Light Waves and Polarization

Xavier Fernando

Ryerson Communications Labhttp://www.ee.ryerson.ca/~fernando

The Nature of Light• Quantum Theory – Light consists of small particles

(photons). This theory better explains light detection and generation processes.

• Wave Theory – Light travels as a transverse electromagnetic wave. This theory better explains light propagation.

• Ray Theory – Light travels along a straight line and obeys laws of geometrical optics – This theory is useful when the objects are much larger than the wavelength of light (Multi Mode Fiber)

Quantum Theory of Light

• Light consists of discrete units called photons. The energy in a photon

h= 6.6256 X10(-34) J.s is the Planck’s constant and

ν is the frequency.• Ex1: Find the energy of a photon travelling

with 200 THz frequency• Ex2: Show eV

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24.1

mEg

hEg

Wave Theory of Light• Electromagnetic light signal has electric and

magnetic fields orthogonal to each other.• The frequency of this EM wave is in the order of

THz. Therefore, it is convenient to measure it in terms of wavelength.

• where, c - speed of light 3 X 108 m/s in air, ν - frequency and λ- wavelength

• Ex: Find the ν when λ = 1550 nm. • Answer: 193.5 THz

c

Wavelength Ranges

Plane Waves

• Most Light waves are plane waves• A plane wave is a constant-frequency wave

whose wave fronts (surfaces of constant phase) are infinite parallel planes.

• The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel).

Field distributions in plane E&M waves

Electric and magnetic fields are orthogonal to each other and to the direction of propagation Z

s

Basics about Plane Waves

/ propagation constant

The combined wave

)cos( kztEE o

vp

Phase Velocity

n

c

kvp

Phase velocity:

co: Speed of light in airn: Refractive index

Phase Velocity• apparent and true

depth

• Light in fiber core travels slower ‘waveguide dispersion’

Medium Ref. Index (n)

Phase Velocity of Light

Air 1 3x108 m/s

Water 4/3 =1.33 2.25x108 m/s

Glass 3/2 = 1.5 2x108 m/s

Changing Refractive Index

• The refractive index n is not constant• It is a function of the wavelength of light, n = n(λ).• Therefore, different wavelengths will travel at

different velocity in glass fiber• The wavelength dependency of n is given by an

empirical formula, the Cauchy or Sellmeier equations

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Group of Waves

Most practical light sources emit group of waves, not just one

2Δω

Carrier and Envelope

vp vg

Group Velocity

• Group of waves travel at group velocity, slightly different from phase velocity

• The group refractive index ng is a function of n, ω and dn/d ω

• If ω proportional to k, then the ng = n and vg = vp.

• Usually it is not the case; This results in “Group Velocity Dispersion“.

• The GVD is important single mode optical fibers.

m/sg

g n

c

kv

)(

n

nng

Sellmeier Equation

• Refractive Index n is a nonlinear function of wavelength

• The slope of this graph is related to ng

Polarization• Polarization of a plane wave is the

orientation of the oscillations of the E field; perpendicular to the direction of propagation

• For a simple harmonic wave, the electric vector in orthogonal directions may have: – Different amplitude – Different phase

• The resulting wave is – Linearly, elliptically or circularly polarized

When the orthogonal components have different phase and amplitude, resulting wave is

Elliptically Polarized (General Case)

When the orthogonal components have 90o phase shift and equal amplitude, the resulting wave is Circularly Polarized(Special Case)

When the orthogonal components have zero phase shift, resulting wave is Linearly

Polarized • More useful • Emitted by

lasers• Polarization

control is possible

• Horizontal and vertical polarizations

Linear Polarization

Faraday Effect • When a magnetic field is applied to linearly

polarized light, the plane of polarization rotates.

• The rotation is proportional to the intensity of the applied magnetic field in the direction of the beam of light

This effect is used in Optical Isolators

Optical Isolator• Vertically polarized light enters

the isolator. • The Faraday rotator rotates it

by 45o. • Output polarizer passes the

light.• Backward traveling (reflected)

light starts with 45o tilt. • It gets horizontal polarization at

the rotator and will be extinguished.

Input Polarizer (allows only vertically polarized light)

Faraday rotator

output polarizer (allows light at 45o)

Polarization Controller (creates vertical polarization)

Polarization Mode Dispersion (PMD)

Each polarization state has a different velocity PMD

Polarization Dependent Modulation