P. Piot, PHYS 630 – Fall 2008Reflection and transmission I• Polarization plays an important role inreflection and transmission at the interfacebetween two media|| = y and ⊥ = x and angles are referenced with respect to normalof the interface.• Note Snell’s law: Medium 1Medium 2(1)(3)(2)P. Piot, PHYS 630 – Fall 2008Reflection and Transmission II• We write• Boundaries condition on E and B gives (Fresnel equations)P. Piot, PHYS 630 – Fall 2008TE (or s) polarization • External reflection (n1<n2)• Internal reflection (n1>n2)θ1(deg)Arg(rx)|rx|θ1(deg)Arg(rx)|rx|P. Piot, PHYS 630 – Fall 2008TM (or p) polarization • External reflection (n1<n2)• Internal reflection (n1>n2)θ1(deg)Arg(rx)|rx|θ1(deg)Arg(rx)|rx|Brewster angleP. Piot, PHYS 630 – Fall 2008Optics in anisotropic crystals• A dielectric medium is said to be anisotropic if its optical propertiesdepends on the direction• Anisotropy depends on the crystal structure– If molecules randomly located in space and are isotropic (ororiented along random directions) the medium is isotropi (gases,liquid and amorphous solids)– If the structure takes the form of disjoined crystalline grainsrandomly oriented, the crystal is a polycrystalline and is ingeneral anisotropic– If the molecules are organized in space according to a regularperioc pattern and oriented in the same direction, as in crystals,the medium is in general anisotropicP. Piot, PHYS 630 – Fall 2008Permittivity tensor• Only anisotropy is considered• The polarization and dielectric displacement are now given by andwherein χ is a tensor (= a 3x3 array)ExEyEzPxPyPzχ11χ21χ31χ12χ22χ32χ13χ23χ33P. Piot, PHYS 630 – Fall 2008Principal axes• The elements of the permittivity tensor depend on the choice ofcoordinate system• However a coordinate system can be found such that the tensor isdiagonal i.e.• This coordinate system define the principal axes and principal planesassociated to the crystal.• The corresponding refractive indexes are known as principalindexes.P. Piot, PHYS 630 – Fall 2008Biaxial, Uniaxial & isotropic crystal• Crystals with three different principal refractive indexes are referredto as biaxial crystals• Crystal with two different principal refractive indexes are referred toas uniaxial crystals• For uniaxial crystals, the refractive indexes are n1=n2=no, and n3=newhere “o” stands for ordinary axis and “e” for extraordinary axis.• If no>ne the crystal is said to be a positive uniaxial
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