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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Interchannel cross-talk in FWM-based phase conjugators

Haiqing Wei, Xin Xue, David V. Plant

Published Jun 17, 2003• 0 citations

Abstract

When a Kerr medium is pumped by a strong laser beam, the nonlinear process of four-wave mixing (FWM) can mix the pump laser and a weak signal to generate a phase-conjugated version of the signal. Optical phase conjugation (OPC) may be employed to compensate the chromatic dispersion and nonlinearity of transmission fibers. It may even serve as a parametric amplifier when the pump is sufficiently intense. Furthermore, the FWM effect is capable of phase-conjugating or amplifying many wavelength-division multiplexed (WDM) signals simultaneously. However, the same FWM effect results in parasitic processes by generating inter-mixing terms among the WDM signals. The center frequency of such unwanted mixing terms may coincide with some of the original or conjugated WDM signals to cause significant interference. This paper studies such interference effect by means of theoretical calculation and computer simulation. It is shown that the coherent interference effect decreases as the pump-power to signal-power ratio (PSR) increases. Unfortunately, there could still be strong interference even with a PSR of 20dB. Some guard-band in the frequency domain is necessary to avoid such coherent interference: if the total bandwidth of the WDM signals is W, then the nearest signal should be more than W away from the pump frequency.

DOI: 10.1117/12.473055

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When a Kerr medium is pumped by a strong laser beam, the nonlinear process of four-wave mixing (FWM) can mix the pump laser and a weak signal to generate a phase-conjugated version of the signal. Optical phase conjugation (OPC) may be employed to compensate the chromatic dispersion and nonlinearity of transmission fibers. It may even serve as a parametric amplifier when the pump is sufficiently intense. Furthermore, the FWM effect is capable of phase-conjugating or amplifying many wavelength-division multiplexed (WDM) signals simultaneously. However, the same FWM effect results in parasitic processes by generating inter-mixing terms among the WDM signals. The center frequency of such unwanted mixing terms may coincide with some of the original or conjugated WDM signals to cause significant interference. This paper studies such interference effect by means of theoretical calculation and computer simulation. It is shown that the coherent interference effect decreases as the pump-power to signal-power ratio (PSR) increases. Unfortunately, there could still be strong interference even with a PSR of 20dB. Some guard-band in the frequency domain is necessary to avoid such coherent interference: if the total bandwidth of the WDM signals is W, then the nearest signal should be more than W away from the pump frequency.

Mutually pumped phase conjugation, a process by which two incident laser beams can mutually pump each other to generate the phase-conjugate replica of the other beam, is studied in a transparent Kerr medium with an electrostrictive nonlinearity. The nonlinear medium acts as a phase-conjugating mirror to both of the incident beams and generates their Stokes-shifted phase-conjugated outputs by the nearly degenerate four-wave mixing process. Our results show that this process will occur only if the coupling strength, defined by the product of the Kerr amplitude gain coefficient, the total input intensity, and the interaction length, is above the threshold value of 2. If the intensity of one of the input beams exceeds the threshold value and the second input beam is weaker than the first, then the weak beam is phase conjugated with a large reflectivity that has a maximum value of the intensity ratio of the strong to the weak input beam. For negligible absorption in the medium, a complete transfer of energy of both the incident beams into the phase-conjugate beams can occur for finite interaction lengths that are only slightly larger than the threshold value. Seeding the oscillation beams tends to lower the phase-conjugate power reflectivities, probably because of increased contribution from the competing two-wave mixing process.

Nondegenerate four-wave mixing (FWM) of picosecond optical pulses in semiconductor optical amplifiers is investigated theoretically, taking into account various carrier processes, probe depletion, and cross-gain modulation effects. Analytical solutions for greatly simplified coupled-wave mixing equations are obtained from which conditions where probe depletion and cross-gain modulation effects cannot be neglected are found. On the other hand, the frequency detuning dependence of optimum input pump pulse energy and shaping of output conjugate pulses are observed from numerical simulations. In particular, calculations show that the frequency symmetry of conjugate and probe pulses with respect to the pump pulse does not hold for optical pulse FWM. Two-photon absorption and ultrafast nonlinear refraction effects are shown to decrease the FWM conversion efficiency.

This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.

A calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators. PACS Code 42. 65. Bp; 42. 60. Da

Theory and experiments are reviewed which suggest that optical-beam phase conjugation by four-wave mixing in a waveguide has the following advantages over four-wave mixing of unguided waves: (1 ) pump power requirements are reduced; (2) the pump beams can contain many transverse modes, both outside and inside the waveguide; (3) pump beam alignment is not critical; (4) the image-wave, being conjugated, can serve simultaneously as its own pump beam; (5) many frequencies can be conjugated simultaneously without intermixing of signals; and (6) frequency- and angle-response characteristics of the conjugator as an optical filter are extended. Frequency depen-dent resonances in the phase-conjugate signal may be employed in spectroscopy of small samples.