Iec Tr 61282-9-2016.Pdf

IEC TR 61 282 9 Edition 2 0 201 6 03 TECHNICAL REPORT Fibre optic communication system design guides – Part 9 Guidance on polarization mode dispersion measurements and theory IE C T R 6 1 2 8 2 9 2 0[.]

I EC TR 61 282-9 ® Ed i ti on 201 6-03 TECH N I CAL REPORT colour in sid e Fi bre opti c com mu n i cati on system desi gn gu i des – I EC TR 61 282-9: 201 6-03(en ) Part 9: Gui dan ce on pol ari zati on m ode di spersi on m easu rem en ts an d th eory Copyright International Electrotechnical Commission TH I S P U B L I C ATI O N I S C O P YRI G H T P RO TE C T E D C o p yri g h t © I E C , G e n e va , S w i tze rl a n d Al l or ri g h t s by re s e rv e d an y e i th e r m ean s, I EC c o p y ri g h t yo u r I EC 3, or or l o ca l IEC C e n t l ru e de CH -1 1 I E C's h a ve U n l ess o t h e rwi s e e l e c t ro n i c or m em ber an N a ti o n a l e n q u i ry m em ber s p e c i fi e d , m e ch a n i ca l , abou t N a ti o n a l no p a rt i n cl u d i n g C o m m i tte e o b ta i n i n g C o m m i tte e th e p u b l i ca ti o n c o u n t ry a d d i ti o n a l fo r O ffi c e in o f th i s p h o to co p yi n g fu rt h e r ri g h t s an d o f th e to th i s Te l : +41 22 91 02 1 F a x: +41 22 91 03 00 G e n e va i n fo @ i e c c h 20 be re p ro d u c e d re q u e s t e r wi t h o u t If p u b l i ca ti o n , yo u h a ve pl ease or u ti l i z e d p e rm i s s i o n an y co n ta c t in in q u e s ti o n s th e an y fo rm wri t i n g fro m abou t a d d re s s IEC bel ow or i n fo rm a t i o n V a re m b é S wi t z e rl a n d may m i c ro fi l m , ww w i e c c h Ab ou t th e I E C Th e I n t e rn a t i o n a l I n t e rn a t i o n a l E l e c t ro t e c h n i c a l S t a n d a rd s fo r al l Com m i ssi on e l e c t ri c a l , (I E C) e l e c t ro n i c and is th e re l a t e d l ead i n g g l obal o rg a n i z a t i o n th a t p re p a re s an d pu bl i sh es te ch n o l o g i e s Ab o u t I E C p u b l i c a ti o n s Th e te c h n i ca l l a te s t e d i ti o n , co n te n t a of IEC c o rri g e n d a p u b l i ca ti o n s or an is ke p t amend ment u n d er might co n s ta n t h a ve been I E C C atal og u e - webs tore i ec ch /catal og u e Th e s ta n d - a l o n e b i b l i o g p h i ca l Te ch n i ca l a p p l i ca ti o n i n fo rm a ti o n on S p e ci fi ca ti o n s , d o cu m e n ts Ava i l a b l e fo r fo r I EC PC, M ac th e I n te rn a ti o n a l An d ro i d e n ti re S ta n d a rd s , Re p o rts OS , an d o th e r Ta b l e ts an d i Pad a d va n ce d va ri e ty of s e a rch en abl es cri te ri a co m m i tte e , … ) an d th e Th e wo rl d ' s e l e ctri ca l wi th d wn It to ( re fe re n ce al so g i ve s fi n d I EC i n fo rm a ti o n on Pl ease m a ke s u re th a t yo u h a ve th e E n g l i sh an d l an g u ag es on l i n e co n ta i n i n g F re n ch , Al s o wi th kn o wn as d i cti o n a ry 20 000 e q u i va l e n t th e of te rm s e l e ctro n i c an d te rm s I n te rn a ti o n a l an d d e fi n i ti o n s in in a d d i ti o n a l E l e ctro te ch n i ca l on l i n e I E C G l os s ary - s td i ec ch /g l os s ary p u b l i ca ti o n s n u m b e r, I E C l ead i n g te rm s Vo ca b u l a ry ( I E V) I E C pu bl i cati on s s earch - www i ec ch /s earch pu b Th e by E l ectroped i a - www el ectroped i a org co n s u l ti n g Te ch n i ca l re v i e w pu bl i sh ed te xt, by a te ch n i ca l p ro j e cts , re p l a ce d 65 000 F re n ch I EC e l e ctro te ch n i ca l e xtra cte d p u b l i ca ti o n s co l l e cte d p u b l i ca ti o n s fro m fro m i ssu ed e a rl i e r te rm i n o l o g y th e Te rm s s i n ce 2002 p u b l i ca ti o n s e n tri e s an d S om e of in E n g l i sh D e fi n i ti o n s I EC e n tri e s TC 37, an d cl a u s e h a ve 77, of been 86 an d C I S P R I E C J u s t P u bl i s h ed - webs tore i ec ch /j u s u bl i s h ed S ta y up d e ta i l s al so to al l o n ce d a te n ew a on al l n ew p u b l i ca ti o n s m o n th by em l I EC p u b l i ca ti o n s re l e a s e d J u st Ava i l a b l e Pu bl i sh ed on l i n e an d I E C C u s to m er S ervi ce C en tre - web s tore i ec ch /cs c If yo u n eed wi s h fu rth e r C e n tre : Copyright International Electrotechnical Commission to g i ve us a s s i s ta n ce , cs c@ i e c ch yo u r fe e d b a ck pl ease co n ta ct on th e th i s p u b l i ca ti o n or C u s to m e r S e rvi ce I E C TR 61 82 -9 ® Ed i ti on 201 6-03 TE C H N I C AL RE PORT colour in sid e Fi bre opti c com m u n i cati on s ys tem d esi g n g u i d es – Part 9: G u i d an ce on pol ari zati on m od e d i spersi on m eas u rem en ts an d th eory I N TERN ATI ON AL ELECTROTECH N I CAL COM M I SSI ON I CS 33 80 01 I SBN 978-2 -832 2-3236-1 Warn i n g ! M ake s u re th at you obtai n ed th i s pu bl i cati on from an au th ori zed d i stri bu tor ® Reg i stered trad em ark of th e I n tern ati on al El ectrotech n i cal Com m i ssi on Copyright International Electrotechnical Commission – – I E C TR - : © I E C C O N TE N TS F O RE WO RD I N TR O D U C TI O N S co p e N o rm a ti ve re fe re n ce s T e rm s , d e fi n i ti o n s , a n d a b b re vi a ti o n s T e rm s a n d d e fi n i ti o n s Ab b re vi a ti o n s T h e o re ti ca l fra m e wo rk L i m i ta ti o n s a n d o u tl i n e O p ti ca l fi e l d a n d s ta te o f p o l a ri z a ti o n S O P m e a s u re m e n ts , S to ke s ve cto rs , a n d P o i n ca ré s p h e re ro ta ti o n s 1 4 F i rs t o rd e r p o l a ri z a ti o n m o d e d i s p e rs i o n 4 B i re fri n g e n ce ve cto r, co n ca te n a ti o n s , a n d m o d e co u p l i n g 6 T h e s ta ti s ti cs o f P M D a n d s e co n d o rd e r P M D 7 M a n a g i n g ti m e M e a s u re m e n t m e th o d s G e n e l S to ke s p a m e te r e va l u a ti o n 2 E q u i p m e n t s e tu p a n d p ro ce d u re 2 2 J o n e s m a tri x e i g e n a n a l ys i s P o i n ca ré s p h e re a n a l ys i s O n e e n d e d m e a s u re m e n ts b a s e d o n S P E [3 ] P h a s e s h i ft b a s e d m e a s u re m e n t m e th o d s G e n e l M o d u l a ti o n p h a s e s h i ft – F u l l s e a rch 3 M o d u l a ti o n p h a s e s h i ft m e th o d – M u e l l e r s e t a n a l ys i s [4 ] P o l a ri z a ti o n p h a s e s h i ft m e a s u re m e n t m e th o d [5 ] I n te rfe ro m e tri c m e a s u re m e n t m e th o d s 3 G e n e l 3 G e n e l i z e d i n te rfe ro m e tri c m e th o d [6 ] 5 5 Tra d i ti o n a l i n te rfe ro m e tri c m e a s u re m e n t m e th o d F i xe d a n a l ys e r 5 G e n e l 5 E xtre m a co u n ti n g 5 F o u ri e r tra n s fo rm 5 C o s i n e F o u ri e r tra n s fo rm 4 5 5 6 S p e ctra l d i ffe re n ti a ti o n Wa ve l e n g th s ca n n i n g O TD R a n d S O P a n a l ys i s ( WS O S A) m e th o d [7 ] 6 G e n e l 6 C o n ti n u o u s m o d e l L a rg e d i ffe re n ce m o d e l S cra m b l i n g fa cto r d e ri va ti o n L i m i ta ti o n s G e n e l Am p l i fi e d s p o n ta n e o u s e m i s s i o n a n d d e g re e o f p o l a ri z a ti o n P o l a ri z a ti o n d e p e n d e n t l o s s ( o r g a i n ) Copyright International Electrotechnical Commission I E C TR - : © I E C – – C o h e re n ce e ffe cts a n d m u l ti p l e p a th i n te rfe re n ce T e s t l e a d fi b re s 6 Ae ri a l ca b l e s te s ti n g 5 B i b l i o g p h y F i g u re – Two e l e ctri c fi e l d ve cto r p o l a ri z a ti o n s o f th e H E 1 m o d e i n a S M F F i g u re – A ro ta ti o n o n th e P o i n ca ré s p h e re F i g u re – S tro n g m o d e co u p l i n g – F re q u e n cy e vo l u ti o n o f th e S O P F i g u re – Ra n d o m D G D va ri a ti o n vs wa ve l e n g th F i g u re – H i s to g m o f D G D va l u e s fro m F i g u re F i g u re – S P E e q u i p m e n t d i a g m 2 F i g u re – Re l a ti o n s h i p o f o rth o g o n a l o u u t S O P s to th e P D V F i g u re – S to ke s ve cto r ro ta ti o n wi th fre q u e n cy ch a n g e F i g u re – S e tu p fo r m o d u l a ti o n p h a s e s h i ft F i g u re – S e tu p fo r p o l a ri z a ti o n p h a s e s h i ft F i g u re 1 – O u u t S O P re l a ti o n to th e P S P F i g u re – I n te rfe ro m e tri c m e a s u re m e n t s e tu p 3 F i g u re – I n te rfe ro g m re l a ti o n s h i p s F i g u re – M e a n s q u a re e n ve l o p e s F i g u re – F i xe d a n a l ys e r s e tu p F i g u re – F i xe d a n a l ys e r ti o F i g u re – P o we r s p e ctru m 4 F i g u re – F o u ri e r tra n s fo rm 4 F i g u re – WS O S A s e tu p F i g u re – F re q u e n cy g ri d Ta b l e – M a p o f te s t m e th o d s a n d I n te rn a ti o n a l S ta n d a rd s 2 Ta b l e – M u e l l e r S O P s Copyright International Electrotechnical Commission – – I E C TR - : © I E C I N TE RN ATI O N AL E L E C TRO TE C H N I C AL C O M M I S S I O N FI BRE OPTIC COM M U N I CATION SYSTEM DESIGN GU IDES – Part 9: Gui dan ce on pol arization mode di spersi on measurements and theory F O RE WO RD 1) T h e I n t e rn a ti o n a l E l e c tro te ch n i c a l C o m m i s s i o n ( I E C ) i s a wo rl d wi d e o rg a n i z a ti o n fo r s ta n d a rd i z a ti o n c o m p ri s i n g all n a ti o n a l e l e c tro te ch n i c a l c o m m i tte e s (I E C N a ti o n a l C o m m i t te e s ) Th e o b j e ct of IEC is to p ro m o te i n t e rn a ti o n a l c o - o p e ti o n o n a l l q u e s ti o n s c o n c e rn i n g s ta n d a rd i z a ti o n i n th e e l e c tri c a l a n d e l e c tro n i c fi e l d s T o th i s end an d Te ch n i ca l in a d d i ti o n R e p o rts , to o th e r a c ti vi ti e s , P u b l i cl y Ava i l a b l e I E C p u b l i s h e s I n te rn a t i o n a l S p e c i fi c a t i o n s ( P AS ) an d S ta n d a rd s , Gu i d es T e ch n i c a l ( h e re a fte r S p e ci fi ca ti o n s , re fe rre d to as “I EC P u b l i c a ti o n ( s ) ” ) T h e i r p re p a ti o n i s e n tru s te d t o te c h n i c a l co m m i tt e e s ; a n y I E C N a ti o n a l C o m m i tt e e i n t e re s te d in th e s u b j e ct d eal t wi th may p a rti ci p a t e in th i s p re p a to ry wo rk I n t e rn a ti o n a l , g o v e rn m e n ta l and n on - g o v e rn m e n ta l o rg a n i z a t i o n s l i a i s i n g wi th t h e I E C a l s o p a rti c i p a te i n t h i s p re p a ti o n I E C c o l l a b o te s cl o s e l y wi t h th e I n te rn a t i o n a l O rg a n i z a ti o n fo r S t a n d a rd i z a t i o n (I SO) in a cc o rd a n ce wi t h co n d i ti o n s d e te rm i n e d by a g re e m e n t b e twe e n th e two o rg a n i z a ti o n s 2) T h e fo rm a l d e ci s i o n s o r a g re e m e n ts o f I E C o n t e c h n i c a l m a tte rs e xp re s s , a s n e a rl y a s p o s s i b l e , a n i n t e rn a ti o n a l co n s e n s u s of opi ni on on th e re l e v a n t s u b j e c ts s i n ce e a ch te ch n i ca l c o m m i tt e e h as re p re s e n t a ti o n fro m all i n te re s te d I E C N a ti o n a l C o m m i tt e e s 3) I E C P u b l i c a ti o n s h a v e th e fo rm o f re c o m m e n d a ti o n s fo r i n te rn a ti o n a l u s e a n d a re a c ce p te d b y I E C N a ti o n a l C o m m i tte e s i n th a t s e n s e W h i l e a l l re a s o n a b l e e ffo rts a re m a d e to e n s u re t h a t th e te ch n i c a l c o n te n t o f I E C P u b l i c a ti o n s is a cc u te , IEC can n o t be h el d re s p o n s i b l e fo r th e wa y in wh i ch th e y a re used or fo r an y m i s i n te rp re ta ti o n b y a n y e n d u s e r 4) In o rd e r to p ro m o te tra n s p a re n tl y to i n t e rn a ti o n a l th e m a xi m u m u n i fo rm i ty, e xte n t IEC possi bl e N a ti o n a l in th ei r C o m m i tte e s n a ti o n a l an d u n d e rta ke re g i o n a l to appl y I EC p u b l i c a ti o n s P u b l i ca ti o n s An y d i ve rg e n c e b e twe e n a n y I E C P u b l i c a t i o n a n d th e c o rre s p o n d i n g n a ti o n a l o r re g i o n a l p u b l i c a ti o n s h a l l b e cl e a rl y i n d i ca te d i n th e l a tte r 5) I E C i ts e l f d o e s n o t p ro vi d e a n y a tte s t a ti o n o f c o n fo rm i ty I n d e p e n d e n t c e rti fi c a ti o n b o d i e s p ro vi d e co n fo rm i ty a s s e s s m e n t s e rv i c e s a n d , i n s o m e a re a s , a c ce s s to I E C m a rks o f c o n fo rm i ty I E C i s n o t re s p o n s i b l e fo r a n y s e rvi c e s c a rri e d o u t b y i n d e p e n d e n t c e rti fi c a ti o n b o d i e s 6) 7) Al l u s e rs s h o u l d e n s u re th a t th e y h a v e t h e l a t e s t e d i ti o n o f th i s p u b l i ca ti o n N o l i a b i l i ty s h a l l a tt a c h to I E C o r i ts d i re c t o rs , e m p l o ye e s , s e rv a n ts o r a g e n t s i n cl u d i n g i n d i v i d u a l e xp e rts a n d m e m b e rs o f i ts te c h n i c a l c o m m i tt e e s a n d I E C N a ti o n a l C o m m i tte e s fo r a n y p e rs o n a l i n j u ry, p ro p e rty d a m a g e o r o th e r d a m a g e e xp e n s e s o f a n y n a t u re a ri s i n g ou t of th e wh a t s o e ve r, wh e th e r d i re ct o r i n d i re ct, p u b l i ca ti o n , use o f, or re l i a n c e u pon, o r fo r c o s t s th i s IEC (i n cl u d i n g P u b l i c a ti o n or l eg al fe e s ) and any o th e r IEC P u b l i ca ti o n s 8) Att e n t i o n i s d wn to t h e N o rm a ti v e re fe re n c e s ci t e d i n th i s p u b l i c a t i o n U s e o f th e re fe re n c e d p u b l i c a ti o n s i s 9) Att e n ti o n i s d wn t o th e p o s s i b i l i t y th a t s o m e o f th e e l e m e n ts o f th i s I E C P u b l i c a ti o n m a y b e th e s u b j e ct o f i n d i s p e n s a b l e fo r th e c o rre c t a p p l i ca ti o n o f th i s p u b l i c a ti o n p a t e n t ri g h ts I E C s h a l l n o t b e h e l d re s p o n s i b l e fo r i d e n ti fyi n g a n y o r a l l s u ch p a te n t ri g h ts Th e m a i n ta s k o f I E C te ch n i ca l co m m i tte e s i s to p re p a re I n te rn a ti o n a l S ta n d a rd s H o we ve r, a te ch n i ca l co m m i tte e m a y p ro p o s e th e p u b l i ca ti o n o f a te ch n i ca l re p o rt wh e n i t h a s co l l e cte d d a ta o f a d i ffe re n t ki n d fro m th a t wh i ch i s n o rm a l l y p u b l i s h e d a s a n I n te rn a ti o n a l S ta n d a rd , fo r e xa m p l e " s ta te o f th e a rt" I E C TR - , wh i ch i s a Te ch n i ca l Re p o rt, h a s b e e n p re p a re d b y s u b co m m i tte e C : F i b re o p ti c s ys te m s a n d a cti ve d e vi ce s , o f I E C te ch n i ca l co m m i tte e : F i b re o p ti cs Th i s s e co n d e d i ti o n ca n ce l s a n d re p l a ce s th e fi rs t e d i ti o n p u b l i s h e d i n 0 Th i s s e co n d e d i ti o n i n cl u d e s th e fo l l o wi n g s i g n i fi ca n t te ch n i ca l ch a n g e s wi th re s p e ct to th e p re vi o u s e d i ti o n : a) m u ch o f th e th e o ry h a s b e e n co n d e n s e d – fo cu s i n g on l y on e xp l a i n th e te s t m e th o d ; b) s ym b o l s h a ve b e e n re m o ve d , b u t a b b re vi a ti o n s a re re ta i n e d ; Copyright International Electrotechnical Commission co n te n t th a t i s n e e d e d to I E C TR - : © I E C c) – – th e m a te ri a l i n th e C l a u s e h a s b e e n s i g n i fi ca n tl y re d u ce d i n a n e ffo rt to a vo i d re p e a ti n g wh a t i s a l re a d y i n th e a ctu a l I n te rn a ti o n a l S ta n d a rd s I n s te a d , th e fo cu s i s o n e xp l a i n i n g th e I n te rn a ti o n a l S ta n d a rd s ; d) m e a s u re m e n t m e th o d s th a t a re n o t fo u n d i n I n te rn a ti o n a l S ta n d a rd s h a ve b e e n re m o ve d ; e) th e re a re s i g n i fi ca n t co rre cti o n s to th e m o d u l a ti o n ph ase s h i ft m e th o d , p a rti cu l a rl y in re g a rd to th e M u e l l e r s e t te ch n i q u e ; f) th e re a re s i g n i fi ca n t co rre cti o n s to th e p o l a ri za ti o n p h a s e s h i ft m e th o d ; g) th e p ro o f o f th e G I N T Y i n te rfe ro m e tri c m e th o d i s p re s e n te d Th i s p ro o f a l s o e xte n d s to th e F i xe d An a l ys e r C o s i n e tra n s fe r te ch n i q u e ; h) a n o th e r F i xe d An a l ys e r m e th o d i s s u g g e s te d T h i s i s b a s e d o n th e p ro o f o f th e G I N T Y m e th o d a n d i s ca l l e d " s p e ctra l d i ffe re n ti a ti o n m e th o d " ; i) Cl au se h as been re n a m e d " L i m i ta ti o n s " and re fo cu s e d on th e l i m i ta ti o n s o f th e te s t m e th o d s Th i s Te ch n i ca l Re p o rt i s n o t i n te n d e d to b e a n e n g i n e e ri n g m a n u a l ; j) th e a n n e xe s h a ve b e e n re m o ve d ; k) th e b i b l i o g p h y h a s b e e n m u ch re d u ce d i n s i z e ; l) th e i n tro d u cti o n h a s b e e n e xp a n d e d to i n cl u d e s o m e i n fo rm a ti o n o n s ys te m i m p a i rm e n ts Th e te xt o f th i s T e ch n i ca l Re p o rt i s b a s e d o n th e fo l l o wi n g d o cu m e n ts : E n q u i ry d ft R e p o rt o n vo ti n g C /1 /D T R C /1 6 /R V C F u l l i n fo rm a ti o n o n th e vo ti n g fo r th e a p p ro va l o f th i s Te ch n i ca l Re p o rt ca n b e fo u n d i n th e re p o rt o n vo ti n g i n d i ca te d i n th e a b o ve ta b l e Th i s p u b l i ca ti o n h a s b e e n d fte d i n a cco rd a n ce wi th th e I S O /I E C D i re cti ve s , P a rt A list of all p a rts in th e I EC 61 282 communication system design guides , s e ri e s , pu bl i sh ed u n d er th e g e n e l ti tl e Fibre optic ca n b e fo u n d o n th e I E C we b s i te Th e co m m i tte e h a s d e ci d e d th a t th e co n te n ts o f th i s p u b l i ca ti o n wi l l re m a i n u n ch a n g e d u n ti l th e s ta b i l i ty d a te i n d i ca te d on th e I EC we b s i te u nder " h ttp : //we b s to re i e c ch " in th e d a ta re l a te d to th e s p e ci fi c p u b l i ca ti o n At th i s d a te , th e p u b l i ca ti o n wi l l b e • re co n fi rm e d , • wi th d wn , • re p l a ce d b y a re vi s e d e d i ti o n , o r • amended A b i l i n g u a l ve rs i o n o f th i s p u b l i ca ti o n m a y b e i s s u e d a t a l a te r d a te I M P O RT AN T th a t it – Th e c o n ta i n s u n d e rs t a n d i n g c o l o u r p ri n t e r Copyright International Electrotechnical Commission of 'col ou r i n s i d e' c o l o u rs i ts wh i ch c o n te n ts l og o a re U s e rs on th e c o ve r p a g e c o n s i d e re d shou l d to t h e re fo re of th i s be p u bl i cati on u s e fu l p ri n t th i s fo r i n d i c a te s th e d ocu m en t c o rre c t using a – – I E C TR - : © I E C I N TRO D U C TI O N Th i s Te ch n i ca l p ro ce d u re s Re p o rt is co m p l e m e n ta ry (I EC 0793-1 -48, to th e I E C 280-4-4 , I n te rn a ti o n a l S ta n d a rd s I EC 90-1 -1 , d e s cri b i n g PM D I E C 61 90-1 -2 and I E C 0 - - ) a n d o th e r d e s i g n g u i d e s o n P M D ( I E C - a n d I E C - ) , a s we l l a s I TU - T Re co m m e n d a ti o n G Th e s ys te m p o we r p e n a l ty a s s o ci a te d wi th P M D va ri e s d e p e n d i n g o n tra n s m i s s i o n fo rm a t a n d bi t te It al so va ri e s wi th o p ti ca l fre q u e n cy and s ta te o f p o l a ri z a ti o n (SOP) o f th e light s o u rce At th e o u u t o f a l i n k, th e s i g n a l ca n s h i ft fro m a m a xi m u m d e l a y to a m i n i m u m d e l a y a s a re s u l t o f u s i n g d i ffe re n t S O P s a t th e s o u rce Th e d i ffe re n ce i n th e s e d e l a ys i s ca l l e d th e d i ffe re n ti a l g ro u p d e l a y ( D G D ) , wh i ch i s a s s o ci a te d wi th two e xtre m e s o f i n p u t S O P At th e s e e xtre m e s , a s i g n a l i n th e fo rm o f a s i n g l e p u l s e a p p e a rs s h i fte d u p o r d o wn b y h a l f th e D G D , a b o u t a m i d p o i n t, a t th e o u u t At i n te rm e d i a te S O P s , th e s i n g l e p u l s e a p p e a rs a s a we i g h te d to ta l o f two p u l s e s a t th e o u u t, o n e s h i fte d u p b y h a l f th e D G D a n d o n e s h i fte d d o wn b y h a l f th e D G D Th i s we i g h te d to ta l o f two s h i fte d p u l s e s i s wh a t ca u s e s s i g n a l d i s to rti o n Th e s ys te m p o we r p e n a l ty i s p a rtl y d e fi n e d i n te rm s o f a m a xi m u m a l l o we d b i t e rro r te a n d a m i n i m u m re ce i ve d th a t wi l l p ro d u ce p o we r th e I n th e a b s e n ce o f d i s to rti o n , m a xi m u m a l l o we d bi t e rro r th e re i s a m i n i m u m re ce i ve d p o we r te In th e p re s e n ce of d i s to rti o n , th e re ce i ve d p o we r s h o u l d b e i n cre a s e d to p ro d u ce th e m a xi m u m b i t e rro r te Th e m a g n i tu d e o f th e re q u i re d i n cre a s e o f re ce i ve d p o we r i s th e p o we r p e n a l ty o f th e d i s to rti o n Th e te rm P M D i s u s e d to d e s cri b e two d i s ti n ctl y d i ffe re n t i d e a s O n e i d e a i s a s s o ci a te d wi th th e s i g n a l d i s to rti o n i n d u ce d b y tra n s m i s s i o n m e d i a fo r wh i ch th e o u u t S O P va ri e s wi th o p ti ca l fre q u e n cy Th i s i s th e fu n d a m e n ta l s o u rce o f s i g n a l d i s to rti o n Th e o th e r i d e a i s th a t o f a n u m b e r ( va l u e ) a s s o ci a te d wi th th e m e a s u re m e n t o f a s i n g l e - m o d e fi b re tra n s m i s s i o n l i n k o r e l e m e n t o f th a t l i n k T h e re a re s e ve l m e a s u re m e n t m e th o d s wi th d i ffe re n t s tre n g th s an d ca p a b i l i ti e s Th e y a re all based on q u a n ti fyi n g th e m a g n i tu d e of p o s s i b l e va ri a ti o n i n o u u t S O P wi th o p ti ca l fre q u e n cy Th e o b j e cti ve o f th i s Te ch n i ca l Re p o rt i s to e xp l a i n th e co m m o n a l i ty o f th e d i ffe re n t m e th o d s Th e D G D a t th e s o u rce ’ s o p ti ca l fre q u e n cy i s wh a t co n tro l s th e m a xi m u m p e n a l ty a cro s s a l l p o s s i b l e S O P s H o we ve r, an d ti m e s ta ti s ti ca l Th e PM D m e tri c a ve g e a n d i n m o s t l i n ks , va l u e th a t a s s o ci a te d d e s cri b e s ro o t- m e a n th e th e D G D va ri e s n d o m l y a cro s s o p ti ca l fre q u e n cy wi th DGD s q u a re ( RM S ) , m e a s u re m e n ts , d i s tri b u ti o n th a t e xi s t i n and Th e re a re wh i ch two th e l i te tu re a n d is s p e ci fi e d , main in m e tri cs , is a l in ear th e m e a s u re m e n t m e th o d s F o r m o s t s i tu a ti o n s , o n e m e tri c ca n b e ca l cu l a te d fro m th e o th e r u s i n g a co n ve rs i o n fo rm u l a Th e re a s o n fo r th e d u al m e tri cs is an a cci d e n t of h i s to ry If h i s to ry co u l d be co rre cte d , th e R M S d e fi n i ti o n wo u l d b e th e m o s t s u i ta b l e F o r th e n o n - re tu rn a p p ro xi m a te l y to dB z e ro tra n s m i s s i o n m a xi m u m p e n a l ty fo rm a t, DGD B e ca u s e eq u al DGD to va ri e s 0, o f th e n d o m l y, e m e rg e d i n th e s ys te m s ta n d a rd i z a ti o n g ro u p s : ke e p P M D l e s s th a n , b i t p e ri o d a ru l e of yi e l d s th u m b o f th e b i t p e ri o d fo r l e s s th a n d B p e n a l ty T h i s a s s u m e s th a t D G D l a rg e r th a n th re e ti m e s th e P M D , a n d th a t th e s o u rce o u u t S O P p ro d u ce s th e wo rs t ca s e d i s to rti o n , i s n o t ve ry l i ke l y F o r G b i t/s n o n re tu rn to ze ro , th i s ru l e yi e l d s a d esi g n ru l e : ke e p th e link PM D l ess th a n 10 I TU - T G s u p [1 ] h a s m o re i n fo rm a ti o n o n th e re l a ti o n s h i p o f P M D a n d s ys te m p e n a l ti e s _ N u m b e rs i n s q u a re b c ke ts re fe r t o th e B i b l i o g p h y Copyright International Electrotechnical Commission ps I E C TR - : © I E C – – F I B RE O P T I C C O M M U N I C AT I O N P a rt : S YS T E M G u i d a n c e o n p o l a ri z a t i o n DESI G N GU IDES – m o d e d i s p e rs i o n m e a s u re m e n t s a n d t h e o ry Scope Th i s p a rt of I EC 61 282, wh i ch is a Te ch n i ca l Re p o rt, d e s cri b e s e ffe cts and th e o ry of p o l a ri z a ti o n m o d e d i s p e rs i o n ( P M D ) a n d p ro vi d e s g u i d a n ce o n P M D m e a s u re m e n ts N o rm a t i v e re fe re n c e s Th e fo l l o wi n g d o cu m e n ts , i n wh o l e o r i n p a rt, a re n o rm a ti ve l y re fe re n ce d i n th i s d o cu m e n t a n d a re i n d i s p e n s a b l e fo r i ts a p p l i ca ti o n F o r d a te d re fe re n ce s , o n l y th e e d i ti o n c i te d a p p l i e s F o r u n d a te d re fe re n ce s , th e l a te s t e d i ti o n of th e re fe re n ce d d o cu m e n t ( i n cl u d i n g an y a m e n d m e n ts ) a p p l i e s Optical fibres – Part -48: Measurement methods and test procedures – Polarization mode dispersion I E C 60793-1 -48, I E C - - , Fibre optic communication subsystem test procedures – Part 4-4: Cable plants and links – Polarization mode dispersion measurement for installed links I E C - 1 - , Optical amplifier – Test methods – Part 1 -1 : Polarization mode dispersion parameter – Jones matrix eigenanalysis (JME) Optical amplifier – Test methods – Part 1 -1 : Polarization mode dispersion parameter – Poincaré sphere analysis method I E C 61 90-1 -2 , I E C 0 - - , Fibre optic interconnecting devices and passive components – Basic tests and measurement procedures – Part 3-32: Examinations and measurements – Polarization mode dispersion measurement for passive optical components T e rm s , d e fi n i t i o n s , T e rm s a n d an d a b b re v i a t i o n s d e fi n i t i o n s F o r th e p u rp o s e s o f th i s d o cu m e n t, th e fo l l o wi n g te rm s a n d d e fi n i ti o n s a p p l y 1 PMD ph en om en on p o l a ri z a t i o n si gn al m o d e d i s p e rs i o n o f fi b re - o p ti c ph en om en on tra n s m i s s i o n signal i n d u ce d by va ri a ti o n in th e sig n al o u u t s ta te of p o l a ri z a ti o n wi th o p ti ca l fre q u e n cy N o t e to e n try: P M D c a n l i m i t th e b i t te - l e n g t h p ro d u c t o f d i g i ta l s ys te m s PMD va l u e p o l a ri z a t i o n m o d e d i s p e rs i o n va l u e m a g n i tu d e o f p o l a ri z a ti o n m o d e d i s p e rs i o n p h e n o m e n o n a s s o ci a te d wi th a s i n g l e - m o d e fi b re , o p ti ca l co m p o n e n t a n d s u b - s ys te m , o r i n s ta l l e d l i n k Copyright International Electrotechnical Commission – – N o t e to e n try: I E C TR - : © I E C T h e p o l a ri z a ti o n m o d e d i s p e rs i o n v a l u e i s u s u a l l y e xp re s s e d i n p s Ab b re vi a t i o n s CFT co s i n e F o u ri e r tra n s fo rm DGD d i ffe re n ti a l g ro u p d e l a y DOP d e g re e o f p o l a ri z a ti o n EC e xtre m a co u n ti n g FA fi xe d a n a l ys e r FT F o u ri e r tra n s fo rm G I N TY g e n e l i n te rfe ro m e tri c m e th o d JME J o n e s m a tri x e i g e n a n a l ys i s M PS m o d u l a ti o n p h a s e s h i ft O TD R o p ti ca l ti m e d o m a i n re fl e cto m e te r PDL p o l a ri z a ti o n d e p e n d e n t l o s s PDV p o l a ri za ti o n d i s p e rs i o n ve cto r PMD p o l a ri za ti o n m o d e d i s p e rs i o n PPS p o l a ri za ti o n p h a s e s h i ft PSA P o i n ca ré s p h e re a n a l ys i s PSP p ri n ci p a l s ta te o f p o l a ri z a ti o n SMF s i n g l e - m o d e fi b re SOP s ta te o f p o l a ri z a ti o n SPE S to ke s p a m e te r e va l u a ti o n TI N TY tra d i ti o n a l i n te rfe ro m e tri c m e th o d WS O S A wa ve l e n g th s ca n n i n g O TD R a n d S O P a n a l ys i s m e th o d T h e o re t i c a l fra m e wo rk Li m i tati o n s a n d o u tl i n e Th e th e o ry p re s e n te d i n C l a u s e d o e s n o t i n cl u d e th e e ffe cts o f p o l a ri z a ti o n d e p e n d e n t l o s s o r g a i n , o r n o n l i n e a r e ffe cts S e e fo r i n fo rm a ti o n o n p o l a ri za ti o n d e p e n d e n t l o s s Th e o u tl i n e fo r C l a u s e i s • o p ti ca l fi e l d a n d s ta te o f p o l a ri z a ti o n ; • m e a s u re m e n t o f S O P , S to ke s ve cto r, a n d ro ta ti o n ; • fi rs t o rd e r p o l a ri z a ti o n m o d e d i s p e rs i o n ; • b i re fri n g e n ce ve cto r, co n ca te n a ti o n s , a n d m o d e co u p l i n g ; • th e s ta ti s ti cs o f P M D a n d s e co n d o rd e r P M D O p ti c a l fi e l d an d s t a t e o f p o l a ri z a t i o n Th i s s u b cl a u s e i s i n te n d e d to s h o w th e l i n ka g e b e twe e n th e p ro p a g a ti o n o f a n o p ti ca l fi e l d i n a si n g l e-mod e i n fo rm a ti o n is fi b re (SM F) fu n d a m e n ta l and to th e th e tra n s m i s s i o n PM D sign al ph en om en a s ta te b e ca u s e of p o l a ri za ti o n va ri a ti o n in (SOP) o u u t SOP Th i s wi th o p ti ca l fre q u e n cy i s th e d i s to rti o n i n d u ci n g m e ch a n i s m Th e s o l u ti o n o f th e wa ve e q u a ti o n h a s d e g e n e te d e i g e n va l u e s T h i s m e a n s th a t e ve n th e fu n d a m e n ta l s o l u ti o n is d e g e n e te d m o n o ch ro m a ti c l i g h t s o u rce Copyright International Electrotechnical Commission In A SMF p a rti cu l a r, th e s u p p o rts a p a i r o f p o l a ri z a ti o n l o we s t o rd e r m o d e , n a m e l y th e mod es fo r a fu n d a m e n ta l I E C TR - : © I E C I n te n s i t y (au ) – 44 – 460 480 500 520 540 560 W a v e l e n g th 580 600 620 640 (nm ) IEC I n te n s i t y (au ) F i g u re – P o w e r s p e c t ru m Del ay 10 (ps) IEC F i g u re – F o u ri e r t n s fo rm F i g u re s 17 an d 18 a re a ca s e of s tro n g m od e co u p l i n g an d high P( τ) I E C - - ca l l s fo r ca l cu l a ti n g a we i g h te d RM S u s i n g th e PM D For th i s ca s e , o u u t fu n cti o n , a vo i d i n g th e re g i o n n e a r z e ro a n d th e re g i o n i n th e n o i s e , th e n ta ke s th e s q u a re ro o t a n d re p o rts i t a s th e l i n e a r a ve g e – b u t wi th o u t th e For th e ca s e of neg l i g i ble m od e π m u l ti p l i e r co u p l i n g , I EC 61 82 -4-4 tre a ts th e p o we r va l u e s as a h i s to g m o f D G D va l u e s a n d a p o we r we i g h te d a ve g e i s re p o rte d a s th e l i n e a r a ve g e Wh i l e th i s i s n o t e xa ctl y co rre ct, i t m a y b e a d e q u a te fo r s i m p l e b i re fri n g e n t e l e m e n ts 5 Th i s C o s i n e F o u ri e r t n s fo rm m a th e m a ti ca l d e ve l o p m e n t is based on th e G I N TY m e th o d th a t h as been p ro ve n to p ro d u ce th e p o we r- s q u a re d we i g h te d P M D R M S I t i s fo u n d i n I E C - - b u t n o t i n a n y o f th e o th e r I n te rn a ti o n a l S ta n d a rd s Th e s e ca l cu l a ti o n s a re m o s t a p p ro p ri a te fo r h i g h P M D , i n wh i ch th e e xtre m a ca n b e q u i te d e n s e , a s i n F i g u re F o r l o w to m o d e te P M D , wh e n th e ti o p l o t l o o ks s i m i l a r to F i g u re , th e s p e ctra l d i ffe re n ti a ti o n te ch n i q u e ( s e e ) m i g h t b e b e tte r L i ke th e F T te ch n i q u e , th e d a ta m u s t b e a va i l a b l e i n e q u a l fre q u e n cy i n cre m e n ts T h e wi n d o wi n g fu n cti o n , ( PA + PB ) W( ν ) , i s a p p l i e d to th e ti o o f p o we r d i ffe re n ce ( PA - PB ) to p o we r to ta l I t s h o u l d b e cl a ri fi e d th a t wh e n a b ro a d b a n d s o u rce i s u s e d , th e wi n d o wi n g fu n cti o n ca n b e s e t to th e p o we r to ta l I n th i s ca s e , th e re s u l t wi l l b e e q u i va l e n t to th e G I N T Y Th e ca l cu l a te d i n te rfe ro g m s co s i n e tra n s fo rm s o n W( ν ) an d fo r a g i ve n W( ν ) R ( ν ) , I /O - S O P , E0 i ( τ ) re s p e cti ve l y, wh e re an d R Exi ( τ) , a re p ro d u ce d b y fa s t i s th e ti o o f p o we r d i ffe re n ce o ve r p o we r to ta l F o l l o wi n g th i s , th e ca l cu l a ti o n s fo r G I N T Y a re co m p l e te d to p ro d u ce s p e ctra l p o we r- s q u a re d we i g h te d P M D R M S Copyright International Electrotechnical Commission I E C TR - : © I E C Doin g th e d e s cri b e d fa s t in co s i n e F o u ri e r I E C 60 793 -1 -48 – 45 – tra n s fo rm i n cl u d e s Th e re a s o n fre q u e n cy s h i fti n g fo r fre q u e n cy s h i fti n g th a t is n ot ve ry we l l i s th a t th e m a th e m a ti cs o f G I N T Y i n cl u d e fre q u e n cy i n te g l s fro m Th e a rra y p u t i n to th e fa s t co s i n e tra n s fo rm a l g o ri th m m u s t co n ta i n wi l l a l m o s t a l wa ys be l a rg e r th a n th e a ctu a l n k = +1 n u m b e r o f m e a s u re m e n ts e l e m e n ts Th i s F re q u e n cy s h i fti n g re s u l ts i n p l a ci n g th e m e a s u re m e n ts i n to th e i n p u t a rra y a n d m a ki n g th e o th e r e l e m e n ts e q u a l to z e ro Th e fre q u e n cy s h i fti n g ca l cu l a ti o n s wi l l i n d i ca te wh e re , i n th e a rra y, th e d a ta s h o u l d b e p l a ce d D e fi n e ∆ ν a s th e fre q u e n cy i n cre m e n t, e g , i n TH z T h e N yq u i s t fre q u e n cy, E q u a ti o n ( ) ν Fi nd m NYQ i s d e fi n e d a s n ∆ν = (1 08) , a n i n te g e r, s u ch th a t: m − )ν NYQ ≤ ν ( wh e re ν NYQ , νm i n an d νm a x < ν m ax ≤ mν NYQ (1 09) d e fi n e th e m e a s u re d fre q u e n cy b o u n d a ri e s T h e l o we r b o u n d a ry fo r th e N yq u i s t i n te rva l d e fi n e d i n E q u a ti o n ( ) , th e m i n i m u m m e a s u re d fre q u e n cy, a n d th e fre q u e n cy i n cre m e n t d e fi n e th e l o ca ti o n wi th i n th e i n p u t a rra y fo r th e fi rs t m e a s u re d va l u e Afte r th e fa s t co s i n e tra n s fo rm i s d o n e , th e fi rs t e l e m e n t o f th e o u u t a rra y co rre s p o n d s to ti m e ze ro an d th e i n cre a s i n g e l e m e n ts co rre s p o n d to i n cre a s i n g ti m e , wi th i n cre m e n t, t ∆ , g i ve n a s : t ∆ = 2ν (1 0) NYQ B e ca u s e th e co s i n e tra n s fo rm i s e ve n , th e va l u e s a t n e g a ti ve ti m e s a re e q u a l to th e va l u e s o f p o s i ti ve ti m e s Wh e n I E C 60793-1 -4 is re vi s e d , it is re co m m e n d e d th a t th e a b o ve m a te ri a l re p l a ce th e re g i o n a ro u n d E q u a ti o n s ( A ) a n d ( A ) o f I E C - - 5 Th i s S p e c t l d i ffe re n t i a t i o n m a th e m a ti ca l s i m u l a ti n g d e ve l o p m e n t i n te rfe ro g m s , is E q u a ti o n also based (1 02) is on u sed th e m a th e m a ti cs d i re ctl y Th i s of wi l l G I N TY be b e tte r I n s te a d of s u i te d to s i tu a ti o n s wh e re th e re a re a m o d e te n u m b e r o f e xtre m a , b u t wi l l g e n e l l y n e e d s o m e fi tti n g o f th e d a ta I n th i s s u b cl a u s e , o p ti ca l fre q u e n cy i s e xp re s s e d a s a n g u l a r o p ti ca l fre q u e n c y , ω, b e ca u s e th e d e ri va ti ve s a n d i n te g l s fo u n d i n E q u a ti o n ( 9 ) a re wi th re g a rd to th i s p a m e te r Ag a i n , th e re i s a wi n d o wi n g fu n cti o n Wω ( ) th a t i s a p p l i e d to th e ti o o f p o we r d i ffe re n ce s to p o we r to ta l F o r th e b ro a d b a n d s o u rce , th e wi n d o wi n g fu n cti o n ca n b e th e to ta l p o we r F o r th e tu n e a b l e l aser ca s e , a wi n d o wi n g fu n c t i o n is s ti l l n eed ed or th e σ p a m e te r wi l l d i s a p p e a r Th e wi n d o wi n g fu n cti o n re fl e cts th e fa ct th a t th e fre q u e n cy e xte n t i s fi n i te Copyright International Electrotechnical Commission – 46 – F o r a g i ve n I /O - S O P , Siω ( Sxi ω ) an d ( ) a re g i ve n I E C TR - : © I E C as Wω ( ) and Wω R ω ( g e n e l l y b e fi tte d to a vo i d n o i s e a n d to yi e l d th e d e ri va ti ve fu n cti o n s , ) ( ) Th e d a ta s h o u l d dS i (ω ) dω and dS xi (ω ) dω C a l cu l a te th e p o we r s q u a re d a ve g e s a s : S (ω ) = S (ω ) S N∑ i 0ω N∑ =    dS i (ω )  S (ω ) S (ω ) S x dω  x N ∑ xi 2 = 2 ω = N∑    dS xi (ω )  dω  (1 1 ) T h e s e a ve g e s th e n n e e d to b e i n te g te d wi th re s p e ct to fre q u e n cy C a l cu l a te th e RM S e xp re s s i o n s a s E q u a ti o n ( 1 ) : ∫ S0ω (ω )dω Th e PM D rm s = ∫ S0 (ω )dω ∫ S xω (ω )dω 2 σ0 σ x (ω ) = (1 2) ∫ S x (ω )dω i s n o w g i ve n a s E q u a ti o n ( ) Wa ve l e n g th s c a n n i n g O TD R a n d S O P a n a l ys i s ( WS O S A) m e th o d [7 ] G e n e l T h i s m e th o d a p p e a rs i n I E C - - Th e m e th o d u s e s e q u a ti o n s th a t a re s i m i l a r to th o s e i n th e o th e r te s t m e th o d s a n d i n th e th e o ry; h o we ve r, th e n o ta ti o n o f I E C - - a n d i n [6 ] wi l l b e u s e d fo r th i s s u b cl a u s e F i g u re s h o ws th e s e tu p TL Ci r P Pol Dx PC DUT M Dy O /E O /E A Py Px IEC Ke y TL p u l s e d tu n e a b l e l i g h t s o u rc e P p o l a ri z e r Ci r c i rc u l a to r Pol p o l a ri z a ti o n b e a m s p l i tte r PC I /O - S O P s c m b l e r M o p e n c o n n e c to r o r o p ti c a l re fl e c to r D x, D y d e te c ti o n s ys t e m A c o m p u te r / a n a l yz e r F i g u re – WS O S A s e tu p Copyright International Electrotechnical Commission I E C TR - : © I E C Th e p u l s e d – 47 – tu n e a b l e l i g h t s o u rce i s s yn ch ro n i z e d l i g h t re fl e cte d fro m th e e n d o f th e D U T wi th th e d e te cti o n Th i s a vo i d s th e p ro b l e m s ys te m to ca p tu re th e o f ca p tu ri n g d e p o l a ri ze d Ra yl e i g h s ca tte ri n g l i g h t, a n i s s u e a s s o ci a te d wi th S o m e o f th e s a m e m a th o f wi l l b e i m p o rta n t fo r th i s m e th o d b e ca u s e th e re tu rn p a th P M D ( RM S ) i s ca l cu l a te d fi rs t, a n d th e fo rwa rd p a th P M D i s th e n ca l cu l a te d u s i n g fo rm u l a s s i m i l a r to th o s e i n F o r a p a rti cu l a r fre q u e n cy, th e p u l s e s a re typ i ca l l y a ve g e d fo r s o m e ti m e to re d u ce n o i s e Th e e ffe ct o f th i s a ve g i n g i s i n te cti ve wi th th e l e n g th o f th e p u l s e Th e o p ti ca l fre q u e n ci e s fo r wh i ch re fl e cte d p o we r, b o th Px an d Py , i s m e a s u re d fo rm a n a rra y o f fre q u e n cy p a i rs , a s s h o wn i n F i g u re Th e p o l a ri z a ti o n s cra m b l e r s e tti n g s a re th e s a m e fo r b o th fre q u e n ci e s o f a p a i r, b u t a re n d o m i z e d fro m o n e p a i r to th e n e xt F o r e a ch p a i r, a s e co n d , i n d e p e n d e n t, p a i r o f p o we r m e a s u re m e n ts i s m e a s u re d u sin g th e s a m e s cra m b l e r s e tti n g s a s th e fi rs t p a i r o f p o we r m e a s u re m e n ts Th i s s e co n d p a i r o f p o we r m e a s u re m e n ts , m a rke d wi th a p ri m e , i s u s e d to m i n i m i z e th e e ffe cts o f m e a s u re m e n t n o i s e F re q u e n c y ( I O /S O P ) k = ( I O /S O P ) k = ( I O /S O P ) k = … k k =1 k N = =2 ν N - δ ν /2 ν N + δ ν /2 ν - δ ν /2 ν + δ ν /2 ν - δ ν /2 ν + δ ν /2 IEC Fi g u re 20 – Freq u en cy g rid J u s t a s a l l th e fre q u e n cy d o m a i n m e th o d s , th e ch a n g e i n o u u t S O P wi th fre q u e n cy i s th e b a s i s o f th e m e a s u re m e n t Th e o ve l l n g e i s typ i ca l l y a ro u n d , TH z wi th th e n u m b e r o f fre q u e n cy m i d p o i n ts a ro u n d 0 I n th e o ry, a n y va l u e o f th e s o u rce p u l s e wi d th m a y b e u s e d , fo r i n s ta n ce fro m n s to µ s H o we ve r, i n p cti ce , to o s h o rt p u l s e s wi l l te s t o n l y o ve r s h o rte r l i n k l e n g th s , u n l e s s th e l i n k i s p ro p o rti o n a l l y s h o rt; to o l on g pu l ses m a y m i x wi th s e ve l re fl e cti o n s ; at th e l i m i t, th i s is e xa ctl y th e ca s e wi th co n ti n u o u s wa ve l i g h t s o u rce s Th e th e o ry i s b a s e d o n th e ch a cte ri s ti cs o f th e n o rm a l i z e d tra n s m i s s i o n va l u e s , T , u si n g fo rm u l a s ve ry s i m i l a r to E q u a ti o n s ( ) a n d ( ) I n E q u a ti o n ( 1 ) , th e tra n s m i s s i o n va l u e i s d epen d en t on th e fre q u e n cy p a i r, co n s e q u e n tl y th e I O-S OP s ta te , an d th e p a rti cu l a r fre q u e n cy o f th e p a i r T (ω ) =   (1 + s (ω ) ⋅ sa ) = s (1 + (ω )) =   +   Px (ω ) − Py (ω )  Px (ω ) =  Px (ω ) + Py ( )  Px (ω ) + Py (ω ) wh e re  s (ω )  sa s(ω) P x (ω)an d i s th e o u u t S to ke s ve cto r a t o n e o f th e fre q u e n ci e s o f a p a i r; i s n d o m o ri e n ta ti o n o f th e a n a l ys e r fo r th e fre q u e n cy p a i r; P i s th e d o t p ro d u ct; y (ω) Copyright International Electrotechnical Commission a re th e m e a s u re d p o we rs (1 3) – For e a ch same fre q u e n c y ti m e s q u a re d of a v e g i n g d i ffe re n c e e a ch and p a i r, pu l se ca l cu l a ti o n a s e co n d l e n g th wh i ch is ∆ W h e re th e ∆ T p a i r Th e n oi se E q u a ti o n ∆ an d Th e T ’ a re th e e xp e c te d re d u c t i o n (1 4) e xp a n d e d , ca n th e co m e s be p a rt s o p e t o r of it wi th u sed N∑ k = th i s by I EC t n s m i s s i o n is b e twe e n as – e x p re s s e d in abou t c o n s i d e re d Th i s T2 d i ffe r e n c e s va l u e 48 to as i n d epen d en t ’, th e is © m e a s u re d n oise e ffe c t s I EC 201 u sing in th e th e mean (1 4) (∆Tk ∗ ∆Tk ) ' (1 4) t n s m i s s i o n ca s e t ru e 61 282-9: 201 T va l u e , re d u c e E q u a ti o n is o ve r c o n s i d e ri n g th e TR va l u e n oi se th a t plu s t e rm s va l u e s b o th th e a fo r I O /S O P two n oise th e and t e rm s t e rm d i sappear two in on Wh e n th e fre q u e n c i e s c e n t l th e th e sen se of fr e q u e n c y ri g h t of p ro d u c t of is e xp e c te d va l u e Th e n e xt s u b cl a u s e s • co n ti n u o u s • l a rg e • s c m b l i n g Th e d i ffe r e n c e a re d i ffe r e n c e o p ti c a l 6 I n is wi l l be is n eed ed n eed ed co n s ta n ts in t h re e p a rts : d e ri v a t i o n m od el in [7 ] fo r wi l l ω , be th a t wh i l e a re u n d e rs t a n d s o m e wh a t by I EC w ri t t e n to th e l a rg e d i ffe re n c e m od el Th e s c m b l i n g b o th t i o n a l i z e d fre q u e n c y , to [7 ] m od el ; fa c t o r d e ri v a t i o n T h e re e l a b o te mod el ; co n ti n u o u s fa c t o r wi l l in d i ffe re n t c o n s i d e ri n g 80-4-4 te rm s of is th a t w ri t t e n ang u l ar fro m [6 ] in o p ti ca l th o s e w o rk s t e rm s in I EC 80-4-4 e xc l u s i ve l y of in fre q u e n c y , te rm s ν , Th e of w h e re m n angu lar ω = π ν fr e q u e n c y C o n ti n u o u s m o d e l th e limit δω as - > 0, and u si n g E q u a ti o n s (1 3) an d (1 8), th e fo l l o w i n g e q u a ti o n ca n be d e ri v e d : ∆ T=    ds δω = s ⋅ (Ω × s )δω a RT dω  (1 5) w h e re  Ω  RT =  DGD RT u u S i n ce th e DGD is is th e ro u n d t ri p P D V; is th e ro u n d t ri p PSP i n d epen d en t ∆ T of th e = F ro m 4, th e t e rm i n vo l vi n g th e   t e rm s ,  [sa ⋅ (u × s )] S to ke s Copyright International Electrotechnical Commission o th e r   a l l o ws [sa ⋅ (u × s )] w ri t i n g DGDRT IO − SOP v e c t o rs  th i s ca n be IO − SOP = w w ri t t e n δω as E q u a ti o n (1 6) (1 6) E q u a ti o n (1 7) (1 7) I E C TR - : © I E C – 49 – C o n s e q u e n tl y, th e ro u n d tri p P M D ca n b e wri tte n a s E q u a ti o n ( 1 ) PMDRT DGDRT = α dT ∆ = w δω T2 (1 8) wh e re α dT = N O TE I n I E C - - , th e re i s a c o n s ta n t, α R S = s q rt( /4 ) , δν th e r th a n to th e fa c t th a t i n I E C - - , t h e d i vi s i o n i s b y t h a t i s th e e q u i v a l e n t o f δω by α dT T h e fa c to r o f i s d u e F ro m E q u a ti o n ( ) , th e fo rwa rd P M D ( RM S ) i s re l a te d to th e re tu rn tri p P M D a s : PMDF2 − RMS = PMDRT (1 9) U s i n g th e re l a ti o n s h i p b e twe e n RM S a n d l i n e a r a ve g e , E q u a ti o n s ( ) a n d ( ) , th e fo rwa rd P M D l i n e a r a ve g e ca n b e wri tte n a s : PMDF2 − AVG N O TE E q u a ti o n s ( 1 ) a n d (1 20) d epen d on = PMDRT π t h e a s s u m p ti o n (1 20) o f n d o m m o d e co u p l i n g an d th a t th e fo rwa rd D G D fo l l o ws a M a xwe l l d i s tri b u ti o n wh i l e th e b a c k wa rd D G D fo l l o ws a R a yl e i g h d i s t ri b u ti o n T h e y a re va l i d i n th e s e n s e o f e xp e c te d v a l u e N O TE E q u a ti o n s (1 9) an d (1 20) a re a pp l i cab l e t o b o th th e c o n ti n u o u s model and th e fi n i te l a s e r l i n e wi d th ca l cu l a ti o n s o f L a rg e d i ffe re n c e m o d e l Th i s cl a u s e l e a d s to th e a ctu a l fo rm u l a fo r P M D RT u sed i n I E C 80-4-4 I t i s based on an a u to co rre l a ti o n fu n cti o n th a t i s d e fi n e d a s E q u a ti o n ( ) fo r a g e n e l i z e d n d o m p ro ce s s , y( ω ) I t i s d e fi n e d s o th a t R y( ) = R y (ω Th e e xp re s s i o n fo r th e mean − ω1 ) = s q u a re σ   y y (ω1 ) y (ω ) d i ffe re n ce wi th a − y fi n i te    (1 21 ) fre q u e n cy d i ffe re n ce ca n be wri tte n a s E q u a ti o n ( 2 ) ∆ Th e Th e ω + and ω co m m o n _ T2 = (s (ω + ) − s (ω − )) = s2 −2 s (ω + )s (ω − ) (1 22) s ym b o l s re p re s e n t th e u p p e r a n d l o we r fre q u e n ci e s o f a p a i r te rm fo r s (ω + )2 an d s (ω − )2 is u sed b e ca u s e th e s e e xp e cte d va l u e s a re i n d e p e n d e n t o f fre q u e n cy A n ew va ri a b l e , x = s-, re wri tte n a s E q u a ti o n ( ) Copyright International Electrotechnical Commission wh i ch has z e ro mean , is i n tro d u ce d so E q u a ti o n (1 22) ca n be – 50 – ∆ Th e te rm , d e ri ve d T ∆ Th e =σ σ s s s = p o l a ri z a ti o n s, x(ω )x(ω + x −σ σ ) − =σ x s [1 − R x (δω )] (1 23) x wh i ch i s th e s a m e a s th e va ri a n ce o f s cra m b l i n g (see 4) and is u sed to I t h a s a va l u e d e fi n e a co n s ta n t, / = / 45 , u s e d i n I E C - - a u to co rre l a ti o n fu n cti o n is th e fre q u e n cy n g e g o e s to i n fi n i ty wh i ch s − , i s th e va ri a n ce o f fro m T I E C TR - : © I E C th e G I N TY m e th o d based For R ( δω ) s h a p e d , a n d h e n ce , s o i s Th e a u to co rre l a ti o n is s q u a re o f th e F o u ri e r tra n s fo rm of × i n th e l imit as th e Th i s i s th e s a m e a s th e m e a n - s q u a re i n te rfe ro g m u p o n n d o m l y m od e co u p l e d fi b re s , th i s is ( C δω G au ssi an x fu n cti o n i s assu med to b e G a u s s i a n , o f th e fo rm exp − 2 ), an d is e xp a n d e d i n T a yl o r s e ri e s to th e s e co n d d e ri va ti ve R z (δω ) ≈ + R x′ (0 )δω + Combi n i n g E q u a ti o n (1 24) an d E q u a ti o n yi e l d th e s a m e re s u l t a s E q u a ti o n ( 1 ) R x′ ′ (0 )δω (1 23), fo r and =1 − C δω co n s i d e ri n g δω, smal l 2 (1 24) th a t th i s co m b i n a ti o n C yi e l d s a va l u e fo r sh al l Th i s i s s h o wn i n E q u a ti o n ( ) ∆ Th e e xp re s s i o n fo r th e mean TC PMDRTδω 2 δω = α s q u a re (1 25) dT d i ffe re n ce u sing th i s e xp re s s i o n of R ( δω ) is x E q u a ti o n ( ) ∆ Re a rra n g i n g E q u a ti o n (1 26) T = ∆ l ead s T    − exp  −      to     E q u a ti o n PMDRTδω   α dT ∆T  (G 2) I E C 61 280-4-4: 2006 (1 26)    of   wh e n th e d i ffe re n ce i n fre q u e n cy u n i ts i s ta ke n i n to a cco u n t Th i s S c m b l i n g fa c t o r d e ri va t i o n s u b cl a u s e wi l l be u sed to e s ta b l i s h th e l i n ka g e s u sed in an d It is a re s ta te m e n t o f Ap p e n d i x A o f [6 ]  I n p a rti cu l a r, th e S to ke s ve cto rs of th e a n a l y s e r, an d o u u t S to ke s   s In , s a , an d v e c t o rs fo r s re p re s e n t th e i n p u t S to ke s ve cto r, a l i g n m e n t ω, re s p e c t i v e l y ( th e d e p e n d e n ce o f th e o u u t S to ke s ve cto r o n fre q u e n cy i s d ro p p e d fo r s i m p l i ci ty) Th e s e a re re l a te d to th e J o n e s ve cto rs wh i ch a re i d e n ti fi e d wi th th e s a m e s u b s cri p ts Th e d o t p ro d u ct, n o ta ti o n ti m e s u sed s, i s g i ve n e l s e wh e re j ( a co m p l e x s ca l a r) , Copyright International Electrotechnical Commission a s E q u a ti o n ( ) , Th e s e co n d u s i n g b o th b cke t n o ta ti o n a n d e xp re s s i o n re a d s : two ti m e s m u l ti p l i e d b y i ts co n j u g a te , m i n u s o n e ja co n j u g a te th e m a tri x tra n s p o s e I E C TR - : © I E C s = B e ca u s e th e s a m e n d o m – 51 –   sa ⋅ s   ja j = p o l a ri za ti o n     * ↑  j  ∗   ja j   ↑ − =  ja  is u sed in    (1 27) −1 th e fo rwa rd and re ve rs e d i re cti o n s , th e fo l l o wi n g re l a ti o n s h i p i s fo u n d fo r th e i n p u t a n d a n a l ys e r S O P s :  sa 0 s In = = [s In1 s In − T s In ]  ja ⇔ =  * j In (1 28) N O TE T h e * i n t h e ri g h tm o s t e xp re s s i o n i n d i c a te s c o n j u g a t i o n o n l y N O TE T h e s u p e rs c ri p t i n d i ca te s th e ve cto r wi t h t h e t h i rd e l e m e n t ch a n g e d i n s i g n E q u a ti o n s ( ) a n d ( ) l e a d to a n o th e r e xp re s s i o n fo r i n p u t to o u u t m a tri x, TIO s th a t i s g i ve n i n te rm s o f th e J o n e s Th e s u b s cri p t i s h e re m e a n t to d i s ti n g u i s h th e J o n e s m a tri x fro m th e tra n s m i tte d p o we r s T h e co m b i n e d m u l ti p l i ca ti o n o f = T, T   * T j In TIO TIO j In tra n s p o s e , −1 (1 29) a n d i n p u t J o n e s ve cto r yi e l d s th e re fl e cte d o u u t J o n e s ve cto r Th e o u u t J ones ve cto r a t th e en d o f th e fi b re is fo rwa rd I t ca n a l s o b e wri tte n a s th e m u l ti p l i ca ti o n o f d e s i g n a te d TI O as  jf , " f" wi th i n d i ca ti n g a n d th e i n p u t J o n e s ve cto r a s th e l e ft o f E q u a ti o n ( ) Th e i m p l i ca ti o n o f co n j u g a ti n g i s th e ri g h t e xp re s s i o n  jf =  ↑ j In TIO ⇒  * T j In TIO =  * jf (1 30) S u b s ti tu ti n g i n to E q u a ti o n ( ) re s u l ts i n E q u a ti o n ( ) , th e re l a ti o n s h i p o f s wi th th e o u u t fo rwa rd S to ke s ve cto r a t th e e n d o f th e fi b re : s T h e va l u e o f s ca n = th e re fo re b e g i ve n   * jf jf in −1 = 0  sf ⋅ sf (1 31 ) te rm s o f th e th i rd e l e m e n t o f th e o u u t S to ke s ve cto r, wi th a n i m p l i ca ti o n fo r th e fre q u e n cy d e ri va ti ve a s s h o wn i n E q u a ti o n ( ) s Th e φ1 , = − 2s f3 ⇒ s′ ( = −4 s f s ′f = −4 s f − Ω s f1 + Ω s f ) (1 32) va l u e s a re th e fi rs t two e l e m e n ts o f th e fo rwa rd P D V a t th e e n d o f th e fi b re Th e te rm th a t i n cl u d e s th e s e va l u e s i s d e ri ve d fro m E q u a ti o n ( ) F ro m th e d e ri va ti ve p a rt of E q u a ti o n (1 32 ), th e I O -S OP e xp e cte d va l u e of th e s q u a re d d e ri va ti ve i s E q u a ti o n ( 3 ) s′ IO − SOP 16 Copyright International Electrotechnical Commission = Ω1 2 s f s f3 IO − SOP + Ω2 2 s f1 s f IO − SOP − 2Ω1 Ω 2 s f1 s f s f IO − SOP (1 33) – 52 – I E C TR - : © I E C S i n ce th e i n p u t S to ke s ve cto r i s u n i fo rm l y d i s tri b u te d , s o i s th e o u u t fo rwa rd S to ke s ve cto r, a n d th e p ro p e rti e s o f th e a b o ve e xp e cte d va l u e s a re s o l e l y d e te rm i n e d b y th e p ro p e rti e s o f th e s cra m b l e r A u n i fo rm d i s tri b u ti o n o f th e i n p u t S to ke s ve cto r i s e q u i va l e n t to th e fo l l o wi n g , wh e re th e p a m e te r, a, is u n i fo rm l y d i s tri b u te d ±1 b e twe e n and th e p a m e te r, Φ , is u n i fo rm l y d i s tri b u te d b e twe e n ± π  s In N O TE = b si n φ a ]T b = [b cos φ f( s ) = T h e p d f o f th e e l e m e n ts o f th e i n p u t S t o k e s v e c to r i s − s [8 (1 - )] a /2 (1 34) F ro m th e s e p ro p e rti e s , th e fo l l o wi n g e xp e cte d va l u e re l a ti o n s h i p s ca n b e d e m o n s tra te d : si s j = si s j = 0, si s j F ro m th e re l a ti o n s h i p s in E q u a ti o n s 0, = (1 35) i≠ j i= j (1 35) i≠ j (1 36) / 3, i≠ j / 5, i = j / 5, to (1 37) (1 37) an d E q u a ti o n (1 33), E q u a ti o n (1 38) e m e rg e s s′ F ro m E q u a ti o n s q u a re o f D G D (45), RT th e e xp re s s i o n Re ca l l i n g th a t T’ = IO − SOP 15 [4 (Ω o f E q u a ti o n = s ’ /2 , +Ω (1 38) 2 )] (1 38) wi th i n th e b cke ts is eq u al to th e yi e l d s E q u a ti o n ( ) , wh i ch i s o n e wa y to wri te E q u a ti o n ( 1 ) H e re , th e e xp e cte d va l u e i s o ve r b o th I O - S O P a n d fre q u e n cy: T′ F ro m th e l e ftm o s t e xp re s s i o n in ∆ = l i m δω → T δω E q u a ti o n = (1 32), 15 th e PMD RT e xp e cte d (1 39) va l u e an d s q u a re of th e e xp e cte d va l u e a re g i ve n i n E q u a ti o n ( ) s Th e va ri a n ce o f = s a n d ∆T s = − sf + sf = − / + / = /1 (1 40) a re th e re fo re g i ve n a s E q u a ti o n ( ) σ s = s2 − s = Th i s co n cl u d e s th e d e ri va ti o n o f a n d Copyright International Electrotechnical Commission 16 45 T2 = ⇒ ∆ 45 (1 41 ) I E C TR - : © I E C 6 – 53 – L i m i ta ti o n s G e n e l I t i s th e i n te n t o f C l a u s e to h i g h l i g h t s o m e s p e ci fi c l i m i ta ti o n s to th e te s t m e th o d s Am p l i fi e d s p o n ta n e o u s e m i s s i o n a n d d e g re e o f p o l a ri z a ti o n Am p l i fi e d s p o n ta n e o u s e m i s s i o n i s ca u s e d b y o p ti ca l a m p l i fi ca ti o n a n d re s u l ts i n o p ti ca l n o i s e co ve ri n g a s i g n i fi ca n t s p e ctru m Th e n oi se l ead s to d e p o l a ri z a ti o n th a t ca n d e g d e th e q u a l i ty o f P M D m e a s u re m e n ts T h e s ta n d a rd s ca l l fo r a d e g re e o f p o l a ri za ti o n , wh i ch s h a l l b e m e a s u re d a t th e o u u t, o f % o r m o re , b u t th e n s ta te th a t d e g re e o f p o l a ri z a ti o n a s l o w a s % co u l d b e m e a s u re d , b u t wi th a l o s s o f a ccu cy M e th o d s to m i ti g a te d e p o l a ri z a ti o n d u e to o p ti ca l a m p l i fi e rs i n cl u d e : • C o n tro l o f O A s a tu ti o n co n d i ti o n s Th i s te ch n i q u e ca n be u sed m o s t e ffe cti ve l y wi th tu n e a b l e l a s e r s o u rce s , wh i ch h a ve h i g h e r p o we r d e n s i ti e s th a n s o m e o th e r s o u rce s I f th e s o u rce ca n d ri ve th e a m p l i fi e r i n to s a tu ti o n , th e n n o i s e i s m i n i m i s e d a n d s i g n a l o u u t m a xi m i s e d Th i s m a i n ta i n s b o th a g ood o p ti ca l s i g n a l to n o i s e ti o a t th e i n s tru m e n t d e te cto r a n d a l a rg e D O P fo r S O P m e a s u re m e n ts • Re d u ci n g th e d e te cti o n o p ti ca l b a n d wi d th T h e d e te cto r b a n d wi d th ca n b e l i m i te d to ve ry e ffe cti ve l y fi l te r th e n o i s e F o r e xa m p l e , th e u se of a tu n e a b l e o p ti ca l fi l te r at th e d e te cto r, tra cki n g in ta n d e m wi th th e s o u rce wa ve l e n g th , a l l o ws a m u ch l o we r n o i s e p o we r to a rri ve a t th e i n s tru m e n t T h e d e te cto r i s n o l o n g e r s u b j e ct to s a tu ti o n , a n d th e a m o u n t o f n o i s e a ffe cti n g th e wa n te d s i g n a l i s re d u ce d Th e i n s tru m e n t p e rfo rm a n ce i s co n s e q u e n tl y m a i n ta i n e d a t h i g h e r o p ti ca l s i g n a l to - n o i s e ti o l e ve l s • Re d u ci n g th e d e te cti o n e l e ctri ca l b a n d wi d th T h e o p ti ca l i n p u t m u s t a l wa ys b e d e te cte d wi th o u t th e d e te cto r ci rcu i t b e co m i n g s a tu te d o r o ve rl o a d e d , o r e l s e P M D m e a s u re m e n t l i n e a ri ty o r b i a s p ro b l e m s o ccu r H o we ve r, o n ce th e s i g n a l h a s b e e n co n ve rte d to a n e l e ctri ca l s i g n a l , th e e l e ctri ca l fi l te ri n g m e th o d s ca n b e u s e d to l i m i t th e e ffe cti ve s ys te m b a n d wi d th Th i s typ i ca l l y re q u i re s th e l i g h t s o u rce to b e m o d u l a te d a t a h i g h fre q u e n cy ( e g wh e n u s i n g th e M P S m e th o d ) Th i s e n a b l e s th e si g n al p o we r to be d e te cte d using tu n e d fi l te rs , s yn ch ro n o u s d e m o d u l a ti o n , l o ck- i n a m p l i fi e r, e tc , a n d th e b ro a d b a n d n o i s e i s re j e cte d e xce p t wi th i n th e s i g n a l tra n s m i s s i o n wi n d o w • D i s cri m i n a ti n g th e l i g h t s o u rce fro m th e n o i s e Th i s is e s s e n ti a l l y th e same as re d u ci n g th e e l e ctri ca l b a n d wi d th , by m o d u l a ti n g th e s o u rce a n d d e te cti n g o n l y th e m o d u l a ti o n , o b s e rve d a t th e d e te cto r Th e " m o d u l a ti o n " m a y ta ke m a n y fo rm s , typ i ca l l y i n te n s i ty m o d u l a ti o n , o r d i g i ta l ke yi n g o r e n co d i n g m e th o d s P o l a ri z a ti o n d e p e n d e n t l o s s ( o r g a i n ) Th i s i s a p h e n o m e n o n wh e re th e tra n s m i tte d p o we r a t a n o p ti ca l fre q u e n cy va ri e s d e p e n d i n g on th e SOP l a u n ch e d i n to th e fi b re It is 0l og1 0( T m a x/ T min), wh e re T m a x/ T a re th e m a xi m u m a n d m i n i m u m tra n s m i tte d p o we rs I E C 0 - - [8 ] co n ta i n s m e a s u re m e n t m e th o d s fo r u s e o n co m p o n e n ts , o n e o f wh i ch i s " a l l s ta te s " , wh i ch i s a s e a rch o ve r a l a rg e n u m b e r o f i n p u t s ta te s An o th e r m e th o d i s b a s e d o n l a u n ch i n g M u e l l e r s ta te s I E C - - s ta te s th a t n o n e o f th e P M D te s t m e th o d s wo rk wh e n th e P D L i s i n e xce s s o f d B , b u t i f th e P D L i s l e s s th a n d B , re a s o n a b l e P M D re s u l ts ca n b e o b ta i n e d O n e o f th e a s p e cts o f P D L i s th a t o rth o g o n a l i n p u t S O P s m a y n o l o n g e r b e o rth o g o n a l a t th e o u u t Copyright International Electrotechnical Commission – 54 – Th e a cti o n of PDL E q u a ti o n ( ) ca n F i rs t be m u l ti p l y u n d e rs to o d th e I E C TR - : © I E C s o m e wh a t, T e s ti m a te d m a tri x or by e va l u a te d , th e fro m m issin g co n s i d e ti o n co m p l e x co n s ta n t, of vy, ( e i th e r s i g n m a y b e u s e d ) T h e n n o te th a t a n y m a tri x ca n b e re p re s e n te d wi th a s i n g u l a r va l u e d e co m p o s i ti o n , s i m i l a r to E q u a ti o n ( ) , a s : T U Th e m a tri ce s V and F o r th e g e n e l ca s e , wh e re V, S a re o rth o n o rm a l , a n d m a g n i tu d e o f th e d i a g o n a l e l e m e n ts o f o f th e co l u m n s o f = USV * U S (1 42) i s d i a g o n a l Wh e n U = V, th e re i s n o P D L , th e a re o n e , a n d th e re s u l t i s th e s a m e a s E q u a ti o n ( ) V, i s n o t e q u a l to wh e n th e i n p u t J o n e s ve cto r i s e q u a l to o n e th e o u u t J o n e s ve cto r i s th e co rre s p o n d i n g co l u m n o f g i ve n a s th e s q u a re o f th e m a g n i tu d e o f th e co rre s p o n d i n g m a g n i tu d e o f U wi th p o we r S T h e o u u t p o we r i s g i ve n a s : Th e e i g e n va l u e s T* T of yi e l d   * * j In T Tj In Pout = th e Tm i n =   * * * j InVS SV j In Tm a x an d (1 43) tra n s m i tte d p o we r wh i ch ca n th e n be co n ve rte d to P D L C o h e re n c e e ffe c t s a n d C o h e re n ce i n te rfe re n ce m u l ti p l e p a th e ffe cts an d m u l ti p l e i n t e rfe re n c e p a th i n te rfe re n ce a re al so ca l l e d F a b ry- P e ro t e ffe cts o r F a b ry- P e ro t e ta l o n e ffe cts C o m p o n e n ts , i n p a rti cu l a r, m a y co n ta i n b u l k o p ti ca l e l e m e n ts , fi b re - wa ve g u i d e s p l i ce s , fi b re l e n s i n te rfa ce s , e tc th a t ca n g i ve ri s e to re fl e cti o n s d u e to o p ti ca l i n d e x m i s m a tch b e twe e n e l e m e n ts Th e tra n s fe r fu n cti o n m e a s u re m e n ts a re s e n s i ti ve to ca vi ty e ffe cts i f th e l e n g th s o f th e s e ca vi ti e s a re s h o rte r th a n th e co h e re n ce l e n g th o f th e tu n e a b l e l a s e r s o u rce Th e l o n g e r th e n g e b e twe e n two re fl e cti o n s , th e l a rg e r th e e ffe cts wi l l be F o r i n s ta n ce , i f two p a s i te re fl e cti o n s a re s e p a te d b y th re e m e tre s o f S M F , a fl u ctu a ti o n o f a q u a rte r o f a wa ve o f th e ca vi ty l e n g th s p e ctru m , wi l l be en ou g h a p p ro xi m a te l y 0, 25 to µm go fro m in th e a m a xi m u m SM F A to a minimum te m p e tu re in fl u ctu a ti o n th e of tra n s m i s s i o n th e o rd e r of , ° C m a y a l s o b e e n o u g h to g e n e te s u ch e ffe cts Th e e ffe ct o f th e s e re fl e cti o n s m a y a l s o b e to i n d u ce m u l ti - p a th d i s p e rs i o n s th a t a re e i th e r P M D re l a te d ( i e th e p a th d i ffe re n ce i s p o l a ri z a ti o n s e n s i ti ve ) o r n o t ( p o l a ri z a ti o n i n s e n s i ti ve p a th d i ffe re n ce s ) Re fl e cti o n s an d re m o ve d fro m m u l ti p l e ∆τ d e l a y p a th s th a t a re n o t p o l a ri z a ti o n s e n s i ti ve ca n be s e p a te l y An y ki n d o f p o l a ri z a ti o n - s e n s i ti ve d i ffe re n ti a l d e l a y ( b i re fri n g e n ce e ffe cts ) , h o we ve r, wi l l a ffe ct th e va l u e re p o rte d a s D G D Test l ead fi b re s Th e S M F te s t l e a d s ( s o m e ti m e s ca l l e d p i g ta i l s ) a d d P M D o f th e i r o wn , wh i ch va ri e s a s th e l e a d s a re b e n t, co i l e d o r twi s te d Th e l e a d s i n to a n d o u t o f th e tra n s m i s s i o n m e d i a ( typ i ca l l y wi th l i ttl e n d o m co u p l i n g ) a l wa ys co n tri b u te s o m e P M D N O TE T yp i c a l P M D v a l u e s fo r a fe w m e te rs o f S M F a re o f th e o rd e r o f p a rti a l l y a d d s to , o r p a rti a l l y s u b tra c t s fro m , th e ∆τ th e l e a d b i re fri n g e n ce a n d th a t o f t h e c o m p o n e n t Copyright International Electrotechnical Commission fs /m o r l e s s Th e P M D i n th e l e a d s o f th e S M F c o m p o n e n t i ts e l f a c c o rd i n g t o th e a xi a l a l i g n m e n t o f I EC TR - : S i n ce th e SM F d e t e rm i n i s t i c , by ke e p i n g to D e vi ce s th e being in wi th m i s a l i g n m e n t wi l l It h as been p re fe rre d 6 V i b t i o n s d e vi ce i n t ro d u c e wi th l ead s wi l l th e n fi b re is if d i u s th a t be so th e th e l ead s In e a ch a re fu l l 50 DGD ti m e o f th e n g e th e l ead s be ke p t mm to is e ffe c t , th e to SM Fs or minimum a vo i d n d o m i s e re s u l t s ta ke n of PM D d e vi ce s a bend i n g m e a s u re m e n t s p o l a ri z a t i o n th e s e e s s e n ti a l l y to a xi s h a ve l o o s e - tu b e th e is be PM D mu st be c o v e re d s e n s i ti ve o f th e high may C a re v a ri a t i o n n o rm a l l y h i g h l y p o l a ri z a t i o n wi th u n ca b l e d in may th a n th e a v e g e th a t th e PM D Th i s l ess re q u i re d , al i g n ed s i g n i fi c a n t P M D n o ti ce d a re c o n fi g u re d a rra n g e d l ead l on g , d e t e rm i n a t i o n a d d i ti o n , m a i n ta i n i n g o f th e th e t n s m i s s i o n re s u l t s d epen d i n g of d e vi ce an d An y PDL ca b l e d SM Fs may be th e th a t on ca n th e m ed i a, be p i d i t y t n s m i s s i o n s u ch d i ffe re n t of m a t ri c e s th e wi th as may fro m be i n d u ce d re s u l t s m e a s u re m e n t o p ti ca l th a t an d fre q u e n c y by wo u l d th e is wi n d s , be l ead m e a s u re m e n t c o n fu s e d to o b ta i n e d wi th PM D wi th o u t m e th o d th e Th e v a ri a t i o n o t h e r s o u rc e s ca n be a rg u e d m o d u l a te d wi l l a re m e t e rs ∆τ ca b l e s te s ti n g of v i b t i o n s , It DGD e x p e ri m e n t a l l y m e a s u re m e n t fro m Th e l ead s fe w th e – fo r t e s t l e a d s Ae ri a l v a ri a t i o n th e a in ben t In wi th lead s th a t th e a xi s on l y bei n g i n t ro d u c e d p o l a ri z a t i o n p o l a ri z a t i o n – 55 t yp i ca l l y fro m ti m e s , th e e n s u re 201 o f u n c e rt a i n t y p i g ta i l s many c o n t ri b u t i o n ta ke n a re s o u rc e th e b i re fri n g e n c e re p e a t e d l ead s a © I EC al so si gn al lead B e ca u s e of m e th o d s , bu t to th a t due o p ti ca l s i n ce it on Copyright International Electrotechnical Commission t n s m i s s i o n o th e r th e t n s fo rm , ta ke s i n t e rfe ro m e t ri c m e t h o d s , Depen d i n g th e s o m e th i n g m a t ri c e s th a n a re o p ti ca l v a ry i n g fre q u e n c y o ve r an d th e p u re s p e c t ru m PMD, th e s e of th e e ffe c t s d i s t o rt i o n th e s ta b i l i ty o f th e if to a th e fi n i t e e ffe c t s m e a s u re m e n t t n s m i s s i o n med i a th e ti m e e ffe c t s to o f v i b t i o n m e th o d , – al l a re m u ch co m p l e te h a ve t h e re o f wh i ch a been a re i n vo l ve re d u c e d s ca n , th e y l i ke n e d som e to fo r a re i n t e rfe ro m e t ri c p re s e n t p o l a ri z a t i o n d i ffe re n t m u l ti p l e th e s ti l l wa ys to m e a s u re m e n t s For th e s c m b l i n g q u a n t i fy th e – 56 – I E C TR - : © I E C B i b l i o g p h y [1 ] I TU - T G sup39, G s e ri e s , Su ppl emen t 39, " O p ti ca l s ys te m d esi g n an d e n g i n e e ri n g co n s i d e ti o n s " , 2 [2 ] N G i s i n , B G i s i n , J P Vo n d e r We i d , a n d R P a s s y, " H o w a ccu te l y ca n o n e m e a s u re a s ta ti s ti ca l q u a n ti ty l i ke P o l a ri z a ti o n M o d e D i s p e rs i o n " , I E E E P h o to n i cs Te ch n o l L e tt , Vo l , N , D e c 9 [3 ] F C o rs i , A G a l ta ro s s a , B a ckre fl e cti o n L P a l m i e ri , M e a s u re m e n t of M S ch i a n o , P o l a ri za ti o n T M od e Ta m b o s s o , " C o n ti n u o u s - Wa ve D i s p e rs i o n " , I EEE P h o to n i cs Te ch n o l L e tt , Vo l 1 , N , Ap ri l 9 , p p - [4 ] P Wi l l i a m s , p o l a ri za ti o n " M o d u l a ti o n p h a s e - s h i ft m e a s u re m e n t o f P M D u s i n g o n l y fo u r l a u n ch e d s ta te s : a n e w a l g o ri th m " , E l e ctro n i c L e tte rs O n l i n e N o : 9991 068, DOI ; /E L : 9 , [5 ] K S a n o , T Ku d o u a n d T O ze ki , " S i m u l ta n e o u s M e a s u re m e n t o f M o d e G ro u p D e l a y D i s p e rs i o n a n d P o l a ri z a ti o n M o d e D i s p e rs i o n " , 2 n d E u ro p e a n C o n fe re n ce o n O p ti ca l C o m m u n i ca ti o n – E C O C ’ , O s l o [6 ] N C yr, " P o l a ri za ti o n - M o d e D i s p e rs i o n M e a s u re m e n t: G e n e l i za ti o n of th e I n te rfe ro m e tri c M e th o d To An y C o u p l i n g Re g i m e " , J L T , 0 [7 ] N C yr, H C h e n , a n d G S ch i n n , " Ra n d o m - S cra m b l i n g Tu n a b l e P O TD R fo r D i s tri b u te d M e a s u re m e n t o f C u m u l a ti ve P M D " , J L T, 0 [8 ] I E C 0 - - , F i b re o p ti c i n te rco n n e cti n g d e vi ce s a n d p a s s i ve co m p o n e n ts – B a s i c te s t and m e a s u re m e n t p ro ce d u re s – P a rt -2 : E xa m i n a ti o n and m e a s u re m e n ts – P o l a ri za ti o n d e p e n d e n t l o s s i n a s i n g l e - m o d e fi b re o p ti c d e vi ce [9 ] I E C TR - , F i b re o p ti c co m m u n i ca ti o n s ys te m d esig n g u i d es – P a rt 3: C a l cu l a ti o n o f l i n k p o l a ri za ti o n m o d e d i s p e rs i o n [1 ] I E C TR - , O p ti ca l a m p l i fi e rs – P a rt : P o l a ri z a ti o n m o d e d i s p e rs i o n p a m e te r – G e n e l i n fo rm a ti o n _ Copyright International Electrotechnical Commission Copyright International Electrotechnical Commission INTERNATIONAL ELECTROTECHNICAL COMMISSION 3, rue de Varembé PO Box 31 CH-1 21 Geneva 20 Switzerland Tel: + 41 22 91 02 1 Fax: + 41 22 91 03 00 info@iec.ch www.iec.ch Copyright International Electrotechnical Commission