Optical Rogue Waves and Nonlinear Effects in Hollow-Core Photonic Crystal Fibers

Abstract

In this dissertation, we theoretically study nonlinear optical effects inside hollow core photonic crystal fibers (HCPCFs). In particular, we explore the formation of optical rogue waves near resonance in stimulated Raman scattering inside HCPCF. We further examine the role of coherence time, coherent memory and source noise in the formation of a long-tailed probability density function (PDF) as a signature of ORWs. We also investigate the design of highly nonlinear liquid-filled PCFs for different nonlinear applications. The research performed throughout this thesis leads to the following results. 1. In the case of noisy Stokes pulses, we show that the degree to which the PDF deviates from Gaussian, sharply increases as the source coherence time decreases. Our results establish a clear link between optical coherence and rogue wave theories. 2. In the case of noisy pump pulses, we demonstrate that Stokes power PDF tail increases as the system coherent memory is enhanced. We show that the maximum attainable power level strongly depends on the pump noise level. We develop the analytical theory of noise transfer in the system in the initial stage of SRS within the undepleted pump approximation. 3. We demonstrate that RWs can be excited in a self-similar asymptotic regime of integrable turbulence and they appear as giant fluctuations away from the average (self-similar) evolution of the system. 4. We design a highly nonlinear liquid-filled PCF with a nonlinear coefficient of 7700 W−1km−1 and a total loss lower than 0.3 dB/m. Using the proposed PCF, we theoretically show the possibility of slowing down the group velocity of light to c/50 with a required power of only 25 mW via stimulated Brillouin scattering. 5. We design a carbon-disulfide-filled PCF with nearly-zero dispersion of 0.00007 ps/(nm km) and a dispersion slope of 0.0000018 near 1550 nm. We demonstrate theoretically widely tunable wavelength conversion based on four-wave mixing using the proposed PCF. A 3-dB tunable wavelength conversion bandwidth is about 108 nm and the conversion efficiency is about -10.6 dB.