Inverse design in photonics: Combining the resonant-state expansion with machine learning

Electromagnetic resonances are widely exploited in modern technologies, and significant advance in their simulation and underlying understanding has an extensive field of applications with a potential impact on society. For example, nanoplasmonics, dealing with optical phenomena in the nanoscale vicinity of metallic surfaces, has yielded practical applications in physics, engineering, biomedicine, and even for environmental monitoring and homeland security. Plasmonic resonances can probe nanoscale regions close to of a metallic nanoparticle (NP), enabling nano-spectroscopy for biomedical sensing. Dielectric resonators with long-lived modes, such as whispering-gallery modes reaching the quality factor of billions, are another example. They can be used as biosensors with single molecule detection sensitivity, providing access to sensing the structure of individual biomolecules, such as DNA. They are also the basis of spectral filters and frequency comb generation in integrated photonics. Furthermore, integrated optical circuits are increasingly relevant in computing, and building blocks such as beam-splitters, resonators need to be designed and optimised.

A host of methods in computational electrodynamics are presently employed for calculating resonances in optical systems and modelling light scattering, and their computational codes have been optimised over the past decades to increase their accuracy and speed. However, the forward design of complex resonators or solving the inverse problem using these methods is still severely restricted by available computational power. The resonant-state expansion (RSE), developed [1] by the supervisors, provides an alternative method for accurate and efficient calculation of resonances in arbitrary open optical systems, which can be orders of magnitude more computationally efficient [2] than other methods. Its continuous development over the last decade, reported in over 30 original publications, has opened up a new field attracting other research groups in the UK and worldwide.

The RSE enables accurate and efficient calculation of all relevant resonances of a system and their use for determining the measurable optical properties, such as absorption and scattering cross-sections [3]. Although the formalism of the RSE is analytically advanced, its practical application is technically straightforward. In fact, using a complete set of the resonant states of a simpler system as a basis, the RSE maps Maxwell’s equations onto a linear eigenvalue problem, which determines the resonant states of the target system by established matrix diagonalisation methods.

The RSE development has improved the accuracy and speed in solving the forward problem, from structure to optical response. However, solving the inverse problem, from optical response to structure requires an iterative minimisation using forward solutions, and is notoriously slow. You will address this issue, by using the high speed of the RSE to provide a forward data set sampling the structural parameter space and train machine learning /artificial intelligence (ML/AI) models for solving the inverse problem of determining the structure from the optical properties. A platform based on the RSE and ML/AI will be developed and made publicly available.

Aligned with ongoing experimental activity and the development of the Nanosizer technology [4] in the supervisors groups, the project will use as examples the extinction and absorption cross-section spectra of plasmonic NPs of various shapes, such as decahedra, tetrahedra, etc [5]. Presently, modelling the response of a single NP shape at a given excitation wavelength, direction and polarisation takes a few tens of seconds with COMSOL on a workstation, so calculating an experimental spectral response being an average over many excitation parameters take days. Creating a sufficiently large training set to cover a small structural parameter space, for example three parameters with 10 values each, takes years, and even supercomputers would require hours to days. 

You will be trained in electromagnetism, the RSE and the commercial solvers COMSOL and Lumerical, as well as in using ML/AI and programming in python and matlab. You will work with experimental methods to measure optical responses. You will present at international conferences, improving your communication skills, and benefit from training in transferable skills offered by the Doctoral Academy. You will join a vibrant multi-disciplinary supervisory team and their groups, across the School of Physics and Astronomy and School of Biosciences, offering cross-disciplinary training and development opportunities. The principles of Responsible Research and Innovation are embedded in the project, providing training on the legal ethical frameworks, publication ethics and responsible research behaviour.

How to apply:

Applicants should apply to the Doctor of Philosophy in Physics and Astronomy with a start date of 1st January 2025. 

Applicants should submit an application for postgraduate study via the Cardiff University webpages

• your academic CV

• Your degree certificates and transcripts to date including certified translations if these are not in English 

• two references, at least one of which should be academic. Your references can be emailed by the referee to [email protected]  

Please note: We are do not contact referees directly for references for each applicant due to the volume of applications we receive.  

 • personal statement

The typical academic requirement is a minimum of a 2:1 physics and astronomy or a relevant discipline. 

Applicants whose first language is not English are normally expected to meet the minimum University requirements (e.g. IELTS 6.5 Overall with 5.5 minimum in sub-scores) (https://www.cardiff.ac.uk/study/international/english-language-requirements) 

In the “Research Proposal” section of your application, please specify the project title and supervisors of this project.

In the funding section, please select that you will not be self-funding and write that the source of funding will be EPSRC. 

Once the deadline for applications has passed, we will review your application and advise you within a few weeks if you have been shortlisted for an interview. 

Eligibility :

EPSRC DTP studentships are available to home and international students. Up to 30% of our cohort can comprise international students, once the limit has been reached we are unable to make offers to international students. International students will not be charged the fee difference between the UK and international rate. Applicants should satisfy the UKRI eligibility requirements.

For more information, or if there are any questions, please contact Physics and Astronomy PGR Student Support team at [email protected]

Please also check the following link: https://www.cardiff.ac.uk/study/postgraduate/funding/research-councils/epsrc-studentships