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 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) is a remarkably powerful tool if implemented correctly - it allows amplification with a noise figure lower than quantum mechanics normally dictates, and also allows the development of systems that coherently process the phase of their optical inputs. PSA at infrared wavelengths can be achieved using second or third order optical nonlinearities - indeed the first demonstrations of PSA utilised degenerate three photon mixing in bulk crystals, allowing the observation of effects such as quantum quadrature squeezing. This PhD research project was aimed at translating the fascinating science of PSAs into applications, based on Kerr nonlinearity in optical fibres, capable of being deployed in modern core optical networks runnning at 40 Gbit/s and higher. This objective was an integral part of the European Union FP7 project PHASORS. Studies, both theoretical and experimental, were carried out on wideband non-degenerate PSAs. The inline cascaded fiber optic parametric amplifier (FOPA), in which a first phase insensitive FOPA is used to generate phase locked signal-idler pairs, followed by a second FOPA in which PSA takes place, was used to experimentally demonstrate PSA gain characteristics in linear and saturated modes of operation, with PSA obtained over 20 nm in the telecom C-band. Focus was then re-directed towards applying a dual pump PSA to DPSK regeneration. The amplitude and phase limiting characteristics of these devices were experimentally studied, in particular revealing that amplitude saturation arises due to an interplay between input phase and nonlinear phase matching along the nonlinear fibre. This feature was used to identify a regime of operation for DPSK regeneration combining simultaneous phase and amplitude regeneration. A practical DPSK regenerator based on a degenerate dual pump phase sensitive FOPA was built. The device advanced the state of the art by incorporating a pump synthesis stage that allowed black-box operation. Detailed measurements using noise sources with varying frequency distributions in both amplitude and in phase, are presented, and the ability of the system to improve the phase and amplitude characteristics of signals at its input was verified. Also presented are results showing the regenerator installed in the middle of an 800 km dark fiber link. Finally, a novel scheme was proposed and demonstrated that utilised parametric mixing to perform arbitrary phase quantization. This relied on the coherent addition of an M-level PSK signal with a conjugated (M-1)th phase harmonic, scaled by a coefficient m, to achieve M-level phase quantization. The concept was successfully demonstrated with QPSK data signals at 56 Gbaud, as well as used to quantize lower bandwidth test signals from 2 to 6 phase levels.
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.
The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.
Optical communication links are usually made with erbium-doped fiber amplifiers, which amplify the signal waves in a phase-insensitive (PI) manner. They can also be made with parametric fiber amplifiers, in which the signal waves interact with idler waves. If information is transmitted using only the signals, parametric amplifiers are PI and their noise figures are comparable to those of erbium amplifiers. However, transmitting correlated information in the signals and idlers, or copying the signals prior to transmission, allows parametric amplifiers to be phase-sensitive (PS), which lowers their noise figures. The information capacities of two-mode PS links exceed those of the corresponding PI links by 2 b/s-Hz.
Parametric processes in materials presenting a second- or third-order nonlinearity have been widely used to demonstrate a wide range of all-optical signal processing functionalities, including amplification, wavelength conversion, regeneration, sampling, switching, modulation format conversion, optical phase conjugation, etc.. The recent evolution of optical fiber communication systems towards advanced modulation formats making use of the phase dimension, as well as polarization and, more recently, space-multiplexing, has created new requirements, as well as new opportunities, for parametric all-optical signal processing. In this presentation, we will review our recent results on the demonstration of all-optical parametric signal processing using different nonlinear platforms, including highly nonlinear optical fibers (HNLFs), silicon nanowires, and periodically-poled lithium niobate (PPLN) waveguides. In particular, we will show how phase-sensitive processes can be engineered to demonstrate phase-quadrature separation, which we have recently demonstrated in HNLFs and PPLN waveguides. Silicon nanowires are particularly attractive for signal processing thanks to their compact size, CMOS compatible fabrication process, degrees of freedom in dispersion engineering, and high nonlinear coefficient. However, the detrimental effect of free-carrier absorption induced by two-photon absorption has so far prevented them from being used for the demonstration of phase-sensitive processing. Thanks to the introduction of p-i-n junctions across silicon waveguides, we have recently been able to demonstrate phase-sensitive extinction ratios as high as 20 dB, allowing the phase regeneration of phase-modulated signals under continuous wave pumping operation. One of the well-known limitations of planar waveguide devices for all-optical signal processing is their inherent polarization sensitivity. We will show how the introduction of polarization-diversity circuits relying on efficient and wideband polarization splitters and rotators can overcome this limitation. Finally, we will also discuss the introduction of signal processing functionalities that are compatible with the novel dimension of space multiplexing. More specifically, we will show how mode-selective wavelength conversion based on four-wave mixing can be realized in a multimode silicon waveguide.
We investigate the possibility of obtaining phase-sensitive amplification (PSA) in a fiber-optic parametric amplifier (OPA), with gain independent of the state of polarization of the input signal, i.e., polarization-independent amplification. We consider both a single OPA with two orthogonal pumps and a polarization-diversity scheme. In either case, PSA with maximum gain is possible, provided that the signal and idler are in suitably matched polarization states; this condition is naturally satisfied by the output fields of an upstream polarization-insensitive amplifier of the same type. Two polarization-multiplexed signals can then be simultaneously amplified in the PSA. The low noise figure can also be obtained with these types of PSA. However, in general, this favorable situation is not maintained if the signal and idler states of polarization drift together due to birefringence fluctuations in a transmission fiber preceding the PSA.