Coupled Wave Theory And Experimental Study On Second Harmonic Generation In Nonlinear Photonic Crystals

Many novel phase-matched processes have been found in nonlinear photonic crystals such as nonlinear Cherenkov radiation,nonlinear Raman-Nath diffraction and nonlinear Bragg diffraction.Nonlinear Cherenkov radiation satisfies the auto-longitudinal-phase-matched condition,and nonlinear Raman-Nath diffraction meets the transverse phase matching condition.What is more,nonlinear Bragg diffraction satisfies both the transverse and longitudinal phase matching conditions.The main content of this article is about the theoretical study of the second harmonic generation in nonlinear photonic crystals.We introduce the development of nonlinear optics,the concept of phase matching,the birefringence matching and quasi-phase-matching theories.Then we summarize the physical structure and the optical characteristics of ferroelectric crystal.We present the technology of making domain-inversion afterwards.We review the nonlinear enhanced Cherenkov radiation in domain wall and nonlinear Raman-Nath diffraction in one-dimensional nonlinear photonic crystal.The nonlinear physical modes are generalized to one-dimensional nonlinear photonic crystal interface,two-dimensional and three-dimensional photonic crystals.We obtain the quantitative expressions of nonlinear second harmonic generation in one dimensional photonic crystal interface,two-dimensional and three-dimensional photonic crystals by solving the coupled wave equations.The analytical expressions combine nonlinear Cherenkov radiation,nonlinear Raman-Nath diffraction,nonlinear Bragg diffraction,birefringence matching process and quasi-phase-matching process.Theoretical study is shown for one dimensional nonlinear photonic crystal interface,and we analyze the nonlinear process in normal and anomalous dispersion condition,respectively.Then the circularly,squarely and hexagonally poled two-dimensional photonic crystals are analyzed,and we obtain the dependence of second harmonic generation intensity on the duty ratio,modulation period and incident angle.We perform the experimental verification of one dimensional nonlinear photonic crystal interface and two-dimensional photonic crystal afterwards.Finally we theoretically study the second harmonic generation in three-dimensional photonic crystals,and the quantitative analysis is achieved in the simple cubic three-dimensional photonic crystals.