EPSRC DLA: Topological monopole in 3D metamaterials

In recent advancements in optics, topology has played a pivotal role in enabling unprecedented light propagation, such as unidirectional modes. Topological photonics focuses on the concept of topological photonic band gaps, which facilitate robust edge and corner states in two-dimensional photonic crystals or metamaterials. These localised states, whether dipolar or quadrupolar, are spatially confined in two dimensions. Similar principles have been extended to three-dimensional optical structures featuring more diverse topological states, known as higher-order topological insulators, which are based on multipole expansions accounting for dipolar polarizations and higher-order effects. However, no theoretical or experimental evidence of topologically protected optical monopoles in 3D structures has been reported so far.

A valuable framework for describing one-dimensional or two-dimensional photonic topological structures involves engineering mass terms in the Dirac equation. Using this theoretical approach, known as the Jackiw-Rebbi model, conventional lasers like distributed feedback (DFB) lasers and vertical-cavity surface-emitting lasers (VCSELs) can be interpreted as topological structures characterized by different signs of the mass parameter. This approach to engineering photonic bands can be extended to three dimensions by incorporating three-dimensional mass terms into the Jackiw-Rebbi model. Recent research has demonstrated the existence of topological monopole modes in acoustic metamaterials [H. Cheng et al., Nat. Comm. 15, 7327 (2024)], but their optical counterparts have yet to be realized.

This project aims to design and fabricate optical monopoles in 3D optical metamaterials operating at visible wavelength working within the groups of Oh (https://profiles.cardiff.ac.uk/staff/ohs2 )and Ladak (www.ladaklab.com)

Specifically, the PhD student will employ the 3D Jackiw-Rebbi model and numerical simulation tools such as the finite-element-method (FEM) and the finite-difference time-domain (FDTD) method to design nanowire metamaterials. The student will then use two-photon lithography and deposition at Cardiff University in order to realise designed structures with features at a scale of approximately 100nm.

Finally, the optical properties of these samples will be characterised using near-field scanning optical microscopy (NSOM) at the National Physical Laboratory. Overall, we expect the project to yield for the first time, 3D optical metamaterials which are home to topological monopoles.

How to apply:

Applicants should apply to the Doctor of Philosophy in Physics and Astronomy with a start date of 1st October 2026.

Applicants should submit an application for postgraduate study via the Cardiff University webpages (https://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/physics-and-astronomy) including:

• your academic CV (Guidance on CVs for a PhD position can be found on the FindAPhD website)

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

• a personal statement/covering letter

Ensure your personal statement (as part of the university application form, or as a separate attachment, if you prefer) provides a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Your personal statement should be no more than 500 words, and address the following questions:

1. What are your scientific research interests and ambition?

2. How has your academic and/or professional journey prepared you for PhD study? (for instance, give examples of work you particularly enjoyed, of challenges you overcame, of connecting with others about your work or ideas, of showing inventiveness, of developing new skills and knowledge)

3. Why do you think this project is important?”

• two references (applicants are recommended to have a third academic referee, if the two academic referees are within the same department/school). Your references can be emailed by the referee to physics-admissions@cardiff.ac.uk

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

Candidates should hold or expect to gain a first-class degree or a good 2.1 (or their equivalent) in Engineering, Physics or a related subject. Desirable skills are knowledge of Quantum Physics, Optics, Semiconductors, Technology, Physics, Engineering.

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 and copy the project description in the text box provided.

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 :

This studentships are available to home and 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 re application process, please contact Physics and Astronomy PGR Student Support team at Physics-PG@cardiff.ac.uk

Cardiff University and the School of Physics and Astronomy are committed to supporting and promoting equality and diversity. Our inclusive environment welcomes applications from talented people from diverse backgrounds. We strongly welcome female applicants and those from any ethnic minority group, as they are underrepresented in our School. The School of Physics & Astronomy has a Juno Practitioner accreditation that recognises good employment practice and a commitment to develop the careers of women working in science. The University is committed to ensuring that we sustain a positive working environment for all staff to flourish and achieve. As part of this commitment, the University has developed a flexible and responsive framework of procedures to support staff in managing their work and personal commitments wherever possible. Applications are welcome from individuals who wish to work part-time or full time.

Cardiff University is a signatory to the San Francisco Declaration on Research Assessment (DORA), which means that in hiring and promotion decisions we will evaluate applicants on the quality of their research, not publication metrics or the identity of the journal in which the research is published. More information is available at: Responsible research assessment – research – Cardiff University.

Applications may be submitted in Welsh, and an application submitted in Welsh will not be treated less favourably than an application submitted in English.