Study On Entangled Photons Generation In Spontaneous Parametric Down-conversion Of BiB₃O₆Crystal

Since the first realization of entangled photons using atomic sources, manystudies of the generation and observation of entangled photons have been carried out.One of the most successful and popular methods to generate entangled photons isusing the spontaneous parametric down conversion (SPDC) in nonlinear crystals, andmost of them were based on uniaxial crystals. In this dissertation, the author focusedon the generation of entangled photons employing biaxial crystal BIBO, and hascompleted the following works:1. The entanglement properties and concepts of quantum states induced bycombined quantum particles are introduced from a historical viewpoint. Variousmedia and the corresponding technologies for generation of entangled photons arethen compared for their superiorities and drawbacks.2. Based on a review of the entangled photons production and the lightpropergation properties in nonlinear crystals, the phase matching conditions in biaxialcrystals are introduced. From the SPDC Hermitian in interaction picture, the biphotonstate wave function and the phase matching function of the generated photons arederived out.3. The optimal phase-matching conditions of SPDC in biaxial nonlinear crystalBiB3O6(BIBO) are investigated theoretically, and the fundamental parameters aredetermined. By analyzing the relations of the effective nonlinear coefficientd effwiththe phase-matching angles, the Fresnel equations, and the relation of thephase-matching angles (, I)in the collinear degenerate down-convertedconfiguration, we obtain the conditions for getting a larger effective nonlinearcoefficientd eff. Then, the influencing factors on the SPDC process in BIBO crystal forboth type I and type II phase-matching are discussed, including the temporal andspatial walk-offs, the acceptance angles, and spectral acceptance bandwidth.Moreover, a new method for determining the maximal phase matching conditions ispresented. The method is based on angle-dependent refractive index in biaxial crystals, and can avoid the complexity for solving the quadratic Fresnel equations.4. Taking into account the geometrical relations between the refractive indexellipsoids and the anisotropy of photon angular distributions in near and far zones, weemphasize on the anisotropic effects on photon angular distributions of the collinearSPDC configuration in BIBO. The wave packets of biphoton pairs, exhibit moreextensive anisotropic characters compared with those in uniaxial crystals. And ahigher degree of entangled photon state is generated, which can be attributed to thefact that the anisotropic structure of the refractive index acts as an orientation filter forpump beam. The calculations are simplified by predigesting the expressions oflongitudinal detuning in the condition of paraxial approximation. Based on thederivation of angular gradient of the refractive index with perfect phase matching, themomentum distribution of entangled photons in cases of parallel and perpendicularare obtained.