PROPAGATION OF SIGNALS IN
OPTICAL FIBER
9/20/11
Light Characteristics
• Particle Characteristics
• Light has energy
• Photons are the smallest quantity of monochromatic light
• That is light with single frequency
• The energy of a photon is described by E= hf (h=6.6260755E-34
joule-sec) and f is the frequency of light
• Energy of light depends on its speed: E=mc^2 (Einstein’s Eqn.)
• The relationship between frequency and speed: v=c/λ
•  Speed of light changes as it enters denser materials
• Wave Characteristics
• Described by a series of equations
Photometric Terms
• Flux
• Rate of optical energy flow (number of photons emitted per
second)
• Illuminous density
• Rate emitted in a solid angle
Light Properties
• Light is electromagnetic radiation
• Impacted by many parameters: reflection, refraction, loss,
polarization, scattering, etc.
• Light of a single frequency is termed monochromatic
• Any electromagnetic wave is governed by a series of
equations
• In this case ε and μ are relative
** Wave Equation
• Phase velocity
• Group velocity
• Velocity at which pulses propagate: 1/β1
• Change of rate of group velocity is proportional to β2
• When β2=0  pulse does not broaden! Propagation constant for
monochromatic wave
• Defined by β=ωn/c = 2πn/λ = kn
• k is the wave number k=2π/λ (spatial frequency)
• Thus, for core β1 = k.n1
• That is kn2 < β <kn1
• Effective index = neff = β/k
• The speed at which light travels is c/neff
Polarization
• Remember: light is an electromagnetic wave
• Electric field and magnetic field
• When E and H fields have the same strength in all directions light is
un-polarized
• As light propagates through medium field interact and
their strengths changes  light become polarized
• If the E field associate with the EM wave has no
component in the direction of propagation is said to be
Traverse E-field (TE)
• Thus, only Ex and Ey exist n the fundamental mode
• Same for TM
• Collectively, it is called a TEM wave
Directional Relation Between E and H
For Any TEM Wave
k (x,y,z)
E (x,y,z)
H (x,y,z)
Phasor Form
Note:
E and H may have x & y components
However, they travel in Z direction and
They are perpendicular to each other!
Polarization - General
• Polarization is the orientation of electric field component of an electromagnetic wave
relative to the Earth’s surface.
• Polarization is important to get the maximum performance from the propagating signal
• There are different types of polarization (depending on existence and changes of
different electric fields)
• Linear
• Horizontal (E field changing in parallel with respect to earth’s surface)
• Vertical (E field going up/down with respect to earth’s surface)
• Dual polarized
• Circular (Ex and Ey)
• Similar to satellite communications
• TX and RX must agree on direction of rotation
• Elliptical
• Linear polarization is used in WiFi communications
Polarization - General
(x,z)
z
E-Field is
Going up/down
respect to Earth!
(Vertical
Polarization)
(y,z)
E-Field is
Rotating (or
Corkscrewed) as
they are
traveling
Propagating parallel to earth

Polarization is important to get the maximum performance from the antennas
 The polarization of the antennas at both ends of the path must use the same
polarization
 This is particularly important when the transmitted power is limited
Factors Impacting Polarization
• A number of factors can impact polarization
• Reflection
• Refraction
• Scattering
• These factors in turn depend on material property
• Transparent materials
• Isotropic
• Refractive index, polarization, and propagation constant do not change along the
medium
• Anisotropy
• Electrons move with different freedom in different directions
• As light hits the medium the refracted light splits, each having a different polarization
• This property is referred to as Birefringence in fiber – modes of propagation have
different propagation constants (polarization modes Ex & Ey)
• Birefringence in fiber can be used for filtering
Example – Fiber Birefringence
• The birefringence property  pulse spreading
• Lithium Niobate
• We refer to this as polarization-mode dispersion
Numerical Example – Fiber Birefringence
Dispersion
• Different components of light travel with different velocity ,
thus, arriving at different time
• This results in pulse broadening
• Dispersion types
• Polarization Mode Dispersion
• Intermodal Dispersion
• Chromatic Dispersion
Chromatic Dispersion
• So how much a pulse is broadened?
• Depends on the pulse shape
• Let’s assume a specific family of pulses called chirped Gaussian
Pulses (chirped means frequency is changing with time)
• They are not rectangular!
• Used in RZ modulation
• Chirped pulses are used in high-performance systems
• If To is the initial width, Tz is pulse width after distance z,
with κ being the chirp factor:
Tz
kb2 z 2 b2 z 2
= (1+ 2 ) + ( 2 )
To
To
To
Chromatic Dispersion
• In a single mode fiber different spectral components travel with
different velocities (proportional to β2)
• Chromatic Dispersion parameter D = 1(2πc/λ^2)β2
• Expressed in terms of ps/nm-km
• No chromatic dispersion when β2 = second derivative = 0
• D=Dm + Dw
• Due to material dispersion nλ
• Different wavelengths travel at different speeds
• More significant
• Due to waveguide dispersion n2<neff<n1; Pneff
• neff depends on how propagated power is distributed in cladding or core
• Power distribution in core and cladding is a function of wavelength
• Longer wavelength  more power in cladding
• Thus, even if n(λ) = constant  wavelength change result in power distribution change 
neff change
•
Chromatic Dispersion
The total dispersion D is zero about 1.31 um
We want to operate around 1.55um (low loss)
let’s shift the zero-dispersion point to 1.55um!
This is done by changing Dw (Dm cannot be changed too much)
Negative dispersion
Example
• Consider a 2.5 Gb/s SONET system operating over a
single mode fiber at 1.55 um with dispersion length of
1800 km. Find Tz/To after Z = 2LD. Assume an unchirped
Gaussian pulse
• LD = To^2/β2
• Z=2(LD)  Tz/To = sqrt(1+4)=2.24
• Note To=0.2 nsec (half bit interval)
• What if κ is negative?
Tz
kb2 z 2 b2 z 2
= (1+ 2 ) + ( 2 )
To
To
To
Chirp Factor
• If chirp factor is negative the pulse goes under
compression first and then it broadens
Example of Single Mode
Chromatic Dispersion
Dealing with Dispersion
• Different approaches
• Dispersion-shifted Fiber
• Dispersion Compensated Fiber
• Dispersion Flattened Fiber
• Basic idea
• Change the refractive index profile in cladding and core
• Thus introducing negative dispersion
References
• http://www.gatewayforindia.com/technology/opticalfiber.ht
m
• Senior: http://www.members.tripod.com/optic1999/