P. Piot, PHYS 630 – Fall 2008• Index ellipsoid• Introducing the impermeability tensor• The index ellipsoid rewrites• In the present of an external electric field• And the index ellipsoid isPockel effectKerr effect+p.EEElectro-optics effect in non-anisotropic mediaP. Piot, PHYS 630 – Fall 2008Electro-optics effect in non-anisotropic media• The tensor is symmetric i.e.• So generally it is custom to replacethe two first indices by one indice• Consider the ZnTe crystal,when E=0:andso the index ellipsoid is distorted by the electric field:P. Piot, PHYS 630 – Fall 2008applications• The difference between the index of refraction (assuming an uniaxialcrystal) are going to give rize the a phase shift between the twonormal (or principal) polarization that are linearly dependent on theElectric field:• An application of such an effect is a variable waveplate: these arereferred to as Pockel cell! " =2#$%n(E ) & EP. Piot, PHYS 630 – Fall 2008Applications II• Application of EO effects using low frequency applied voltageincludes– Pulse picker– Phase modulator– Polarization rotator– Amplitude modulatorP. Piot, PHYS 630 – Fall 2008• THz pulse propagating along U3Propagation of THz pulse in a EO crystalP. Piot, PHYS 630 – Fall 2008Propagation of THz pulse in a EO crystal• The THz pulse E-field in the crystal coordinate system is• The index ellipsoid is then given by• Let’s compute• The eigenvalues areP. Piot, PHYS 630 – Fall 2008Propagation of THz pulse in a EO crystal• The associated eigenvector• The refractive index are given byP. Piot, PHYS 630 – Fall 2008Propagation of THz pulse in a EO crystal• Phase shift isP. Piot, PHYS 630 – Fall 2008Application in ultra-fast diagnostics for charged particle beamsP. Piot, PHYS 630 – Fall 2008Application in ultra-fast diagnosticsfor charged particle beams• An ultra-relativistic bunch ofcharged particle moving alongz produce a radial E-field ofthe formP. Piot, PHYS 630 – Fall 2008Optical activity• Some material act as natural polarizer• Property knows as optical activity• Phase shift is of the form• Can be demonstrated by decomposingan incoming linearly polarized wave asa sum of RCP and LCP• Optical activity occurs in materialwith helical structure (e.g. amino-acid)EIkMk×MRCPLCPP. Piot, PHYS 630 – Fall 2008Optical activity: normal modes I• A magnetic field induce a current that in turn induce a dipole momenton the molecules• The dielectric permittivity tensor is writtenor often• So E and D are not parallel• Considering a wave propagating along z [k=(0,0,k) and G=(0,0,G)]givesP. Piot, PHYS 630 – Fall 2008Optical activity: normal modes II• The eigenvectors are• With eigenvaluesP. Piot, PHYS 630 – Fall 2008Magneto optics• In magneto-optics the dielectric permittivity is altered by applying astatic magnetic field.• The gyration vector is taken to be proportional to the appliedmagnetic field• The rotation angle is then given byVerdet constantdmedium thicknessP. Piot, PHYS 630 – Fall 2008Magneto optics: application• Optical