The non-instantaneous response of the Kerr nonlinearity couples noise to parametric processes in fibers through Raman scattering. We describe theoretical and experimental progress in understanding this noise and its effect on phase-insensitive and phase-sensitive applications.
Wavelength dependence of quantum noise in nondegenerate phase-sensitive amplification in an optical fiber, where signal and its phase-conjugated idler lights are incident into a fiber together with pump light, is theoretically investigated. An analytical formula of the quantum-limited noise figure, that takes Raman scattering into account as well as parametric amplification, is derived based on full quantum mechanical treatment. Using the obtained formula, a calculation example of the noise figure spectrum is also presented, where the pump light phase is adjusted so that the signal gain is maximum at a phase-matched wavelength, supposing multichannel amplification.
Optical parametric amplifiers rely on second-order susceptibility (three-wave mixing) or third-order susceptibility (four-wave mixing) in a nonlinear process where the energy of incoming photons is not changed (elastic scattering). In the latter case, two pump photons are converted to a signal and to an idler photon. Under certain conditions, related to the phase evolution of the waves involved, this conversion can be very efficient, resulting in large amplification of an input signal. As the nonlinear process can be very fast, all-optical applications aside from pure amplification are also possible. If the amplifier is implemented in an optical input-phase-sensitive manner, it is possible to amplify a signal wave without excess noise, i.e., with a noise figure of 0 dB. In this paper, we will provide the fundamental concepts and theory of such amplifiers, with a focus on their implementation in highly nonlinear optical fibers relying on four-wave mixing. We will discuss the distinctions between phase-insensitive and phase-sensitive operation and include several experimental results to illustrate their capability. Different applications of parametric amplifiers are also discussed, including their use in optical communication links.
Phase-sensitive amplification (PSA) can provide low-noise signal amplification, and a quantum-limited noise figure of 0 dB, that is, additional noise-free amplification, is theoretically achievable. However, in fiber-based single-pumped PSA systems, it has been reported that Raman scattering in the fiber degrades the noise figure from the ideal 0 dB. In the present study, the influence of Raman scattering on quantum noise in dual-pumped degenerate PSA in a fiber is investigated. A quantum mechanical treatment starting from the Heisenberg equation of motion is developed, considering the parametric interaction and Raman interaction simultaneously, and an analytical expression for the noise figure is derived. An example of calculation is also presented, which quantitatively indicates the degradation in the noise figure due to Raman scattering.