Optical wave propagation in periodic systems, guided wave optics, nonlinear optics, optical solitons, discrete solitons in optical lattices, nonlinear surface waves, time-dependent hamiltonians, scalar and vector diffraction theory, superoscillations, disk microlasers, random lasers, self-consistent ab initio laser theory, optical microcavities, non-hermitian optical physics, semiclassical quantum optics.
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Superoscillatory diffractionless optical beams
A recent research topic I am working on is that of optical superoscillations. An open question of fundamental as well as, technological importance in the area of nano-optics and imaging is the transfer of subwavelength information into the far field. Such an important goal is hintered by the inevitable existence of evanescent waves that contain this subwavelength information. Since the evanescent waves cannot propagate into the far field, any subwavelength information is always confined to the near field. A solution to this problem is proposed by the introduction of superoscillatory diffractionless optical beams. In particular, localized diffraction-free beams can propagate undistorted carrying subwavelegth information into the far field. By using the concept of superoscillations we can create superpositions of Bessel beams in order to construct such superoscillatory beams. The applications to subwavelength imaging and fabrication are immediate. This work is in collaboration with the experimental groups of Prof. Psaltis at EPFL, Switzerland, the group of Prof. Segev at Technion, Israel, and the group of Profs. Tzortzakis and Papazoglou at University of Crete, Greece. The group of Prof. M. Segev demonstrated experimentally (2013) for the first time such superoscillatory beams.
Parity-time (PT) symmetry in Optics
Another major research direction was the introduction of the parity-time (PT) symmetry in the framework of Optics. In the seminal work of Bender in 1998 it was shown that it is in fact possible even for non-Hermitian Hamiltonians to exhibit an entirely real eigenvalue spectrum, as long as they are parity-time symmetric. The question posed was whether these ideas could be realized in the context of wave guided optics. Indeed this can be achieved through a judicious design that involves a combination of optical gain or loss regions. We developed the basic theory of PT-symmetric lattices, in both the linear and nonlinear regime. Abrupt phase transitions, band merging, double refraction, beam splitting, power oscillations, non-reciprocity, phase-dislocations and discrete solitons are some of the peculiar characteristics of these exotic PT-optical lattices. Appropriate combination of tools and methods from abstract disciplines such as non-Hermitian operator theory and physics of exceptional points where combined with traditional optical methods to account for a series of experiments, in collaboration with experimental groups of Prof. Kip in Germany and Prof. Segev in Israel. This work opened the way for the first experimental observation of PT-symmetry in any physical system.
Rabi oscillations in z-modulated waveguide arrays
A different direction of my work was the theoretical study of Rabi oscillations in z-dependent Hamiltonians in the context of wave optics. The motivation was the fact that in solid state physics experiments with indirect Rabi transitions are possible only at extremely low temperatures, and as such, they have never been observed before. Our group showed that optical Rabi inter-band transitions are possible in periodically modulated array structures. More interestingly, nonlinear power exchange between two different gap solitons is also possible in that kind of optical systems. The theoretical analysis resulted in the experimental observation of spatial Rabi oscillations occurring in an optical photonic lattice. This work was in collaboration with the experimental groups of Prof. Kip at Clausthal University of Technology, Germany and Prof. Segev at Technion, Israel.
Surface solitons in optical waveguide lattices
Surface waves are known to display properties that have no analogue in the bulk, and over the years have been the subject of intense investigation in various fields of physics. Yet, so far, direct observation of these nonlinear optical surface waves has been hindered by experimental difficulties. The solution to this problem of nonlinear surface-wave physics was given in 2005 by introducing the concept of discrete surface solitons. This approach is attractive because the power response is determined by two easily controllable fabrication parameters, namely the difference between the propagation constants of the channels and the continuous region, and the coupling strength between adjacent waveguides. As a result, our theoretical work led to the first experimental observation of discrete surface solitons at the interface between a Kerr-nonlinear waveguide AlGaAs lattice and a continuum medium. A series of theoretical and experimental papers were published exploring surface solitons in two-dimensional geometries, in hetero-structures, in semi-infinite LiNbO3 lattices with quadratic nonlinearities, in photorefractive two-dimensional lattices always in close collaboration with the experimental groups of Prof. Stegeman at CREOL, of Prof. Segev at Technion, Israel and of Prof. Chen at San Francisco State University, California, USA.
