MODULATION OF LIGHT

Elliptical polarization A beam of light may consist of two plane-polarized wave trains A beam of light may consist of two plane-polarized wave trains Planes of polarization at right angles to each other Planes of polarization at right angles to each other May also be out of phase May also be out of phase Electric vector at a given point in space is constant in amplitude but rotates with angular frequency  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 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 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 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 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 Electro-, magneto- and acousto-optic modulation Anisotropic crystal: induced polarization and the electric field are not necessarily parallel 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 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 Crystals with cubic symmetry exhibit no birefringence Noncubic crystals: birefringence effects 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 axisIn 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 Polycrystalline optical solids: internal scattering effects

Birefringence

Birefringence 1 st synthetic crystals developed in the 1930s, commercially available for IR spectroscopy: LiF, NaCl, CsBr, KBr 1 st synthetic crystals developed in the 1930s, commercially available for IR spectroscopy: LiF, NaCl, CsBr, KBr 1960s: lasing crystals 1960s: lasing crystals Ruby (Al 2 O 3 doped with 0.5% Cr)Ruby (Al 2 O 3 doped with 0.5% Cr) YAG (Y 3 Al 5 O 12 + Nd) for 1.06 m lasing crystalsYAG (Y 3 Al 5 O 12 + Nd) for 1.06 m lasing crystals

Birefringence Anisotropy in crystals: arrangement of atoms being different in different directions through the crystal Anisotropy in crystals: arrangement of atoms being different in different directions through the crystal Electric polarization P: dipole moment per unit volume 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 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 )^1/2Relative permittivity  r and refractive index n = (  r )^1/2

Natural birefringence Displacement D Displacement D Electric susceptibility  Electric susceptibility  In isotropic media and cubic crystals, direction in the medium is not important In isotropic media and cubic crystals, direction in the medium is not important E, D and P are parallel, r, n and  are scalar quantitiesE, D and P are parallel, r, n and  are scalar quantities Speed of propagation of EM waves is constant irrespective of directionSpeed 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 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 fieldInduced polarization may be in a different direction from that of the field Principal axes, principal permittivities Principal axes, principal permittivities In general, the three permittivities are differentIn general, the three permittivities are different Principal refractive indices Principal refractive indices

Anisotropic crystals Uniaxial: two principal refractive indices Uniaxial: two principal refractive indices Principal axis  33,  22 =  11Principal axis  33,  22 =  11 Optic axis (z direction): velocity of propagation is independent of polarization Optic axis (z direction): velocity of propagation is independent of polarization Biaxial: crystals of lower symmetry Biaxial: crystals of lower symmetry n x, n y and n z all differentn x, n y and n z all different Birefringence: only two states of polarization can propagate for any crystal direction Birefringence: only two states of polarization can propagate for any crystal direction

The index ellipsoid Energy density in a dielectric W Energy density in a dielectric W Ellipsoid with semi-axes n x, n y and n zEllipsoid with semi-axes n x, n y and n z Uniaxial: n x = n y  n z Uniaxial: n x = n y  n z n x = n y : ordinary refractive index n on x = n y : ordinary refractive index n o n z : extraordinary refractive index n en z : extraordinary refractive index n e

Optical Activity Ability to rotate plane of polarization of light Ability to rotate plane of polarization of light Right-handed (dextro-rotatory): clockwiseRight-handed (dextro-rotatory): clockwise Left-handed (laevo-rotatory): counter- clockwiseLeft-handed (laevo-rotatory): counter- clockwise The velocity of propagation of circularly polarized light is different for different directions of rotation The velocity of propagation of circularly polarized light is different for different directions of rotation

Optical activity Refractive indices n r and n l for right- and left-circularly polarized light Refractive indices n r and n l for right- and left-circularly polarized light Quarter-wave plate: |n o d – n e d| =/4 Quarter-wave plate: |n o d – n e d| =/4 Phase change of /2Phase change of /2 Plane polarized light emerges as circularly polarizedPlane polarized light emerges as circularly polarized

Electro-optic effect Introduces new optic axes into naturally birefringent crystals or makes isotropic crystals birefringent Introduces new optic axes into naturally birefringent crystals or makes isotropic crystals birefringent r: linear electro-optic coefficientr: linear electro-optic coefficient P: quadraticP: quadratic Pockels effect: linear variation in refractive index Pockels effect: linear variation in refractive index Kerr effect: quadratic term Kerr effect: quadratic term

Pockels effect Depends on crystal structure and symmetry of material Depends on crystal structure and symmetry of material Ex. KDP Ex. KDP Electric field is applied along the z directionElectric field is applied along the z direction x and y principal axes are rotated 45 o into x’ and y’x and y principal axes are rotated 45 o into x’ and y’