This effect was explained by Christiaan Huygens 1629 1695 Dutch physicist as double refraction of what he called an ordinary and an extraordinary wave With the help of a polarizer we can easily see what these ordinary and extraordinary beams are Ob ID: 26127 Download Pdf

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This effect was explained by Christiaan Huygens 1629 1695 Dutch physicist as double refraction of what he called an ordinary and an extraordinary wave With the help of a polarizer we can easily see what these ordinary and extraordinary beams are Ob

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Halite cubic sodium chloride crystal , optically isotropic Calcite optically anisotropic Calcite crystal with two polarizers at right angle to one another Birefringence was first observed in the 17th century when sailors visiting Iceland brought back to Europe calcite cristals that showed double images of objects that were viewed through them. This effect was explained by Christiaan Huygens (1629 1695, Dutch physicist ), as double refraction of what he called an ordinary and an extraordinary wave. With the help of a polarizer we can easily see what these ordinary and

extraordinary beams are Obviously these beams have orthogonal polarization , with one polarization ordinary beam ) passing undeflected throught the crystal and the other extraordinary beam ) being twice refracted

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linear anisotropic media: [2] [3] and as n depends on the direction , is a tensor ij ji ij principal axes coordinate system off diagonal elements vanish D is parallel to E 11 22 33 [4] inverting [4] yields defining in the pricipal coordinate system is diagonal with principal values [5] Birefringence Birefringence optically isotrop crystal cubic symmetry constant phase

delay uniaxial crystal (e.g. quartz , calcite , MgF Birefringence extraordinary / optic axis

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the index ellipsoid ij ij is in the principal coordinate system: a useful geometric representation is [6] [7] uniaxial crystals (n =n sin cos [8] 90 Birefringence the index ellipsoid Birefringence the index ellipsoid

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refraction of a wave has to fulfill the phase matching condition modified Snell's Law ): sin sin air two solutions do this ordinary wave: sin sin extraordinary wave: sin sin Birefringence double refraction Birefringence double refraction

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How to build a waveplate input light with polarizations along extraordinary and ordinary axis , propagating along the third pricipal axis of the crystal and choose thickness of crystal according to wavelenght of light Phase delay difference Birefringence uniaxial crystals and waveplates Birefringence uniaxial crystals and waveplates

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Friedrich Carl Alwin Pockels (1865 1913) Ph .D. from Goettingen University in 1888 1900 1913 Prof. of theoretical physics in Heidelberg for certain materials n is a function of E, as the variation is only slightly we can Taylor expand n(E): ...

linear electro optic effect Pockels effect , 1893): quadratic electro optic effect Kerr effect , 1875): Electro Optic Effect Electro Optic Effect

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the electric impermeability (E): dn ... explains the choice of r and s. Kerr effect typical values for s: 10 18 to 10 14 /V n for E=10 V/m 10 to 10 crystals 10 10 to 10 liquids Pockels effect typical values for r: 10 12 to 10 10 m/V n for E=10 V/m 10 to 10 crystals

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Electro Optic Effect theory galore Electro Optic Effect theory galore from simple picture [9] to serious theory kl ijkl ijk ij ij [10] ij ijk ij ijkl

Symmetry arguments ij = ji and invariance to order of differentiation ) reduce the number of independet electro optic coefficents to: 6x3 for r ijk 6x6 for s ijkl a renaming scheme allows to reduce the number of indices to two see Saleh, Teich "Fundamentals of Photonics ") and crystal symmetry further reduces the number of independe t elements diagonal matrix with elements 1/n

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Pockels Effect doing the math Pockels Effect doing the math How to find the new refractive indices Find the principal axes and principal refractive indices for E=0 Find the r ijk from the crystal

structure Determine the impermeability tensor using ijk ij ij Write the equation for the modified index ellipsoid ij ij Determine the principal axes of the new index ellipsoid by diagonalizing the matrix ij (E) and find the corresponding refractive indices n (E) Given the direction of light propagation , find the normal modes and their associated refractive indices by using the index ellipsoid as we have done before

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Pockels Effect what it does to light Pockels Effect what it does to light Phase retardiation (E) of light after passing through a Pockels Cell of lenght L: [11]

[12] with this is EL [13] with the retardiation is finally a Voltage applied between two surfaces of the crystal [14]

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Longitudinal Pockels Cell (d=L) scales linearly with large apertures possible Transverse Pockels Cell scales linearly with aperture size restricted Pockels Cells building a pockels cell Pockels Cells building a pockels cell Construction from Linos Coorp

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Pockels Cells Dynamic Wave Retarders / Phase Modulation Pockels Cells Dynamic Wave Retarders / Phase Modulation Pockels Cell can be used as dynamic wave retarders Input light is vertical ,

linear polarized with rising electric field applied Voltage ) the transmitted light goes through elliptical polarization circular polarization @ V /2 (U /2 elliptical polarization (90°) linear polarization (90°) @ V

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Pockels Cells Phase Modulation Pockels Cells Phase Modulation Phase modulation leads to frequency modulation dt definition of frequency [15] with a phase modulation sin frequency modulation at frequency with 90° phase lag and peak to peak excursion of 2m Fourier components : power exists only at discrete optical frequencies w± k dt dt

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Pockels

Cells Amplitude Modulation Pockels Cells Amplitude Modulation Polarizer guarantees , that incident beam is polarizd at 45° to the pricipal axes Electro Optic Crystal acts as a variable waveplate Analyser transmits only the component that has been rotated > sin transmittance characteristic

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Pockels Cells the specs Pockels Cells the specs preferred crystals LiNbO LiTaO KDP (KH PO KD*P (KD PO ADP (NH PO BBO (Beta BaB longitudinal cells Half wave Voltage O(100 V) for transversal cells O(1 kV) for longitudinal cells Extinction ratio up to 1:1000 Transmission 90 to 98 % Capacity

O(100 pF switching times O(1 µs) can be as low as 15ns)

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Pockels Cells temperature "stabilization" Pockels Cells temperature "stabilization" an attempt to compensate thermal birefringence

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Electro Optic Devices Electro Optic Devices

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Liquid Crystals Liquid Crystals

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Optical activity Faraday Effect Faraday Effect Faraday Effect

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hotorefractive Materials Photorefractive Material

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Acousto Optic Acousto Optic

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