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IEEE Journal of Quantum Electronics

Limitations and optimization of (near) two-photon-resonant frequency up-converters

E. A. Stappaerts

Published Feb 1, 1979• 18 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1979.1069969

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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.
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.
We present a theoretical and experimental study of IR image upconversion using two-photon resonant optical four-wave mixing in alkali metal vapors. A closed form solution for the upconversion efficiency which includes Doppler broadening of the two-photon transition and a finite bandwidth pump laser is given. Experimental results for two types of image upconverters using Cs are presented. The first upconverts 2.94 μm to 4558 Å with a power efficiency of 32 percent and1.6 \times 10^{4}resolvable spots. The second is IR tunable, but of lower efficiency and resolution. Finally, the optimized characteristics of the Cs upconverter are compared to crystal upconverters and to the requirements of various applications.
We demonstrate theoretical conditions for highly efficient degenerate four-wave mixing in triply resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ${\ensuremath{\omega}}_{0}\ensuremath{-}\ensuremath{\Delta}\ensuremath{\omega}$ can, in the presence of pump light at ${\ensuremath{\omega}}_{0}$, be converted with quantum-limited efficiency into an output shifted signal of frequency ${\ensuremath{\omega}}_{0}+\ensuremath{\Delta}\ensuremath{\omega}$, and we derive expressions for the critical input powers at which this occurs. We find the critical powers in the order of 10 mW, assuming very conservative cavity parameters (modal volumes  10~10 10 cubic wavelengths and quality factors  1000~1000 1000). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting ``quantum'' arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.
Quantum frequency conversion (QFC), a critical technology in photonic quantum information science, requires that the quantum characteristics of the frequency-converted photon must be the same as the input photon except for the color. In nonlinear optics, the wave mixing effect far away from the resonance condition is often used to realize QFC because it can prevent the vacuum field reservoir from destroying the quantum state of the converted photon effectively. Under conditions far away from resonance, experiments typically require strong pump light to generate large nonlinear interactions to achieve high-efficiency QFC. However, strong pump light often generates additional noise photons through spontaneous Raman or parametric conversion processes. Herein, we theoretically study another efficient QFC scheme based on a resonant four-wave mixing system. Due to the effect of electromagnetically induced transparency (EIT), this resonant QFC scheme can greatly suppress vacuum field noise at low light levels; consequently, the converted photon can inherit the quantum state of the input photon with high fidelity. Our research demonstrates that if the conversion efficiency of the EIT-based QFC is close to 100%, the wave function and quadrature variance of the converted photon are almost the same as the input probe photon.
Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double- Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of 91.2 % ± 0.6 % by using this backward FWM system at an optical depth of 130 in cold 87 Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.