Lecture19

# Lecture19 - Physical origin of the electro-optical effect...

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Lecture 19 Electro-optic Acousto-optic Physical origin of the electro-optical effect The applied electric ﬁeld changes the band structure of the material and thereby the absorption of the sample is changed Franz Keldish Effect Kramers-Kronig Change in refractive index Franz Keldish Effect • Photons with energy somewhat below the gap can make a transition into a virtual state (or the tail of the density of states distribution) and tunnel into the conduction band ! 1 n 2 " # \$ % i = r ij j = 1 3 ( E j ! 1 n 2 " # \$ % 1 ! 1 n 2 " # \$ % 2 ! 1 n 2 " # \$ % 3 ! 1 n 2 " # \$ % 4 ! 1 n 2 " # \$ % 5 ! 1 n 2 " # \$ % 6 " # \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ % = r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 r 41 r 42 r 43 r 51 r 52 r 53 r 61 r 62 r 63 " # \$ \$ \$ \$ \$ \$ \$ \$ \$ % E 1 E 2 E 3 " # \$ \$ \$ % The refractive indexes and therefore the principle axis change. This is usually expressed as a changed index ellipsoid. Pockels Effect electro-optic tensor 1 = x 2 n x 2 + y 2 n y 2 + z 2 n z 2 + ! 1 n 2 " # \$ % 1 x 2 + ! 1 n 2 " # \$ % 2 y 2 + ! 1 n 2 " # \$ % 3 z 2 + 2 ! 1 n 2 " # \$ % 4 yz + 2 ! 1 n 2 " # \$ % 5 xz + 2 ! 1 n 2 " # \$ % 6 xy ! 1 n 2 " # \$ % i = r ij j = 1 3 ( E j r ij

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triclinic monoclinic tetragonal hexagonal Example: KDP Let’s assume E-ﬁeld in z-direction ! 1 n 2 " # \$ % 1 ! 1 n 2 " # \$ % 2 ! 1 n 2 " # \$ % 3 ! 1 n 2 " # \$ % 4 ! 1 n 2 " # \$ % 5 ! 1 n 2 " # \$ % 6 " # \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ % = 0 0 0 0 0 0 0 0 0 r 41 0 0 r 51 r 41 0 0 0 r 63 " # \$ \$ \$ \$ \$ \$ \$ \$ \$ % 0 0 E 3 " # \$ \$ \$ % = 0 0 0 0 0 r 63 E 3 " # \$ \$ \$ \$ \$ \$ \$ \$ \$ % We need to ﬁnd new coordinate system such that; 1 = x ' 2 n x ' 2 + + y ' 2 n y ' 2 + z ' 2 n ' z z remains unchanged Rotation in x-y plane 1 = x 2 n 0 2 + y 2 n 0 2 + 2 r 63 E 3 xy + z 2 n e 2
x 2 + y 2 = x ' 2 cos 2 ! + y ' 2 sin 2 " x ' y ' cos sin + x ' 2 sin 2 + x ' 2 cos 2 + x ' y ' cos sin = x ' 2 + y ' 2 xy = + x ' 2 sin cos

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Lecture19 - Physical origin of the electro-optical effect...

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