M.-R. Khodja's Research Interests (1)
Electromagnetic Inverse Source Problem in Antenna Substrate Media: Radiation Enhancement.
In my PhD thesis I investigated, both analytically and numerically, a non-antenna-specific analysis of radiation and source inversion in generally lossy substrate media. This research was motivated by the identified possibility of embedding an antenna in a metamaterial substrate so as to generate a certain field or performance level that may be unachievable, under comparable physical constraints including antenna size. The study was performed via inverse source and constrained optimization theories. This framework complements in analytical and computational tools and insight the pioneering work by some of the leading groups in this area. The adoption of the inverse-source-theoretic approach was aimed at enabling intrinsic, i.e., non-antenna-specific, and fair characterization of different substrate configurations by comparing optimal radiation in either configuration. This characterization is governed by a formally tractable source-energy cost function that is physically motivated by ohmic loss control.
Electromagnetic Inverse Scattering in Substrate Media: Super-resolution Imaging.
At the moment, I am also working on the scalar inverse scattering counterpart of the abovementioned inverse source problem in metamaterial backgrounds. In particular, my goal is to investigate possible enhancements in the imaging resolution of an object embedded in a metamaterial background. I expect that imaging resolution enhancement will be possible in this case due to multiple scattering interactions of the object with a helper substrate that acts as a near-field agent (i.e., a “re-transmitting station”) that facilitates communication to the far field of evanescent field information about the object. In fact, the achieving of super-resolution thanks to multiple scattering, and the re-evaluation of the so-called “diffraction limit” in imaging, is an area that has been receiving much attention in recent years, and is closely connected to the developments in radiation and scattering enhancement due to metamaterials. Like in the metamaterial field, subwavelength resonances in rather simple multiple scattering systems (including systems of only two closely-spaced small scatterers) have also been of interest.
Extensions to the Inverse Source Problem in Antenna Substrate Media
I am interested in the development of a broadband inverse theory, which can be derived as a stepped-frequency approach or as a theory directly in the time domain. Extension to the full-vector context and dispersive embedding media is an important open problem of my interest. Potential future directions for my research also include the development of a general multiport antenna theory for small antennas formed by a number of independently addressable feeding ports which may benefit, e.g., from nano-technology.
Extensions to the Inverse Scattering Problem in Substrate Media
I am interested in expanding my investigation of metamaterial-engendered imaging super-resolution to the full-vector inverse scattering problem in metamaterial substrates including multiple scattering. Another interesting open area for further exploration is the utilization of metamaterials in optical imaging with phaseless data, particularly in the imaging with far-field data.
Electrodynamics of Metamaterials
On account of the identified exciting potential applications of metamaterials, a better understanding of their electrodynamics is in order. For instance, one major problem that plagues the manufacturing of metamaterials is the ubiquitous lossy nature of the meta-cells. I am interested in exploring the effects that replacing ordinary conductors as a base material for the meta-cells with superconducting ones would have on the overall response of these materials. Another area that is still almost completely open and where I believe I can make a difference is the development of a quantum electrodynamical theory in metamatarial backgrounds.
Because of the very promising interplay between metamaterial research and nanotechnology, there is another important topic related to the study of the electrodynamics of metamaterials that I find very interesting. That is nanoelectromagnetics. As a matter of fact, new theoretical models supplemented by numerical studies are essential for the understanding of electromagnetic-wave propagation in media embedded with nanostructures. At a more fundamental level, but no less important and relevant, one may need to recur to quantum electrodynamics not just electromagnetics to elucidate some of the physical properties of these media. This already is an active line of research pursued in connection with the study of carbon nanotubes and graphene sheets and I am interested in exploring it in the context of metamaterials.