Transcript CRYSTALLINE MATERIALS

MODULATION OF
LIGHT
Elliptical polarization




A beam of light may consist of two
plane-polarized wave trains
Planes of polarization at right angles
to each other
May also be out of phase
Electric vector at a given point in
space is constant in amplitude but
rotates with angular frequency 
Birefringence


Anisotropy is due to the arrangement
of the atoms being different in
different directions through the
crystal
Refractive index depends on not only
the direction of propagation of the
waves but also the direction of
polarization
Birefringence


Doubly refracting: in general there
are two different directions of
propagation through the crystal,
depending on the direction of
propagation
Optic axes: directions in the crystal
along which the velocities of the two
orthogonally polarized waves are the
same
Propagation of EM waves in
anisotropic crystals



Electro-, magneto- and acousto-optic
modulation
Anisotropic crystal: induced
polarization and the electric field are
not necessarily parallel
Along an arbitrary direction of
propagation s, there can exist two
independent plane wave, linearly
polarized propagation modes
Birefringence


Crystals with cubic symmetry exhibit
no birefringence
Noncubic crystals: birefringence
effects
• In single crystals main effect is the
splitting of a light ray unless ray is in
the direction of a crystal axis

Polycrystalline optical solids: internal
scattering effects
Birefringence
www.dkimages.com
Birefringence


1st synthetic crystals developed in
the 1930s, commercially available for
IR spectroscopy: LiF, NaCl, CsBr, KBr
1960s: lasing crystals
• Ruby (Al2O3 doped with 0.5% Cr)
• YAG (Y3Al5O12 + Nd) for 1.06 m lasing
crystals
Birefringence



Anisotropy in crystals: arrangement of
atoms being different in different
directions through the crystal
Electric polarization P: dipole moment per
unit volume
P produced in a crystal by a given electric
field E depends on the direction of the
field
• Relative permittivity r and refractive index n =
(r)^1/2
Natural birefringence



Displacement D
Electric susceptibility 
In isotropic media and cubic crystals,
direction in the medium is not
important
• E, D and P are parallel, r, n and  are
scalar quantities
• Speed of propagation of EM waves is
constant irrespective of direction
Birefringent materials

Polarization in response to an applied
E depends on magnitude and
direction of the field
• Induced polarization may be in a
different direction from that of the field

Principal axes, principal permittivities
• In general, the three permittivities are
different

Principal refractive indices
Anisotropic crystals



Uniaxial: two principal refractive
indices
• Principal axis 33, 22 = 11
Optic axis (z direction): velocity of
propagation is independent of polarization
Biaxial: crystals of lower symmetry
• nx, ny and nz all different

Birefringence: only two states of
polarization can propagate for any crystal
direction
The index ellipsoid

Energy density in a dielectric W
• Ellipsoid with semi-axes nx, ny and nz

Uniaxial: nx = ny  nz
• nx = ny: ordinary refractive index no
• nz: extraordinary refractive index ne
Optical Activity

Ability to rotate plane of polarization
of light
• Right-handed (dextro-rotatory):
clockwise
• Left-handed (laevo-rotatory): counterclockwise

The velocity of propagation of
circularly polarized light is different
for different directions of rotation
Optical activity


Refractive indices nr and nl for rightand left-circularly polarized light
Quarter-wave plate: |nod – ned| =
/4
• Phase change of /2
• Plane polarized light emerges as
circularly polarized
Electro-optic effect

Introduces new optic axes into
naturally birefringent crystals or
makes isotropic crystals birefringent
• r: linear electro-optic coefficient
• P: quadratic


Pockels effect: linear variation in
refractive index
Kerr effect: quadratic term
Pockels effect


Depends on crystal structure and
symmetry of material
Ex. KDP
• Electric field is applied along the z
direction
• x and y principal axes are rotated 45o
into x’ and y’