Resonant-state Expansion for Periodic Open Optical Systems
Lead Research Organisation:
Cardiff University
Department Name: School of Physics and Astronomy
Abstract
The resonant state expansion (RSE) is a rigorous perturbative method recently invented in Cardiff School of Physics and Astronomy. The RSE has been developed and used for relativistic wave equations describing such open systems as planar, cylindrical and spherical optical resonators with various perturbations. The method was demonstrated to be particularly suitable for calculating high-quality modes in such open system and efficient and accurate in calculating their perturbations. It has been shown that the RSE is a few orders of magnitude quicker computational tool as compared to existing commercial software packages like ComSol or Lumerical.
One of the main aims of the project is to apply the RSE to non-relativistic wave equations and develop a theory of resonant states in quantum-mechanical systems. In particular, the RSE will be applied to Schrödinger's wave equation describing an electron/exciton in various nanostructures with effectively one-, two- and/or three-dimensional potentials and various perturbations. The efficiency and the quality of the new method will be investigated and tested against the existing finite difference methods and ab initio calculations. The concept of resonant states will also be used to investigate the short and long-time behaviour of quantum states and to calculate a non-quadratic (non-exponential) decay of the survival probability of quantum states at short (long) times.
The project will also consider some further applications of the RSE in relativistic problems. This may include calculation of eigenstates in optical planar waveguides and photonic crystal fibres where everlasting waveguide modes contribute to expansions of the Green's function. Finally, there will be made attempts towards generalisation of the RSE for relativistic Dirac wave equation with a potential application of the method to narrow-band semiconductor nanostructures.
One of the main aims of the project is to apply the RSE to non-relativistic wave equations and develop a theory of resonant states in quantum-mechanical systems. In particular, the RSE will be applied to Schrödinger's wave equation describing an electron/exciton in various nanostructures with effectively one-, two- and/or three-dimensional potentials and various perturbations. The efficiency and the quality of the new method will be investigated and tested against the existing finite difference methods and ab initio calculations. The concept of resonant states will also be used to investigate the short and long-time behaviour of quantum states and to calculate a non-quadratic (non-exponential) decay of the survival probability of quantum states at short (long) times.
The project will also consider some further applications of the RSE in relativistic problems. This may include calculation of eigenstates in optical planar waveguides and photonic crystal fibres where everlasting waveguide modes contribute to expansions of the Green's function. Finally, there will be made attempts towards generalisation of the RSE for relativistic Dirac wave equation with a potential application of the method to narrow-band semiconductor nanostructures.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509449/1 | 01/10/2016 | 30/09/2021 | |||
| 1796606 | Studentship | EP/N509449/1 | 01/10/2016 | 30/04/2020 | Sam Neale |
| Description | Expanded the application of the resonant state expansion (RSE) method, a rigorous perturbative method developed to find the resonant states in optical and dispersive systems, to include photonic crystal structures. Resonant states are discrete complex modes that contain all the information required to study light's transmission through a structure and how strongly it is bound the structure. Used the RSE method to find and investigate bound states in the continuum in photonic crystals which are modes of the system which are bound yet exist at frequencies which should radiate energy away into the conintuum. These states have gained a lot of interest in recent years and the RSE provides an efficient way to find them and also can reveal some information about their formation. |
| Exploitation Route | The fastest method of finding resonant states in optical systems currently in mainstream research is the scattering matrix method (SMM). The RSE is much faster and able to handle much more complex permittivities. We hope that RSE will become the new mainstream method for finding resonant states. Photonic crystal structures are particularly useful in their ability to guide light, the photonic crystal RSE developed here can allow researchers to find just how much light is being guided and how much energy is lost to the surrounding environment. Bound states in the continuum are high Q-factor modes with extremely sharp features in the transmission spectrum, this is useful for applications such as lasers, sensing and filtering. The RSE provides insight into these modes and can easily find their frequencies since it is so computationally lightweight. |
| Sectors | Digital/Communication/Information Technologies (including Software),Electronics |