Transcript Fig. 2-1: Spherical and plane wave fronts

Light Waves and
Polarization
Xavier Fernando
Ryerson Communications Lab
http://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
E g  h
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
1.24
Eg 
eV
• Ex2: Show
 ( m)
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.
c  
• 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
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
Basics about Plane Waves
/ propagation constant
The combined wave
s
E  Eo cos(t  kz)
Phase Velocity
vp

c

Phase velocity: v p 
k n
co: Speed of light in air
n: 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
red   yellow  blue
Group of Waves
Most practical light sources emit group of waves, not just one
2Δω
Carrier and Envelope
vp
vg
Group Velocity

c
vg 

m/s
k
ng
n
n g  (n  
)

• 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.
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
output polarizer
(allows light at 45o)
Faraday rotator
Input Polarizer
(allows only vertically
polarized light)
Polarization
Controller (creates
vertical polarization)
• 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.
Polarization Mode Dispersion (PMD)
Each polarization state
has a different
velocity  PMD
Polarization Dependent Modulation