Analogue event horizons in dielectric medium

Abstract

In this thesis I numerically study an optical pulse travelling in a dielectric medium as an analogue event horizon. A novel numerical method is developed to study the scattering properties of this optical system. Numerical solutions of scattering problems often exhibit instabilities. The staircase approximation, in addition, can cause slow convergence. We present a differential equation for the scattering matrix which solves both of these problems. The new algorithm inherits the numerical stability of the S matrix algorithm and converges faster for a smoothly varying potential than the S matrix algorithm with the staircase approximation. We apply our equation to solve a 1D stationary scattering of plane waves from a non-periodic smoothly varying pulse/scatterer travelling with a constant velocity in a lossless medium. The properties of stability and the convergence of the Riccati matrix equation are demonstrated. Furthermore, we include a relative velocity between the scatterer and the wave medium to generalise the algorithm further where the number of right and left going modes are not equal. The algorithm is applicable for stationary scattering process from arbitrarily shaped smooth scatterers, periodic or non-periodic, even when the scatterer is varying at the scale of wavelengths. This method is used to present numerical results for a sub-femtoseconds optical pulse travelling in bulk silica. We calculate the analogue hawking radiation from the analogue system. The temperature of the hawking radiation is studied systematically with many different profiles of pulses. We find out steepness, intensity and duration of the pulse are most important in producing analogue hawking radiation in these systems. A better numerical and theoretical understanding will make the experiments better suited to detect hawking radiation.