Parametric interactions in ordered and disordered nonlinear photonic crystals

Abstract

Parametric interactions are one of the oldest studied phenomenon in nonlinear optics. The nonlinear light-matter-light interaction allows one to generate light at any wavelength within the transmission band of a nonlinear crystal. It is known that the efficiency of the harmonic generation process strongly depends on the phase mismatch between interacting waves and, in order to observe harmonic generation, some technique has to be implemented. The spatially periodic modulation of the sign of nonlinearity is one of the solutions to this phase mismatch problem. Such structures, called nonlinear photonic crystals, are nowadays widely realized. Proper design of the nonlinearity modulation gives one a great control over the properties of a newly generated harmonic. The purpose of this thesis is the theoretical analysis of possible phase matching schemes and the experimental investigation of nonlinear scattering processes. The nonlinear structures under consideration in this work are periodic and strongly disordered 1D nonlinear gratings; 2D random nonlinear photonic crystals; and a single boundary between two regions of different nonlinearity. Chapter 1 provides a general introduction to aspects of frequency conversion relevant to the topic of this thesis. Basic terms used in quadratic parametric processes are defined. The fundamental theory of harmonic generation in nonlinear crystals is presented. Phase matching techniques in homogeneous and periodic structures are reviewed followed by an introduction to nonlinear diffraction mechanisms in one and two dimensional nonlinear gratings. Chapter 2 contains a theoretical study of parametric wave interaction in nonlinear optical media with a randomized distribution of quadratic nonlinearity. In particular, it shows how the transition from an ideal periodic structure to a fully random structure affects properties of the second and cascaded third harmonic generation. Analytical formulas describing properties of such harmonics in the presence of nonlinearity disorder are derived. In chapter 3 we study theoretically and numerically the second harmonic generation in a two dimensional nonlinear crystal with a random distribution of ferroelectric domains. We numerically generate a disordered structure composed of semi-circular ferroelectric domains of random size and random position. Aside from presenting numerical simulations, we show that the strict model presented in chapter 2 can be successfully applied to 2D random structures. We show that the specific features of disordered domain structures greatly affect the emission pattern of the generated harmonics. In chapter 4 and chapter 5 we study, experimentally and theoretically, the Cerenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vectors of the crystal can be used to compensate for the phase mismatch in the transverse direction. We also experimentally investigate the Cerenkov second harmonic tuning response to a wavelength and the position of the incident beam. We reveal that, in contrast to the classic second harmonic generation whose tuning response is determined by the superlattice itself, the sensitivity of the Cerenkov harmonic intensity depends strongly on the width of the incident beam.