Inverse scattering designs of optical waveguides and fibres

Abstract

Optical fibres and waveguides have become vital components in communication systems ranging from on-chip interconnects in datacentres, to trans-oceanic submarine communication cables. Typically, they are designed in a trial-and-error manner and the objective of this thesis was to investigate their inverse design using a method known as inverse-scattering. In contrast to methods of design optimisation where an initial refractive form of index profile of some kind must be chosen, inverse-scattering makes no such assumptions other than that of which modes are carried by the structure and what their respective propagation constants are.

Initially, the control over group-velocity dispersion in a single-mode planar waveguide with fixed propagation constant was investigated by considering the form of the transverse reflection response by which the modal properties of the waveguide may be specified, as discussed in the literature. It was demonstrated that common features of dispersion-engineered waveguides were obtained corroborating their use in the existing literature and further understanding of these features was developed.

Extending the study to multimode planar waveguides through the application of an inverse-scattering method rooted in the quantum mechanical community, the properties of multiple guided modes, such as their group-velocities and modal gain were controlled. The realisation that both gain and loss are required in a refractive index profile to have exact equalisation of modal gain across multiple modes was novel and differed from existing approaches using genetic algorithms. In addition to this, the design of waveguide couplers by which power can be transferred from one waveguide to another was considered by an approach differing from that of the increasingly popular supersymmetric (SUSY) approach in the literature.

Attention turned to the design of few-mode optical fibres which are at the forefront of technology. Since the planar waveguide designs above were found to contain ‘depressions’ and ‘rings’, similar such features were investigated in an optical fibre based upon the knowledge that there were similarities in the modal intensity profiles of the first few linearly polarised (LP) modes in a fibre, and that of the TE modes in planar waveguides. Core depressions and ‘rod-like’ refractive index perturbations were implemented and found to increase the spacing between mode groups.

Following on from the above successes, inverse-scattering techniques were applied directly to the cylindrical symmetry of optical fibres and their associated LP modes. A particular feature of this work was the realisation that the propagation constants of such modes can only be specified at the start of the design process for a fixed value of the azimuthal symmetry of the fibre mode. A finding by other researchers using the SUSY technique had been that the modes in coupled fibres (trunk-partner pairs) could only be ‘matched’ when the azimuthal symmetry of the trunk and partner modes differed. The inverse-scattering method in this thesis, on the other hand, does not have this limitation.

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Identifiers

ORCID for Michael Zervas: orcid.org/0000-0002-0651-4059

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