PROPAGATION OF SIGNALS IN
OPTICAL FIBER
9/13/11
Summary
• See notes
Single Mode Fiber
• Avoids the delay between different rays
• Only one mode (ray) is propagated
• Thus, we need to select the right relationship between the
wavelength and core diameter
2p a × n1(2D)
l =
2.405
1/2
Note that modes propagating near
c
The critical wavelength (cutoff) will not
Be fully guided within the core.
NOTE: Single mode operation (with step index) occurs only above λc.
n1 - n2
D=
;
2
2n1
2
2
Single Moe Fiber - Example
• See notes
Attenuation
• Transmission loss is the main limiting factor in optical
communication systems
• Limiting how far the signal can be transmitted
• Transmission loss in fiber is much less than copper (<5
dB/km)
• Loss in dB = 10log Pi / Po
• Pi/Po = 10 ^(dB/10)
• Attenuation (dB) = αL = 10log(Pi/Po) ;
• Loss per unit length is represented by α is in dB/km
• Also represented as follow (z=length from the source, and P(z) is
the power at point z.
• Example
Loss - Example
• OTDR Example
• Numerical Example
Fiber Bend Loss
• Radiation loss due to any type of
bending
• There are two types bending
causing this loss
• micro bending
• small bends in the fiber created by
crushing, contraction etc causes the loss
• macro bending
• fiber is sharply bent so that the light
traveling down the fiber can not make the
turn and gets lost
Radiation attenuation
coefficient = αr = C1 exp(C2 x R)
R = radius of the
curvature; C1 & C2 are
constants
Fiber Bend Loss
3× n1 × l
Rcm =
2
2 3/2
4p (n1 - n2 )
2
• Multimode Fibers
• Critical Radius of curvature
• Large bending loss occurs at Rcm
• Single-Mode Fibers
20 l
l -3
Rcs = 2
(2.748
0.996
)
2 3/2
(n1 - n2 )
lc
2p a × n1(2D)
l =
2.405
1/2
Note that modes propagating near
c
The critical wavelength (cutoff) will not
Be fully guided within the core.
NOTE: Single mode operation (with step index) occurs only above λc.
Fiber Bend Loss - Example
• In general, the refractive index difference:
n1 - n2
n1- n2
D=
; D=
<<1
2
2n1
n1
2
2
Example of cutoff Wavelength
• Find the cutoff wavelength for a step index fiber to exhibit
single mode operation when n1=1.46 and core
radius=a=4.5 um. Assume Δ=0.25%
2p a × n1(2D)
lc =
2.405
1/2
2p
lc
a n1 - n2 < V = 2.405
2
2
λc = 1.214 um
Typical values are a=4μm,
Δ=0.3%, λ=1.55 μm
Note that if V becomes larger than 2.405  multimode fiber
Other factors impacting loss
• Notes - map
Scattering
• When some of the power in one propagation mode is
transferred into a different mode  Loss of power in the
core
• Power Scattering
• Linear : Po is proportional to Pi, and there is no frequency change –
thus the power propagated is proportional to mode power
• Two types: Rayleigh and Mie
• Nonlinear : The power propagation results in frequency change
• Type types: Stimulated Brillouin Scattering & Stimulated Roman
Scattering
Rayleigh Scattering
• Due to density fluctuation in
refractive index of material
• Represented by ϒR (Rayleigh
scattering factor) – (1/m)
• ϒR is a function of 1/(λ)^4
• Transmission loss factor for one km (unit
less) αR= exp(-ϒR.L); L is the fiber
length
• Attenuation (dB/km) = 10log(1/αR)
• Rayleigh scattering is dominant in
low-absorption window
Example
• Assume for Silica ϒR = 1.895/(λ^4); and we are operating
at wavelength 0.63um. Find attenuation due to Rayleigh
scattering in a 1-km of fiber. Repeat the same problem for
wavelengths of 1 um and 1.3 um.
Mie Scattering
• Linear scattering can be due to inhomogeneities in fiber
• This is due to having non-perfect cylindrical structure or codecladding refractive index difference along the fiber
• When such inhomogeneities > λ/10  Mie Scattering is
significant
• Mie scattering can be removed by removing imperfections
in the glass manufacturing or increasing Δ.
Nonlinear Scattering
• Nonlinearity is primarily due to high power level, high bit-rate (when
we have to transmit over long distances)
• Resulting in frequency change
• Stimulated Brillouin Scattering (SBS)
• A backward gain (emission is stimulated), opposite to direction of
propagation when a threshold power is reached depleting the
transmitted power
• The stimulated light has a shorter wavelength  creating interfering with
similar possible wavelengths
• Exists only above a certain power threshold
• PB (in watts) = 4.4*10-3*d^2*λ^2*α( in dB/km)*V
• [this is relatively low threshold]
• V is Bandwidth in GHz; d is code diameter (2a) in um; λ in um
• Beyond PB optical frequency shifts
• More critical than SRS
Nonlinear Scattering
• Stimulated Roman Scattering (SRS)
• Power from lower wavelength channels is transferred to higher
wavelengths
• Exists only above a certain power threshold
• PR = 5.9*10-2*d^2 (in um)*λ (in um)*α( in dB/km) [in watts]
• d is code diameter (2a);
Example
Material Absorption
• A major loss factor is material absorption
• Dissipation of optical power in the waveguide due to material
composition and fabrication process
• Absorption can be Intrinsic or Extrinsic
• Intrinsic
• Interaction of different components of the glass (due to impurities)
• Has two components
• Ultra violate absorption – high energy excitation (lower wL  high eV
higher excitation  more heat  more loss
• Infrared Absorption – molecular vibration within the glass  heat
Material Absorption
Photon Energy increasing (eV)
molecular vibration
within the glass
 prop. to WL
high energy excitation
 prop. to eV
Material Absorption – Extrinsic
• Due to waveguide impurities (the glass) – major source of
attenuation
• Metallic impurities – metallic ions e.g., copper and chromium);
depending on their WL
• This is why some glasses are colored (e.g., they have copper ion –
thus, absorbing some lights passing through others)
• Hydroxyl (OH) impurities (main factor)
• Key factors in generating overtones
Overtones due to Hydroxyl Impurities
Material Absorption – Extrinsic
• Using lower-water-peak fiber (dry fiber); also known as
zero-water peak (by Lucent) the peaks can be eliminated!
Polarization
• Introduction
References
• http://www.gatewayforindia.com/technology/opticalfiber.ht
m
• Senior: http://www.members.tripod.com/optic1999/
Communication Systems
Basic Blocks
• Three basic components
• Source and Transmitter
• Destinations and Receiver
• Communication channel
(medium)
• Communication channel
• Wired
• Wireless
• Glass
• Water and or materials
Coverage and Topology
• Coverage (public network)
• LAN
• MAN
• WAN
• Topology
• Bus
• Ring
• Mesh
• Star