Research On The Third-order Nonlinear Effects And Field Localization Of Photonic Crystals

In recent years,photonic crystals have received a lot of attention from researchers.Similar to the control of electron motion by periodic arrangement of atoms or molecules in electronic materials,the regulation of photons can be realized in photonic crystals by periodically arranging macroscopic media with different dielectric constants,which provides a new platform for artificially modulating various characteristics of light.Meanwhile,various exotic optical localization phenomena are being revealed in photonic crystals,especially the bound states in the continuum(BICs),which have been extensively investigated in photonic crystals recently and bring more opportunities to enhance the light-matter interactions.BICs are also demonstrated as polarization singularities in the momentum space of photonic crystals,providing a new insight for controlling the polarization and localization of light.In addition,for the conventional materials in nature,one cannot flexibly manipulate their nonlinear effects due to the inherent optical properties,while the intersection and combination of photonic crystals and nonlinear materials open up more possibilities for the flexible modulation of the nonlinear effects of light.In this thesis,we first achieve a phase-matched third harmonic generation based on the dispersion engineering of photonic crystals,and then realize a polarization-tunable optical Kerr effect by utilizing the distinct electric field distributions of TE and TM modes in photonic crystals.Moreover,we further study the special field localization phenomenon in photonic crystals,i.e.,bound states in the continuum.Finally,we investigate the polarization singularities in the momentum space of the photonic crystals and achieve two different optical field localizations from the perspective of polarization singularity tuning.The main contents and novelties are summarized as follows:1.For the phase mismatch in the third harmonic generation process,we achieve a perfect phase matching in a two-dimensional photonic crystal,which is independent of the polarization and propagation direction of the incident light,providing a new avenue for high-efficiency third harmonic generation.Specifically,in the isotropic frequency region of the photonic crystal,by tuning the structural parameters of the photonic crystal,we make the TM and TE modes have equal effective refractive indices at the fundamental and triple frequency,thus satisfying the requirement of phase matching for the third harmonic generation.Meanwhile,we derive the formula of the third harmonic generation of Gaussian pulses and simulate the nonlinear propagations of Gaussian pulses in the photonic crystal by FDTD numerical simulation.The results show that the third harmonic generation conversion efficiency increase with propagation length like a parabola,further demons trating the realization of phase matching.2.We achieve a sign switching of the effective nonlinear coefficient of photonic crystals by exploiting the distinct electric field distributions of TM and TE modes in the isotropic frequency region of the phot onic crystals,providing a new way for flexible control of nonlinear propagations of high-power laser pulses.In the designed nonlinear Kerr photonic crystal,when the incident light is TM polarized,the photonic crystal exhibits a negative effective nonlinear coefficient,and if the incident light is TE polarized,the photonic crystal shows a positive effective nonlinear coefficient.In addition,we demonstrate polarization-dependent self-focusing and self-defocusing,as well as spectral broadening and narrowing in the photonic crystal.3.The symmetry-protected BICs in photonic crystal slabs are generally located at the band edges,and the optical density of states at their frequencies is usually limited by the steep dispersion characteristics.Here,we achieve a BIC with flatband dispersion by breaking the vertical mirror symmetry of a photonic crystal slab to hybridize the zero-and first-order waveguide modes therein.Meanwhile,we demonstrate that the BIC on flatband have stronger light-matter interaction compared to the normal BIC.In addition,we present a Hamiltonian model that can accurately describe the dispersion properties of the photonic crystal slab and validate it.Our results introduce a new dimension to further enhance the performance of BICs and provide an avenue for improving optical devices.4.Analogous to polarization singularities in real space,various polarization singularities have been found in the momentum space of photonic crystal slabs.Here,by misaligning two superimposed dielectric gratings,we show a complete evolution process of two pairs of circularly polarization singularities in momentum space starting from zero topological charge,including their generation,merging,and annihilation.Interestingly,we observe two merging and splitting processes of the circularly polarization singularities during the evolution,and based on this,two resonances with unidirectional radiation properties and a perfect BIC are achieved.Our results provide a new insight and method for creating various polarization singularities in momentum space and flexibly regulating the quality factor,radiative channels,and far-field polarization properties of resonances.