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Journal of Modern Optics

Graphical Representation of Self-phase Modulation Noise

Keith J. Blow, R. Loudon, Simon J. D. Phoenix

Published Dec 1, 1993• 9 citations
Publisher

Abstract

We develop graphical representations of the noise characteristics imposed on initially coherent light by the process of self-phase modulation in an optical fibre. The graphical methods provide physical understanding of the squeezing that sets in at the shorter propagation distances, and the subsequent desqueezing that occurs as the distance of propagation is increased. They also provide quantitative agreement with the results of the quite complicated analytical theory of self-phase modulation.

DOI
10.1080/09500349314552501

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We develop graphical representations of the noise characteristics imposed on initially coherent light by the process of self-phase modulation in an optical fibre. The graphical methods provide physical understanding of the squeezing that sets in at the shorter propagation distances, and the subsequent desqueezing that occurs as the distance of propagation is increased. They also provide quantitative agreement with the results of the quite complicated analytical theory of self-phase modulation.
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Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
Polarisation squeezing in optical fibres is an efficient means of producing highly squeezed light. Because the experiments operate in a very nonclassical regime, the results are very sensitive to additional nonlinear and thermal effects in the fibre. To quantitatively characterise such experiments, we perform first-principles, quantum dynamical simulations of intense, ultrashort pulses in a fibre, including all significant quantum and thermal noise. We compare simulation and experiments to find excellent agreement over a wide range of pulse energies and fibre lengths.
Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.
We develop a travelling-wave formulation of the theory of quantum optics and apply it to the description of the self-phase modulation of a short coherent pulse of light. The infinite nonlinear phase shift that is produced by the vacuum fluctuations is treated, within our approach, through a renormalization procedure. The renormalized theory successfully describes the nonlinear chirp that the pulse undergoes in the course of its propagation and permits the calculation of the squeezing characteristics of self-phase modulation.
The part played by higher-order optical nonlinearities in self-squeezing of intense light propagating in a nonlinear Kerr medium is discussed. An analytical formula for the normally ordered variances of the field is derived under the assumption that the nonlinearity parameters of the medium are small and the number of photons is very great. The saddle-point approach is used to evaluate the sums over large numbers of photons. The analytical formula is illustrated graphically for several sets of nonlinearity coefficients. It is shown that, for large numbers of photons, the higher-order contributions are substantial and can modify the magnitude of squeezing as well as the range of the parameters over which squeezing can be observed.