Reflection and transmission I Polarization plays an important role - - PowerPoint PPT Presentation

• P. Piot, PHYS 630 – Fall 2008

Reflection and transmission I

• Polarization plays an important role in

reflection and transmission at the interface between two media || = y and ⊥ = x and angles are referenced with respect to normal

• f the interface.
• Note Snell’s law:

Medium 1 Medium 2 (1) (3) (2)

• P. Piot, PHYS 630 – Fall 2008

Reflection and Transmission II

• We write
• Boundaries condition on E and B gives

(Fresnel equations)

• P. Piot, PHYS 630 – Fall 2008

TE (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 2008

TM (or p) polarization

• External reflection (n1<n2)
• Internal reflection (n1>n2)

θ1(deg) Arg(rx) |rx| θ1(deg) Arg(rx) |rx| Brewster angle

• P. Piot, PHYS 630 – Fall 2008

Optics in anisotropic crystals

• A dielectric medium is said to be anisotropic if its optical properties

depends on the direction

• Anisotropy depends on the crystal structure

– If molecules randomly located in space and are isotropic (or

• riented along random directions) the medium is isotropi (gases,

liquid and amorphous solids) – If the structure takes the form of disjoined crystalline grains randomly oriented, the crystal is a polycrystalline and is in general anisotropic – If the molecules are organized in space according to a regular perioc pattern and oriented in the same direction, as in crystals, the medium is in general anisotropic

• P. Piot, PHYS 630 – Fall 2008

Permittivity tensor

• Only anisotropy is considered
• The polarization and dielectric displacement are now given by

and wherein χ is a tensor (= a 3x3 array)

Ex Ey Ez Px Py Pz

χ11 χ21 χ31 χ12 χ22 χ32 χ13 χ23 χ33

• P. Piot, PHYS 630 – Fall 2008

Principal axes

• The elements of the permittivity tensor depend on the choice of

coordinate system

• However a coordinate system can be found such that the tensor is

diagonal i.e.

• This coordinate system define the principal axes and principal planes

associated to the crystal.

• The corresponding refractive indexes are known as principal

indexes.

• P. Piot, PHYS 630 – Fall 2008

Biaxial, Uniaxial & isotropic crystal

• Crystals with three different principal refractive indexes are referred

to as biaxial crystals

• Crystal with two different principal refractive indexes are referred to

as uniaxial crystals

• For uniaxial crystals, the refractive indexes are n1=n2=no, and n3=ne

where “o” stands for ordinary axis and “e” for extraordinary axis.

• If no>ne the crystal is said to be a positive uniaxial crystal