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Optics Express

Optical filtering enabled by cascaded parametric amplification

Colin J. McKinstrie, James M. Dailey, Anjali Agarwal, P. Toliver

Published Jun 15, 2016• 5 citations

Abstract

A cascaded parametric amplifier consists of a first parametric amplifier, which amplifies an input signal and generates an idler, which is a copy of the signal, a signal processor, which controls the phases of the signal and idler, and a second parametric amplifier, which combines the signal and idler in a phase-sensitive manner. In this paper, cascaded parametric amplification is modeled and the conditions required to maximize the constructive-destructive extinction ratio are determined. The results show that a cascaded parametric amplifier can be operated as a filter: A desired signal-idler pair is amplified, whereas undesired signal-idler pairs are deamplified. For the desired signal and idler, the noise figures of the filtering process (input signal-to-noise ratio divided by the output ratios) are only slightly higher than those of the copying process: Signal-processing functionality can be achieved with only a minor degradation in signal quality.

DOI: 10.1364/oe.24.014242

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A cascaded parametric amplifier consists of a first parametric amplifier, which amplifies an input signal and generates an idler, which is a copy of the signal, a signal processor, which controls the phases of the signal and idler, and a second parametric amplifier, which combines the signal and idler in a phase-sensitive manner. In this paper, cascaded parametric amplification is modeled and the conditions required to maximize the constructive-destructive extinction ratio are determined. The results show that a cascaded parametric amplifier can be operated as a filter: A desired signal-idler pair is amplified, whereas undesired signal-idler pairs are deamplified. For the desired signal and idler, the noise figures of the filtering process (input signal-to-noise ratio divided by the output ratios) are only slightly higher than those of the copying process: Signal-processing functionality can be achieved with only a minor degradation in signal quality.

We investigate the beating of signal and idler waves, which have imbalanced signal to noise ratios, in a phase-sensitive parametric amplifier. Imbalanced signal to noise ratios are achieved in two ways; first by imbalanced noise loading; second by varying idler to signal input power ratio. In the case of imbalanced noise loading the phase-sensitive amplifier improved the signal to noise ratio from 3 to 6 dB, and in the case of varying idler to signal input power ratio, the signal to noise ratio improved from 3 to in excess of 20 dB.

Quantum fluctuations in an optical amplifier are of fundamental as well as technological significance and lead to basic limitations on noise performance. It is well-known that the signal-to-noise ratio (SNR) of an injected signal is degraded in the amplification process due to added noise from thermal or (at best) vacuum fluctuations of the internal modes of the amplifier.[1] However, if the internal modes are coupled to a squeezed vacuum, the added noise in amplification can be reduced.[2] With this motivation, we have constructed a nondegenerate parametric amplifier whose idler mode is itself coupled to a squeezed vacuum, which is generated by a second parametric amplifier. Phase-sensitive noise amplification of a vacuum input to the signal mode is observed with the minimum amplified noise level 0.5dB below the usual phase-insensitive amplified noise level for the amplified signal of the same amplifier but with the idler mode coupled to a vacuum state. Prospects for improvement by increasing the squeezing that is coupled into the idler mode of the amplifier beyond the current level of 2dB as well as surprising results from our theoretical analysis which includes losses will be discussed.

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.

Optical parametric amplifiers (PAs) utilize highly efficient nonlinear effects in an optical fiber and they have the ability to operate in phase-sensitive mode. The inclusion of PAs in optical systems can give an ultimate limit for lumped amplified links in terms of achievable signal to noise ratio. The drawback is the complexity stemming from the requirement of phase matching a number of waves at each amplifier, phase lock, and the extra spectrum consumed by idler waves. In this chapter, the theories of a parametric amplifier, including the quantum-optical equations, are given. The properties of the gain saturation and the noise figure are presented. Practical amplifier systems and their applications in phase-sensitive amplification, all-optical signal regeneration, and squeeze state generation are outlined.