Polarization and devices |
Feb. 1, 2018 |
•
Polarization:
`vec e = hat x E_x cos ( omega t -k z ) + hat y E_y cos (omega t -k z + phi )`,
`phi = phi_y - phi_x`
is the relative phase between the 2 components.
Unpolarized `-phi`
is a random variable.
Linearly polarized `- phi = 0`
or `pi`
Circularly polarized `- E_x = E_y`
, `phi = pm pi/2`
Elliptically polarized `- E_x ne Ey`
, `phi ne 0`
or `pi`
Polarization devices - , birefringent polarizers,
rotator.
• :
based on optical activity or Faraday effect
Put in terms of right circular unit
vector `hat e_R = {hat x - j hat y}/sqrt(2)`
and left circular unit
vector `hat e_R = {hat x + j hat y}/sqrt(2)`,
`vec E = E_R e^{-jk_R z) hat e_R + E_L e^{-jk_L z) hat e_L`;
angle of rotation `= rho z = (k_L - k_R ) z /2`; `rho`
is rotatory power. For example, Faraday
effect `rho = V H`
where `H` is magnetic field intensity
and `V`
is the Verdet constant, i.e. magneto-optics.
• Anisotropic materials: causes birefringence since
refractive indices are different along different axes, i.e.
directional
dependent. `P_i = sum_j epsilon_o chi_{ij} E_j`
In general, the refractive indices are different in all 3
axes (x, y, z) in biaxial crystals. More common are uniaxial
crystals which have one axis with refractive index different
from those of the other two axes. This unique axis is called
optic axis and refractive index along this axis is
called `n_e`
or `n_{||}`
The refractive index along the other 2 axes
is `n_o`
or `n_{_|_}`
They are used to make polarization devices, e.g.
quarter wave plate causes
a `pi/2`
phase difference between x and y components,
i.e. `Delta phi = pi/2 (2 m + 1 )`
It can be a polarization converter.
Half wave plate causes
a `pi`
phase difference between x and y components,
i.e. `Delta phi = pi (2 m + 1 )`
• Inhomogeneous media: refractive index is a function
of
position, `P = epsilon_o chi (r) E`
Applications - grade index fiber, mirage.
• Nonlinear
media: `P = epsilon_o ( chi ^{(1)} E + chi ^{(2)} E^2 + chi ^{(3)} E^3 )`
Nonlinear effects result in harmonic generation.
Four-wave mixing (FWM), Stimulated Raman Scattering (SRS),
and Stimulated Brillouin Scattering (SBS) rob energy from
signal into different freq. channels.
• Dispersive medium: Different frequency components
travel with different speeds, e.g. Prisms.