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Optics Letters

Phase conjugation based on single backward second-order nonlinear parametric process

Yujie J. Ding

Published Nov 15, 2012• 17 citations
Publisher

Abstract

We show that backward difference-frequency generation can be exploited to achieve phase conjugation in a second-order nonlinear medium. The backward configuration can be utilized to achieve broadband quasi-phase-matching, compared with the forward counterpart. Our calculation shows that a nonlinear reflectivity of close to 100% is achievable from a laser emitting an output power of ~1 mW. Such an efficient phase conjugator is made feasible by placing the nonlinear medium inside a pump laser cavity. In addition, a Fabry-Perot resonator at the input frequency is used to significantly improve the nonlinear reflectivity.

DOI
10.1364/ol.37.004792

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We show that backward difference-frequency generation can be exploited to achieve phase conjugation in a second-order nonlinear medium. The backward configuration can be utilized to achieve broadband quasi-phase-matching, compared with the forward counterpart. Our calculation shows that a nonlinear reflectivity of close to 100% is achievable from a laser emitting an output power of ~1 mW. Such an efficient phase conjugator is made feasible by placing the nonlinear medium inside a pump laser cavity. In addition, a Fabry-Perot resonator at the input frequency is used to significantly improve the nonlinear reflectivity.
Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>
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.
We present a theoretical analysis of second-order nonlinear difference frequency generation (DFG) in a generalized mirrorless quasi-phase-matching (QPM) frame, aimed at a comparison of counterpropagating DFG configuration (CDFG) to other DFG schemes, in view of all-optical processing applications. Field nonlinear coupling equations have been numerically solved under the hypothesis of phase-matched interaction. The evolution of propagating fields within the material and the wavelength conversion efficiency have been calculated in dependence of operating parameters. The increased complexity in the evolution of amplitude and phase for fields interacting in CDFG with respect to forward-propagating DFG (FDFG) is at the basis of a dramatic increase in the wavelength conversion efficiency under particular settings of device parameters.
A nonlinear process based on backward quasi-phase matching (BQPM) can be used to realize mirrorless optical parametric oscillation, the generation of paired photons with a separable joint spectral amplitude and narrow wavelength bandwidth, and the preparation of counterpropagating polarization-entangled photons, which shows distinct advantages over some applications based on forward quasi-phase matching. In this work, three types of BQPM in a bulk periodically poled potassium titanyl phosphate crystal with a single period are theoretically analyzed. Experimentally, the harmonic wave generated by second-harmonic generation in type 0 and type I exhibits a narrow bandwidth of 15.5 GHz. Furthermore, photon pairs generated by spontaneous parametric downconversion in all types of BQPM (type 0, type I, and type II) at 7th order are observed and characterized. Their coincidence-to-accidental ratios are all greater than 5 × 10 3 in the pump power range from 10 mW to 500 mW. This research lays the foundation for further applications of BQPM in nonlinear optics, quantum optics, and quantum information processing.
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.