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Lightwave Transmission and Amplification
1. Optical fibers
Principle: total reflection between two dielectric materials with different refractive index:
n1 and n2 (< n1).
Features: EM field is not fully confined in the core – leading to radiation loss from the
structure incompleteness; - possible coupling from waveguide to waveguide through
evanescent wave.
Behavior model:
EM field in fiber (propagating along z ) can be written as:
E (r ,  , z, t )  A( z, t )(r ,  )e j (ot   o z )
It can be viewed as the superposition of many single frequency harmonic waves:
E (r ,  , z, t ) 
1
E (r ,  , z ,  )e jt d

2
Hence:
E (r ,  , z ,  )  A( z ,    o ) (r ,  )e  j o z
A( z , t ) 
1
2
 A( z,  
o
)e j (  o ) t d 
1
2
 A( z, )e
jt
d
Substituting E (r ,  , z,  ) into Helmholtz equation (wave propagation equation in
frequency domain, directly derived from Maxwell equation) yields:
A( z, )  2   o2

A( z, )  0
z
2 j o
plus an eigen value equation that governs  (r ,  ) .
Since    o ,  can be expanded as:
  o  j
n 

2
  1 
1
1
 2  2   3  3  ......
2
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 
|
 n o
n
1
where  is the fiber loss,  1, 2,3,...... are the group delay, the chromatic (2nd) dispersion and
the higher order (>3rd) dispersions, respectively.
Therefore, the governing equation for lightwave propagation along fiber in time domain
can be obtained:
  2 A( z, t )  3  3 A( z, t ) 
A( z, t )
A( z, t )
 1
j 2

 A( z, t )  0
z
t
2
6
2
t 2
t 3
Characteristics:
Ge-SiO2/SiO2 fiber loss characteristics
Loss (dB/km)
OH- Absorption
Metal Ion
Absorption
Transmission
Windows
Rayleigh Scattering
Infrared
Absorption
1100nm
1200nm
1300nm
1400nm
1500nm
Wavelength
Ge-SiO2/SiO2 fiber chromatic dispersion characteristics
Mode dispersion: different propagation speed from different mode.
Polarization dispersion: different propagation speed from different polarized mode.
Material dispersion: from material inherent property.
Waveguide dispersion: from waveguide structure.
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Dispersion (ps/nm.km)
Material
dispersion
G. 652/G. 654 SMF
Waveguide
dispersion
G. 653 SMF
1300nm
1550nm
Wavelength
Numerical aperture
NA  n1 2
n1  n2
 sin 
n1
From connection and guidance point of view: larger NA is better. However, larger NA
may excite high order modes, hence introduce mode dispersion and reduce the
transmission bandwidth. In SMF, larger NA yields more negative dispersion. This can be
utilized to cancel the positive material dispersion. (DCF is such designed.)
Cut-off wavelength
Fundamental mode (LP01) has no cut-off wavelength, higher (1st) order mode (LP11) has
cut-off wavelength given by: c  2aNA/ Vc , where Vc is calculated from the eigen
value equation for LP11 mode, Vc  2.4 for any fiber with step-index profile (the 1st root
of zero-order Bessel function).
In order to guarantee single mode transmission in fiber, the cut-off wavelength must be
designed smaller than the transmission wavelength.
Please note that any wavelength can be transmitted in the fiber through at least one
spatial pattern (the fundamental mode). The cut-off wavelength only gives the criteria
how many spatial patterns are allowed. If the wavelength transmitted in the fiber is longer
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than the cut-off wavelength, there is only one spatial pattern (the fundamental mode) in
the fiber. Otherwise, there are more than one spatial patterns (the fundamental mode plus
the higher order mode) in the fiber.
For a given index profile, the cut-off wavelength is only determined by the core-size of
the fiber. This indicates that the waveguide can be viewed as a “spatial pattern filter”
controlled by its size (cut-off wavelength).
Fiber products:
Transmission
Wavelength
Loss
Dispersion
G. 652 SMF
1310nm or 1550nm
G. 653 DSF
1550nm
G. 654
1550
0.35dB at 1310nm
0.2dB at 1550nm
3.5ps/nm.km at 1310nm
20ps/nm.km at 1550nm
0.22dB
0.15dB
3.5ps/nm.km
20ps/nm.km
Application requirement:
NA
c
Loss
small
to be optimized
Dispersion
to be optimized
small
Bending
large
large
Connection
large
large
Mode Profile
to be optimized
to be optimized
small
large
2. Other passive photonic devices
Passive photonic devices: optical connector, optical isolator, optical coupler, optical
attenuator, optical filter.
3. Optical amplifiers
1. Erbium Doped Fiber Amplifier (EDFA)
Principle:
EDF Energy Level
EDF Cross-sectional Structure
4I(11/2)
1S
Cladding
4I(13/2)
Core
Er 3
980nm
1480nm
1550nm/10mS
Doped
Area
4
Gain spectrum:
S-Band
L-Band
C-Band
20dB
1535nm
1550nm
1570nm
Wavelength
Configuration:
Optical Signal Input
EDF
ISO
Optical Signal Output
ISO
Pump
Laser
PhotoDetector
PhotoDetector
Gain Control Unit
Behavior model:
dN up
dt
(
(
 p pa Pp
Ahv p
 p pe Pp
Ahv p


s sa Ps M ni nai Pni

)( N o  N up )
Ahvs
Ahvni
i 1
N up
s se Ps M ni nei Pni

) N up 
Ahvs
Ahvni
 up
i 1
dPni
1
 {v g ni [( nai   nei ) N up   nai N o ]  }Pni  Rspi , i  1,2,......M
dt
n
where N up is Er 3 density at exited state 4I 13 / 2 ; N o is Er 3 doping density; A is the
fiber core area,  p , s , ni are the optical field confinement factor of the pump light, the
signal light, and the spontaneous emission light at i_th wavelength, respectively;  pa, sa,nai
are the stimulated absorption cross-section of the pump light, the signal light, and the
spontaneous emission light at i_th wavelength, respectively;  pe, se,nei are the stimulated
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emission cross-section of the pump light, the signal light, and the spontaneous emission
light at i_th wavelength, respectively; v p , s ,n are the frequency of the pump light, the
signal light, and the spontaneous emission light at i_th wavelength, respectively; h is
Planck constant; Pp , s ,ni are the optical power of the pump light, the signal light, and the
spontaneous emission light at i_th wavelength, respectively;  up, n are the lifetime of Er 3
at its exited state 4I 13 / 2 and the spontaneous emission photon lifetime, respectively; R spi
is the spontaneous emission rate at i_th wavelength; i  1,2,......M indicates all the
possible wavelengths at which spontaneous emission is generated.
Pp is given as the steady state pump power. Ps is the averaged signal power. Both of
them can be viewed as constants in solving above rate equations.
Characteristics:
Optical gains for the signal and the spontaneous noise are given by:
Gs  s [( sa   se ) N up   sa N o ]
Gni  ni [( nai   nei ) N up   nai N o ]
Hence signal light output power can be related to signal light input power:
PsO  PsI e Gs L
where L is the length of EDF.
At input end, the signal-to-noise ratio (SNR) can be estimated as:
SNRin 
PsI
hv s v
The spontaneous noise is also amplified in EDF and its value in the signal band at the
output end can be given as:
Pns  2nsp (e GnsL  1)hvs v
where n sp is the population inversion factor. Hence SNR at output end can be estimated
as:
SNRout 
PsO
PsI
e Gs L

(
)
hv s v  Pns 1  2nsp (e GnsL  1) hv s v
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Therefore, the noise figure of EDFA can be given as:
G L
SNRin 1  2nsp (e ns  1)
NF 

 2nsp  2
SNRout
e Gs L
Applications:
Requirement
small signal gain >
In-line
20dB
Amplification
noise figure < 5dB
PreAmplification
output optical power >
Power
10dBm
Booster
Pump
980nm
1480nm
980nm
Remark
980nm pump for better noise figure
1480nm pump for in-line monitoring
980nm pump for better noise figure
980nm
1480nm
980 pump for high efficiency
1480nm pump for stability
2. Semiconductor Optical Amplifier (SOA)
Structure:
Current Injection
Optical Signal Output
Optical Signal Input
Semiconductor Gain Medium
Anti-Reflection Coatings
Application:
Gain Block Configuration
EDFA
DEMUX
……
SOA
DEMUX
SOA
……
SOA
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