Dr Mark Doost


e: DoostM@Cardiff.ac.uk
t: 029 208 76782
w: http://www.astro.cardiff.ac.uk/contactsandpeople/?page=full&id=570

The main goal of my research has been has been to develop the RSE for treatment of effectively 1D, 2D, and 3D systems to cover all physically relevant structures. My contribution can be summarized as follows. The projects fall into three areas which have produced four papers: • I applied the RSE to planar, effectively one-dimensional optical systems, such as layered dielectric slabs including Bragg reflector microcavities. I demonstrated that the RSE converges with a power law in the basis size. I presented and evaluated algorithms for error estimation and their reduction by extrapolation. I calculated complex eigenfrequencies, electromagnetic fields, and the Green's function of a selection of optical systems, as well as the observable transmission spectra, I showed that the transmission calculated using the RSE reproduces the results of the established transfer- or scattering-matrix methods. • I applied the RSE to effectively two-dimensional open optical systems. I used the analytically solvable homogeneous dielectric cylinder as an unperturbed system, and I found it’s Green’s function contains a cut in the complex frequency plane, which I included in the RSE basis. The complex eigenfrequencies of modes were calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film, and thin-wire perturbation, demonstrating the accuracy and convergency of the method. I showed resonant states for the thin-wire perturbation reproduce an approximative analytical solution. I proved mathematically that the spectral representation of the Green’s function in terms of resonant states is valid for a system of arbitrary dielectric profile. • I applied the RSE to three-dimensional open optical systems. I used the analytically solvable homogeneous dielectric sphere as an unperturbed system. I included the pole at zero frequency important for TM modes. I calculated complex eigenfrequencies of modes using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum and azimuthal momentum, such as half-sphere and quarter sphere perturbations, demonstrating the accuracy and convergence of the method. I proved mathematically that the flux volume normalisation of resonant states required for their use in the spectral Green’s function is valid for an arbitrary system. Publications M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to planar open optical systems”, Phys. Rev. A 85, 023835 (2012). M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant-state expansion applied to planar open optical systems”, Phys. Rev. A 85, 023835 (2012). L. J. Armittage, M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant state expansion applied to planar waveguides”, Phys. Rev. A 89, 05382 (2014). M. B. Doost, W. Langbein, and E. A. Muljarov, “Resonant state expansion applied to three-dimensional open optical systems” (accepted for publication in Phys. Rev. A). Presentations Poster - Resonant state expansion applied to planar open optical systems 2011 Conference on cold atoms, semiconductor polaritons and nanotechnology Poster - Resonant state expansion applied to two-dimensional open optical systems 2013 Symposium on Bio-Nano-Photonics

Dr Mark Doost is (or has formerly been) affiliated with Cardiff University and Condensed Matter and Photonics Group, Cardiff University.

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