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Optics Express

Noise-induced nonlinear frequency chirping in χ^(3) nonlinear media

Slaven Moro, Aleksandar Daničić, Nikola Alić, Bryan J. Stossel, Stojan Radic

Published Oct 22, 2010• 1 citation
Publisher

Abstract

We theoretically and experimentally analyze the dominant impairment mechanisms affecting the fidelity of optical phase in parametric amplifiers and converters in media characterized by third-order (Kerr) optical nonlinearity. The critical role of narrow-band pump filtering in parametric mixers is quantified with respect to frequency stability of amplified and converted waves. The analysis is generally applicable to all four-photon devices used to generate new frequencies or translate spectral bands.

DOI
10.1364/oe.18.023413

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We theoretically and experimentally analyze the dominant impairment mechanisms affecting the fidelity of optical phase in parametric amplifiers and converters in media characterized by third-order (Kerr) optical nonlinearity. The critical role of narrow-band pump filtering in parametric mixers is quantified with respect to frequency stability of amplified and converted waves. The analysis is generally applicable to all four-photon devices used to generate new frequencies or translate spectral bands.
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The non-zero response time of the Kerr (χ (3) ) nonlinearity determines the quantum-limited noise figure of χ (3) parametric amplifiers and wavelength converters. This non-zero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss. The effect of this excess noise on the noise figure of the amplifier can be significant. We derive analytical expressions for this quantum-limited noise figure in the case of non-degenerate phase-insensitive operation of a χ (3) parametric amplifier and show excellent agreement with experiment without any fitting parameter. We also derive analytical expressions for the quantum limited noise figure for χ (3) -based wavelength converters.
Microwave parametric amplifiers based on Josephson junctions have become indispensable components of many quantum information experiments. One key limitation which has not been well predicted by theory is the gain saturation behavior which limits the amplifier's ability to process large amplitude signals. The typical explanation for this behavior in phase-preserving amplifiers based on three-wave mixing, such as the Josephson Parametric Converter, is pump depletion, in which the consumption of pump photons to produce amplification results in a reduction in gain. However, in this work, we present experimental data and theoretical calculations showing that the fourth-order Kerr nonlinearities inherent in Josephson junctions are the dominant factor. The Kerr-based theory has the unusual property of causing saturation to both lower and higher gains, depending on bias conditions. This work presents an efficient methodology for optimizing device performance in the presence of Kerr nonlinearities while retaining device tunability and points to the necessity of controlling higher-order Hamiltonian terms to make further improvements in parametric devices.
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.