Optoelectronics Lecture notes

1. n1
2
1
3
n
n2
O
O' O''
n2
2
3
 GRIN fibre does not have a constant refractive index in the core
but decreases from n1 at the centre, as a power law, to n2 at the
cladding.
Graded index (GRIN) fibre
2n
2
1
1 21
















a
r
n ; r < a
; r = a
n(r)
∆ = relative refractive index
difference, (n1-n2)/n1
 = profile parameter

2. n1
n2
2
1
3
n
O
n1
2
1
3
n
n2
O
O' O''
n2
(a) Multimode step
index fiber. Ray paths
are different so that
rays arrive at different
times.
(b) Graded index fiber.
Ray paths are different
but so are the velocities
along the paths so that
all the rays arrive at the
same time.
2
3
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)

3. Dispersion in GRIN fibre
• In the GRIN fibre, the index changes continuously, which
is analogous to having ray travel from layer to layer
almost immediately.
– After many refractions, the angle eventually satisfies the
critical angle to have TIR.
– The ray paths in the graded index core are therefore curved
trajectories as shown in Fig.17
• The intermodal dispersion is minimum when
 = (4+2)/(2+3)  2(1 – )
If  is small so that  ~ 2 (parabolic). This is optima profile index
• With this optima profile index, the rms dispersion
sintermode/L  n12/(20 3 c)

4. n decreases step by step from one layer
to next upper layer; very thin layers.
Continuous decrease in n gives a ray
path changing continuously.
TIR TIR
(a) A ray in thinly stratifed medium becomes refracted as it passes from one
layer to the next upper layer with lower n and eventually its angle satisfies TIR.
(b) In a medium where n decreases continuously the path of the ray bends
continuously.
(a) (b)
© 1999 S.O. Kasap, Optoelectronics(Prentice Hall)
Fig. 17:

5. The Decibel
• The decibel unit is used to express gain or loss in a system or
component. It is used to compare the power entering a system,
circuit or component to the power leaving it.
• A useful figure to remember is 3dB, which represents a loss of
one half of the power.
• Decibel expressing loss is a negative unit.
• dBm means “decibels referenced to a milliwatt”
dB
P
P
Gain
in
out






 10log10







mW
P
dBm
1
log10 10
dB
P
P
Loss
out
in






 10log10

6. Attenuation in Optical Fibres
• Suppose that the input optical power into a fibre of length L
is Pin and the output power is Pout and power anywhere in
the fibre at a distance x from the input is P.
• The attenuation coefficient a is defined as the fractional
decrease in the optical power per unit distance
 LPP
P
P
L
dP
P
dx
dx
dP
P
inout
out
in
P
P
L out
in
a





a
a
a

expln
1
1
1
0

7. Attenuation in dB/length
 
aaa






a
344
10ln
10
log10
1
dB/length,intcoefficiennAttenuatio
km.perdBtypicallydB/length,ofin term
expressedispoweropticalaninnattenuatiopowergeneral,In
.
P
P
L
dB
out
in
dB

8. Attenuation in optical fiber
(glass or silica fiber)
Absorption Scattering Geometrical
effects
Intrinsic
UV IR
Extrinsic
Metal
ions
OH-
ions
Rayleigh
Mie
Raman
Brillouin

9. Attenuation
• Attenuation is a major factor to be considered in the
design of any communication systems due to the fact
that receivers require minimum level of power.
– It determines the maximum length possible before the power
levels drop below its minimum level.
• In a particular optical link, beside the fiber attenuation,
losses can occur at the input/output couplers, splices
and connectors.
– The attenuation is usually expressed in dB/km

11. Absorption
• Optical energy lost when passes through any medium is
called absorption.
• Different material will absorb different amount of light
and a material will absorb different amount of light at
different wavelengths.
• The absorbed light is usually converted into heat energy
within the absorbing material.
– The absorption is the dissipation of some optical power as
heat in the optical fiber.

12. z
A solid with ions
Light direction
k
Ex
Lattice absorption through a crystal. The field in the wave
oscillates the ions which consequently generate "mechanical"
waves in the crystal; energy is thereby transferred from the wave
to lattice vibrations.
© 1999 S.O. Kasap, Optoelectronics(Prentice Hall)

13. Intrinsic Absorption
• This is a natural property of glass.
• It is strong in the short wavelength ultraviolet (UV)
region in the electromagnetic spectrum.
– It is unimportant because the communication wavelength
is far from the UV region.
• Another intrinsic peak occurs in the Infrared region
between 7µm-12µm for typical glass composition.
– Although it is still far from the key wavelengths, the edges
of IR absorption extends toward the key wavelength region.

14. Optical fiber attenuation as a function of wavelength yields nominal
values of 0.5 dB/km at 1300 nm and 0.3 dB/km at 1550 nm for standard
single mode fiber. The attenuation peak was shown at 1440 nm

15. Extrinsic absorption
• It is due to impurities present in the glass.
They are Hydroxyl ion (OH-) and metal
ions.
• The most significant OH losses occur at
1.38µm, 0.95µm and 0.72µm.
• The purity has been achieved for silica
fibres nowadays.

16. Scattering losses
• Linear scattering: Rayleigh scattering, Mie scattering.
• Non-linear scattering: Brillouin scattering, Raman
scattering.
• Mie Scattering:
– It is caused by imperfections such as irregularities in the
core cladding interface, core cladding refractive index
differences along the fiber length, diameter
fluctuations, strains and bubbles.

17. Rayleigh scattering
• It occurs due to the random distribution of
individual molecules within the medium.
• Molecules moves randomly in molten state are
frozen into solid state in the making of fiber.
• This will result in a localized variation of the
refractive index throughout the glass due to
clumping of the molecules.
• Rayleigh scattering is inversely proportional to the
wavelength.

18. Scattered waves
Incident wave Through wave
A dielectric particle smaller than wavelength
Rayleigh scattering involves the polarization of a small dielectric
particle or a region that is much smaller than the light wavelength.
The field forces dipole oscillations in the particle (by polarizing it)
which leads to the emission of EM waves in "many" directions so
that a portion of the light energy is directed away from the incident
beam.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)

19. The attenuation due to Rayleigh
scattering in dB/km:
FBcR TkPn 


 28
4
3
3
8







 = optical wavelength,
n = refractive index of the medium,
P = average photoelastic coefficient,
c = isothermal compressibility at temp TF
kB =Boltzman’s constant (1.381×10-23JK-1)
 
)/exp(
1log10 10
L
nAttenuatio
R


The Rayleigh scattering coefficient is:

20. Stimulated Brillouin Scattering (SBS)
)(104.4 223
wattsBdP dBB a 
• SBS is due to modulation of light through thermal vibration
within the fiber. The scattered light appears as upper and lower
sideband which are separated from the incident light by the
modulation frequency.
• The threshold power, PB above which Brillouin scattering occurs
is given as:
– d=fibre core diameter in µm, =operating wavelength in µm, adB=fibre
attenuation in dB/km, B=source bandwidth in GHz
– From this formula, the maximum power which can be launched into a
SMF before SBS occurs can be calculated.
*SMF : single mode fibre

21. Stimulated Raman Scattering (SRS)
)(109.5 222
wattsBdP dBR a 
• SRS is similar to SBS but occurs at higher
threshold power, PR:
• SBS and SRS are usually seen in SMF since
the MMF with higher core size allows
higher power to be traveling in the
waveguide.
*SMF: Single Mode Fibre
MMF: Multi Mode Fibre

22. Geometrical Effect – Bend losses
• Bending the fiber causes attenuation.
– This is due to the energy in the evanescent field at the bend
exceeding the velocity of light in the cladding
– and hence the guidance mechanism is inhibited, which
causes light energy to be radiated from the fiber.
• Macroscopic bending losses due to small changes in
the refractive index of the fiber due to induced strains
when it is bent during its use.
– It is a large scale bending loss like wrapping fiber on a spool
or pulling (laying) fiber around a corner.
• Microscopic bending can occur during the cabling
process due to stress.

23. Escaping wave
 
  

  c 
Microbending
R
Cladding
Core
Field distribution
Sharp bends change the local waveguide geometry that can lead to waves
escaping. The zigzagging ray suddenly finds itself with an incidence
angle  that gives rise to either a transmitted wave, or to a greater
cladding penetration; the field reaches the outside medium and some light
energy is lost.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)

24. Fundamental mode field in
a curved optical waveguide
Small scale fluctuations in the
radius of curvature of the fiber
axis leads to micro bending
losses. Microbends can shed
higher order modes can cause
power from low order modes to
couple to high order modes.

25. Bend radius for macroscopic bending losses
• For multimode fibers, the minimum bend
radius or the critical radius for curvature is:
• For single mode fiber, it is given by:
where c=[2 an1(2∆)1/2]/2.405
2
3
2
2
2
1
2
1 )(4/)3( nnnRc  
32
3
21 )/996.0748.2]()/(20[ 
 ccs nnR 