A statistical treatment of cross-polarization modulation in DWDM systems & its application [Elektronische Ressource] / vorgelegt von Marcus Winter

A Statistical Treatment of Cross-Polarization Modulation in DWDM Systems its Applicationvorgelegt von Diplom-Ingenieur Marcus Winter aus Potsdamvon der Fakultät IV - Elektrotechnik und Informatik - der Technischen Universität Berlin zurErlangung des akademischen Grades (.-.)genehmigte DissertationP Vorsitzender Prof. Dr.-Ing. Heino Henke Berichter Prof. Dr.-Ing. Klaus Petermann Berichter Prof. Dr.-Ing. Peter Krummrich Tag der wissenschalichen Aussprache 26. Juni 2010Berlin 2010D83D a s, wo bei u nse r e B e r e c h nu n g e n ve r sag e n, n e n n e n wir Zu f a ll.– A l b e r t E i n s t ei nP R E F A C Ee p r ese n t w o r k is t he cu lm i n a t io n of a n a lmos t t h r e e - a nd - a - h a l f yea r r esea r ch effo r t o n a t o p ic t h a ti n it ia l ly se e me d (a t lea s t t o me) not m uch mo r e t h a n a cu r iou s no n l i nea r side effe ct of m u l t i- w a v ele n g t hd a t a t r a n s m is sio n . P r e v iou s r esea r ch me r ely i nd ic a t e d t h a t c o m p e n sa t io n of  m a y b e affe ct e d , a ndt he p r oj e ct i n it ia l ly s t a r t e d ou t i n t h is d i r e ct io n .
Publié le : vendredi 1 janvier 2010
Lecture(s) : 35
Source : D-NB.INFO/1009105868/34
Nombre de pages : 196
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A Statistical Treatment of
Cross-Polarization Modulation
in DWDM Systems its
Application
vorgelegt von
Diplom-Ingenieur Marcus Winter aus Potsdam
von der Fakultät IV - Elektrotechnik und Informatik - der Technischen Universität Berlin zur
Erlangung des akademischen Grades (.-.)
genehmigte Dissertation
P
Vorsitzender Prof. Dr.-Ing. Heino Henke
Berichter Prof. Dr.-Ing. Klaus Petermann
Berichter Prof. Dr.-Ing. Peter Krummrich
Tag der wissenschalichen Aussprache 26. Juni 2010
Berlin 2010
D83D a s, wo bei u nse r e B e r e c h nu n g e n ve r sag e n, n e n n e n wir Zu f a ll.
– A l b e r t E i n s t ei nP R E F A C E
e p r ese n t w o r k is t he cu lm i n a t io n of a n a lmos t t h r e e - a nd - a - h a l f yea r r esea r ch effo r t o n a t o p ic t h a t
i n it ia l ly se e me d (a t lea s t t o me) not m uch mo r e t h a n a cu r iou s no n l i nea r side effe ct of m u l t i- w a v ele n g t h
d a t a t r a n s m is sio n . P r e v iou s r esea r ch me r ely i nd ic a t e d t h a t c o m p e n sa t io n of  m a y b e affe ct e d , a nd
t he p r oj e ct i n it ia l ly s t a r t e d ou t i n t h is d i r e ct io n .  is ch a n g e d w it h t he r e n a is sa nc e of c o he r e n t r e c e p -
t io n, w h ich a l lo w e d p o w e rf u l c o m p e n sa t io n of t r a n s m is sio n - r el a t e d d is t o r t io n s, bu t a lso p e r m it t e d a
chea p doub l i n g of t he d a t a r a t e b y m a k i n g u se of b ot h o r t ho g o n a l eig e n mo des of t he fib e r t o t r a n s m it
i nde p e nde n t d a t a . E n t e r 100 Gb ps E t he r net a nd t he desi r e t o k e e p t he   50 G H z ch a n nel s p aci n g
a nd t he r e se e me d t o b e no w a y a r ou nd p o l a r iza t io n - d iv isio n m u l t i p lex. S udde n ly , p o l a r iza t io n effe ct s
w h ich h a v e not yet p l a ye d a m aj o r r o le i n d i r e ct o r d iffe r e n t ia l det e ct io n s ys t e m s b e c a me r ele v a n t a nd
c r os s- p o l a r iza t io n mo d u l a t io n b e c a me i n t e r es t i n g t o a m uch l a rg e r a ud ie nc e. I n t h is w a y , I c o n side r
m ysel f l uck y , a s it m ade it ea sie r t o pub l ish m y w o r k .
I a m afr a id t h a t t he fo l lo w i n g ch a pt e rs c o n t a i n m uch mo r e m a t he m a t ics t h a n I i n it ia l ly i n t e nde d
t he m t o h a v e. H o w e v e r , w he n I s t a r t e d ou t t he r e w a s no si n g le not a t io n i n u se – p e o p le dea l i n g w it h
 h ad t hei r w a ys of w r it i n g t he p r o p a g a t io n e q u a t io n s ( o e n Di r ac’ s b r a - k et not a t io n ) a nd p e o p le
dea l i n g w it h no n l i nea r it ies h ad t hei rs . F i nd i n g m ysel f a t t he i n t e rse ct io n of b ot h a r ea s, I de cide d t o u se
t he b es t of b ot h w o r lds a nd c o me u p w it h a si n g le w a y of w r it i n g t h i n g s .  is m ade it ne c es sa r y t o mo r e
o r les s s t a r t fr o m sc r a t ch, w h ich r es u l t e d i n r a t he r ex t e n siv e ch a pt e rs dea l i n g w it h t he b a sics . M y desi r e
t o w r it e e v e r y t h i n g do w n a s fo r m a l ly c o r r e c t a s p os sib le c e r t a i n ly m ade o ne o r t he ot he r p a s sa g e q u it e
le n g t h y . H o w e v e r , mos t of t he e q u a t io n s g iv e n he r ei n se r v e a pu rp ose r el a t e d t o t he t o p ic.
A  e r r ead i n g t h is t ex t, t he r eade r shou ld h a v e a p r ofou nd u nde rs t a nd i n g of t he effe ct of c r os s-
p o l a r iza t io n mo d u l a t io n, ho w it c a n b e mo dele d , a nd ho w t h is mo del c a n b e q u a n t ifie d . F u r t he r mo r e,
a nd p e r h a ps mos t i n t e r es t i n g , he o r she w il l se e ho w c r os s- p o l a r iza t io n mo d u l a t io n affe ct s o pt ic a l c o m -
m u n ic a t io n . F o r so me si m p le ex e m p l a r y s ys t e m s l i m it s o n t he l a u nch p o w e r a r e de r iv e d , bu t I b el ie v e
t he g r ea t es t b e nefit of t h is w o r k is t o sho w ho w s uch l i m it s c a n b e det e r m i ne d fo r q u it e a rb it r a r y s ys t e m s .
A t t he ex p e n se of ac cu r ac y m a n y si m p l if yi n g a s s u m pt io n s w e r e m ade t o a r r iv e a t ex p r es sio n s t h a t c a n b e
ea sie r u nde rs t o o d a nd fr o m w h ich c o ncl u sio n s c a n b e dr a w n w it hou t t he ne e d fo r n u me r ics . H o w e v e r ,
c o m p a r iso n t o c o m pu t e r si m u l a t io n s sho w t h a t t he r es u l t s a r e r e m a r kab ly ac cu r a t e. I w ou ld h a v e l ik e d
t o c o n fi r m t hose r es u l t s i n a l ab o r a t o r y , bu t t he r ele v a n t b ou nd a r y c o nd it io n s w e r e u n f a v o r ab le. I m u s t
t he r efo r e r ely o n t he ac cu r ac y of t he (sel f- p r o g r a m me d ) si m u l a t io n s fo r c o n fi r m a t io n .
La rg e p a r t s of C h a pt e r 3 h a v e b e e n p r e v iou sly pub l ishe d i n a n a r t icle i n t he J ou r n a l of L ig h t w a v e
T e ch no lo g y [Wi n t e r   b], a nd p o r t io n s of C h a pt e rs 3 a nd 5 h a v e b e e n p r ese n t e d a t v a r iou s c o n fe r -
e nc es a nd w o r k sho ps . M os t of t he p a p e rs a nd sl ides a r e a v a il ab le o n m y w eb sit e a t
h t t p ://www .m a r cu sw i n t e r . de/r esea r ch     -                      
I w ou ld l ik e t o t h a n k P r of. D r .- I n g . Kl a u s P et e r m a n n fo r h is c o n t i n u i n g s u p p o r t, b ot h t e ch n ic a l
a nd adm i n is t r a t iv e, t h r ou g hou t t hese yea rs . H is not es o n t he fi rs t dr a of t h is t hesis – o e n not mo r e
t h a n a fe w w o r ds fo l lo w e d b y a q ues t io n m a r k – h a v e r e g u l a r ly r es u l t e d i n r e w r it i n g of c o m p let e p a s-
sa g es, i ncl ud i n g t he add it io n of yet mo r e e q u a t io n s . I w ou ld a lso l ik e t o t h a n k m y c o l lea g ues C h r is t ia n
W eb e r , J o h a n nes F ische r , a nd S t ef a n W a r m fo r l is t e n i n g t o m y m u si n g s a nd c o n t e m p l a t io n s o n a nd
off t he t o p ic (a nd a t lea s t p r et e nd i n g t o b e i n t e r es t e d ) a nd a lso D r .- I n g . C h r is t ia n - A lexa nde r B u n g e
fo r fr u it f u l d iscu s sio n s w it h i n t he fi rs t yea r . F u r t he r mo r e, I o w e t h a n k s t o N o k ia Sie me n s N et w o r k s
fo r f u nd i n g f u nd a me n t a l r esea r ch w it hou t a n i m me d ia t e r et u r n o n i n v es t me n t a nd i n p a r t icu l a r D a r io
S et t i fo r h is s u p p o r t t h r ou g hou t t he p r oj e ct. P r of. P et e r K r u m m r ich, i n it ia l ly o n t he p r oj e ct t ea m a t
N o k ia Sie me n s N et w o r k s a nd l a t e r a s r efe r e e of t h is t hesis, a lso dese r v es m y g r a t it ude. I a lso w ou ld l ik e
t o t h a n k t he a no n y mou s r e v ie w e rs of m y s ub m it t e d p a p e rs fo r t hei r hel p i n m a k i n g t he t o p ic clea r e r
a nd mo r e u nde rs t a nd ab le. La s t bu t c e r t a i n ly not lea s t, I w ou ld l ik e t o t h a n k t he p e o p le t h a t m ade m y
p r iv a t e l ife a g r e eab le i n o r de r fo r me t o b e ab le t o f u l ly c o nc e n t r a t e o n m y w o r k – fo r e mos t m y p a r t ne r
J u l ia S e m mel , bu t a lso m y p a r e n t s L e o a nd R o l f , a nd m y sis t e r H eik e.
W a ld b r o n n, N ov e mb e r 2009
i vC O N T E N T S
M e m o r an d u m o n N ota t io n … 1
I n t r o d u ct io n … 3
1 P olariz a t io n i n F i b e r- Opt ic Co m m u nic a t io n … 11
1.1 C l a s sic a l D esc r i pt io n of t he P o l a r iza t io n of L ig h t … 11
1.2 e S t o k es P a r a met e rs  t he P o i nc a r é S p he r e … 14
1.3 J o nes  M uel le r M a t r ic es … 22
2 P r opa g a t io n of G uide d W a v es … 27
2.1 e F u nd a me n t a l E v o l u t io n Eq u a t io n … 27
2.2 L i nea r E ffe ct s … 32
2.2.1 Gr ou p - V elo c it y Dis p e rsio n … 32
2.2.2 B i r efr i n g e nc e … 36
2.2.3 P o l a r iza t io n - M o d e Dis p e rsio n … 49
2.3 N o n l i nea r E ffe ct s … 63
2.3.1 F ou r - W a v e M ixi n g … 6 5
2.3.2 S el f- P h a s e M o d u l a t io n … 67
2.3.3 C r os s- P h a se  C r os s- P o l a r iza t io n M o d u l a t io n … 69
3 A S ta t i st ic a l M o de l of X P olM … 73
3.1 R a ndo m R ot a t io n s i n S t o k es S p ac e … 74
3.2 E s t i m a t io n of t he P a r a met e r  … 85
3.2.1 A u t o c o v a r ia nc e of t he S t o k es S u m … 88
3.2.2 W a l k - Off … 91
3.2.3 M ea n   D e c o r r el a t io n … 96
3.2.4 Co - P o l a r ize d  M u t u a l ly O r t ho g o n a l La u nch … 99
3.2.5 A m p l i fie r N o ise … 104
3.3 A p p l ic a t io n of t he M o del … 106
3.3.1 D e p e n de nc e o n F ib e r P a r a met e rs … 106
3.3.2 D e p e n de nc e o n C h a n nel L o ad … 115
4  e P olariz a t io n E n se m ble … 119
4.1 e V a r ia nc e of t he   … 119
4.2 e Dis t r ibu t io n of t he   … 127     -                      
4.3 Dis t r ibu t io n of t he  s w it h i n Si n g le E n se mb le M e mb e rs … 129
5 D et ri m e n ta l E ff e ct s of X P olM … 133
5.1 Opt ic a l Diffe r e n t ia l D et e ct io n … 134
5.2 P o l a r iza t io n - Div isio n M u l t i p lex … 146
5.2.1     P e n a l t y E s t i m a t e … 151
5.2.2 N u me r ic a l R es u l t s … 154
O u t lo ok … 165
S u m m ar y … 167
Z u sam m e n f as su n g … 169
A c r o n ym s … 171
L i st of N ota t io n … 173
Bi bl iogr a ph y … 175
A u t h o r ’ s Bi bl iogr a ph y … 187
v iM E M O R A N D U M O N N O T A T I O N
  a r e t w o p r i nci p a l t yp es of v e ct o rs t h a t a r e u se d t h r ou g hou t t h is t hesis . e fi rs t is t he c o m p lex -
⟩ ⟨

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