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Journal of the Optical Society of America B

Optimization of two-photon-resonant four-wave mixing: application to 1302-nm generation in mercury vapor

Arlee V. Smith, W. J. Alford, George Ronald Hadley

Published Jul 1, 1988• 28 citations

Abstract

A detailed model of two-photon-resonant four-wave mixing that includes the consideration of efficiency-limiting processes is presented. The model provides a generally applicable systematic approach for maximizing conversion efficiencies for both exact and near two-photon resonance. For exact two-photon resonance, an interference effect limits efficiency to a value determined by ratios of nonlinear susceptibilities and input intensities. For near two-photon resonance, nonlinear refractive indices limit efficiencies unless input intensities are properly balanced. For the specific case of 130.2-nm generation in Hg, we examine a number of potential additional efficiency-limiting processes, including amplified spontaneous emission, stimulated Raman and hyper-Raman gain, parametric gain, linear absorption, and population transfer. We include isotopic effects and Gaussian-profile beams. From our analysis, we conclude that efficiencies of approximately 10% should be feasible by using collimated light beams in an energy-scalable system.

DOI: 10.1364/josab.5.001503

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A detailed model of two-photon-resonant four-wave mixing that includes the consideration of efficiency-limiting processes is presented. The model provides a generally applicable systematic approach for maximizing conversion efficiencies for both exact and near two-photon resonance. For exact two-photon resonance, an interference effect limits efficiency to a value determined by ratios of nonlinear susceptibilities and input intensities. For near two-photon resonance, nonlinear refractive indices limit efficiencies unless input intensities are properly balanced. For the specific case of 130.2-nm generation in Hg, we examine a number of potential additional efficiency-limiting processes, including amplified spontaneous emission, stimulated Raman and hyper-Raman gain, parametric gain, linear absorption, and population transfer. We include isotopic effects and Gaussian-profile beams. From our analysis, we conclude that efficiencies of approximately 10% should be feasible by using collimated light beams in an energy-scalable system.

Previously we showed1 that two-photon-resonant sum- and difference-frequency mixing in Hg vapor is a practical means of generating coherent light over the 140-120- and 230-185-nm wavelength ranges. Here we consider optimization of the conversion efficiency for such a two-photon-resonant mixing process in general and for generation of 130.2-nm atomic oxygen resonance light in particular. We predict that conversion efficiencies (defined as the energy of the sum frequency divided by the total input light energy) of 5-10% should be possible for 130.2-nm production using unfocused mixing beams. This prediction is being tested in experiments at Spectra Technologies, Inc. Their results are described in a companion paper.

This paper considers the limitations of (near) two-photon-resonant frequency up-conversion due to quadratic Kerr effect, two-photon absorption, and Raman scattering. These processes, which are intimately tied to the four-wave mixing process, limit the efficiency and/or the pulse length due to breaking of phase-matching, attenuation, and (de)focusing. General expressions are derived for the limits on the efficiency and the pulse length resulting from these processes. The results of the theoretical analysis are applied to three examples of great practical interest; i.e., tripling of the CO2laser in liquid CO, mixing of IR photons using vibrational nonlinearities, and IR image up-conversion in alkali metal vapors. Several new, important properties of these systems are derived.

If an extended Na vapor column (heat pipe configuration) is subjected to strong laser pumping near two-photon resonance with 3D3/2,5/2 or 4D3/2,5/2 states at pressures above tens of millitorr, strong stimulated emissions are produced by amplified spontaneous emission (ASE) or stimulated electron in hyper-Raman scattering (SEHRS) and by phase matched parametric four-wave mixing (PFWM). These new electromagnetic fields that are generated within the near-resonant nonlinear medium can strongly influence the total atomic response and produce several saturation and total cancellation types of effect.

Four-wave mixing (FWM) in silicon photonics offers promising applications in optical signal processing, wavelength conversion, and quantum photonics, necessitating a comprehensive understanding of its underlying physics and limitations. Stimulated four-wave mixing in silicon photonic wire waveguides has been investigated theoretically by considering two-photon absorption, free carrier absorption, and free carrier dispersion, etc., operating near λ∼1550 nm. It has been shown that these effects severely degrade the performance when operating at higher pump power levels. We present exact numerical calculations of idler wavelength conversion efficiency and bandwidth taking into account the abovementioned nonlinearities, to show the effects of various parameters within the waveguide structure. We extended to investigate silicon photonic microring resonators in terms of the four-wave mixing performance of high-Q-value microring resonators, which are very promising as photon sources (spontaneous four-wave mixing) for large-scale quantum photonic circuits. Our analysis illustrates the limitations of analytical models in describing FWM in ring resonator behavior at a moderate input power level, necessitating a rigorous numerical approach. Experimentally, we demonstrate stimulated FWM (1525 nm≤λp≤1575 nm) in a silicon photonic wire with a cross-section of 500 nm×220 nm and with a small waveguide length of 2 mm. The idler-to-signal conversion efficiency of about −35 dB has been measured for an approximate launched pump power of 30 mW. The conversion efficiency is improved further in the microring resonator as predicted by the simulation results.