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Effect of modal noise on single mode fiber optic networks
Volume 65, number 5
OPTICS COMMUNICATIONS
1 March 1988
EFFECT OF MODAL NOISE ON SINGLE MODE FIBER OPTIC NETWORKS P. M o h a n a S H A N K A R Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104, USA
Received 15 July 1987; revised manuscript received 2 November 1987
Modal noise may arise in single mode fiber optic networks from the random coupling of the fundamental model LPol and the higher order mode LPt ~. The higher mode LP~ is generated in the fiber optic link from imperfect connectors. A model for the modal noise generated in a single mode fiber optic network consisting of a number of connectors or splices is presented. The effect of modal noise on the link is discussed and expression for signal to noise ratio has been obtained. Suggestions for the reduction of modal noise are given.
1. Introduction High capacity, high speed fiber optic c o m m u n i cation links use lasers with a high degree o f coherence. The coherence o f the source makes it possible for the different m o d e s propagating in the fiber to retain the phase relationship between t h e m leading to interference between m o d e s when p e r t u r b a t i o n a n d m o d e coupling occur. This interference produces a speckle p a t t e r n at the o u t p u t end o f the fiber. The pattern so generated fluctuates with changes in the e n v i r o n m e n t , changes in the source characteristics etc. a n d hence the a m o u n t o f power coupled to the next fiber or detector fluctuates, thus introducing yet a n o t h e r r a n d o m parameter, called m o d a l noise [ 1-5] in the detection process. The m o d a l noise is thus inherent and u n a v o i d a b l e in fiber optic systems a n d is a manifestation o f the r a n d o m coupling o f m o d e s in a fiber. M o d a l noise poses serious p r o b l e m s in m u l t i m o d e fibers, as it arises from p e r t u r b a t i o n s such as source frequency fluctuations, microbending, m o d e selective losses, reflections at fiber connectors/splices etc. The m o d a l noise ceases to exist as the length o f the fiber increases a n d consequently the delay between the different m o d e s exceeds the coherence time o f the source a n d the m o d e s no longer have phase coherence to p r o d u c e interference. It has been established that even single m o d e fibers are susceptible to m o d a l noise [ 6 - 8 ] . M o d a l noise in single m o d e fi-
bers arises from the presence o f the LP 11 m o d e generated in the link from an imperfect connector. If this lossy m o d e is not completely a t t e n u a t e d before it reaches the next connector, interference between the LPo~ and LPtt modes takes place across the connector. W h e n p e r t u r b a t i o n s such as source frequency changes take place, this interference pattern fluctuates leading to m o d a l noise. M o d a l noise will therefore be a limiting factor in fiber optic systems in terms o f achieving the required signal to noise ( S / N ) or bit error rate [ 6 - 8 ] . The effect o f m o d a l noise on system performance has been studied in systems where a m u l t i m o d e fiber is used. Some results are available for single m o d e fibers too [ 6,7 ]. These analyses have been limited to a discussion o f m o d a l noise in a single p o r t network systems. H o w e v e r with the increased use o f single m o d e fibers for c o m m u n i c a t i o n and for local area networks ( L A N ) [9] for analog as well as digital transmission, problems o f modal noise become much m o r e serious due to the use o f a large n u m b e r o f connectors/splices in the link over a short length. The presence o f these large n u m b e r o f connectors/splices makes the m o d a l noise situation critical, as the LPt~ m o d e generated at one j u n c t i o n is not totally attenuated before it reaches the next j u n c t i o n and so on, leading to worsening noise. As the connectors are seld o m ideal, m o d a l noise will therefore be the limiting factor in achieving the ultimate i n f o r m a t i o n capacity o f the fiberoptic link. These p r o b l e m s posed by
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
347
Volume 65, number 5
OPTICS COMMUNICATIONS
the presence of a large n u m b e r of optical components have not been explored fully. The purpose of this study is to investigate the effects of modal noise on a single mode fiber optic link and evaluate the performance of the model noise limited systems.
nector is assumed to be a no loss device; any loss in LP01 mode appears as LP~ mode. However there is an overall loss in the system as the LP~ mode is a lossy one. The noise model is shown in fig. lb. Ao and Bo are the incident amplitudes of the modes LPo~, LPI~ respectively at TI. (We assume that only the LPo~ mode is launched, i.e., Ao= 1, B 0 = 0 . ) Ax, BN are the amplitude transmission of the respective modes across the Nth j u n c t i o n Tx. Due to the generation of LP~ mode at the connector, the transmission across T~ is
2. Noise considerations A typical single mode fiber optic link is shown in fig. la. It has N sections of fiber, each of length L, connected through terminal ports such as connectors or couplers. Because the connector is not an ideal one, the LPII mode is generated at the connector and propagates as a lossy mode. If this mode is not completely attenuated before it reaches the next j u n c tion, interference between these two modes takes place across the next connector [1,6,7]. The con-
1
Al=cAo,
Bl=dAo,
(1) (2)
where c the amplitude coupling coefficient across the j u n c t i o n for the LPoL mode (assumed to be the same for LPl~ mode as well) and d is the cross coupling coefficient between LPo~ and LP~ modes. I f q is the transmission efficiency of the connector, then q=c 2
2
AIjt}) ]AfB1
input
l March 1988
]A2'B2
I (I)
.................. ]AI~BN
N+I
L
output
TI
TN
T2
TN.I
(a) 5 j
O1 ,
splice loss /
t
01
modal noise
f~:::::::::::::
LP
LP 11
::::::::::::spliceloss
I
"'"
,~4u.e... ~.%.,..,Fiberlength
to otherconnectors
(b) Fig. 1.(a) The single mode fiber optic network configuration. The network has N sections each of length L. T~, 7"2.... etc. are the connec tors. Ao, B~ are the input amplitudes of the LPo> LP~ modes respectively to T~. A~, BN are the amplitude transmission of LPm, LP~ modes respectivelyacross the Nth junction Tx. In.+z(t) will be the intensity transmission of the LPo. mode after N sections of length L. (b) The model for the modal noise. Initially only the gP0~ mode is present. The connector loss leads to the excitation of the LP~ which propagates as a lossy mode, finally leading to the generation of modal noise as shown [7,8]. 348
V o l u m e 65, n u m b e r 5
OPTICS COMMUNICATIONS
and (I - t / ) = d 2. Let us define the phase factors El, E2 and the attenuation factor E a a s El = exp(-iflo~L) , E2 = e x p ( - i f l ~ L ) , Ea= e x p ( - a L ) ,
(3)
flo~ and fll~ are the propagation constants of the LPot and LP 11 mode respectively, a is the attenuation per unit length of the LP~ mode. The amplitude transmission across 7"2 will be given by A2=cA~E~ +dBIE2E a
(for the LPm mode) ,
(4)
B2=dAjEI +cB~E2Ea
(fortheLPl~ mode) .
(5)
Proceeding similarly the amplitude transmission of the LPm mode across the ( N + 1)th junction will be (6)
AN+I =CANEI +dBNE2Ea •
Using eqs.(1 ) through (6), Au+l
can
be expressed as
AN+ 1 = cN+ 1Err + N c N - 1E N- l E z E a d 2 .
(7)
1 M a r c h 1988
Normally one would have very little information on the phase. However if the source has a high degree of coherence, it is fair to assume that the phase 0 is uniformly distributed between - n and + n [ 10,11 ] and hence the variance a~ of cos 0 is 1/2. The signal to noise ratio S/Nout at the end of N sections, each of length L can now be written as
S/N°ut =
=
mean Of lN+ l ( t) standard deviation of modal noise
q 21/2 N (1 --q) e x p ( - c ~ L ) "
(9)
This is a worst case signal to noise ratio because coherence goes down as the number of sections N increases. Consequently 0 will no longer be uniformly distributed as N increases. The variance a~ will hence decrease as the length of the fiber, ( N L ) increases and the S/Nout will always be better than that given in eq.(9).
The intensity across this junction can now be written as
3. Discussion and conclusions
IN+~(t) = IAN+I I 2
=qN+l
+2N~/N ( l - q ) cos(Aft L) e x p ( - c ~ L ) ,
(8)
where Aft=tim--fl~. In arriving at eqs.(7) and (8), terms involving powers OfEa are neglected as the LPI~ mode is highly attenuating. Also terms containing d 3 and higher powers in d are neglected as the connectors generally have good transmission efficiency (q is about 90% or more). Normally the phase factor in the third term, cos(Aft L) does not vary or varies very slowly. However, changes in the source spectrum, changes in environment etc. combined with a high degree of coherence lead to random fluctuations of this phase term [4-8] resulting in modal noise (fig. lb). The phase factor cos(Aft L) may hence be represented by cos(0), where 0 is a random variable whose randomness will depend on the degree of coherence, the number of sections N and distance between the sections L etc. [ 1,10,11 ]. The first term is the signal and the second term is the modal noise. The signal to noise ratio S/Nora, given by the ratio of the mean OflN+~(t) to the standard deviation of the modal noise, can now be obtained. This requires a knowledge of the behavior of the phase term which depends on the probability density function of 0.
In a link with a number of nonideal connectors/splices, any spectral fluctuations of the source [ 1,7,8,11 ] lead to modal noise and eq.(9) gives the system performance in terms of the signal to noise ratio S/Nout. This is the worst case S/Nout as we have assumed that the source has a high degree of coherence. The S/Nout falls as N, the number of sections increases. For a given number N of sections, performance depends mainly on two parameters, namely the transmission efficiency t/ of the connector and the attenuation c~ of the LP~ mode. So the modal noise can be reduced if the splice loss t/o (q= 10-t"°/~°), ~/o in dB) is very small. For a given splice loss, S/Nou, can be improved by using a fiber with a larger value of the attenuation coefficient o~ of the LP~j mode. This can be achieved either by proper choice of the physical and geometrical characteristics of the fiber or by introducing small bends between the junctions so as to increase the attenuation of the LP~ mode. Increasing the length L of the fiber between the connectors also improves the S/N because this leads to reduced modal noise in two ways, nameley that of increased attenuation of the LP~ mode and reduced phase coherence between the 349
Volume 65, number 5
OPTICS C O M M U N I C A T I O N S
modes. Eq.(9) can therefore be used as a means of achieving a trade-off in choosing the link parameters such as the transmission efficiency q, the number of connectors/splices N and the seperation L between the junctions so as to maintain the S/Nout at any desired level.
References [ l ] R.E. Epworth, Laser Focus 17 ( 1981 ) 109. [2] A.M.J. Koonen, J. Opt. Comm. 5 (1981) 141.
350
1 March 1988
[3] A.M.J. Koonen, IEEE J. Selected Areas in Comm. SAC-4 (1986) 1515. [4] H. Shinohara, IEEE J. Lightwave Tech. LT-I (1983) 535. [ 5 ] B. Crosignani and A. Yariv, J. Opt. Soc. Am. 73 (1983) 1022. [ 6 ] S. Heckman, Optics Lett. 6 (1981 ) 201. [ 7 ] F.T. Stone, in: Fiber optics~ short- haul and long-haul measurements and applications, SPIE, Vol. 500, pp. 17-22, 1984. [8] C.M. Miller, S.C. Mettler and I.A. White, Optical fiber splices and connectors ( Marcel Dekker, New York, 1986). [9] C.A. Villarruel, C.C. Wang, R.P. Moeller and W.K. Burns, IEEE J. Ligbtwave Tech. LT-3 (1985) 472. [ 10 ] H. Olesen, Electr. Lett. 16 (1980) 217. [ 11 ] E.G. Rawson, J.W. G o o d m a n and R.E. Norton, J. Opt. Soc. Am. 70 (1980) 968.
OPTICS COMMUNICATIONS
1 March 1988
EFFECT OF MODAL NOISE ON SINGLE MODE FIBER OPTIC NETWORKS P. M o h a n a S H A N K A R Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104, USA
Received 15 July 1987; revised manuscript received 2 November 1987
Modal noise may arise in single mode fiber optic networks from the random coupling of the fundamental model LPol and the higher order mode LPt ~. The higher mode LP~ is generated in the fiber optic link from imperfect connectors. A model for the modal noise generated in a single mode fiber optic network consisting of a number of connectors or splices is presented. The effect of modal noise on the link is discussed and expression for signal to noise ratio has been obtained. Suggestions for the reduction of modal noise are given.
1. Introduction High capacity, high speed fiber optic c o m m u n i cation links use lasers with a high degree o f coherence. The coherence o f the source makes it possible for the different m o d e s propagating in the fiber to retain the phase relationship between t h e m leading to interference between m o d e s when p e r t u r b a t i o n a n d m o d e coupling occur. This interference produces a speckle p a t t e r n at the o u t p u t end o f the fiber. The pattern so generated fluctuates with changes in the e n v i r o n m e n t , changes in the source characteristics etc. a n d hence the a m o u n t o f power coupled to the next fiber or detector fluctuates, thus introducing yet a n o t h e r r a n d o m parameter, called m o d a l noise [ 1-5] in the detection process. The m o d a l noise is thus inherent and u n a v o i d a b l e in fiber optic systems a n d is a manifestation o f the r a n d o m coupling o f m o d e s in a fiber. M o d a l noise poses serious p r o b l e m s in m u l t i m o d e fibers, as it arises from p e r t u r b a t i o n s such as source frequency fluctuations, microbending, m o d e selective losses, reflections at fiber connectors/splices etc. The m o d a l noise ceases to exist as the length o f the fiber increases a n d consequently the delay between the different m o d e s exceeds the coherence time o f the source a n d the m o d e s no longer have phase coherence to p r o d u c e interference. It has been established that even single m o d e fibers are susceptible to m o d a l noise [ 6 - 8 ] . M o d a l noise in single m o d e fi-
bers arises from the presence o f the LP 11 m o d e generated in the link from an imperfect connector. If this lossy m o d e is not completely a t t e n u a t e d before it reaches the next connector, interference between the LPo~ and LPtt modes takes place across the connector. W h e n p e r t u r b a t i o n s such as source frequency changes take place, this interference pattern fluctuates leading to m o d a l noise. M o d a l noise will therefore be a limiting factor in fiber optic systems in terms o f achieving the required signal to noise ( S / N ) or bit error rate [ 6 - 8 ] . The effect o f m o d a l noise on system performance has been studied in systems where a m u l t i m o d e fiber is used. Some results are available for single m o d e fibers too [ 6,7 ]. These analyses have been limited to a discussion o f m o d a l noise in a single p o r t network systems. H o w e v e r with the increased use o f single m o d e fibers for c o m m u n i c a t i o n and for local area networks ( L A N ) [9] for analog as well as digital transmission, problems o f modal noise become much m o r e serious due to the use o f a large n u m b e r o f connectors/splices in the link over a short length. The presence o f these large n u m b e r o f connectors/splices makes the m o d a l noise situation critical, as the LPt~ m o d e generated at one j u n c t i o n is not totally attenuated before it reaches the next j u n c t i o n and so on, leading to worsening noise. As the connectors are seld o m ideal, m o d a l noise will therefore be the limiting factor in achieving the ultimate i n f o r m a t i o n capacity o f the fiberoptic link. These p r o b l e m s posed by
0 030-4018/88/$03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
347
Volume 65, number 5
OPTICS COMMUNICATIONS
the presence of a large n u m b e r of optical components have not been explored fully. The purpose of this study is to investigate the effects of modal noise on a single mode fiber optic link and evaluate the performance of the model noise limited systems.
nector is assumed to be a no loss device; any loss in LP01 mode appears as LP~ mode. However there is an overall loss in the system as the LP~ mode is a lossy one. The noise model is shown in fig. lb. Ao and Bo are the incident amplitudes of the modes LPo~, LPI~ respectively at TI. (We assume that only the LPo~ mode is launched, i.e., Ao= 1, B 0 = 0 . ) Ax, BN are the amplitude transmission of the respective modes across the Nth j u n c t i o n Tx. Due to the generation of LP~ mode at the connector, the transmission across T~ is
2. Noise considerations A typical single mode fiber optic link is shown in fig. la. It has N sections of fiber, each of length L, connected through terminal ports such as connectors or couplers. Because the connector is not an ideal one, the LPII mode is generated at the connector and propagates as a lossy mode. If this mode is not completely attenuated before it reaches the next j u n c tion, interference between these two modes takes place across the next connector [1,6,7]. The con-
1
Al=cAo,
Bl=dAo,
(1) (2)
where c the amplitude coupling coefficient across the j u n c t i o n for the LPoL mode (assumed to be the same for LPl~ mode as well) and d is the cross coupling coefficient between LPo~ and LP~ modes. I f q is the transmission efficiency of the connector, then q=c 2
2
AIjt}) ]AfB1
input
l March 1988
]A2'B2
I (I)
.................. ]AI~BN
N+I
L
output
TI
TN
T2
TN.I
(a) 5 j
O1 ,
splice loss /
t
01
modal noise
f~:::::::::::::
LP
LP 11
::::::::::::spliceloss
I
"'"
,~4u.e... ~.%.,..,Fiberlength
to otherconnectors
(b) Fig. 1.(a) The single mode fiber optic network configuration. The network has N sections each of length L. T~, 7"2.... etc. are the connec tors. Ao, B~ are the input amplitudes of the LPo> LP~ modes respectively to T~. A~, BN are the amplitude transmission of LPm, LP~ modes respectivelyacross the Nth junction Tx. In.+z(t) will be the intensity transmission of the LPo. mode after N sections of length L. (b) The model for the modal noise. Initially only the gP0~ mode is present. The connector loss leads to the excitation of the LP~ which propagates as a lossy mode, finally leading to the generation of modal noise as shown [7,8]. 348
V o l u m e 65, n u m b e r 5
OPTICS COMMUNICATIONS
and (I - t / ) = d 2. Let us define the phase factors El, E2 and the attenuation factor E a a s El = exp(-iflo~L) , E2 = e x p ( - i f l ~ L ) , Ea= e x p ( - a L ) ,
(3)
flo~ and fll~ are the propagation constants of the LPot and LP 11 mode respectively, a is the attenuation per unit length of the LP~ mode. The amplitude transmission across 7"2 will be given by A2=cA~E~ +dBIE2E a
(for the LPm mode) ,
(4)
B2=dAjEI +cB~E2Ea
(fortheLPl~ mode) .
(5)
Proceeding similarly the amplitude transmission of the LPm mode across the ( N + 1)th junction will be (6)
AN+I =CANEI +dBNE2Ea •
Using eqs.(1 ) through (6), Au+l
can
be expressed as
AN+ 1 = cN+ 1Err + N c N - 1E N- l E z E a d 2 .
(7)
1 M a r c h 1988
Normally one would have very little information on the phase. However if the source has a high degree of coherence, it is fair to assume that the phase 0 is uniformly distributed between - n and + n [ 10,11 ] and hence the variance a~ of cos 0 is 1/2. The signal to noise ratio S/Nout at the end of N sections, each of length L can now be written as
S/N°ut =
=
mean Of lN+ l ( t) standard deviation of modal noise
q 21/2 N (1 --q) e x p ( - c ~ L ) "
(9)
This is a worst case signal to noise ratio because coherence goes down as the number of sections N increases. Consequently 0 will no longer be uniformly distributed as N increases. The variance a~ will hence decrease as the length of the fiber, ( N L ) increases and the S/Nout will always be better than that given in eq.(9).
The intensity across this junction can now be written as
3. Discussion and conclusions
IN+~(t) = IAN+I I 2
=qN+l
+2N~/N ( l - q ) cos(Aft L) e x p ( - c ~ L ) ,
(8)
where Aft=tim--fl~. In arriving at eqs.(7) and (8), terms involving powers OfEa are neglected as the LPI~ mode is highly attenuating. Also terms containing d 3 and higher powers in d are neglected as the connectors generally have good transmission efficiency (q is about 90% or more). Normally the phase factor in the third term, cos(Aft L) does not vary or varies very slowly. However, changes in the source spectrum, changes in environment etc. combined with a high degree of coherence lead to random fluctuations of this phase term [4-8] resulting in modal noise (fig. lb). The phase factor cos(Aft L) may hence be represented by cos(0), where 0 is a random variable whose randomness will depend on the degree of coherence, the number of sections N and distance between the sections L etc. [ 1,10,11 ]. The first term is the signal and the second term is the modal noise. The signal to noise ratio S/Nora, given by the ratio of the mean OflN+~(t) to the standard deviation of the modal noise, can now be obtained. This requires a knowledge of the behavior of the phase term which depends on the probability density function of 0.
In a link with a number of nonideal connectors/splices, any spectral fluctuations of the source [ 1,7,8,11 ] lead to modal noise and eq.(9) gives the system performance in terms of the signal to noise ratio S/Nout. This is the worst case S/Nout as we have assumed that the source has a high degree of coherence. The S/Nout falls as N, the number of sections increases. For a given number N of sections, performance depends mainly on two parameters, namely the transmission efficiency t/ of the connector and the attenuation c~ of the LP~ mode. So the modal noise can be reduced if the splice loss t/o (q= 10-t"°/~°), ~/o in dB) is very small. For a given splice loss, S/Nou, can be improved by using a fiber with a larger value of the attenuation coefficient o~ of the LP~j mode. This can be achieved either by proper choice of the physical and geometrical characteristics of the fiber or by introducing small bends between the junctions so as to increase the attenuation of the LP~ mode. Increasing the length L of the fiber between the connectors also improves the S/N because this leads to reduced modal noise in two ways, nameley that of increased attenuation of the LP~ mode and reduced phase coherence between the 349
Volume 65, number 5
OPTICS C O M M U N I C A T I O N S
modes. Eq.(9) can therefore be used as a means of achieving a trade-off in choosing the link parameters such as the transmission efficiency q, the number of connectors/splices N and the seperation L between the junctions so as to maintain the S/Nout at any desired level.
References [ l ] R.E. Epworth, Laser Focus 17 ( 1981 ) 109. [2] A.M.J. Koonen, J. Opt. Comm. 5 (1981) 141.
350
1 March 1988
[3] A.M.J. Koonen, IEEE J. Selected Areas in Comm. SAC-4 (1986) 1515. [4] H. Shinohara, IEEE J. Lightwave Tech. LT-I (1983) 535. [ 5 ] B. Crosignani and A. Yariv, J. Opt. Soc. Am. 73 (1983) 1022. [ 6 ] S. Heckman, Optics Lett. 6 (1981 ) 201. [ 7 ] F.T. Stone, in: Fiber optics~ short- haul and long-haul measurements and applications, SPIE, Vol. 500, pp. 17-22, 1984. [8] C.M. Miller, S.C. Mettler and I.A. White, Optical fiber splices and connectors ( Marcel Dekker, New York, 1986). [9] C.A. Villarruel, C.C. Wang, R.P. Moeller and W.K. Burns, IEEE J. Ligbtwave Tech. LT-3 (1985) 472. [ 10 ] H. Olesen, Electr. Lett. 16 (1980) 217. [ 11 ] E.G. Rawson, J.W. G o o d m a n and R.E. Norton, J. Opt. Soc. Am. 70 (1980) 968.