1、Beam propagation in anizotropic crystals,Optic axis of a crystal is the direction in which a ray of transmitted light suffers no birefringence (double refraction). Light propagates along that axis with a speed independent of its polarization,However, if the light beam is not parallel to the optical
2、axis, then, when passing through the crystal the beam is split into two rays: the ordinary and extraordinary, to be mutually perpendicular polarized.,A crystal which has only one optic axis is called uniaxial crystal. An uniaxial crystal is isotropic within the plane orthogonal to the optical axis o
3、f the crystal. A crystal which has only two optic axis is called biaxial crystal.,The refractive index of the ordinary ray is constant for any direction in the crystal, and of the extraordinary ray is variable and depends on the direction. In a uniaxial crystal for the direction parallel to the opti
4、cal axis the refractive indices are equal.,Positive birefringence,Negative birefringence,BBO is negative uniaxial crystal,Fast Axis Direction having a low refractive index is the fast axis; at right angles to it is the slow axis, with a high index of refraction.,Type I cut,kp =ks +ki,npwp=2nswscosqs
5、,Index of refraction of BBO (negative uniaxial crystal): blue solid curve: ordinary polarization; red/dash-dot curve: full extraordinary polarization; green/dash curve: extraordinary polarization at the phase matching angle (29o),for ws = wp/2,np=nscosqs,For collinear down-conversion the index of re
6、fraction at wavelengths differing by a factor of two must be equal. For isotropic material it is impossible, but by using birefringent material we can achieve this condition via the different indices of refraction of orthogonal linear polarizations.,Calculating Characteristics of Noncollinear Phase
7、Matching in Uniaxial and Biaxial Crystals N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Gurin, G. Jaeger, A. Muller, A. Migdall Originally published in: Opt. Eng. 39(4), 1016-1024 (April 2000).,http:/units.nist.gov/Divisions/Div844/facilities/cprad/index.html,Polarization of light,Malus law, whi
8、ch is named after Etienne-Louis Malus(1775 1812) , says that when a perfect polarizer is placed in a polarized beam of light, the intensity, I, of the light that passes through is given bywhere I0 is the initial intensity, and i is the angle between the lights initial polarization direction and the
9、axis of the polarizer.,His discovery of the polarisation of light by reflection was published in 1809 and his theory of double refraction of light in crystals, in 1810.,RetardersA retarder, or waveplate, is an optical device that resolves a light wave into two orthogonal linear polarization componen
10、ts and produces a phase shift between them. The resulting light wave generally is of a different polarization form. Ideally, retarders do not polarize, nor do they induce an intensity change in the light beam. They simply change its polarization form. Retarders are used in applications where control
11、 or analysis of polarization states is required.,Half wave plate A retarder that produces a /2 phase shift is known as a half wave retarder. Half wave retarders can rotate the polarization of linearly polarized light to twice the angle between the retarder fast axis and the plane of polarization. Pl
12、acing the fast axis of a half wave retarder at 45 to the polarization plane results in a polarization rotation of 90. Passing circularly polarized light through a half wave plate changes the “handedness“ of the polarization.,Quarter waveplate,If the orthogonal electric field components are equivalen
13、t, a phase shift /4 in one component will result in circularly polarized light. Retarders that cause this shift are known as quarter wave retarders. They have the unique property of turning elliptically polarized light into linearly polarized light or of transforming linearly polarized light into circularly polarized light when the fast axis of the quarter wave plate at 45 to the incoming polarization plane. (Light polarized along the direction with the smaller index travels faster and thus this axis is termed the fast axis. The other axis is the slow axis).,
