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Polarization Mode Dispersion in Distributed Erbium-Doped Fibers
Optical Fiber Technology 5, 75]81 Ž1999. Article ID ofte.1998.0274, available online at http:rrwww.idealibrary.com on
Polarization Mode Dispersion in Distributed Erbium-Doped Fibers X. Shan,1 R. E. Schuh,2 A. Altuncu,3 and A. S. Siddiqui Department of Electronic Systems Engineering, Uni¨ ersity of Essex, Colchester CO4 3SQ, United Kingdom E-mail: [email protected] Received March 11, 1998; revised June 23, 1998
In the design of distributed erbium-doped fibers ŽDEDFs. for ultra-high bit-rate Ž) 40 Gbitrs. soliton transmission, polarization mode dispersion ŽPMD. is an important design parameter. We have measured the PMD values of DEDFs from two different sources and found them to be an order of magnitude higher than those suitable for G 40 Gbitrs soliton transmission. Theoretical modeling and microscopic inspection of fiber core ellipticity have been carried out to understand the high PMD values in these DEDFs. It is believed that core ellipticity and erbium doping process-induced stress are the main reasons for the high PMD values in these fibers. This highlights an important design and fabrication problem which must be solved before DEDFs can fulfil their promise as a channel for long-haul ultra-high bit-rate soliton transmission. Q 1999 Academic Press
I. INTRODUCTION
Dispersion shifted distributed erbium doped fibers ŽDEDFs. are a very promising transmission medium for ultra-high bit-rate ŽG 40 Gbitsrs. long-haul soliton communication systems w1x. They can form a nearly lossless optical pipe and ameliorate the trend toward shrinking amplifier spacing as the bit rate is increased in soliton systems using lumped erbium-doped fiber amplifiers. PMD is an important design parameter in such systems and numerical simulation w2x gives an 1
Current address: Alcatel Submarine Networks Ltd, Christchurch Way, Greenwich, London SE10 0AG, UK. 2 Current address: GMD FOKUS, Research Institute for Open Communication Systems, 10589 Berlin, Germany. 3 Current address: Department of Electronics, Dumlupinar University, Kutahya, Turkey. 75 1068-5200r99 $30.00 Copyright Q 1999 by Academic Press All rights of reproduction in any form reserved.
76
SHAN ET AL.
approximation for the range of benign PMD value for such links as PMD F 0.3'D ,
Ž 1.
where the PMD and the chromatic dispersion coefficient, D, are both in their usual units Žpsr 'km and psrnm km.. In ultra-high bit-rate ŽG 40 Gbitrs. soliton systems, the pulsewidth is limited to only a few picoseconds. Therefore D normally has to be 0.1 psrnm km or less in order to achieve an acceptably long soliton period Že.g., G 50 km.. This low value of D and Eq. Ž1. then require that the DEDF PMD should be lower than 0.1 psr 'km . DEDFs being developed at present are based on the standard dispersion-shifted fiber ŽDSF. design with the addition of erbium ion doping. We have measured the differential group delay ŽDGD., which together with mode coupling determines the PMD w3x, of several DEDFs from different manufacturers and found that their DGD values are around 10 times higher than those of low PMD DSFs. In this article we report our measurements and theoretical modeling, and indicate how the PMD might be reduced in the next generation of DEDFs. II. FIBER PMD MEASUREMENT
Fiber PMD depends strongly on fiber twist w4x. A comparison of the PMD values of different fibers is meaningful only when the fibers have the same amount of twist. Samples of standard step index fibers ŽS-SMF. type ŽG652., DSFs ŽG653., some early research-type erbium-doped fiber ŽEDF., and DEDFs from two different sources were measured using Jones matrix eigenanalysis techniques w4, 5x. One type of the DEDFs has segmented refractive index profile, in order to get zero dispersion at 1.55 m m, manufactured using outside vapor deposition ŽOVD. method, and the other has triangular profile made with modified chemical vapor deposition ŽMCVD.. DGD results for one sample of each type of fiber except the EDF are shown in Fig. 1 as a function of twist, and Fig. 2 shows the intrinsic Žat zero twist. DGD values. The lowest DEDF intrinsic DGD value in Fig. 2 is ; 7.5 psrkm, which is about 10 times higher than the values for step index and the nonspun DS fibers. To further confirm this difference between the DEDF and the other fibers we measured the PMD of different fibers wound tightly on shipping bobbins, and the results are shown in Fig. 3. This shows that the S-SMF, DSFs, and spun DSFs on their shipping bobbins all have nearly the same PMD value of around 0.05 psr 'km , whereas the DEDFs seem to reflect their high intrinsic DGD values in exhibiting a PMD of ) 0.15 psr 'km . Now, DGD values for short lengths Ž l < LC . of fiber can be related to long length Ž l 4 LC . fiber PMD values through w3x PMD s
'L
C
DGD,
Ž 2.
where LC is the average random mode coupling length. Using the measured DGD and PMD values Eq. Ž2. then yields LC values for the DSFs and DEDFs on the fiber bobbins lying between 0.1 and 5 m, which agrees with w3x.
POLARIZATION MODE DISPERSION
77
FIG. 1. Measured and calculated DGD values versus twist for different types of fibers: Ža. step index, Žb. DS, Žc. DS spun, and Žd. DS DEDF.
In order to understand the origin of these high DGD values, we then theoretically modeled the DGD in S-SMF and step index DSFs and examined their core ellipticity with a scanning electronic microscope. III. THEORETICAL MODELING
PMD in single mode optical fibers is caused by a combination of shape and stress birefringence w6, 7x. The stress birefringence may be of external, e.g., cabling-induced PMD, or internal origin due to the thermal expansion mismatch of the core and cladding material, which introduces birefringence w7x. Shape birefringence arises if the fiber possesses some ellipticity, e 2 , defined by e 2 s 1 y b 2ra 2 , where b and a are the minor and major half axes of the elliptic core.
FIG. 2. Measured DGD results for different types of fibers with zero twist.
78
SHAN ET AL.
FIG. 3. PMD on shipping bobbins versus short length DGD for some of the fibers in Fig. 2.
Although the DEDFs under study have nonrectangular index profiles, for simplicity, we used rectangular index profile approximation to calculate shape and stress birefringence. Shape birefringence can be expressed as w6x
dbG s
1 a
e 2 Ž 2D .
3r2
dbGU ,
Ž 3.
where D is the relative index difference, and dbGU is the normalized birefringence
dbGU s
U 2W 2 8V 3
1y
J 02 Ž U . J12 Ž U .
1y
W2 U2
q
W 2 J0 Ž U . UJ1 Ž U .
,
Ž 4.
where J 0, 1 are Bessel functions of the first kind Žof zero and first order.. The birefringence due to internal thermal stress anisotropy, which develops during drawing when the fiber cools through the temperature at which the glass sets, can be expressed as w7x
dbs s
DC
Ž 1 y np .
1
Ž a 1 y a 2 . DTbn Ž l . k 0 O, 2
Ž 5.
where E and C are the Young’s modulus and stress optic coefficient for silica, respectively; bn , the normalized propagation constant, is defined as bn Ž l . s
n2eff y n22 n12 y n22
s1y
U2 V2
s
W2 V2
Ž 6.
and O s 2 Ž a y b . r Ž a q b . f er2;
Ž 7.
a 1 and a 2 are the temperature expansion coefficients of the core and cladding material, respectively; np is Poisson’s ratio; and DT is the difference between the
POLARIZATION MODE DISPERSION
79
glass softening temperature and room temperature. Stress birefringence is proportional to the core ellipticity and depends on the electric field distribution indicated by the normalized propagation constant, which is mainly due to a direction-dependent stress change in the core]cladding interface which arises from the thermal expansion mismatch between the core and cladding w7x. The temperature expansion coefficient is a linear function of the refractive index and doping level, provided that the doping concentration g q , is small and can be estimated at low temperatures through w8x
a qq SiO 2 s g q a q q Ž 1 y g q . a SiO 2 ,
Ž 8.
where a q is the thermal expansion coefficient, whose values at low temperatures can be found for fused silica and some frequently used codopants ŽTable 1. w8x, w9x. The total birefringence is the vectorial sum of the shape and stress birefringences: ª
ª
ª
db s dbG q db S .
Ž 9.
For low birefringence fibers, the shape and stress birefringences can be treated as a simple linear combination w10x. DGD is then derived from the total birefringence as DGD s
d Ž db . dv
s
1 d Ž db . c
dk
.
Ž 10 .
The simulation results using Eqs. Ž3. to Ž10. are shown in Fig. 4 with the simulation values as given in the figure. Figure 4 shows that the DGD increase with increasing ellipticity is faster for the DSF than for the S-SMF, due mainly to the larger refractive index difference, D, and the smaller core diameter, 2 a, in the DSF. We then examined the core of different DEDF samples using a backscatter scanning electron microscope and found that in some samples e 2 could be as large as 5%. For one of the DEDFs, the one with the triangular profile, data on the core ellipticity measured on its parent preform were available, the value being ; 7%. We believe that this ellipticity was impressed into the fiber during drawing. For this ellipticity the calculated DGD for a DSF with step-index profile, as shown in Fig. 4b, would be ; 17 psrkm. This value is higher than the measured value of ; 14.4 psrkm in this DEDF. The difference is due to the nonrectangular profile of the DEDF and the doping of the fiber cladding with P2 O5 , which reduces the thermal expansion mismatch between core and cladding. For the other DEDF with the segmented index profile a far field scan was done on fiber samples in order to
TABLE 1 Thermal Expansion Coefficients a q for Silica and Some of Its Dopants SiO 2 f 0.55 = 10y6 Cy1 GeO 2 f 7 = 10y6 Cy1 B 2 O 3 f 10 = 10y6 Cy1
P2 O5 f 14 = 10y6 Cy1 Al 2 O 3 f 5.9 = 10y6 Cy1
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SHAN ET AL.
FIG. 4. DGD due to shape and thermal stress birefringence both caused by elliptical cores with DT s 10008C for Ža. step-index fiber with zero chromatic dispersion at 1.3 m m and Žb. DS step-index fiber with zero dispersion at 1.55 m m.
determine the core ellipticity. In the far field scans no core ellipticity could be observed within its 2% resolution. We assume that in this fiber the erbium doping-induced stress in the main reason for the high PMD values. IV. DISCUSSION
In the present, first generation of DEDFs, effort has been mainly focused on the optimization of the erbium doping profile to achieve high pumping efficiency, low ASE level, and a flat spectral gain. However, PMD is also a highly significant parameter at bit rates ) 40 Gbitsrs. Unfortunately, little attention has been paid so far to the effects of various doping methods on fiber birefringence, although some of them have been found to lead to irregular refractive index distributions. Therefore in the development of next-generation DEDF, it is essential to reduce its DGD. Before a satisfactory doping method is found which does not introduce excessive birefringence due to either core ellipticity or thermal stress in the fiber, it is recommended that the fiber be spun during drawing to make spun DEDF so as to ensure that the fiber has an acceptably low PMD. V. CONCLUSION
We have measured the intrinsic DGD in distributed erbium-doped fibers. These DGD values are about an order of magnitude higher than the acceptable upper limit for high capacity Ž) 40 Gbitrs. soliton systems. Relatively high core ellipticity values and erbium doping process-induced stress seem to be the main origins of these high DGD values, and therefore it is important not only to reduce the core ellipticity significantly in the next stage of DEDF design but also to use more careful doping processes.
POLARIZATION MODE DISPERSION
81
ACKNOWLEDGMENTS The authors acknowledge J. G. Ellison and B. Diamond from the University of Essex, Colchester, UK, for helping with the measurements, and D. L. Williams and S. R. Sikora from BT Labs, Ipswich, UK, for providing core ellipticity data on the loaned DEDFs and for helpful discussions. This work was carried out under EPSRC Research Grant GRrK49454. The industrial partners are Alcatel Submarine Networks, Greenwich, London, and BT Laboratories, Martlesham Heath, Ipswich.
REFERENCES w1x A. Altuncu and A. S. Siddiqui et al., ‘‘40 Gbitrs error free transmission over a 68 km distributed erbium doped fiber amplifier,’’ Electron. Lett., vol. 32, 233 Ž1996.. w2x L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, ‘‘Resistance of solitons to the effects of polarization in optical fibers,’’ Opt. Lett., vol. 14, 1219 Ž1989.. w3x M. C. de Lignie, H. G. J. Nagel, and M. O. van Deventer, ‘‘Large polarization mode dispersion in fiber optic cables,’’ J. Lightwa¨ e Technol., vol. 12, 1325 Ž1994.. w4x R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Beddington, ‘‘Theoretical analysis and measurement of the effects of fiber twist on the differential group delay of optical fibers,’’ Electron. Lett., vol. 31, 1772 Ž1995.. w5x R. E. Schuh and A. S. Siddiqui, ‘‘A single channel polarimetric OTDR for the measurement of the backscattered SOP evolution along a fiber with twist,’’ Electron. Lett., vol. 33, 2153 Ž1997.. w6x R. A. Sammut, C. D. Hussey, J. D. Love and A. W. Snyder, ‘‘Modal analysis of polarisation effects in weakly-guiding fibers,’’ IEE Proc., vol. 128, 173 Ž1981.. w7x W. Eickhoff, ‘‘Stress-induced single-polarization single-mode fiber,’’ Opt. Lett., vol. 7, 629 Ž1982.. w8x I. P. Kaminow and V. Ramaswamy, ‘‘Single-polarisation optical fibers: Slab model,’’ Appl. Phys. Lett., vol. 34, 268 Ž1979.. w9x D. R. Lide and H. P. R. Frederikse, CRC Handbook of Chemistry and Physics, 75th ed., CRC Press, London, 1994. w10x A. M. Vengsarkar, A. H. Moesle, L. G. Cohen, and W. L. Mammel, ‘‘Polarization mode dispersion in dispersion shifted fibers: An exact analysis,’’ Opt. Lett., vol. 18, 1412 Ž1993..
Polarization Mode Dispersion in Distributed Erbium-Doped Fibers X. Shan,1 R. E. Schuh,2 A. Altuncu,3 and A. S. Siddiqui Department of Electronic Systems Engineering, Uni¨ ersity of Essex, Colchester CO4 3SQ, United Kingdom E-mail: [email protected] Received March 11, 1998; revised June 23, 1998
In the design of distributed erbium-doped fibers ŽDEDFs. for ultra-high bit-rate Ž) 40 Gbitrs. soliton transmission, polarization mode dispersion ŽPMD. is an important design parameter. We have measured the PMD values of DEDFs from two different sources and found them to be an order of magnitude higher than those suitable for G 40 Gbitrs soliton transmission. Theoretical modeling and microscopic inspection of fiber core ellipticity have been carried out to understand the high PMD values in these DEDFs. It is believed that core ellipticity and erbium doping process-induced stress are the main reasons for the high PMD values in these fibers. This highlights an important design and fabrication problem which must be solved before DEDFs can fulfil their promise as a channel for long-haul ultra-high bit-rate soliton transmission. Q 1999 Academic Press
I. INTRODUCTION
Dispersion shifted distributed erbium doped fibers ŽDEDFs. are a very promising transmission medium for ultra-high bit-rate ŽG 40 Gbitsrs. long-haul soliton communication systems w1x. They can form a nearly lossless optical pipe and ameliorate the trend toward shrinking amplifier spacing as the bit rate is increased in soliton systems using lumped erbium-doped fiber amplifiers. PMD is an important design parameter in such systems and numerical simulation w2x gives an 1
Current address: Alcatel Submarine Networks Ltd, Christchurch Way, Greenwich, London SE10 0AG, UK. 2 Current address: GMD FOKUS, Research Institute for Open Communication Systems, 10589 Berlin, Germany. 3 Current address: Department of Electronics, Dumlupinar University, Kutahya, Turkey. 75 1068-5200r99 $30.00 Copyright Q 1999 by Academic Press All rights of reproduction in any form reserved.
76
SHAN ET AL.
approximation for the range of benign PMD value for such links as PMD F 0.3'D ,
Ž 1.
where the PMD and the chromatic dispersion coefficient, D, are both in their usual units Žpsr 'km and psrnm km.. In ultra-high bit-rate ŽG 40 Gbitrs. soliton systems, the pulsewidth is limited to only a few picoseconds. Therefore D normally has to be 0.1 psrnm km or less in order to achieve an acceptably long soliton period Že.g., G 50 km.. This low value of D and Eq. Ž1. then require that the DEDF PMD should be lower than 0.1 psr 'km . DEDFs being developed at present are based on the standard dispersion-shifted fiber ŽDSF. design with the addition of erbium ion doping. We have measured the differential group delay ŽDGD., which together with mode coupling determines the PMD w3x, of several DEDFs from different manufacturers and found that their DGD values are around 10 times higher than those of low PMD DSFs. In this article we report our measurements and theoretical modeling, and indicate how the PMD might be reduced in the next generation of DEDFs. II. FIBER PMD MEASUREMENT
Fiber PMD depends strongly on fiber twist w4x. A comparison of the PMD values of different fibers is meaningful only when the fibers have the same amount of twist. Samples of standard step index fibers ŽS-SMF. type ŽG652., DSFs ŽG653., some early research-type erbium-doped fiber ŽEDF., and DEDFs from two different sources were measured using Jones matrix eigenanalysis techniques w4, 5x. One type of the DEDFs has segmented refractive index profile, in order to get zero dispersion at 1.55 m m, manufactured using outside vapor deposition ŽOVD. method, and the other has triangular profile made with modified chemical vapor deposition ŽMCVD.. DGD results for one sample of each type of fiber except the EDF are shown in Fig. 1 as a function of twist, and Fig. 2 shows the intrinsic Žat zero twist. DGD values. The lowest DEDF intrinsic DGD value in Fig. 2 is ; 7.5 psrkm, which is about 10 times higher than the values for step index and the nonspun DS fibers. To further confirm this difference between the DEDF and the other fibers we measured the PMD of different fibers wound tightly on shipping bobbins, and the results are shown in Fig. 3. This shows that the S-SMF, DSFs, and spun DSFs on their shipping bobbins all have nearly the same PMD value of around 0.05 psr 'km , whereas the DEDFs seem to reflect their high intrinsic DGD values in exhibiting a PMD of ) 0.15 psr 'km . Now, DGD values for short lengths Ž l < LC . of fiber can be related to long length Ž l 4 LC . fiber PMD values through w3x PMD s
'L
C
DGD,
Ž 2.
where LC is the average random mode coupling length. Using the measured DGD and PMD values Eq. Ž2. then yields LC values for the DSFs and DEDFs on the fiber bobbins lying between 0.1 and 5 m, which agrees with w3x.
POLARIZATION MODE DISPERSION
77
FIG. 1. Measured and calculated DGD values versus twist for different types of fibers: Ža. step index, Žb. DS, Žc. DS spun, and Žd. DS DEDF.
In order to understand the origin of these high DGD values, we then theoretically modeled the DGD in S-SMF and step index DSFs and examined their core ellipticity with a scanning electronic microscope. III. THEORETICAL MODELING
PMD in single mode optical fibers is caused by a combination of shape and stress birefringence w6, 7x. The stress birefringence may be of external, e.g., cabling-induced PMD, or internal origin due to the thermal expansion mismatch of the core and cladding material, which introduces birefringence w7x. Shape birefringence arises if the fiber possesses some ellipticity, e 2 , defined by e 2 s 1 y b 2ra 2 , where b and a are the minor and major half axes of the elliptic core.
FIG. 2. Measured DGD results for different types of fibers with zero twist.
78
SHAN ET AL.
FIG. 3. PMD on shipping bobbins versus short length DGD for some of the fibers in Fig. 2.
Although the DEDFs under study have nonrectangular index profiles, for simplicity, we used rectangular index profile approximation to calculate shape and stress birefringence. Shape birefringence can be expressed as w6x
dbG s
1 a
e 2 Ž 2D .
3r2
dbGU ,
Ž 3.
where D is the relative index difference, and dbGU is the normalized birefringence
dbGU s
U 2W 2 8V 3
1y
J 02 Ž U . J12 Ž U .
1y
W2 U2
q
W 2 J0 Ž U . UJ1 Ž U .
,
Ž 4.
where J 0, 1 are Bessel functions of the first kind Žof zero and first order.. The birefringence due to internal thermal stress anisotropy, which develops during drawing when the fiber cools through the temperature at which the glass sets, can be expressed as w7x
dbs s
DC
Ž 1 y np .
1
Ž a 1 y a 2 . DTbn Ž l . k 0 O, 2
Ž 5.
where E and C are the Young’s modulus and stress optic coefficient for silica, respectively; bn , the normalized propagation constant, is defined as bn Ž l . s
n2eff y n22 n12 y n22
s1y
U2 V2
s
W2 V2
Ž 6.
and O s 2 Ž a y b . r Ž a q b . f er2;
Ž 7.
a 1 and a 2 are the temperature expansion coefficients of the core and cladding material, respectively; np is Poisson’s ratio; and DT is the difference between the
POLARIZATION MODE DISPERSION
79
glass softening temperature and room temperature. Stress birefringence is proportional to the core ellipticity and depends on the electric field distribution indicated by the normalized propagation constant, which is mainly due to a direction-dependent stress change in the core]cladding interface which arises from the thermal expansion mismatch between the core and cladding w7x. The temperature expansion coefficient is a linear function of the refractive index and doping level, provided that the doping concentration g q , is small and can be estimated at low temperatures through w8x
a qq SiO 2 s g q a q q Ž 1 y g q . a SiO 2 ,
Ž 8.
where a q is the thermal expansion coefficient, whose values at low temperatures can be found for fused silica and some frequently used codopants ŽTable 1. w8x, w9x. The total birefringence is the vectorial sum of the shape and stress birefringences: ª
ª
ª
db s dbG q db S .
Ž 9.
For low birefringence fibers, the shape and stress birefringences can be treated as a simple linear combination w10x. DGD is then derived from the total birefringence as DGD s
d Ž db . dv
s
1 d Ž db . c
dk
.
Ž 10 .
The simulation results using Eqs. Ž3. to Ž10. are shown in Fig. 4 with the simulation values as given in the figure. Figure 4 shows that the DGD increase with increasing ellipticity is faster for the DSF than for the S-SMF, due mainly to the larger refractive index difference, D, and the smaller core diameter, 2 a, in the DSF. We then examined the core of different DEDF samples using a backscatter scanning electron microscope and found that in some samples e 2 could be as large as 5%. For one of the DEDFs, the one with the triangular profile, data on the core ellipticity measured on its parent preform were available, the value being ; 7%. We believe that this ellipticity was impressed into the fiber during drawing. For this ellipticity the calculated DGD for a DSF with step-index profile, as shown in Fig. 4b, would be ; 17 psrkm. This value is higher than the measured value of ; 14.4 psrkm in this DEDF. The difference is due to the nonrectangular profile of the DEDF and the doping of the fiber cladding with P2 O5 , which reduces the thermal expansion mismatch between core and cladding. For the other DEDF with the segmented index profile a far field scan was done on fiber samples in order to
TABLE 1 Thermal Expansion Coefficients a q for Silica and Some of Its Dopants SiO 2 f 0.55 = 10y6 Cy1 GeO 2 f 7 = 10y6 Cy1 B 2 O 3 f 10 = 10y6 Cy1
P2 O5 f 14 = 10y6 Cy1 Al 2 O 3 f 5.9 = 10y6 Cy1
80
SHAN ET AL.
FIG. 4. DGD due to shape and thermal stress birefringence both caused by elliptical cores with DT s 10008C for Ža. step-index fiber with zero chromatic dispersion at 1.3 m m and Žb. DS step-index fiber with zero dispersion at 1.55 m m.
determine the core ellipticity. In the far field scans no core ellipticity could be observed within its 2% resolution. We assume that in this fiber the erbium doping-induced stress in the main reason for the high PMD values. IV. DISCUSSION
In the present, first generation of DEDFs, effort has been mainly focused on the optimization of the erbium doping profile to achieve high pumping efficiency, low ASE level, and a flat spectral gain. However, PMD is also a highly significant parameter at bit rates ) 40 Gbitsrs. Unfortunately, little attention has been paid so far to the effects of various doping methods on fiber birefringence, although some of them have been found to lead to irregular refractive index distributions. Therefore in the development of next-generation DEDF, it is essential to reduce its DGD. Before a satisfactory doping method is found which does not introduce excessive birefringence due to either core ellipticity or thermal stress in the fiber, it is recommended that the fiber be spun during drawing to make spun DEDF so as to ensure that the fiber has an acceptably low PMD. V. CONCLUSION
We have measured the intrinsic DGD in distributed erbium-doped fibers. These DGD values are about an order of magnitude higher than the acceptable upper limit for high capacity Ž) 40 Gbitrs. soliton systems. Relatively high core ellipticity values and erbium doping process-induced stress seem to be the main origins of these high DGD values, and therefore it is important not only to reduce the core ellipticity significantly in the next stage of DEDF design but also to use more careful doping processes.
POLARIZATION MODE DISPERSION
81
ACKNOWLEDGMENTS The authors acknowledge J. G. Ellison and B. Diamond from the University of Essex, Colchester, UK, for helping with the measurements, and D. L. Williams and S. R. Sikora from BT Labs, Ipswich, UK, for providing core ellipticity data on the loaned DEDFs and for helpful discussions. This work was carried out under EPSRC Research Grant GRrK49454. The industrial partners are Alcatel Submarine Networks, Greenwich, London, and BT Laboratories, Martlesham Heath, Ipswich.
REFERENCES w1x A. Altuncu and A. S. Siddiqui et al., ‘‘40 Gbitrs error free transmission over a 68 km distributed erbium doped fiber amplifier,’’ Electron. Lett., vol. 32, 233 Ž1996.. w2x L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, ‘‘Resistance of solitons to the effects of polarization in optical fibers,’’ Opt. Lett., vol. 14, 1219 Ž1989.. w3x M. C. de Lignie, H. G. J. Nagel, and M. O. van Deventer, ‘‘Large polarization mode dispersion in fiber optic cables,’’ J. Lightwa¨ e Technol., vol. 12, 1325 Ž1994.. w4x R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Beddington, ‘‘Theoretical analysis and measurement of the effects of fiber twist on the differential group delay of optical fibers,’’ Electron. Lett., vol. 31, 1772 Ž1995.. w5x R. E. Schuh and A. S. Siddiqui, ‘‘A single channel polarimetric OTDR for the measurement of the backscattered SOP evolution along a fiber with twist,’’ Electron. Lett., vol. 33, 2153 Ž1997.. w6x R. A. Sammut, C. D. Hussey, J. D. Love and A. W. Snyder, ‘‘Modal analysis of polarisation effects in weakly-guiding fibers,’’ IEE Proc., vol. 128, 173 Ž1981.. w7x W. Eickhoff, ‘‘Stress-induced single-polarization single-mode fiber,’’ Opt. Lett., vol. 7, 629 Ž1982.. w8x I. P. Kaminow and V. Ramaswamy, ‘‘Single-polarisation optical fibers: Slab model,’’ Appl. Phys. Lett., vol. 34, 268 Ž1979.. w9x D. R. Lide and H. P. R. Frederikse, CRC Handbook of Chemistry and Physics, 75th ed., CRC Press, London, 1994. w10x A. M. Vengsarkar, A. H. Moesle, L. G. Cohen, and W. L. Mammel, ‘‘Polarization mode dispersion in dispersion shifted fibers: An exact analysis,’’ Opt. Lett., vol. 18, 1412 Ž1993..