13 research outputs found
Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise
The Ornstein-Uhlenbeck process may be used to generate a noise signal with a
finite correlation time. If a one-dimensional stochastic process is driven by
such a noise source, it may be analysed by solving a Fokker-Planck equation in
two dimensions. In the case of motion in the vicinity of an attractive fixed
point, it is shown how the solution of this equation can be developed as a
power series. The coefficients are determined exactly by using algebraic
properties of a system of annihilation and creation operators.Comment: 7 pages, 0 figure
Fluctuation Relations for Diffusion Processes
The paper presents a unified approach to different fluctuation relations for
classical nonequilibrium dynamics described by diffusion processes. Such
relations compare the statistics of fluctuations of the entropy production or
work in the original process to the similar statistics in the time-reversed
process. The origin of a variety of fluctuation relations is traced to the use
of different time reversals. It is also shown how the application of the
presented approach to the tangent process describing the joint evolution of
infinitesimally close trajectories of the original process leads to a
multiplicative extension of the fluctuation relations.Comment: 38 page
Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime
Numerical simulations are used to study how fiber supercontinuum generation
seeded by picosecond pulses can be actively controlled through the use of input
pulse modulation. By carrying out multiple simulations in the presence of
noise, we show how tailored supercontinuum Spectra with increased bandwidth and
improved stability can be generated using an input envelope modulation of
appropriate frequency and depth. The results are discussed in terms of the
non-linear propagation dynamics and pump depletion.Comment: Aspects of this work were presented in Paper ThJ2 at OECC/ACOFT 2008,
Sydney Australia 7-10 July (2008). Journal paper submitted for publication 30
July 200
Schrodinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrodinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication
Optical wave turbulence
We review recent progress in optical wave turbulence with a specific focus on the fast growing field of fibre lasers. Weak irregular nonlinear interactions between a large number of resonator modes are responsible for practically important characteristics of fibre lasers such as spectral broadening of radiation. Wave turbulence is a fundamental nonlinear phenomenon which occurs in a variety of nonlinear wave-bearing physical systems. The experimental impediments and the computationally intensive nature of simulating of hydrodynamic or plasma wave turbulence often make it rather challenging to collect a significant number of statistical data The study of turbulent wave behaviour in optical devices offers quite a unique opportunity to collect an enormous amount of data on statistical properties of wave turbulence using high-speed, high precision optical measurements during a relatively short period of time. We present recent theoretical, numerical and experimental results on optical wave turbulence in fibre lasers ranging from weak to strong developed turbulence for different signs of fibre dispersion. Furthermore, we report on our studies of spectral wave condensate in fibre lasers that make interdisciplinary links with a number of other research fields
Spherical Ornstein-Uhlenbeck processes
The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterised by only one dimensionless number, the persistence angle, which is the typical angle of rotation during the correlation time of the angular velocity. We first show that the two-dimensional case is exactly solvable. When the persistence angle is large, a series for the correlation function has the surprising property that its sum varies much more slowly than any of its individual terms. In three dimensions we obtain asymptotic forms for the correlation function, in the limits where the persistence angle is very small and very large. The latter case exhibits a complicated transient, followed by a much slower exponential decay. The decay rate is determined by the solution of a radial Schrödinger equation in which the angular momentum quantum number takes an irrational value, namely j=½ (√17-1). Possible applications of the model to objects tumbling in a turbulent environment are discussed