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# Calculations and Measurements of Raman Gain Coefficients of

## Different Fiber Types

Yuhong Kang

Thesis submitted to The Faculty of the Virginia Polytechnic Institute and State University
in partially fulfillment of the requirements for the degree of

Master of Science

In

Electrical Engineering

Roger H. Stolen, Chair,
Ira Jacobs

December 9, 2002
Blacksburg, Virginia

Keywords: Fiber Raman amplifier, stimulated Raman scattering, effective Raman gain
and Raman gain coefficient, GeO
2
concentration, Effective area

Calculations and Measurements of Raman Gain Coefficients of
Different Fiber Types

Yuhong Kang

Abstract

Fiber Raman amplification using the transmission line is a promising technology to
increase the repeater distance as well as the capacity of the communication systems.
Because of the growing importance of fiber Raman amplification, it is desired to predict
the magnitude and shape of the Raman gain spectrum from the doping level and
refractive index profiles of different fiber designs.

This thesis develops a method to predict the Raman gain coefficients and spectra for a
pure silica core fiber and two different types of GeO
2
-doped silica fibers given their
index profiles. An essential feature of the model is the inclusion of the variation in
Raman gain coefficient over the mode field due to the variation in the Ge concentration
across the fiber core. The calculated Raman gain coefficients were compared with
measurements of the peak Raman gain on a step- index GeO
2
-doped fiber and with
published measurements from various sources. Agreement between the calculated and
measured peak gain for the step- index fiber was excellent. There was qualitative
agreement with published measurements but there were significant differences between
the calculated and published gain coefficients, which are not understood.

Part of the work sought a way of predicting Raman gain coefficients from a standard
gain curve given only the fiber type and the effective area. This approach appears
promising for moderately-doped fibers with the proper choice of effective area.

iii
Acknowledgements

I would like to thank all of my committee members for their support and encouragement
before and during my time spent at the fiber optics research group. I would like to
acknowledge my advisor Dr. Roger Stolen for giving me the opportunity to work with
him, for the help and advice, and for the valuable guidance and support of him during

I have enjoyed working with all the students in our group over the past 1 year. Special
thanks to Nitin Goel for his so many advices on my thesis research.

I would also like to thank the continuous support and encouragement provided by my
dear husband and parents.

iv

Abstract ii
Acknowledgements..iii
List of illustrationsv
Chapter 1 - Introduction.................................................................................................... 1
1.1 Significance of Calculation and Measurement of Fiber Raman Amplifier ............ 1
1.2 Overview of Raman Scattering............................................................................... 3
1.2.1 Spontaneous Raman Scattering........................................................................... 3
1.2.2 Raman Amplification using Stimulated Raman Scattering.................................. 6
1.3 Thesis Objective and Overview.............................................................................. 8
Chapter 2 - Calculations of Raman Gain and Raman Gain Coefficients in Different
Fiber Types ..................................................................................................................... 10
2.1 Theoretical Background ....................................................................................... 10
2.2 Calculations .......................................................................................................... 16
2.2.1 Calculation parameters ..................................................................................... 16
2.2.1.1 Pure Silica Raman Gain Spectrum................................................................. 16
2.2.1.2 Fiber Types ..................................................................................................... 17
2.2.2 GeO
2
concentrations and the refractive index................................................... 19
2.2.3 Simulation Results ............................................................................................. 23
2.2.3.1 Raman Gain Spectra for pure silica core fiber, step index fiber and
dispersion-shift fiber................................................................................................... 23
2.2.3.2 Optimized Effective Area Approximation Scheme.......................................... 27
2.2.3.3 A simplified calculation model for standard step index fibers ....................... 32
Chapter 3 - Measurement of Raman Gain in Optical Fibers .......................................... 40
3.1 Experimental Setup of Fiber Raman Gain Measurement ..................................... 40
3.2 Experimental Results ............................................................................................ 42
Chapter 4 Conclusions ................................................................................................. 46
4.1 Conclusions........................................................................................................... 46
4.2 Future Work.......................................................................................................... 47
References....................................................................................................................... 48
Vita ................................................................................................................................. 51

v
Table of Illustrations
Table 1.1 Comparison of commercial EDFA and FRA, data sheets from Amonics  .. 2
Figure 1.1 Spontaneous Raman Scattering....................................................................... 4
Figure 1.2(a) Parallel and Perpendicular Raman Gain Coefficients of ..................... 5
Figure 1.2(b) Parallel and Perpendicular Raman Gain Coefficients of Fused GeO
2
 5
Figure 1.3 The Relative Raman Cross Sections of Vitreous SiO
2
, GeO
2
, P
2
O
5
and B
2
O
5

glasses.  .............................................................................................................. 6
Figure 2.1 Linear regression factor vs frequency shift (cm
-1
).................................. 13
Figure 2.2 Parallel and Perpendicular Raman Gain Spectrum of fused Silica  ....... 17
Table 2.1 Specifications for SMF-28 and SPECTRAN Fibers ...................................... 18
Figure 2.3 Refractive index profile for SPECTRAN fiber ............................................. 18
Figure 2.4 Refractive index profile for dispersion-shift fiber......................................... 19
Table 2.2 Sellmeiers Equation Parameters for Pure and GeO
2
Doped Silica Glass ..... 20
Figure 2.5 Refractive Index vs GeO
2
concentration (Mol %)......................................... 21
Figure 2.6 Index Difference vs GeO
2
concentration (Mol %) ........................................ 21
Figure 2.7 Refractive Index of Pure Silica and GeO
2
-doped Silica vs Wavelength....... 22
Figure 2.8 Effective Raman Gain for dispersion-shift fiber, step index fiber, and pure
silica core fiber ....................................................................................................... 24
Figure 2.9 Normalized Raman Gain in Different Fibers ................................................ 25
Table 2.3 Raman Gain Data in Different Fibers, In the Case of Depolarized Light ...... 25
Figure 2.10 Raman Gain Coefficient with Different Fibers ........................................... 26
Figure 2.11 Comparison of Raman Gains of All Fiber types with Four Effective Area
Approximation Schemes......................................................................................... 29
Figure 2.12 Comparison of Normalized Raman Gains of All Fiber Types with Four
Effective Area Approximation Schemes ................................................................ 30
Figure 2.13 Comparison of Raman Gain Coefficients of All Fiber Types with Four
Effective Area Approximation Schemes ................................................................ 31
Figure 2.14 Comparison of Raman gain curves with the simplified and original
calculation model.................................................................................................... 34
Table 2.4 Measured Raman Gain For Different Transmission Fiber Types .................. 38
Table 2.5 Comparisons between the Calculated and Published Measurement D For
Different Transmission Fiber Types ....................................................................... 38
Figure 3.1 Experimental setup for measuring Raman gain ............................................ 41
Figure 3.2 Spectrum of the pump source........................................................................ 43
Figure 3.3 Pump on/off Optical Gain in dB................................................................... 44

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
1

Chapter 1 - Introduction

1.1 Significance of Calculation and Measurement of Fiber Raman Amplifier

Distributed Fiber Raman Amplifier (FRA) using the transmission line as a Raman gain
medium is a promising technology available for the long haul communication systems,
especially for Wavelength Division Multiplexing (WDM), where simultaneous
amplification of multi-channel lightwave signals is needed, as well as for repeaterless
transmission, where optical gain is required for compensation of the fiber loss -.
FRA is to amplify optical signals in optical fibers, based on transferring the power from
the pump beam to the signal via Raman interaction between the light and vibrational
modes of the glass. Typically, the Raman gain coefficient in fused silica peaks at a
Stokes shift of about 13.2THz with a 3dB bandwidth of about 6THz. FRAs exhibit
several attractive features for applications in transmission systems, which are listed as
follows:

1. Simplicity of amplifier architecture: Raman gain is obtainable in any
conventional transmission fiber. Only high pump lasers are required to be
launched with the signals, and there is no excess loss in the absence of pump
power.
2. Low noise: Distributed Raman amplifiers may deliver negative noise figures ,
while the Erbium Doped Fiber Amplifiers (EDFA) have at least 3dB noise
figure, as shown in Table 1.1.
3. Broad gain spectrum: The Raman gain bandwidth is very broad, around 60nm in
terms of Full Width at Half Maximum (FWHM), which is of significance to the
wavelength division multiplexed system. One unique technique applicable for
RFA is that a broader gain spectrum may be obtained by the use of multi-
wavelength pump sources .
4. Flexibility of transmission window: The pump wavelength determines the gain
spectrum of a Raman amplifier, which means the operation window is
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
2
adjustable. Furthermore, the multi-wavelength pump technique increases and
flattens the bandwidth by pumping simultaneously at different wavelengths.
5. Higher saturation power: Commercial Raman amplifiers have a saturation power
over 100mw, compared to 50 mW with EDFA.

PUMP
POWER
BANDWIDTH

SATURATION
POWER
NOISE
EDFA 35mW 37nm from 1528-1565
with flattening
technology
50mW 5.5 dB
FRA ~350mw 100nm from 1520-1620
with 4 pumps
-2dB (C band)
-3dB (L band)

Table 1.1 Comparison of commercial EDFA and FRA, data sheets from Amonics 

The spontaneous and stimulated Raman scatterings in silica-based glasses and optical
fibers have been studied extensively, since the early work by Stolen , Lin  and
Galeener . The potential applications of Raman amplification in fibers for
communications were first pointed out by Ippen, Patel and Stolen , because of the
long interaction length and high light intensity associated with small core size of fibers.
An early application of fiber Raman amplifier was as a discrete preamplifier to improve
the receiver sensitivity . It also can be used to post-amplify the signal before the
signal is launched into the transmission lines. In 1992, 23 dB signal gain was obtained
from a 140 ns pump pulse with 1.4 W peak power over 20-km- long dispersion shifted
fiber . In 1996, 30 dB gain was obtained when a heavily germanium-doped optical
fiber was pumped with only 350mW . Distributed Raman amplification used in
conjunction with discrete in- line EDFAs can reduce the overall span noise figure more
than 7dB assuming an EDFA noise figure of 4dB . Recently, progress in high power
diode lasers has offered great potential for the development of a multi- wavelength
pumped FRAs to achieve 1dB flatness and ultrawide bandwidth over 100nm .

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
3
The important parameters to describe the gain of the FRA are the Raman gain
coefficient and Raman gain coefficient over effective area, also called effective Raman
gain, which is the desired parameter in a Raman amplifier. Knowing this number can
give us a projection of how much signal gain can be achieved in a specific fiber given
its length and attenuation parameters at pump and signal wavelengths. Recently the
measurements of effective Raman gain of transmission fibers have been performed by
several scientists to investigate the application of distributed Raman amplification -
. However, their results are only qualitatively in agreement with each other. One of
the reasons is that the fibers under test were from various types, different companies,
and even for the same fiber type, the variations appear to be large. Consequently, to
fully understand the material and fiber structure dependences of SRS and develop the
multi- wavelength pumped Raman amplifiers, it is vital to design a reliable numerical
simulation model associated with accurate measurements on Raman gain coefficients to
predict obtainable Raman gains in optical fibers from the fiber designs. It is also
important to find a simplified but sufficiently accurate model to evaluate the Raman
gain spectrum of different fibers from their refractive index profiles.

1.2 Overview of Raman Scattering

Fundamentally, Raman Scattering can be divided into two categories: Spontaneous
Raman Scattering and Stimulated Raman Scattering. To have a complete understanding
of the Raman scattering, this section briefly reviews the history and principle of the
Raman Scattering.

1.2.1 Spontaneous Raman Scattering

When an incident light of frequency
0
is scattering from molecules of a substance, the
scattered light will consist mostly of light with the same frequency as the incident light.
In the meantime, low intensities of light with frequency higher and lower than the
incident light may also be observed. This is called spontaneous Raman scattering, which
was observed independently and simultaneously by Landsberg, Mandelstam and Raman
in 1928.
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
4

Incident
Light
Molecules

Rayleigh
Scattering
-
R
Stokes

shift

+
R
Anti-Stokes

shift
Transmitted Light
Raman
Scattering

Figure 1.1 Spontaneous Raman Scattering

As shown in Figure 1.1, when a photon is incident with frequency
0
upon a molecule
in some arbitrary vibrational state, it will excite the molecule to some intermediate state;
and the molecule will immediately relax its energy state by emitting a photon. The
molecule may return to a higher vibrational energy state than before. The resulting
scattered light will be of a lower energy than the incident light (h
s
< h
i
); This is
called Stokes scattering. The scattered light will have a higher energy (h
s
> h
i
) to
form an anti-Stokes side band if the molecule was already in an excited vibrational
state. Spontaneous Raman Scattering is a very useful analytical tool for the study of
vibrational modes of solids, liquids and gases.

Due to the amorphous nature, fused silica and GeO
2
20THz.The Raman gain spectra in fused silica and GeO
2
are shown in Figure 1.2 (a)
and 1.2 (b), where the gain spectra are a composite of measurements by several authors
of spontaneous Raman scattering in bulk silica, GeO
2
samples and silica-core fibers
. The two curves in each figure are for scattering of light polarized parallel and
perpendicular to the polarization of the exciting light. The perpendicular gain
coefficients in silica and GeO
2
are much less than the parallel ones.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
5
The material related frequency shift dependent stimulated Raman scattering coefficient,
g
R
is related to the Zero Kelvin spontaneous Raman scattering cross section which will
be discussed in detail in Chapter2.

Figure 1.2(a) Parallel and Perpendicular Raman Gain Coefficients of 

Figure 1.2(b) Parallel and Perpendicular Raman Gain Coefficients of Fused GeO
2


200 400 600 800 1000 1200 1400
Frequency Shift (cm
-1
)
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
6
Figure 1.3 The Relative Raman Cross Sections of Vitreous SiO
2
, GeO
2
, P
2
O
5
and B
2
O
5

glasses. 

Figure1.3 shows relative Raman cross sections of vitreous SiO
2,
GeO
2
, P
2
O
5
and B
2
O
5

glasses, normalized to the peak of the silica spectrum. These Oxide glasses are
commonly used as dopants for fiber fabrication. After corrected for effects caused by
different optical index of these glasses, the Raman cross section for pure GeO
2
at the
peak is approximately nine times as high as that for pure SiO
2
. Doping GeO
2
into SiO
2
glass has been proved to significantly increase the Raman cross-section and the Raman
gain coefficient for silica-based fibers.

1.2.2 Raman Amplification using Stimulated Raman Scattering

Optical amplification via stimulated Raman scattering, called Raman amplification, has
advantages of self-phase matching between the pump and the signal, and broad
bandwidth or high speed response, compared with other nonlinear processes.

When a weak signal is launched with a stronger pump, it will be amplified due to SRS.
In the CW case, the signal amplification is described by the following equations in
terms of power transfer from the pump to the signal due to the Raman interaction
between the pump and the signal:

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
7
S S S P R
S
P P P g
dz
dP
(1.1)
P P S P R
S
P P
P P P g
dz
dP

(1.2)

The Raman interaction transfers power from
P
P to
S
P .
P
P and
S
P are the powers of
waves at frequencies
P
and
S
.
P
P and
S
P are functions of propagation distance Z
and
P
,
S
stand for the fiber loss at
P
and
S
.
R
g represents the Raman gain
coefficient in a fiber. If we neglect the pump depletion term on the first right side of
equation (1.2), we can obtain:

( ) ( )

,
_

L L
A
P
g P L P
S eff
eff
R S S

0
exp 0 (1.3)
( )
P
P
eff
L
L

exp 1
(1.4)

The solutions show, because of pump absorption, the effective length L
eff
in place of
the actual fiber length L. For short lengths, the effective length approximates L, and for
long length, it reaches
P
/ 1 . Clearly, high Raman gain can be achieved with high pump
power, long effective lengths, small effective area, high stimulated Raman scattering
gain coefficients as well as low signal and pump attenuations.

1
1
]
1

L
KA
P
L g G
S
eff
eff R

0
34 . 4 (1.5)

Signal gain G in dB depends on the pump intensity, the effective Raman gain
coefficient, the effective length and the polarization state . Since the
polarizations of the pump and signal in conventional transmission fibers vary arbitrarily
along the fiber, the net gain is a mixture of the parallel and perpendicular gains. This is
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
8
described by a polarization factor K, which is 1 if the pump and signal waves are
polarization matched, or 2 if depolarized.

Effective area for Raman gain is determined by mode size and the overlap between
pump and Stokes modes, and defined as:

rdr
rdr rdr
A
S P
S P
eff
2 2
2 2
2

(1.6)

Where
p,

s
represent the mode fields at the pump and Stokes wavelengths.

The effective stimulated Raman gain and gain coefficients in GeO
2
-doped fibers can be
measured based upon the equation (1.5), and independently calculated through the
spontaneous Raman cross section measured from the GeO
2
-doped silica based glass as
discussed in the next chapter.

1.3 Thesis Objective and Overview

The goal of this thesis is to develop a calculation model for predicting the Raman gains
and Raman gain coefficients obtainable in different GeO
2
-doped silica fibers given their
fiber profiles. The measurement of the peak Raman gain using pump on/off method is
performed using a step index GeO
2
-doped silica fiber to support this simulation model.
Some major factors affecting the Raman gain in a fiber are discussed in this thesis to
characterize the distributed fiber Raman amplification and help us come up with a
simplified model to estimate the Raman gain.

Chapter 1 gives a general introduction to the principles of optical amplification using
Stimulated Raman scattering and its potential applications in telecommunications, and
discusses the calculation of Raman gain in fibers. Chapter 2 presents the calculation
model to relating the spontaneous Raman cross-section to the effective Raman gains
and gain coefficients of different GeO
2
-doped fibers. The effect of the mode field
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
9
penetrating into the fiber cladding is included in the calculation model. Also a
simplified but sufficiently accurate calculation model is developed. In the end, the
characteristics of simulated Raman gain spectra of different fiber types are discussed
and compared with published measurement data. Chapter 3 describes the experimental
setup to measure the peak effective Raman gain of a step index fiber. Some
considerations to achieve accurate results and comparisons of experimental results with
simulation results are also covered in this chapter. Chapter 4 gives a summary of this
thesis, and lists the suggestions for future work.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
10
Chapter 2 - Calculations of Raman Gain and Raman Gain
Coefficients in Different Fiber Types

In order to predict the behavior of Stimulated Raman scattering in transmission fibers,
which can be used for distributed amplification in optical fiber links, it is important to
theoretically calculate the Raman gain spectra of the transmission fibers based on their
refractive index profiles as well as attenuation spectra. In this chapter, the Raman gain
spectra, ranging from 30 cm
-1
(0.9 THz) to 700 cm
-1
(21.0 THz) frequency shifts, for
pure silica core fiber (Z-Fiber), Standard single mode fiber (SMF-28 and SPECTRAN)
and dispersion-shifted fiber (DSF) are calculated. This calculation includes the field
averaging effect over the doping profile. In fiber designs, effective area (A
eff
) plays a
crucial role in controlling the Raman gain in fibers, so the effect of a change in A
eff
with
wavelength, on Raman gain is also estimated and discussed. The calculated results for
typical transmission fibers are found to be in qualitative agreement with published
measurement results, but there are several discrepancies with the quantitative data.

2.1 Theoretical Background

A weak Stokes signal launched into a fiber with a stronger pump will be amplified due
to SRS as discussed in the previous chapter. The amplification of the signal is described
through the following equations .

( ) ( )
( )

,
_

L
KA
L P v g
P L P
S
eff
eff R
S S

0
exp 0 (2.1)
2 2
3
0
) (
). ( ) (

hn c
g
S
R
(2.2)

Where c is the velocity of light, h is Plancks constant,
S
is the Stokes wavelength,
) (v n is the refractive index, which is frequency dependent, and K is the polarization
factor, which is 1 if the pump and signal waves are polarization matched, or 2 if
depolarized. The spontaneous zero Kelvin Raman cross section ( ) v
0
is defined as the
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
11
ratio of radiated power at the Stokes wavelengths to the pump power at temperature 0K,
which can be obtained with the measured Raman cross-section ( ) v
T
at temperature
TK and the thermal population factor ( ) T v N ,

( ) ( ) ( ) ( ) 1 , /
0
+ T v N v v
T
(2.3a)
( )

,
_

1 exp
1
,
T K
v hc
T v N
B
(2.3b)

The ) (
R
g in Equation 2.2 is the spontaneous Raman gain coefficient in bulk glass,
where ) (
R
g is uniform in all directions. But for fibers, the Germania concentration,
and hence the stimulated Raman gain coefficient, may vary across the whole fiber. As a
result, ) (
R
g is also a function of the radial distance with respect to the core center. In
addition, in a fiber the mode field penetrates into the cladding so that the effective
Raman gain coefficient is some average over the doping profile. The proper way to
include the increase in Raman gain from Ge-doping is to include Raman gain
coefficients ) , ( r g
R
in the calculation of the overlap integral as shown in Equation 2.4.

Effective area is determined by mode size and the overlap between pump and Stokes
modes as shown in Equation 1.6. Effective Raman Gain (g/A
eff
) is defined as:

rdr rdr
rdr r g
A
g
s p
s p R
eff
R
2 2
2 2
2
) , (

(2.4)

Where
p,

s
represent the mode fields at the pump and Stokes wavelengths and g
R
is
the effective Raman gain coefficient of the fiber shown in Equation 2.1, which can be
obtained by multiplying the effective Raman gain g
R
/A
eff
with A
eff
. ) , ( r g
R
is the
Raman gain coefficient in a fiber with a specific GeO
2
distance to the core center, which is related to spontaneous zero Kelvin Raman cross-
section ( ) v
0
through Equation 2.2.
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
12

Since the cross section ( ) v
0
varies with
4
, it is clearly seen from the equation (2.2)
that Raman gain coefficient varies linearly with signal frequency.

The above equations are obtained under several assumptions. The first is that the
bandwidth of the pump is much less than that of the Raman gain spectra. Secondly the
equations assume that pump depletion due to the amplification of the signal is neglected
in the case of a weak signal with a stronger pump.

Based on the research results of Galeener , Shibata  and Davey , the Raman
cross section peak for pure GeO
2
is about 9 times as high as the pure SiO2, and the
Raman cross section of a GeO
2
doped silica glass is in linear relationship with
Germania concentration.

The change in Raman cross-section with GeO
2
-doping mol% (
2
GeO
x ) in pure silica has
been summarized in the expression:

2
2
0
'
0
'
). ( ) , ( ) , (
2
GeO GeO
x C SiO x + (2.5)

Where ) , (
2
0
'
SiO and ) , (
2
0
'

GeO
x respectively represents the Raman cross-sections
of pure silica and Ge-doped silica, normalized with respect to the peak Raman cross-
section of pure silica and ) ( C is a linear regression factor whose values at different
frequency shifts are obtained from the reference  and illustrated in Figure 2.1.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
13
0.005
0.015
0.025
0.035
0.045
0.055
0.065
0.075
0.085
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750
Raman frequency shift (cm
-1
)
L
i
n
e
a
r

R
e
g
r
e
s
s
i
o
n

f
a
c
t
o
r

C

(
1
/
m
o
l
%
)

Figure 2.1 Linear regression factor vs frequency shift (cm
-1
)

Now, if ) , (
2
0

GeO
x and ) , (
2 0
SiO represent non-normalized cross-sections and
) , (
2 0
SiO
p
represents the silica peak cross section, then equation (2.5) can be written
as:

2
2
). (
) , (
) , (
) , (
) , (
2 0
2 0
2 0
0
GeO
p p
GeO
x C
SiO
SiO
SiO
x

+
or
) , ( . ). ( ) , ( ) , (
2 0 2 0 0
2 2
SiO x C SiO x
p GeO GeO
+ (2.6)

Based on Equation 2.2, the Raman gain coefficients ) , (
2
SiO g
R
and ) , (
2

GeO R
x g for
pure silica and for GeO
2
-doped silica respectively can be written as:

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
14
2
2
2
3
2 0 2
2
1
2
3
0
). , ( ) , (
). , ( ) , (
2 2
hn c
SiO SiO g
hn c
x x g
s
R
s
GeO GeO R

(2.7)

where n
1
and n
2
are the refractive indices in a GeO
2
-doped silica core and a pure silica
cladding of a fiber respectively. Even though refractive index is wavelength dependent,
if the spectra being investigated are within a narrow range from 1457nm to 1614nm, n
1

and n
2
are treated as constant values using the refractive indexes at 1550nm. From
equation (2.5) and (2.7) we get,

1
1
]
1

+
3
3
2 2
2
1
2
2
). , ( . ). ( ) , ( ) , (
2 2
sPeak
s
Rp GeO R GeO R
SiO g x c SiO g
n
n
x g

(2.8)

Equation 2.8 applies to a fiber for which the pump and Stokes waves maintain the same
state of polarization as they travel along the fiber. This is not true for transmission fibers
when the states of polarization of pump and signal waves evolve randomly along the
fibers and are seldom the same. It can be shown rigorously that if the perpendicular
Raman gain is zero then the net Raman gain in a non-PM fiber is the parallel gain
. It is not clear whether this also applies to the perpendicular gain. But in the
absence of full knowledge, a reasonable assumption for the net Raman gain coefficient
in a non-PM fiber is to add half the parallel and half the perpendicular gain coefficients.
The net depolarized peak gain at a Stokes wavelength of 1.0um in pure silica then
becomes
13
10 046 . 1

/2 mW
-1
, equal to
13
10 5023 . 0

mW
-1
. From figure 2.2, it can be
clearly seen that the perpendicular gain coefficients has a large effect for frequency shift
below 200cm
-1
, even though it is much smaller compared to the parallel one.

Very little is known about the perpendicular Raman gain coefficients of GeO
2
-doped
silica. But ideally there would be a ) (

## C for the perpendicular gain. As an

approximation, following equation 2.6, the perpendicular gain of GeO
2
- doped silica
would:
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
15

) , ( . ). ( ) , ( ) , (
2 0 2 0 0
2 2
SiO x C SiO x
p GeO GeO
+ (2.9)

where ) (

## C would be normalized to the peak ) (

||
C . Thus the total Raman gain
coefficient of GeO
2
- doped silica for the average of random polarization states
becomes:
[ ] B A
n
n
x g
GeO TOT
+
2
1
2
2
2
) , (
2
(2.10)
) , ( ) , (
2 2 ||
v SiO g v SiO g A
R R
+ (2.11)
[ ]
3
3
2 || ||
) , ( ) ( ) (
2
sPeak
s
Rp GeO
v SiO g x V C v C B

+

(2.12)

Figure 2.2 shows that the perpendicular gain curve of pure silica is much flatter than
parallel one over the frequency shift ranging from 50-500cm
-1
. By analogy with pure
silica, ) , (
2
0

GeO
x

## will probably be about 1/3 of ) , (

2
|| 0

GeO
x at frequency shift
100 cm
-1
. Thus, ) (

## C can be approximated as a constant about 1/3 of ) (

||
C at
frequency shift of 100 cm
-1
over frequency shift ranging from 50-500cm
-1
.

Also because the Raman gain coefficient varies linearly with signal frequency, the
depolarized Raman gain coefficient obtained through Equation (2.10) at Stoke
wavelength 1micron needs to be converted into the one at actual Stokes wavelengths
s
by dividing the Raman gain coefficient by the Stokes wavelength. So equation (2.10)
can be modified to the following form

1
]
1

+
sPeak s
GeO TOT
B A
n
n
x g

2
1
2
2
2
) , (
2
(2.13)

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
16
where
sPeak

s
values are in units of microns. Equation (2.13) gives us the Raman
gain coefficient as a function of Stokes wavelength and GeO2 concentration in GeO
2

doped silica.

As discussed before, because the Germania concentration in a fiber may vary across the
whole fiber, ) , (
2

GeO TOT
x g is also a function of the radial distance with respect to
the core center.

In our calculations equation (2.13) is used to find ) , , (
2
r x g
GeO TOT
, which is
substituted into equation (2.4) to get the effective Raman gains for all fiber types .
Raman gain coefficient in a fiber can be obtained by multiplying the effective Raman
gain with the calculated effective area.

2.2 Calculations

To investigate the effects of Ge-doping and fiber structure on Raman gain and Raman
gain coefficients of typical transmission fibers, the simulations of Raman gain and
Raman gain coefficients are performed on a pure silica core fiber (PSCF), two standard
step index fibers (SMF-28 and SPECTRAN) and a dispersion-shifted fiber (DSF). All
these fibers except the pure silica core fiber are GeO
2
doped in the core with pure silica

2.2.1 Calculation parameters

In this simulation, pump wavelength is set at 1450.4nm for all fiber types. Referred to
the frequency shift of 30-700cm
-1
, the Stokes wavelength is from 1457nm to 1614nm,
and the peak gain wavelength is 1549.27nm.

2.2.1.1 Pure Silica Raman Gain Spectrum

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
17
Raman gain spectrum for fused silica is shown in Figure 2.2 . This figure forms the
basis for estimation of Raman gain spectra in different fiber types as shown in equations
(2.13) and (2.4). The red and yellow curves stand for scattering of light polarized
parallel and perpendicular to the polarization of the exciting light. The blue curve is for
the total (Parallel + Perpendicular) scattering of light. The absolute value of the total
peak gain coefficient in this curve is 1.046x10
-11
cm/W at a frequency shift of 440 cm
-1

(13.2 THz), with 1.0 micron Stokes wavelength and second gain peak is at about 490
cm
-1
(14.7 THz) frequency shift. Based on this figure, calculations of effective Raman
gain and gain coefficients for pure silica core fiber, standard step index fiber and
dispersion-shifted fiber are addressed in the following sections.
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600 700 800
frequency shift (cm
-1
)
R
a
m
a
n

g
a
i
n

c
o
e
f
f
i
c
i
e
n
t

(
m
/
W
*
1
0
- 1
3
)
Parallel + Perpendicular
Parallel
Perpendicular

Figure 2.2 Parallel and Perpendicular Raman Gain Spectrum of fused Silica 

2.2.1.2 Fiber Types

The numerical simulations are performed on three typical transmission fibers: pure
silica core fiber, standard step index fiber, and dispersion-shifted fiber.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
18
1. Pure silica core fiber (PSCF), also called Z-fiber
For this Z fiber, the core and cladding diameter is respectively 9.7um and 125um.
The index difference is 0.005 at 633nm wavelength. These numbers are based on
measurements of 2 fibers taken at Bell laboratories in 1996 .

2. Standard step index fiber
Two types of standard step index fiber are used for the calculations. The first is
SMF-28, manufactured by Corning cable. The second is a fiber sample donated by
SPECTRAN Inc., which is also used for our measurements to check with the
calculation results. The fiber parameters are listed as followed:

Core
Diameter
(um)
Index
Difference
(632.8nm)
MFD
@1310 nm
(um)
Attenuation
@ 1550 nm
(dB/km)
Cutoff
Wavelength
(nm)
SMF-28 8.2 0.005265
10.4 t 0.8
<0.25 <1260
SPECTRAN 8.3 0.00462 9.2 0.21 1258

Table 2.1 Specifications for SMF-28 and SPECTRAN Fibers

The fiber profile of the SPECTRAN fiber measured by YORK fiber profiler is
shown in Figure 2.3.

Figure 2.3 Refractive index profile for SPECTRAN fiber
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
19
3. Dispersion-shifted fiber (DSF)
The Refractive index profile of this fiber is shown in Figure 2.4. The fiber profile
taken from the reference , is typical of many DSF fibers.

Figure 2.4 Refractive index profile for dispersion-shift fiber

2.2.2 GeO
2
concentrations and the refractive index

This section describes how to find the GeO
2
concentrations given a fiber profile and
discusses the wavelength dependence of the refractive index.

The refractive- index relationship with the wavelength and the concentration is given by
Sellmeiers equation:

+
k
i
i
i
b
a
n
1
2
2
2
1

(2.14)

where k is equal to 3, represents that this is a three term Sellmeiers equation. is in a
unit of micron. In this equation, a certain set of parameters a
i
and b
i
are corresponding
to a specific type of material such as pure silica or GeO
2
-doped silica glass with a
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
20
certain GeO
2
concentration level. A series of a
i
and b
i
have been computed from the
measured data taken from reference , as shown in Table 2.2.

Dopant
(mol%)
a1 a2 a3 b1 b2 b3
Pure Silica 0.6965325 0.4083099 0.8968766 0.004368309 0.01394999 97.93399
GeO
2
6.3 0.7083925 0.4203993 0.8663412 0.007290464 0.01050294 97.93428
GeO
2
8.7 0.7133103 0.4250904 0.863198 0.006910297 0.01165674 97.93434
GeO
2
11.2 0.7186243 0.4301997 0.8543265 0.004026394 0.01632475 97.9344
GeO
2
15.0 0.7249180 0.4381220 0.8221368 0.007596374 0.01162396 97.93472
GeO
2
19.3 0.7347008 0.4461191 0.8081698 0.005847345 0.01552717 97.93484

Table 2.2 Sellmeiers Equation Parameters for Pure and GeO
2
Doped Silica Glass

By adopting Sellmeier equation with parameters given in the above table, we can get a
figure of refractive index vs GeO
2
concentration (Mol %) at a certain wavelength. The
calculated data of refractive index as a function of GeO
2
concentration at two
wavelengths of 632.8nm and 1550nm are shown in Figure 2.5. It indicates a linear
relationship between refractive index and GeO
2
concentration. The linear functions can
be obtained by curve regression. Consequently, once the refractive index is known, the
corresponding GeO
2
concentration can be found through the linear functions.

As shown in Figure 2.6, GeO
2
concentration also is found to increases linearly with the
index difference from the pure silica if the refractive index line in Figure 2.5 at a certain
wavelength is subtracted by the refractive index of pure silica at this wavelength.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
21
0 5 10 15 20
1.44
1.45
1.46
1.47
1.48
1.49
1.5
Mol vs Refractive index n
Mol%
R
e
f
r
a
c
t
i
v
e

i
n
d
e
x

n
0.633um
1.55um

Figure 2.5 Refractive Index vs GeO
2
concentration (Mol %)

0 5 10 15 20
0
0.005
0.01
0.015
0.02
0.025
0.03
Mol vs delta n
Mol%
D
e
l
t
a

n
0.633um
1.55um

Figure 2.6 Index Difference vs GeO
2
concentration (Mol %)

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
22
As seen in Figure 2.6, the index differences between 632.8nm and 1550nm differ more
with higher GeO
2
doping than with lower doping.

Through Sellmeriers Equation, the wavelength dependence of the refractive index can
be obtained as seen in Figure 2.7. The refractive index decreases linearly with the
wavelength from 1457 nm to 1614 nm, while it increases with GeO
2
concentration. In
addition, within a small wavelength range as from 1457nm to 1614nm, the variations in
refractive index are shown in Figure 2.7, to be less than 0.2%. This variation is so small
that the refractive indices of the core and the cladding can both be treated as constant
values at 1550nm throughout this simulation for the step index fibers.

It is concluded that the GeO
2
concentrations across a fiber can be obtained if the fiber
profile is provided.

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1.44
1.45
1.46
1.47
1.48
1.49
1.5
Refractive index vs wavelength
Wavelength(um)
R
e
f
r
a
c
t
i
v
e

i
n
d
e
x
pure silica
6.3%
8.7%
11.2%
15%
19.3%

Figure 2.7 Refractive Index of Pure Silica and GeO
2
-doped Silica vs Wavelength

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
23
2.2.3 Simulation Results

In this section, the calculated effective Raman gain and gain coefficients of different
fibers are presented and compared with published data. Also a simplified model to
predict the effective Raman gain is developed and discussed. It is noted that only LP01
mode exists in all four types of fibers investigated since the transmission window is set
around 1550 nm, far beyond their cutoff wavelengths. The LP01 modes at pump
wavelength 1450.4nm and signal wavelengths ranging from 1457 nm to 1614 nm are
calculated using a commercial fiber program package with input of a fiber profile
measured at 632.8nm; Thereafter, the effective areas and effective Raman gain spectra
over the above wavelength range can be obtained through these LP01 modes.

2.2.3.1 Raman Gain Spectra for pure silica core fiber, step index fiber and dispersion-
shift fiber

Figure 2.8 shows a plot of calculated effective Raman gains vs frequency shift for all
the fiber types we investigated. The effective areas and effective Raman gains are
calculated based on the equations (1.6), (2.4) and (2.13), where ) (
2

GeO R
x g is included
in the overlap integral of the modes fields at the pump and the actual Stokes
wavelengths.

According to the fiber parameters shown in the Table 2.1, Figure 2.3 and Figure 2.4,
through Sellmeier equation (2.10), the dispersion-shifted fiber has the highest GeO
2

concentration, around 8.3 mol% near the core center, the SMF and SPECTRAN have
respectively 3.71 mol% and 3.265 mol% GeO
2
in the core, while Z fiber has no GeO
2
in
the fiber. Since there is no GeO2 doping in the core and cladding of Z fiber, there is no
change in the Raman gain coefficient of Z fiber, but the mode fields do affect the
resultant Raman gain through the effective area A
eff
. A comparison of the effective
areas, GeO
2
concentration and peak Raman gain values for all these fibers can be found
in Table 2.3. The effective areas listed in this table are calculated at pump wavelength
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
24
0 100 200 300 400 500 600 700
0
0.2
0.4
0.6
0.8
1
1.2
x 10
-3
Raman Gains of DSF,SPECTRAN,SMF and ZF
Frequency shift cm-1
R
a
m
a
n

G
a
i
n
(
W
-
1
m
-
1
)
DSF
SPECTRAN
SMF-28
ZF

Figure 2.8 Effective Raman Gain for dispersion-shift fiber, step index fiber, and pure
silica core fiber

of 1450nm and peak gain wavelength of 1550nm. It is clearly visible from Figure 2.8
and Table 2.3 that Raman gain increases with GeO
2
concentration and decreases with
effective area, which depends on the fiber structure as well as GeO
2
concentration. The
increase of Raman gain is the biggest in the case of DSF because of the highest GeO
2
-
doping and the smallest effective area, on the other hand, the Z fiber has the least gain
at 440cm
-1
and the largest effective area. For example, at the frequency shift of 430cm
-1
,
DSF has a peak gain of 10.3*10
-4
W
-1
m
-1
, which is 75% higher than that of the SMF-28;
Peak gain and GeO
2
concentration of SPECTRAN fiber are both 12% less than that of
those of the SMF-28.

Raman gain spectra were normalized to 1.0 at the peak gain to compare the overall gain
profiles. As shown in Figure 2.9, Full Bandwidth Half Maximum (FWHM) decreases
slightly with GeO
2
doping. But The FWHM of the two standard step index fibers (STF)
SMF and SPECTRAN are almost same and both Raman gain curves are observed to be
very close to each other. It implies that GeO
2
concentration in standard step index fibers
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
25
does not affect the gain profile very much even though it does change the effective
Raman gain. FWHM values for all fiber types are also shown in Table 2.3. The second
peak at around 490 cm
-1
(14.7 THz) for Z fiber is observed to be the highest, while the
DSF has the least. We can conclude from Table 2.3 and Figure 2.9 that the second peak
suppresses as the GeO
2
concentration increases. In the meantime, the peak of the
Raman gain curve moves to lower frequency shift associated with higher GeO
2
doping.
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized Raman Gain of DSF,SPECTRAN,SMF and ZF
Frequency shift cm-1
N
o
r
m
a
l
i
z
e
d

R
a
m
a
n

G
a
i
n
DSF
SPECTRAN
SMF-28
ZF

Figure 2.9 Normalized Raman Gain in Different Fibers

DSF SMF-28 SPECTRAN ZF
A
eff
at Peak Gain (*1E-12 m
2
) 46.7 72.8 80.4 85.5
GeO
2
concentration (mol%) 8.3(peak) 3.71 3.265 0
Peak Gain (g/Aeff ) (*1E-4 m
-1
w
-1
) 10.30 5.879 5.175 3.947
Peak Gain Coefficient (*1E-13 mw
-1
) 4.811 4.279 4.172 3.374
Peak Gain frequency shift (cm
-1
) 430 440 440 440
Gain FWHM (nm at 1450nm pump) 52 55 56 62

Table 2.3 Raman Gain Data in Different Fibers, In the Case of Depolarized Light
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
26

The effective Raman gain coefficients shown in Figure 2.10, were calculated by
multiplying the effective Raman gain with the effective areas. Figure 2.10 indicates that
the peak gain coefficients of fibers also increase with GeO
2
doping, but not as
significantly as the effective Raman gain. Pure silica core fiber has the same gain
coefficient as the fused silica as expected.

0 100 200 300 400 500 600 700
0
1
2
3
4
5
x 10
-14
Raman Gain Coefficients of DSF,SPECTRAN,SMF and ZF
Frequency shift cm-1
R
a
m
a
n

G
a
i
n

C
o
e
f
f
i
c
i
e
n
t
(
m
/
W
*
1
0
-
1
3
)
DSF
SPECTRAN
SMF-28
ZF
Pure silica

Figure 2.10 Raman Gain Coefficient with Different Fibers

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
27
2.2.3.2 Optimized Effective Area Approximation Scheme

As effective area depends on not only the mode field of the pump, but also those of the
signals, A
eff
is normally obtained using both
p
and
s
. However, based on the fact that
Raman amplifiers are desired to operate around the peak zone, it is efficient not to find

s
at each Stokes wavelength when calculating Raman gain spectra. To simplify the
calculations, we need to find the optimized effective area approximation scheme by
taking approximated signal wavelengths. The effective areas are obtained by taking the
following four cases into considerations, from which we also can investigate how
effective area affects the effective Raman gain and gain coefficient.

1) Both pump and signals wavelengths are taken to be 1450.4 nm.
2) Both pump and signals wavelengths are taken to be 1550 nm
3) Pump is 1450.4 nm and signal wavelengths are all set at 1550 nm.
4) Pump is 1450.4 nm and signal wavelengths are taken at actual Stokes
wavelengths ranging from 1457 to 1614nm.

Figure 2.11 shows the simulation results of the effective Raman gains of all the fibers
for the above listed 4 cases. Among these four cases, the first three are used to evaluate
approximations and the last one is to get the actual values. For all fibers, the first case
gives the highest effective Raman gain, g
R
/A
eff
, while the second case gives the least.
These results are theoretically justified because the smaller effective area, the bigger
Raman gain, and the effective area at 1450nm is smaller than that at 1550nm.

As to the third and the last case, these two Raman gain curves are very close to each
other except the lower ends of the curves, which gives 5% difference of Raman gain.
Both are kind of average of the first and the second cases. This comparison leads us to
an optimized approximation that we can use the third case, in which pump is at 1450
nm and signal is at 1550 nm, to approximate the actual gain spectrum.

Figure 2.12 compares the normalized Raman gain curves with respect to the peaks for
all four cases to find the change in the gain profiles due to this effective area scheme.
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
28
The comparison demonstrates that the normalized Raman gain curves are very close to
each other in all cases and the effective area affect little on the shape of the Raman gain
curve.

Figure 2.13 shows the Raman gain coefficient curves for the four cases are also very
close to each other. It means the influence of the effective area on the Raman gain
coefficient is neglectable.

In conclusion, an optimized approximation can be achieved by using pump at 1450 nm
and signal at 1550 nm to approximate the actual effective areas.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
29

1) Dispersion Shift Fiber 2) SMF-28

3) SPECTRAN 4) Z Fiber

Figure 2.11 Comparison of Raman Gains of All Fiber types with Four Effective Area
Approximation Schemes

0 100 200 300 400 500 600 700
0
0.2
0.4
0.6
0.8
1
1.2
x 10
-3
Raman gain(DSF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
1
2
3
4
5
6
7
x 10
-4
Raman gain(SMF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
-4
Raman gain(ZF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
1
2
3
4
5
6
x 10
-4
Raman gain(SPECTRON)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
30

1) Dispersion Shift Fiber 2) SMF-28

3) SPECTRAN 4) Z Fiber

Figure 2.12 Comparison of Normalized Raman Gains of All Fiber Types with Four
Effective Area Approximation Schemes
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized Raman gain(DSF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized Raman gain(SMF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized Raman gain(SPECTRON)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized Raman gain(ZF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

W
-
1
m
-
1
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
31

1) Dispersion Shift Fiber
2) SMF-28

3) SPECTRAN
4) Z Fiber

Figure 2.13 Comparison of Raman Gain Coefficients of All Fiber Types with Four
Effective Area Approximation Schemes

0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
-14
Raman gain coefficient(SMF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

c
o
e
f
f
i
c
i
e
n
t
s

m
/
W
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
3
3.5
x 10
-14
Raman gain coefficients(ZF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

c
o
e
f
f
i
c
i
e
n
t
s

m
/
W
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
-14
Raman gain coefficients(SPECTRON)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

c
o
e
f
f
i
c
i
e
n
t
s

m
/
W
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-14
Raman gain coefficients(DSF)
Frequency shift cm-1
R
a
m
a
n

g
a
i
n

c
o
e
f
f
i
c
i
e
n
t
s

m
/
W
Cyan-ps1450
Green-ps1550
Red-p1450,s1550
Blue-p1450,sall
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
32

2.2.3.3 A simplified calculation model for standard step index fibers

This section illustrates an approach to develop a simplified but sufficiently accurate
calculation model to predict the effective Raman gain without having to calculate the
) , (
2
r x g
GeO R
. As discussed in the previous section, the Raman gain profiles of STF,
DSF and PSCF are close to each other. Especially for the two STF fibers, SMF and
SPECTRON have almost the same Raman gain shape. This implies that it is possible to
find a universal standard gain curve applicable to all fibers. The effective Raman gain
of a specific fiber can be found through multiplying this standard gain curve with a
constant factor, which basically is an estimated ratio of the peak gain of the under
investigated fiber over that of the standard fiber.

In this section, a simplified calculation model to estimate the effective Raman gains of
Standard step index fibers is proposed. The result is compared with the one obtained
with the previously presented calculation model. As found in 2.2.3.1, peak gain and
GeO
2
concentration of SPECTRAN fiber are both 12% less than that of the SMF-28 at
440cm
-1
, the peak gain appears to be in linear relationship with the GeO
2
concentration,
which is in fact true because the GeO
2
concentration is constant over the fiber core, and
the overlapped mode fields term
p
2

s
2
in cladding, as shown in equation 2.4, is so
small that the GeO
2
concentration can be treated as a constant over the whole fiber. As a
result, the ) , , (
2
r x g
GeO TOT
from Equation 2.13 substituted into the overlap integral
of Equation 2.4, can be taken out from the integral. As shown in the Equation 2.15, 2.16
and 2.17, the effective Raman gain increases linearly with GeO
2
concentration.

1
]
1

+
sPeak s eff eff
GeO TOT
eff
R
B A
A n
n
A
r v x g
A
g

2
1
2
2
2
) , , (
2
(2.15)
) , ( ) , (
2 2 ||
v SiO g v SiO g A
R R
+ (2.16)
[ ]
3
3
2 || ||
) , ( ) ( ) (
2
sPeak
s
Rp GeO
v SiO g x v C v C B

+

(2.17)

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
33
In this calculation, only peak gain needs to be considered. Thus, by substituting A with
peak total gain coefficient of 1.046*10
-13
m/W,
S
with
sPeak
and
) ( ) (
||
v C v C

+ with the value at the peak gain wavelengt h, which is 0.0833, the
above equations become

13 2
2
1
2
2
10
1 0833 . 0 046 . 1
2

1
]
1

+
sPeak
GeO
sPeak eff eff
Rpeak
x
A n
n
A
g

(2.18)

sPeak
value is in a unit of micron. In the case of small index difference,
2
1
2
2
n
n
can be
approximated to 1. Then Equation 2.18 becomes

[ ]
13
10 04165 . 0 523 . 0
1
2

+
GeO
sPeak eff eff
Rpeak
effpeak
x
A A
g
g

(2.19)

The effective area at the peak gain point can be easily obtained with the mode fields at
the pump wavelength and peak gain Stokes wavelength.

Through the above linear relationship between the Raman gain and GeO
2
concentration,
the ratio of the peak effective Raman gain
1 eff
g of the test fiber over that of the
standard fiber
0 eff
g ,
0
1
eff
eff
g
g
can be easily achieved given a standard Raman gain curve
with its GeO
2
concentration
2
0 GeO
x , the effective peak Raman gain
0 eff
g
,
the
effective area
0 eff
A in um
2
as well as the GeO
2
concentration
2
1 GeO
x , the effective
area
1 eff
A of the test fiber.

1
0 1
1
0
0
1
) ( 004165 . 0
2 2
eff sPeak
GeO GeO
eff
eff
eff
eff
A
x x
A
A
g
g

(2.20)

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
34
Finally the Raman gain curve of the test fiber can be obtained by multiplying the given
standard curve with the above-calculated ratio.

In this section, the SMF-28 and SPECTRAN fibers are used to verify this model. The
Raman gain curve of SMF-28 is set as the standard gain curve to estimate the Raman
gain spectrum of the SPECTRAN fiber. Based on the model described above, the ratio
of SPECTRAN peak gain over SMF peak gain SMF-28s peak gain value is first
calculated, and then multiplied with the SMF Raman gain curve to get the estimated
gain curve of SPECTRON fiber. As shown in Figure 2.14, the resulting curve matches
very well with the original one obtained through the non-simplified model. The
parameters needed in the model such as GeO
2
concentrations, peak gain effective areas
of SPECTRON and SMF-28 can be found in Table 2.3.

0 100 200 300 400 500 600 700
0
1
2
3
4
5
6
x 10
-4
Raman Gains of SPECTRAN, SMF
Frequency shift cm-1
R
a
m
a
n

G
a
i
n
(
W
-
1
m
-
1
SPECTRON
SMF
SPECTRON with SMF profile

Figure 2.14 Comparison of Raman gain curves with the simplified and original
calculation model

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
35
2.2.3.3 Comparison of Calculated Results From the Published Data

The calculated Raman gains for different fiber types were compared with the measured
Raman gain data from several published sources [19-21]. Table 2.4 shows
the measured effective Raman gain values (g/A
eff
) along with the effective area (where
available). Here g
1
represents the Raman gain at 150 cm
-1
frequency shifts and g
2
represents Raman gain at peak (430 cm
-1
/440 cm
-1
frequency shift). The ratio g
1
/g
2
is
calculated to give a measure of the deviation of the effective Raman gain curve from the
standard gain curve for pure silica core fiber. In the comparison, the gain was examined
at the maximum and one point well off the maximum at a frequency shift of 150 cm
-1
.

The data were loosely grouped into three typical fiber categories for comparisons, such
as pure silica core fiber, standard step index fiber and dispersion-shifted fibers.
Considerable variation occurs within the categories. For example, the dispersion shifted
fibers can be divided into four types, including Dispersion Shift Fiber (DSF), Non-Zero
Dispersion Shift Fiber (NZ-DSF), Non-Zero Positive Dispersion Shift Fiber (NZ-
DSF+), and Non- Zero Negative Dispersion Shift Fiber (NZ-DSF-). Each may provide
different Raman gain values. Similar fibers from different manufacturers have different
Raman gains. The effective Raman gain is seen to vary within a relatively large range,
for the same category of fibers. For example, the DSF Raman gain ranges from
4.63*10
-4
W
-1
m
-1
to 8.4*10
-4
W
-1
m
-1
. Much of the variation may be due differences in
measurement techniques, since these procedures have not been standardized.

Table 2.5 summaries the comparison between published measurement data and
calculated values of Raman gain and g
R
for different fibers. For both measured and
calculation cases, the DSF has the highest Raman gain while the PSCF has the least
Raman gain. Calculated Raman gain however appears to be higher than that of averaged
measured ones except that for the pure silica core fiber, where measured and calculated
Raman gains are very close to each other. For standard fiber and dispersion-shifted
fibers there is a big difference between the calculated and published values. This
difference can be attributed to the fact that the calculation is made for typical fiber types
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
36
and not for the same fibers for which measurements are made in different published
sources.

Fiber
A
eff

@1550nm
(um
2
)
g/A
eff

(*10
-4
/W
m)
G
1

(*10
-14

m/w)

g/
Aeff

(*10
-4
/W m)

G
2

(*10
-14
m/w)

g
1
/g
2

f=150cm
-1
f=440/430cm
-1

Grays
Data 
Pump
@1486nm

SMF 1.17 3.80 0.308
NZ-DSF 1.40 4.63 0.302

Fludgers
Data 

Pump
@1455nm

Allwave 80 1.0 0.8 3.59 2.88 0.279
Corning
NZ-DSF
50 2.11 0.93 7.15 3.55 0.295
NDSF 80 1.15 0.84 3.93 3.12 0.292
Truewave
RS
55 1.81 0.825 5.93 3.25 0.305
Corning
DSF
55 2.00 1.018 6.74 3.71 0.297

Kidorfs
Data 
Pump
@1452nm

PSCF 1.33 4.28 0.311

D.Hamoir Pump
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
37
Pump:

@1486nm
NZDSF+ 55 2.43 1.34 8.4 4.62 0.289
NZDSF- 55 2.26 1.24 7.7 4.24 0.294
TeraLight 67 1.69 1.13 5.7 3.82 0.296
SMF 83 1.30 1.08 4.5 3.74 0.289
PSCF 78 1.30 1.01 4.3 3.36 0.302

Puse
Silica
Stolen

Stokes
@1000nm
1.12 3.53 0.318

Tycom(1):


Pump@
1480nm

Truewave
(Average)
50.9 7.18 3.65 0.299
Leaf
(Average)
71.4 4.95

3.53 0.299

LS
(Average)
51.65 7.42 3.83 0.299
Sumitumo
Z
79.4 3.51 2.79 0.299
IDFX 28.7 16.09 4.62 0.299
HFD2 53.7 6.96 3.74 0.299
LMF1 77.6 4.72 3.66 0.299
5D 71.2 3.97 2.83 0.299

Tycom(2)
DSF 0.291
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
38
SMF 0.279
PSCF 0.309

Table 2.4 Measured Raman Gain For Different Transmission Fiber Types

It also can be seen in Table 2.5 that the PSDF has the largest g
1
/g
2
, while the STF has
the least; at the same time, the simulation results indicate that DSF has the least g
1
/g
2
.
However g
1
/g
2
values for STF and DSF in both cases are close to each other. All the
published data shows that the second peak of the gain curve suppresses with Ge-doping,
and the gain peak moves to the low frequency shift side as the GeO
2
increases, which is
in good agreement with the calculation results.

Table 2.5 Comparisons between the Calculated and Published Measurement D For
Different Transmission Fiber Types

Summary

We estimated Raman gain for pure silica core fiber, standard single mode fiber and
dispersion- shifted fiber. It was noticed that dispersion-shifted fiber provides the highest
effective Raman gain among the fibers investigated. It was also observed that pump at
PUBLISHED DATA CALCULATED DATA
Pump=1450nm PSCF STF DSF PSCF STF DSF
g
R
0.305 0.292 0.296 0.327 0.294 0.286
Raman Gain (*1e-4w-1m-1)
Average 4.01 4.07 7.10 3.95 5.53 10.3
Maximum 4.32 4.52 8.43
Minimum 3.51 3.80 4.63
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
39
1450 nm and signal at 1550 nm can be used to approximate the absolute effective area
in calculating the gain spectrum. The calculated results were compared with the
measured results obtained from various published sources. The calculated results are
found to be in good qualitative agreement with the measured ones. Good quantitative
agreement between calculation and published measurements is obtained for the PSCF.
However, the calculated effective Raman gains for the STF and DSF are higher than
even the maximum published values. The discrepancies in quantitative results between
the two might be attributed to the fact that the calculations are made for some typical
fiber types and not for the same fibers which various published sources used for the
measurements. Secondly the published sources themselves have discrepancies in gain
values for the same kind of fibers. Finally, much of the variation may be due differences
in measurement techniques, since these procedures have not been standardized. As a
result, it is necessary to make our own measurements to verify if the calculation model
is valid.
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
40
Chapter 3 - Measurement of Raman Gain in Optical Fibers

In this chapter, the experiment setup for the measurement of Raman gain of a step index
fiber is given. In order to get accurate experimental results, some considerations are
discussed. The measurement results are then analyzed and compared with the
simulation ones.

3.1 Experimental Setup of Fiber Raman Gain Measurement

The purpose of this experiment is to measure the peak Raman gain in optical fibers and
verify the data with the simulation results mentioned in the previous chapter. This
experiment focuses on the effective Raman gain, also called Raman gain coefficient
over effective area,
eff
R
A
g
, which is a more practical parameter than the Raman gain
coefficient in a Raman amplifier. Knowing this number can give us a projection of what
kind of signal gain can be achieved within a specific fiber given its length and
attenuation parameters at pump and signal wavelengths. A measurement of the actual
Raman gain coefficient is more complicated since the gain coefficient depends on GeO
2

concentration, which varies across the index profile. For this reason, only
eff
R
A
g
is
investigated and measured utilizing the so-called pump on and off technique. However,
we may estimate the peak effective Raman gain coefficients by multiplying the
measured
eff
R
A
g
with calculated
eff
A at pump and peak signal wavelengths or the average
of measured
eff
A s at pump and signal peak wavelengths.

Based on the equation 2. 1, the Raman gain is determined. When pump is off, the output
signal power is attenuated due to the fiber loss.

( ) ( ) ( ) L P L P
S S off S
exp 0
_
(3.1)

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
41
When pump is on, the signal is amplified and the output signal power becomes:
( ) ( )
( )

,
_

L
KA
L P v g
P L P
S
eff
eff R
S on S

0
_
exp 0 (3.2)

G, the pump on/off gain in dB, is determined by

( )
( )
) ( log 10
_
_
10
L P
L P
G
off S
on S
(3.3)

By substituting equations (3.1) and (3.2), the effective Raman gain is obtained

pump eff eff
R
P L
G
KA
g

343 . 4
(3.4)

where
eff
L is the effective length calculated by the equation (2.1),
pump
P is the pump
power launched into the fiber spool,
eff
R
KA
g
is depolarized effective Raman gain.

The Raman gain measurement was performed on a step index single mode fiber by
using the setup shown in Figure 3.1.

Tunable
Laser
OSA
MQW Laser
Diode
2
*
WDM Coupler

Isolator
* 3
Connectors
Backward Pumping
at 1450.4nm
Signal 1550nm
Fiber spool
1
*

Figure 3.1 Experimental setup for measuring Raman gain

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
42
Backward pumping was used in order to cancel out polarization effects and amplitude
fluctuations from pump to signal. An isolator was placed in front of the Tunable laser
source to prevent the pump light from entering into this laser source. The optical
spectrum analyzer (OSA) measured the output signal power in the cases of pump-on
and pump-off. The major advantage in this setup is the fact that the signal input power,
the losses due to fiber attenuation at the signal wavelength, imperfect fiber connectors
or system function of the Wavelength Division Multiplexing (WDM) coupler and
isolator need not to be known. All these factors are cancelled out by calculating the
Raman on-off gain.

3.2 Experimental Results

The fiber under test is a 22.195 km long SPECTRAN fiber and has a step index profile
with a pure silica cladding and GeO
2
process so there is no index dip at the center of the core. This is an important feature for
accurate calculation of Raman gain of this fiber because there is no radial variation of
Ge concentration across the core. This fiber is also extremely uniform along its length.
The fiber core diameter is 8.3 microns and the core cladding index difference is 0.00462
as measured with a York fiber index profiler and shown in previous chapter. The cutoff
wavelength and MFD at 1310 nm of this fiber sample were calculated using the above
measured fiber parameters, which are consistent with the manufacturers value for the
cutoff wavelength of 1.216 microns and MFD of 9.2 microns at 1310nm.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
43

Figure 3.2 Spectrum of the pump source

The pump source used was a Multi-Quantum Well (MQW) laser diode with Fiber
Bragg Grating (FBG) centered at a wavelength of 1450.4 nm, its spectrum is shown in
Figure 3.2. The 3dB bandwidth is around 0.8nm (0.114THz). As discussed in the
previous chapter, the pump bandwidth is required to be much less than the bandwidth of
the gain curve, while much larger than the 100 MHz (Spontaneous Brillouin scattering
bandwidth) to prevent stimulated Brillouin scattering occurring in the fiber. SBS would
largely deplete the pump power and cause measurement error. Pump power measured at
one of WDM coupler ends, connector number 2, shown in figure 3.1, was 116.48 mW
and then corrected for the reflection loss, which gives pump power equal to 120.39
mW. The reflection loss caused by the end face of the fiber is about 3.25% of the pump
power.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
44
The signal source was a tunable laser set at 1550 nm (peak Raman gain wavelength). It
is not necessary to know the exact signal power because of the pump on/off method,
however, based on assumption that the amplification of Stokes does not significantly
deplete the pump, the signal power should be much less than the pump power. The
signal power measured from the laser source connector is 50uW.

The measured loss of the fiber at the pump wavelength using cut back method with a
white light source was 0.261 dB/km giving an effective length of 12.249 km.
Figure 3.3 shows the spectra of the pump on/off output signals.

Figure 3.3 Pump on/off Optical Gain in dB

Taking integrals of the spectra of the pump on/off output signals and dividing the
resulting signal pump-on power with the pump-off power gives us the measured pump
on/off signal gain, which was 3.324 in dB. Substituting the measured pump power and
effective length values into equation (3.4), g/A
eff
was calculated to be 5.19x10
-4
m
-1
W
-1
,
while the simulation result is 5.175x10
-4
m
-1
W
-1
as shown in Table 2.3. The 0.29%
difference between the simulation result and the measurement data shows an excellent
agreement.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
45
In conclusion, the calculation model of relating the spontaneous Raman cross-sections
to the stimulated effective Raman gains and gain coefficients are validated by the
measurement result.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
46
Chapter 4 Conclusions

4.1 Conclusions

In this thesis, a calculation model was developed to predict the Raman gains and Raman
gain coefficients achieved in different GeO
2
-doped silica fibers given their fiber
profiles. The following goals have been met:

1) Study of some major factors affecting the Raman gain in a fiber: the theoretical
background for relating the spontaneous Raman cross-section to the effective
Raman gains and gain coefficients of different GeO
2
-doped fibers was studied.
The effect of the mode field penetrating into the fiber cladding was included in
the calculation model.
2) Comparison of the simulation data with the published measurement data: The
calculated results were compared with the measured results from various
published sources. The calculated results are found to be in good qualitative
agreement with the measured ones.
3) Development of the simplified but sufficiently accurate calculation model: To
simplify the calculations, an optimized effective area approximation scheme was
obtained by taking approximated signal wavelengths. Also a simplified
calculation model to estimate the effective Raman gains of Standard step index
fibers without having to calculate the ) , (
2
r x g
GeO R
is proposed and verified.
4) Verification of the calculation model by conducting our own measurements: The
measurement of the peak Raman gain using pump on/off method is performed
upon a step index GeO
2
-doped silica fiber, which is in excellent agreement with
the calculated result and thus supports this Raman gain calculation model.

In conclusion, this calculation model is accurate to get the effective Raman gains in a
GeO
2
-doped fiber given its fiber profile, it can give us a projection of how much signal
gain can be achieved in a specific fiber given its length and attenuation parameters at
Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
47
pump and signal wavelengths. Moreover, this model is of help in understanding the
material and fiber structure dependence of Raman amplification.

4.2 Future Work

This simulation model calculates the small signal Raman gain as a function of GeO2
concentration in optical fibers. From this work, several investigations can be conducted.

The current model investigates the Raman amplification in a fiber when pumping at a
single wavelength. In fact, recent progress in the Raman amplification area is the
application of the multi- wavelength pumped Raman amplifier. This technology can
provide broader and flatter gain spectrum, which is of significance to the wavelength
division multiplexed system. The current model can be modified for the estimation of
the net Raman gain for multi-wavelength pumped Raman amplifier. This is related to
the superposition of the Raman gain spectra from individual pumps. Moreover, efforts
of adjusting the pump wavelengths to flatten and broaden the gain bandwidth are
needed.

Another improvement would be to develop a more simplified but sufficiently accurate
calculation model to predict the effective Raman gain in any fiber type without having
to calculate the ) , (
2
r x g
GeO R
. As discussed in the chapter 2, the shapes of the effective
Raman gains of GeO
2
-doped fibers are similar. This may lead us to a possible solution
of finding the effective Raman gain of a fiber through multiplying a standard gain curve
with a constant factor corresponding to the fiber type, in which the constant factor
depends on the GeO
2
concentration.

Calculations and Measurements of Raman Gain
Coefficients of Different Fiber Types
48
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Vita

Yuhong Kang was born in Hunan Province, P. R. China. After graduating from
Huazhong University of Science and Technology with a Bachelor of Science degree in
Optics Engineering in 1991, she attended Guangdong Nortel Telecommunications
Equipment Ltd. In 1996, she then worked at Xian Institute of Optics and Precision
Mechanics, Academia Sinica as an Optoelectronics Engineer. In 2001, she joined Fiber
and Electro-optics Research Center at Virginia Tech as a Graduate Research Assistant.
She earned her Master of Science degree in Electrical Engineering from Virginia Tech
in December 2002.
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