Melike B. Yucel

Refraction-based photonic crystal diode

A system composed of air holes in a dielectric host to form two square photonic crystals, with the same orientation and lattice constant but different scatterer radii, making an interface along their body diagonals, is numerically demonstrated to facilitate unidirectional light transmission. Band structure computations are carried out via the plane wave expansion method, whereas finite-difference time-domain simulations are carried out to investigate the transient behavior. Unidirectional light transmission is achieved over two adjacent stop bands along the ΓX direction, which are circumvented in the forward direction by scaling down the wave vector and rotating the surface normal. Contrast ratios as high as 0.9 are attained within the lower stop band.

Edge electrostatics revisited

Abstract In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. [1] , which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture are investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.

Polarization-independent self-collimated beam splitting in two-dimensional photonic crystals

Polarization-independent splitting of self-collimated transverse-electric and transverse-magnetic polarized waves in a two-dimensional square photonic crystal are demonstrated. The beam splitting is facilitated by the existence of sharp edges in flat equifrequency contours.

Quantum Dynamics of Brachistochrone Problem

In this study we discuss the quantum dynamics of a particle, which moves classically on the brachistochrone curve corresponding to the minimization of the time functional, in a linear gravity potential. We derive the Lagrangian and the Hamiltonian of the particle, which moves also on the brachistochrone curve by the minimization of the action functional. The solutions of the Schrodinger’s equation for this Hamiltonian give the energy spectrum, and the confluent hypergeometric functions as the wave functions. The problem combines the infinitewell and harmonic oscillator potentials. We also discuss the solutions of the Schrodinger’s equation for the particle in the periodic extension of the original brachistochrone problem. We show that the band structure arised from Floquet theory and the problem is equivalent to the periodic δ-potential problem for the particle with positive energy in the limit of infinite potential.