# Computational "Renaissance man": Humble and Curious!

## PERSONAL STATEMENT

**Dr. Alexander R. May MIET MInstP MIMA**

I currently work as a Research Fellow at the University of Exeter on the TEAM-A Metamaterials project, on secondment to QinetiQ. Prior to this I worked at a start-up company near Oxford where my focus was on the design of diffractive optical elements for the Augmented Reality (AR) market (e.g Google Glasses).

I completed a PhD at the University of Southampton in Optoelectronics where I studied novel inverse-scattering approaches to the design of optical fibres and waveguides. To date I have worked in a variety of fields, including Mechanical and Electrical Engineering, with the common thread being Mathematical Modelling, which is my passion. I like to think that my background gives me 'out of the box' insights ' which I can then use to develop novel solutions to problems. I also find it useful to 'get my hands dirty' and do lab experiments to develop further intuition.

In time I hope to provide some notes on this site to catalog the topics that I have worked on!

My current line-manager refers to me as a '**Computational ****Renaissance man**', and I'd like to think that pretty much sums it up!

**The areas I am currently working on include (but are not limited to!):**

(1) Imaging through atmospheric turbulence (e.g. correcting distorted images?)

(2) The optical response of nanophotonic and nanoplasmonic structures (e.g. Lycurgus Cup?)

(3) The characterisation (and modelling!) of optical scatter from material (e.g. skin in computer games?) surfaces

(4) The modelling of wind-blown sea surfaces and their optical scatter (e.g. detecting pollution from above?)

(5) The microwave characterisation (and modelling!) of dielectrics and their permittivity (e.g. non-destructive testing)

(6) The optical scatter in turbid media (quality of olive oil?)

**I also tend to get intrigued by random problems I find around the home with a wife and two kids, such as:**

(1) What is the most efficient way to sort odd socks?

(2) Is my kids' bad behaviour in some way synonymous to coupled non-linear oscillators?

(3) How might you model the varying 'mood' of someone (me!) on a daily basis

(4) How might you model the oscillations of my car and caravan when towing on a bumpy road?

(5) How might the forces be distributed in the alloy wheel 'spokes' of my family car?

**...**

In the meantime, please take a look at one popular science article I have written on the topic of modelling ocean surfaces:

## SOME PUBLICATIONS (IN THE OPEN LITERATURE)

### INVERSE SCATTERING DESIGNS OF ACTIVE MULTIMODE WAVEGUIDES WITH TAILORED MODAL GAIN

November 2015

Darboux inverse scattering transforms are used to design active waveguides with individually tailored modal gain, introducing areas of distributed gain and loss inside the waveguide. Potential applications of such devices include multimode optical amplifiers for which mode-dependent loss and its associated deleterious effects on channel capacity have been compensated. We also show that the commonly used ring-doping approach to modal gain equalization in fibers is a sub-set of the design approach utilizing gain and loss that derives from inverse scattering theory

### FEW-MODE FIBERS WITH IMPROVED MODE SPACING

June 2015

Presented at ECOC 2015 in Valencia, Spain

### INVERSE SCATTERING DESIGNS OF MODE-SELECTIVE WAVEGUIDE COUPLERS

April 2015

We describe the design of arbitrary mode-selective waveguide couplers through application of the Darboux transform of inverse scattering theory. We demonstrate that contrary to recent SUSY designs, it is not necessary to use complex refractive index profiles to achieve this.

### INVERSE SCATTERING DESIGNS OF DISPERSION-ENGINEERED PLANAR WAVEGUIDES

February 2015

We have introduced a semi-analytical IS technique suitable for multipole, rational function reflection coefficients, and used it for the design of dispersion-engineered planar waveguides. The technique is used to derive extensive dispersion maps, including higher dispersion coefficients, corresponding to three-, five- and seven-pole reflection coefficients. It is shown that common features of dispersion-engineered waveguides such as refractive-index trenches, rings and oscillations come naturally from this approach when the magnitude of leaky poles in increased. Increasing the number of poles is shown to offer a small but measureable change in higher order dispersion with designs dominated by a three pole design with a leaky pole pair of the smallest modulus.

### GROUP VELOCITY EQUALISATION IN MULTIMODE WAVEGUIDES USING INVERSE SCATTERING DESIGNS

August 2014

In this paper, using an inverse scattering approach, we describe how the selection of mode effective indices and thus phase velocities can be used to control group velocity in a waveguide. As such it is shown that differential group delay can be equalised or minimised over a wavelength of choice. A particular feature of the new designs is the development of rings and a peaked core which may split depending upon the number of guided modes. These designs show characteristics comparable with commercially available fibres but with refractive index profiles that differ from typical graded-index designs.

### INVERSE SCATTERING DESIGNS OF DISPERSION-ENGINEERED SINGLE-MODE PLANAR WAVEGUIDES

February 2014

We use an inverse-scattering (IS) approach to design single-mode waveguides with controlled linear and higher-order dispersion. The technique is based on a numerical solution to the Gelfand-Levitan-Marchenko integral equation, for the inversion of rational reflection coefficients with arbitrarily large number of leaky poles. We show that common features of dispersion-engineered waveguides such as trenches, rings and oscillations in the refractive index profile come naturally from the IS algorithm without any a priori assumptions. Increasing the leaky-pole number increases the dispersion map granularity and allows design of waveguides with identical low order and differing higher order dispersion coefficients.

### INFORMATION THEORY: LEARNING THROUGH EXAMPLE

September 2012

In this paper, the perceived difficulty for students learning purely through auditory and visual means, such as via the standard lecture format, is highlighted through a literature review of learning styles and methods, and a solution based upon interactive computer case-based learning through worksheets is proposed. A brief history of Information Theory is discussed and a review of the various software packages available is made and Mathematica selected. The contents of the worksheets are described and conclusions made.