Classical electromagnetism:
On the classical end, I am interested in a variety of subjects, ranging from nonlinear optics, to photonic quasicrystals, to fluctuation-induced interactions. The latter include Casimir forces and thermal properties of photonic media.
Nonlinear optics: Understanding the origins, limitations and applications of these interactions continues to drive the field of nonlinear optics. The dream of a scalable optical computer, and the demand for ultra-fast energy-efficient integrated nonlinear devices has attracted notable theoretical interest; and in particular, on the problem of manipulating the strength and timescales of these interactions. If I were to find a way to enhance and modify photon nonlinearities by orders of magnitude, I would probably dance Cuban conga and "guaguanco" in the middle of 77 Mass Ave for a whole day.
Quasicrystals: Quasicrystals are, as suggested by their name, "almost crystals". They are often informally described as quasiperiodic structures possesing long-range order. It is well known that three-dimensional quasicrystals can offer high degrees of rotational symmetry, raising questions regarding the possibility of obtaining large three dimensional band gaps with low index contrasts. However, the current lack of exact numerical and analytical techniques capable of describing three dimensional quasicrystals has hampered further experimental work, many of which remain questionable and controversial. I along with collaborators have been interested in solving the problem by use of Bloch's theorem in higher dimensions. If we can obtain an exact three-dimensional spectrum, I will consider becoming a vegetarian.
Casimir forces: While I have shamelessly written the following sentence more often than I can remember, and while it may not provide much of a description to the unfamiliar, I feel it impossible to omit, since it has it's place in my list of "cool-sounding" phrases: "Casimir forces arise between uncharged macroscopic bodies due to changes in the zero-point energy associated with quantum and thermal fluctuations of the electromangetic field". In a nutshell, the fluctuations of the electromagnetic field in vaccum or matter depend on the boundary conditions that the fields need satisfy. As turns out, the most usual energetically favorable configuration found so far has given rise to an attractive force between two objects. These have been studied in simple geometries where solutions become analytically tractable. My interests lie in the search for formulations that can adequately and efficiently describe the force in more complex structures. Our recent works describe a general approach to computing Casimir forces that seems to be both efficient and simple. Using this method, we have discovered interesting effects like nonmonotonic and repulsive forces. I am currently working on a different formulation that involves stochastic variables. If such a formulation proves useful, I shall learn flamenco.
Thermal fluctuations: Coming soon.
Quantum electromagnetism: Coming soon.
Single-photon-atom interactions: Coming soon.