This chapter focuses on the effects of loss or gain in a graded-index (GRIN) medium. In Section 6.1, we discuss the impact of losses on the modes of such a medium. Section 6.2 considers the mechanisms used for providing optical gain inside a GRIN medium. Section 6.3 is devoted to Raman amplifiers and Raman lasers, built with GRIN fibers and pumped suitably to provide optical gain. Parametric amplifiers are discussed in Section 6.4, together with the phase matching required for four-wave mixing to occur. The focus of Section 6.5 is on amplifiers and lasers made by doping a GRIN fiber with rare-earth ions. Section 6.6 includes the nonlinear effects and describes the formation of spatial solitons and similaritons inside an active GRIN medium.
This chapter focuses on the effects of loss or gain in a graded-index (GRIN) medium. In Section 6.1, we discuss the impact of losses on the modes of such a medium. Section 6.2 considers the mechanisms used for providing optical gain inside a GRIN medium. Section 6.3 is devoted to Raman amplifiers and Raman lasers, built with GRIN fibers and pumped suitably to provide optical gain. Parametric amplifiers are discussed in Section 6.4, together with the phase matching required for four-wave mixing to occur. The focus of Section 6.5 is on amplifiers and lasers made by doping a GRIN fiber with rare-earth ions. Section 6.6 includes the nonlinear effects and describes the formation of spatial solitons and similaritons inside an active GRIN medium.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
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 solitons are expected to play a key role in single-mode optical-fiber communication systems. However, they are still degraded by the linear fiber loss. Therefore, in order to be realistically feasible, soliton-based systems will need repeaters to enhance the signal, and, from a practical point of view, optical amplifiers are preferable to electro-optical ones. The use of Raman nonlinearity,1 and, more recently, the use of rare-earth-doped fibers,2 have been proposed for such optical amplification. We have numerically simulated pulse propagation through singlemode silica fibers doped with passive two-level atoms in an attempt to cancel the linear fiber loss by the well known doping resonant nonlinearities. Our first results, from experiments carried out in a variety of circum-stances, indicate that the linear rate of loss may be diminished with a proper choice of parameters but that the doped fiber by itself is unable to support steady propagation.
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.
A calculation procedure and various large-signal and numerical solutions are presented for degenerate four-wave mixing in optical Kerr media, and for phase conjugate resonators using degenerate four-wave mixing. The solutions presented take full account of nonlinear refractive index changes, pump depletion, signal saturation, distributed losses, and possible external mirrors with laser gain. We find that including the nonlinear index change generally causes little change in the reflectivity or power output of degenerate four-wave mixing devices, at least with symmetric pumping. The optimum power output from a phase conjugate resonator with and without a laser gain medium is calculated. The results provide some theoretical guidance for designing phase conjugate resonators.
PACS Code 42. 65. Bp; 42. 60. Da
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.