nondegenerate fourwave mixing (NFWM) in a nonlinear Fabry-Perot interferometer (FPI). The principal aims are the development of a theory for intracavity four-wave mixing in complex molecular media in conditions of scattering from dynamic gratings and resonator feedback; determination of a mechanism of light field transformations in dynamic holograms, and also by nonlinear interferometers; working out and introduction of novel nonlinear-optical methods to control the characteristics of light beams. High diffraction efficiency (up to 13.5%) with simultaneous infrared-to-visible frequency conversion of coherent images has been experimentally obtained by intracavity NFWM.