Konstantinos G. Makris

Theory of coupled optical PT-symmetric structures

Starting from Lagrangian principles we develop a formalism suitable for describing coupled optical parity-time symmetric systems.

Discrete surface solitons.

It is theoretically shown that discrete nonlinear surface waves are possible in waveguide lattices. These self-trapped states are located at the edge of the array and can exist only above a certain power threshold. The excitation characteristics and stability properties of these surface waves are systematically investigated.

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.

Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials

We present closed form solutions to a certain class of one- and two-dimensional nonlinear Schr¨ odinger equations involving potentials with broken and unbroken PT symmetry. In the one-dimensional case, these solutions are given in terms of Jacobi elliptic functions, hyperbolic and trigonometric functions. Some of these solutions are possible even when the corresponding PT -symmetric potentials have a zero threshold. In two-dimensions, hyperbolic secant type solutions are obtained for a nonlinear Schr¨ odinger equation with a nonseparable complex potential.

All-optical switching and multifrequency generation in a dual-core photonic crystal fiber.

We demonstrate all-optical switching at 1550 nm between two weakly coupled cores in a photonic crystal fiber for intensities up to 0.5 TW/cm2. Spectrum analysis at higher intensities reveals that the output was dominated by continuum generation primarily towards shorter wavelengths.

Observation of discrete quadratic surface solitons

We report the first observation of discrete quadratic surface solitons in self-focusing and defocusing periodically poled lithium niobate waveguide arrays. By operating on either side of the phase-matching condition and using the cascading nonlinearity, both in-phase and staggered discrete surface solitons were observed. This represents the first experimental demonstration of staggered/gap surface solitons at the interface of a semi-infinite nonlinear lattice. The experimental results were found to be in good agreement with theory.

Constant-intensity waves and their modulation instability in non-Hermitian potentials

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a waves constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

Optical modes at the interface between two dissimilar discrete meta-materials

We have studied theoretically and experimentally the properties of optical surface modes at the hetero-interface between two meta-materials. These meta-materials consisted of two 1D AlGaAs waveguide arrays with different band structures.

Superoscillatory diffraction-free beams

It is widely known that any beam with subwavelength characteristics will diffract very fast and these features will not propagate into the far field. This is due to the existence of evanescent waves, which diffract in the near field. By using the counter-intuitive effect of superoscillations [1] we show that it is possible to create a superoscillatory diffraction free beam by superimposing already known diffraction-free [2] solutions (Bessel beams for example) of Helmholtz equation. Such optical beams do not contain any evanescent waves and can propagate practically undistorted carrying these subwavelength features into the far field. Superoscillations have been recently studied and introduced to optics in the context of superresolution [3], and subwavelength focusing [4].

Scalable numerical approach for the steady-state ab initio laser theory

We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need of setting up a parametrized basis of constant flux states. We validate this approach in one-dimensional as well as in cylindrical systems, and demonstrate its scalability to full-vector three-dimensional calculations in photonic-crystal slabs. Our method paves the way for efficient and accurate simulations of microlasers which were previously inaccessible.