Transcript Modal and Material Dispersion - Northern India Engineering

Optical Fibre Dispersion
By:
Mr. Gaurav Verma
Asst. Prof.
ECE
NIEC
Why does dispersion matter ?
• Understanding the effects of dispersion in optical
fibers is quite essential in optical communications
in order to minimize pulse spreading.
• Pulse compression due to negative dispersion can
be used to shorten pulse duration in chirped pulse
lasers
Dispersion in Multimode Step Index Fiber
θa
Easy Derivation from Senior or Sapna Katyar…
Birefringence in single-mode fibers
Because of asymmetries the refractive indices for the two degenerate modes (vertical
& horizontal polarizations) are different. This difference is referred to as
birefringence,
B:f
Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000
Fiber Beat Length
In general, a linearly polarized mode is a combination of both of the
degenerate modes. As the modal wave travels along the fiber, the difference
in the refractive indices would change the phase difference between these
two components & thereby the state of the polarization of the mode.
However after certain length referred to as fiber beat length, the modal
wave will produce its original state of polarization. This length is simply
given by:
2
Lp 
kB f
[2-35]
Modal Birefringence
Intermodal Dispersion
Intermodal Dispersion
 Exists in multimode fiber cable
 It causes the input light pulse to spread.
 Light Pulse consists of group of modes. The light energy is delayed with different amount
along the fiber.
Graded Index Fiber Structure
• In graded index fiber, core refractive index
decreases continuously with increasing radial
distance r from center of fiber and constant in
cladding
r  1/ 2


n
[
1

2

(
) ]
for 0  r  a
 1

n(r )  
a

n (1  2)1/ 2  n (1  )  n for r  a
1
2
 1

• Alpha defines the shape of the index profile
• As Alpha goes to infinity, above reduces to step
index
n n
n n
• The index difference is


2
1
2n12
2
2
1
2
n1
contd
• NA is more complex that step index fiber since
it is function of position across the core
• Geometrical optics considerations show that
light incident on fiber core at position r will
propagate only if it within NA(r)
• Local numerical aperture is defined as

[n 2 (r )  n22 ]1/ 2  NA(0) 1  (r / a)
NA(r )  

0 for r  0
• And
NA(0)  [n (0)  n ]
2
2 1/ 2
2

for r  a 





2 1/ 2
2
 n n
2
1
 n1 2
contd
• Number of bound modes
M

 2
a k n 
2
2
2
1
Examples
If a = 9.5 micron, find n2 in order to design a
single mode fiber, if n1=1.465.
Solution,
V  2.405  (2a /  ) n12  n22  (2 4.25 /  ) 1.4652  n22
  820nm, n2  1.463
  1300nm, n2  1.46
  1550nm, n2  1.458
The longer the wavelength, the larger refractive
index difference is needed to maintain single
mode condition, for a given fiber
Examples
• Compute the number of modes for a fiber
whose core diameter is 50 micron. Assume
that n1=1.48 and n2=1.46. Wavelength = 0.8
micron.
• Solution
V0.82 m  (2a /  ) n12  n22  (2 25 / 0.82) 1.48 2  1.46 2  46.45
For large V, the total number of modes
supported can be estimated as
M  V 2 / 2  46.452 / 2  1079
Example
• What is the maximum core radius allowed for
a glass fiber having n1=1.465 and n2=1.46 if
the fiber is to support only one mode at
wavelength of 1250nm.
• Solution
Vcritical  2.405  (2a /  ) n12  n22


a  Vcritical /(2 n12  n22 )  2.405x1.25 / 2 1.4652  1.462  3.956m