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Transcript
MODULATION OF LIGHT Elliptical polarization A beam of light may consist of two plane-polarized wave trains Planes of polarization at right angles to each other May also be out of phase Electric vector at a given point in space is constant in amplitude but rotates with angular frequency Birefringence Anisotropy is due to the arrangement of the atoms being different in different directions through the crystal Refractive index depends on not only the direction of propagation of the waves but also the direction of polarization Birefringence Doubly refracting: in general there are two different directions of propagation through the crystal, depending on the direction of propagation Optic axes: directions in the crystal along which the velocities of the two orthogonally polarized waves are the same Propagation of EM waves in anisotropic crystals Electro-, magneto- and acousto-optic modulation Anisotropic crystal: induced polarization and the electric field are not necessarily parallel Along an arbitrary direction of propagation s, there can exist two independent plane wave, linearly polarized propagation modes Birefringence Crystals with cubic symmetry exhibit no birefringence Noncubic crystals: birefringence effects • In single crystals main effect is the splitting of a light ray unless ray is in the direction of a crystal axis Polycrystalline optical solids: internal scattering effects Birefringence www.dkimages.com Birefringence 1st synthetic crystals developed in the 1930s, commercially available for IR spectroscopy: LiF, NaCl, CsBr, KBr 1960s: lasing crystals • Ruby (Al2O3 doped with 0.5% Cr) • YAG (Y3Al5O12 + Nd) for 1.06 m lasing crystals Birefringence Anisotropy in crystals: arrangement of atoms being different in different directions through the crystal Electric polarization P: dipole moment per unit volume P produced in a crystal by a given electric field E depends on the direction of the field • Relative permittivity r and refractive index n = (r)^1/2 Natural birefringence Displacement D Electric susceptibility In isotropic media and cubic crystals, direction in the medium is not important • E, D and P are parallel, r, n and are scalar quantities • Speed of propagation of EM waves is constant irrespective of direction Birefringent materials Polarization in response to an applied E depends on magnitude and direction of the field • Induced polarization may be in a different direction from that of the field Principal axes, principal permittivities • In general, the three permittivities are different Principal refractive indices Anisotropic crystals Uniaxial: two principal refractive indices • Principal axis 33, 22 = 11 Optic axis (z direction): velocity of propagation is independent of polarization Biaxial: crystals of lower symmetry • nx, ny and nz all different Birefringence: only two states of polarization can propagate for any crystal direction The index ellipsoid Energy density in a dielectric W • Ellipsoid with semi-axes nx, ny and nz Uniaxial: nx = ny nz • nx = ny: ordinary refractive index no • nz: extraordinary refractive index ne Optical Activity Ability to rotate plane of polarization of light • Right-handed (dextro-rotatory): clockwise • Left-handed (laevo-rotatory): counterclockwise The velocity of propagation of circularly polarized light is different for different directions of rotation Optical activity Refractive indices nr and nl for rightand left-circularly polarized light Quarter-wave plate: |nod – ned| = /4 • Phase change of /2 • Plane polarized light emerges as circularly polarized Electro-optic effect Introduces new optic axes into naturally birefringent crystals or makes isotropic crystals birefringent • r: linear electro-optic coefficient • P: quadratic Pockels effect: linear variation in refractive index Kerr effect: quadratic term Pockels effect Depends on crystal structure and symmetry of material Ex. KDP • Electric field is applied along the z direction • x and y principal axes are rotated 45o into x’ and y’