On the theory of Helmholtz solitons

Christian, JM

Abstract

This thesis is concerned with spatial optical solitons in (quasi-two
dimensional) planar waveguides, where there is a single longitudinal and
(effectively) a single transverse dimension, and whose symmetry the solutions
respect consistently. A key feature of Helmholtz soliton theory is that, by
recognizing the physical equivalence of the longitudinal and transverse dimensions
in uniform media, it can access experimental contexts involving broad, moderately
intense beams that propagate and interact at arbitrarily large angles. It thus provides
an ideal platform for the systematic generalization of established paraxial results
(restricted to applications involving vanishingly-small angles) to the finite-angle
domain. Helmholtz soliton theory is expected to play a fundamental role in the
design of any futuristic integrated-optic device exploiting the propagation and
interaction of spatial soliton beams at oblique angles relative to a reference direction.
Exact analytical soliton solutions are derived for a variety of newly-proposed
scalar and vector Non-Linear Helmholtz equations. These solutions are valid for a
wide variety of media, such as some semiconductors, doped glasses and non-linear
polymers. Different types of solution classes have been obtained, including
hyperbolic (exponentially localized), algebraic (with power-law asymptotics),
amplitude-kink (where the intensity varies monotonically), and spatially-extended
(such as trigonometric and cnoidal) waves. Exact analytical solutions have also been
obtained in the presence of some higher-order effects - for example, gain/absorption
and saturation of the non-linear refractive index.
Helmholtz solitons are found to exhibit generic features (such as angular
beam broadening), and they reduce to their paraxial counterparts when an
appropriate multiple limit (defining rigorously a paraxial beam) is enforced. Each new solution has been tested under a numerical perturbative analysis that examines
its stability. Helmholtz solitons have been classified largely as robust attractors, in a
non-linear dynamical sense, and this stability is crucial if they are to be exploited
successfully in practical applications.

Citation

Christian, J. On the theory of Helmholtz solitons. (Thesis). Salford : University of Salford

• Thesis Type: Thesis
• Deposit Date: Oct 3, 2012
• Award Date: Jan 1, 2006