164 research outputs found
Self-consistent multi-mode lasing theory for complex or random lasing media
A semiclassical theory of single and multi-mode lasing is derived for open
complex or random media using a self-consistent linear response formulation.
Unlike standard approaches which use closed cavity solutions to describe the
lasing modes, we introduce an appropriate discrete basis of functions which
describe also the intensity and angular emission pattern outside the cavity.
This constant flux (CF) basis is dictated by the Green function which arises
when formulating the steady state Maxwell-Bloch equations as a self-consistent
linear response problem. This basis is similar to the quasi-bound state basis
which is familiar in resonator theory and it obeys biorthogonality relations
with a set of dual functions. Within a single-pole approximation for the Green
function the lasing modes are proportional to these CF states and their
intensities and lasing frequencies are determined by a set of non-linear
equations. When a near threshold approximation is made to these equations a
generalized version of the Haken-Sauermann equations for multi-mode lasing is
obtained, appropriate for open cavities. Illustrative results from these
equations are given for single and few mode lasing states, for the case of
dielectric cavity lasers. The standard near threshold approximation is found to
be unreliable. Applications to wave-chaotic cavities and random lasers are
discussed.Comment: 18 pages, 9 figure
Sub-kHz lasing of a CaF_2 Whispering Gallery Mode Resonator Stabilized Fiber Ring Laser
We utilize a high quality calcium fluoride whispering-gallery-mode resonator
to stabilize a simple erbium doped fiber ring laser with an emission frequency
of 196 THz (wavelenght 1530 nm) to a linewidth below 650 Hz. This corresponds
to a relative stability of 3.3 x 10^(-12) over 16 \mus. In order to
characterize the linewidth we use two identical self-built lasers and a
commercial laser to determine the individual lasing linewidth via the
three-cornered hat method.Comment: 4 pages, 3 figure
Discrete and fuzzy dynamical genetic programming in the XCSF learning classifier system
A number of representation schemes have been presented for use within
learning classifier systems, ranging from binary encodings to neural networks.
This paper presents results from an investigation into using discrete and fuzzy
dynamical system representations within the XCSF learning classifier system. In
particular, asynchronous random Boolean networks are used to represent the
traditional condition-action production system rules in the discrete case and
asynchronous fuzzy logic networks in the continuous-valued case. It is shown
possible to use self-adaptive, open-ended evolution to design an ensemble of
such dynamical systems within XCSF to solve a number of well-known test
problems
Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators
We study lasing emission from asymmetric resonant cavity (ARC) GaN
micro-lasers. By comparing far-field intensity patterns with images of the
micro-laser we find that the lasing modes are concentrated on three-bounce
unstable periodic ray orbits, i.e. the modes are scarred. The high-intensity
emission directions of these scarred modes are completely different from those
predicted by applying Snell's law to the ray orbit. This effect is due to the
process of ``Fresnel filtering'' which occurs when a beam of finite angular
spread is incident at the critical angle for total internal reflection.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, submitted to Phys. Rev. Lett;
corrected a minor (transcription) erro
Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity
We have investigated quasi-eigenmodes of a quadrupolar deformed microcavity
by extensive numerical calculations. The spectral structure is found to be
quite regular, which can be explained on the basis of the fact that the
microcavity is an open system. The far-field emission directions of the modes
show unexpected similarity irrespective of their distinct shapes in phase
space. This universal directionality is ascribed to the influence from the
geometry of the unstable manifolds in the corresponding ray dynamics.Comment: 10 pages 11 figure
Squeeze-and-Breathe Evolutionary Monte Carlo Optimisation with Local Search Acceleration and its application to parameter fitting
Motivation: Estimating parameters from data is a key stage of the modelling
process, particularly in biological systems where many parameters need to be
estimated from sparse and noisy data sets. Over the years, a variety of
heuristics have been proposed to solve this complex optimisation problem, with
good results in some cases yet with limitations in the biological setting.
Results: In this work, we develop an algorithm for model parameter fitting
that combines ideas from evolutionary algorithms, sequential Monte Carlo and
direct search optimisation. Our method performs well even when the order of
magnitude and/or the range of the parameters is unknown. The method refines
iteratively a sequence of parameter distributions through local optimisation
combined with partial resampling from a historical prior defined over the
support of all previous iterations. We exemplify our method with biological
models using both simulated and real experimental data and estimate the
parameters efficiently even in the absence of a priori knowledge about the
parameters.Comment: 15 Pages, 3 Figures, 6 Tables; Availability: Matlab code available
from the authors upon reques
An efficient Fredholm method for calculation of highly excited states of billiards
A numerically efficient Fredholm formulation of the billiard problem is
presented. The standard solution in the framework of the boundary integral
method in terms of a search for roots of a secular determinant is reviewed
first. We next reformulate the singularity condition in terms of a flow in the
space of an auxiliary one-parameter family of eigenproblems and argue that the
eigenvalues and eigenfunctions are analytic functions within a certain domain.
Based on this analytic behavior we present a numerical algorithm to compute a
range of billiard eigenvalues and associated eigenvectors by only two
diagonalizations.Comment: 15 pages, 10 figures; included systematic study of accuracy with 2
new figures, movie to Fig. 4,
http://www.quantumchaos.de/Media/0703030media.av
Application of Permutation Genetic Algorithm for Sequential Model BuildingâModel Validation Design of Experiments
YesThe work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient Design of Experiment (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to support an exploration-based sequential DoE strategy for complex real-life engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of Model BuildingâModel Validation (MB-MV) sequences, by generating optimal infill sets of test points as OLH DoEs, that preserve good space filling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB-MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back (SHCB) function, as well as the Gasoline Direct Injection (GDI) engine steady state engine mapping problem that motivated this research. The case studies show that the algorithm is effective at delivering quasi-orthogonal space-filling DoEs with good properties even after several MB-MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The practical importance of this work, demonstrated through the engine case study, also is that significant reduction in the effort and cost of testing can be achieved.The research work presented in this paper was funded by the UK Technology Strategy Board (TSB) through the Carbon Reduction through Engine Optimization (CREO) project
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