| Abstract [eng] |
This work investigates the possibility of compensating the optical Kerr-induced self-focusing by precise control of spatial dispersion using photonic crystals. To this end, a split-step beam propagation method algorithm was written. The spatial dispersion curves formed by photonic crystals were analysed. The effects of photonic crystal parameters on spatial dispersion curvature were investigated. The interaction of the modified spatial dispersion and nonlinear self-focusing was analysed. Finally, attempts to fabricate photonic crystals as those described were made. Using the beam propagation method, the spatial dispersion curves formed by various photonic crystals were investigated. As expected, it was shown that a photonic crystal with a constant period and a geometric constant near 1 induces spatial dispersion with three separate curves. It is shown that applying an adiabatic chirp to the start of the photonic crystal makes it possible to project the radiation to a specific spatial dispersion curve. It was determined that while chirping both the longitudinal period and the scattering coefficient is the best way to do it, chirping solely the longitudinal period also provides good results, whereas chirping only the scattering coefficient is ineffective. Five distinct spatial dispersion regimes are attainable using such photonic crystals, though most importantly, for geometric constant values Q > 1 – strengthened diffraction is possible, while for values Q < 1 – strengthened anti-diffraction is possible, with the strongest diffraction being at values closer to the Talbot resonance. 2D linear simulations show that chirping helps control the strength of diffraction and reduces the amount of energy scattered at the front interface of the photonic crystal. 3D nonlinear simulations with photonic crystals with a geometric constant Q > 1 show promise for compensation of nonlinear self-focusing. Indeed, using a photonic crystal with Q = 1,20 an almost perfectly collimated beam is achieved, retaining reasonably high peak intensity as far as 8 mm from the start while successfully preventing spatial beam collapse even using beam power 30 % higher than designed. The high beam intensity localization is a good sign for potential supercontinuum generation. Simulations with photonic crystals with Q < 1 show poorer results. Nonlinear self-focusing compensation was only achievable with significant energy losses. This is likely because to reach the strengthened anti-diffraction regime; we first have to pass the zero-diffraction regime. In conclusion, varying the photonic crystal geometric constant Q allows the fine-tuning of spatial dispersion, giving control of beam diffraction. Chirping the longitudinal period allows most incident radiation to project to the desired spatial dispersion curve. Proper selection of photonic crystal parameters allows for full compensation of nonlinear self-focusing. |
