Kerr Nonlinear Instability: Classical and Quantum Optical Theories - Nesrallah, Michael (Université d'Ottawa / University of Ottawa, 2019)
An important aspect of third-order optical nonlinearity is the intensity-dependent refractive index, where the intensity of the light itself affects the refractive index. This nonlinear effect is known as Kerr nonlinearity. In this work, a theory of amplification based on Kerr nonlinearity is developed. Kerr nonlinearity is well known to exhibit instability. Our amplification theory is based on seeding this instability. The full theory is developed to obtain the vectorial wave equations of the instability. It is shown that for materials of interest, vectorial effects are negligible across the instability regime and the scalar theory gives an accurate account of Kerr instability amplification. It is also shown that this instability analysis is a spatiotemporal generalization to four-wave mixing, modulation instability, and filamentation instability. It fact, it can be considered a seeded conical emission process. Subsequently, the theory of plane wave Kerr instability is explored. Quantitatively, the importance of pump wavelength, linear dispersive properties, and non-collinear angles for optimal amplification are demonstrated. Next, the seed beam is generalized to a finite Gaussian pulse in both time and space; the effect of a finite seed beam is quantitatively analyzed. Our analysis of Kerr instability in bulk dielectric crystals demonstrates the potential to amplify pulses in the wavelength range of ~1-14 μm. Whereas plane wave amplification is shown to extend to 40 μm in the example materials shown, material damage limits finite pulse Kerr instability amplification to about 14μm. There, seed pulse output energies in the 50 μJ range appear feasible with a ratio of pump to seed pulse energy in the range 400-500. Three key aspects of Kerr amplification are the capacity for single cycle pulse amplification, that it is intrinsically phase-matched, and its simplicity and versatility. As the Kerr instability gain profile is of Bessel-Gaussian nature in the transverse space domain, it lends itself naturally to the amplification of Bessel-Gauss beams. It is shown that pump-to-seed energy amplification that is more effcient than the Gaussian case by a factor of about 5-7. Whereas in the Gaussian case, the efficiency is on the order of about 0.15-0.2%, in the Bessel-Gaussian case it is on the order of about 1%. It is also demonstrated that Bessel-Gaussian seed beams centered at longer wavelengths than ordinary Gaussian beams may be amplified. Lastly, Bessel-Gauss beams are known to have favourable properties, such as being diffraction-free over a certain propagation range. Finally, a quantum optical theory of Kerr instability is developed. In particular, we explore a theory of the generation of ultrashort photon pairs (biphotons) from vacuum with Kerr instability.
Keywords: Nonlinear Optics; Quantum Optics; Light-Matter Interaction; Laser Amplification