!
Polarization-mode dispersion is defined and characterized, using
Poincaré sphere and Jones matrix concepts. Interferometric, wavelength
scanning, and Jones matrix eigenanalysis measurement methods are
described. Instrumentation, especially the HP 8509B lightwave
polarization analyzer, is discussed.
(: *(1(5$7,216 2) +,*+?63((' 81'(56($ 7(/(&20081,&$7,21
6<67(06 $1' &$%/( ! ',675,%87,21 6<67(06 )($785( $1 ,0325?
7$17 1(: 3/$<(5 7+( (5%,80?'23(' ),%(5 $03/,),(5 25 29,1* 48,&./< )520 /$%25$725< 72 0$,1/,1( $33/,&$7,21 7+(
:,// /2:(5 7+( &267 $1' ,1&5($6( 7+( 5(/,$%,/,7< 2) /21*?
+$8/ 7(/(&20081,&$7,216 $1' *5($7/< ,1&5($6( +($'?(1'
',675,%87,21 32:(5 )25 !
1 &2175$67 72 2/'(5 6<67(06 ,1 :+,&+ 3523$*$7,21 /266 :$6
&203(16$7(' %< '(7(&7,1* 7+( 237,&$/ 6,*1$/ $1' 5(75$160,7?
7,1* ,7 $7 +,*+(5 32:(5 5(*(1(5$7,21 7+( ?%$6(' 6<6?
7(0 ,6 $ &217,18286 */$66 3$7+:$< :,7+ $03/,),&$7,21 352?
9,'(' $7 ,17(59$/6 %< 6+257 /(1*7+6 2) 3803(' (5%,80?'23('
),%(5 +( $%6(1&( 2) 38/6( 5(*(1(5$7,21 0867 %( 2))6(7 %<
,03529(0(176 ,1 7+( ',63(56,9( &+$5$&7(5,67,&6 2) 7+(
3$7+:$<
7+( 32/$5,=$7,21 02'(6 &255(6321' 72 3+<6,&$/ $;(6 2) 7+(
&20321(17 $1' 7+( ',))(5(17,$/ *5283 '(/$< $1' 7+(5()25(
7+( ,6 1($5/< ,1'(3(1'(17 2) :$9(/(1*7+ 1 35$&7,&$/
/(1*7+6 2) 237,&$/ ),%(5 ',))(5(17,$/ *5283 '(/$< 9$5,(6 5$1?
'20/< :,7+ :$9(/(1*7+ $1' 7+( 63(&,),&$7,21 2) 0867 %(
67$7,67,&$//< %$6(' 21*?),%(5 ,6 &20021/< (;35(66(' $6
(,7+(5 7+( $9(5$*( 9$/8( 25 7+( 506 9$/8( 2) ',))(5(17,$/ *5283
'(/$< 29(5 $ :,'( :$9(/(1*7+ 5$1*( 25 ),%(56 7+$7 (;+,%,7 $
/$5*( '(*5(( 2) &283/,1* 2) (1(5*< %(7:((1 32/$5,=$7,21
02'(6 6&$/(6 :,7+ 7+( 648$5( 5227 2) ),%(5 /(1*7+ $1'
,6 2)7(1 63(&,),(' ,1 3,&26(&21'6 3(5 5227 .,/20(7(5
2: 08&+ ,6 722 08&+ 25 02'(67 ,03$&7 7+( ,167$1?
7$1(286 ',))(5(17,$/ *5283 '(/$< 2) $ 7(/(&20081,&$7,21 6<6?
7(0 0867 %( .(37 %(/2: 21( 7(17+ 2) $ %,7 3(5,2' 25 36
)25 $ ?%,76 # 38/6( 675($0
,6725,&$//< 32/$5,=$7,21?02'( ',63(56,21 25 ,6 7+(
7+,5' 2) $ 6(5,(6 2) ',63(56,9( ())(&76 ,1 237,&$/ ),%(5 +(
%$1':,'7+ 2) 08/7,02'( ),%(5 ,6 /,0,7(' %(&$86( /,*+7 6(3$?
5$7(6 ,172 63$7,$/ 02'(6 2) 0$1< ',))(5(17 /(1*7+6 ,1*/(?
02'( ),%(5 62/9(6 7+$7 352%/(0 %87 ,6 /,0,7(' %< &+520$7,&
',63(56,21 ,1 :+,&+ 7+( 75$160,66,21 0(',80 $//2:6 $'-$?
&(17 :$9(/(1*7+6 72 75$9(/ $7 6/,*+7/< ',))(5(17 63(('6 $ 025( 68%7/( ())(&7 $5,6(6 )520 6/,*+7 3+<6,&$/ $6<00(75< ,1
7+( ,1'(; 2) 5()5$&7,21 &$//(' %,5()5,1*(1&( 1 ),%(5 ,7 ,6
&$86(' %< 675(66(6 ,1'8&(' %< ),%(5 0$18)$&785( 3$&.$*,1*
$1' '(3/2<0(17 $1' ,6 67521*/< ,1)/8(1&(' %< (19,5210(17
,1 0$1< 5($/ 6<67(06 9$5,(6 29(5 7,0( $1' ,6 %(67 &+$5?
$&7(5,=(' %< $ 67$7,67,&$/ 3,&785( 72 $&&2817 )25 ,76 &+$1*,1*
'(7$,/6 25 7+( 020(17 +2:(9(5 /(76 &216,'(5 +2: 72 &+$5?
$&7(5,=( 7+( 2) $ 67$%/( '(9,&( 25 6<67(0 7+$7 (;+,%,76
12 7,0( 9$5,$7,21 ,))(5(17,$/ *5283 '(/$< 7+( 0267 ',5(&7
0($685( 2) 7+( 6,*1$/?',67257,1* ())(&76 2) '2(6 127 7(//
7+( :+2/( 6725< +( 2) $ 6<67(0 ,6 &203/(7(/< &+$5$&?
7(5,=(' %< 63(&,)<,1* $1< 2) 7+( )2//2:,1* 7+5(( 48$17,7,(6 $6
$ )81&7,21 2) :$9(/(1*7+ 25 237,&$/ )5(48(1&<
• 3$,5 2) 35,1&,3$/ 67$7(6 2) 32/$5,=$7,21 $1' $ ',))(5(17,$/
*5283 '(/$<
"+(1 &+520$7,& ',63(56,21 ,6 68)),&,(17/< 5('8&(' 7+( 38/6(
• 7+5((?',0(16,21$/ 32/$5,=$7,21 ',63(56,21 9(&725
',67257,21 $1' 6,*1$/ )$',1* 352'8&(' %< &$1 %( 2%?
• 21(6 0$75,; 6(( 3$*( 6(59(' 1 ! 6<67(06 7+( &20%,1$7,21 2) ,1 ),%(5
$1' &20321(176 )5(48(1&< &+,53 ,1 7+( 75$160,77(5 $1'
) $ 32/$5,=(' 781$%/( 237,&$/ :$9( ,6 75$160,77(' 7+528*+ $
32/$5,=$7,21 '(3(1'(17 /266 1($5 7+( 5(&(,9(5 352'8&(6 &20?
'(9,&( 7+( 32/$5,=$7,21 $7 7+( '(9,&( 287387 :,// ,1 *(1(5$/
326,7( 6(&21'?25'(5 ',67257,21 25 +,*+?63((' /21*?+$8/
75$&( 287 $1 ,55(*8/$5 3$7+ 21 7+( 2,1&$5> 63+(5( 6(( 3$*(
7(/(&20081,&$7,216 $1' +,*+?&+$11(/?&$3$&,7< ! 6<6?
$6 7+( 237,&$/ 5$',$1 )5(48(1&< ,6 781(' $6 6+2:1 ,1
7(06 72 5($/,=( 7+(,5 327(17,$/ 0867 %( 81'(56722' $1'
,* 9(5 $ 60$// 5$1*( 2) )5(48(1&< $1< 6(&7,21 2) 7+(
&21752//('
,55(*8/$5 3$7+ &$1 %( $3352;,0$7(' $6 $1 $5& 2) $ &,5&/( 21
7+( 685)$&( 2) 7+( 63+(5( +( &(17(5 2) 68&+ $ &,5&/( 352?
2/$5,=$7,21?02'( ',63(56,21 ,6 $ )81'$0(17$/ 3523(57< 2)
-(&7(' 72 7+( 685)$&( 2) 7+( 63+(5( /2&$7(6 $ 35,1&,3$/ 67$7( 2)
6,1*/(?02'( 237,&$/ ),%(5 $1' &20321(176 ,1 :+,&+ 6,*1$/
32/$5,=$7,21 6(&21' 257+2*21$/ 35,1&,3$/ 67$7( 2) 32/$5,=$?
(1(5*< $7 $ *,9(1 :$9(/(1*7+ ,6 5(62/9(' ,172 7:2 257+2*21$/
7,21 ,6 /2&$7(' ',$0(75,&$//< 23326,7( 21 7+( 63+(5( +(
32/$5,=$7,21 02'(6 2) 6/,*+7/< ',))(5(17 3523$*$7,21 9(/2&,7<
35,1&,3$/ 67$7(6 2) 32/$5,=$7,21 $5( 6,*1,),&$17 %(&$86( 7+(<
+( 5(68/7,1* ',))(5(1&( ,1 3523$*$7,21 7,0( %(7:((1 32/$5?
,=$7,21 02'(6 ,6 &$//(' 7+( ',))(5(17,$/ *5283 '(/$< &20021/< 6800$5,=( +2: $1< 287387 67$7( 2) 32/$5,=$7,21 (92/9(6 :,7+
)5(48(1&< 6 $ )81&7,21 2) )5(48(1&< $// 287387 67$7(6
6<0%2/,=(' $6 * 25 6,03/< 1 0267 237,&$/ &20321(176
 Hewlett-Packard Company 1995
(%58$5< (:/(77?$&.$5' 2851$/
Between 1941 and 1948, R. Clark Jones published a series of papers describing a
new polarization calculus based upon optical fields rather than intensities. This
approach, although more removed from direct observation than previous methods,
allowed calculation of interference effects and in some cases provided a simpler
description of optical physics. A completely polarized optical field can be represented by a two-element complex vector, each element specifying the magnitude
and phase of the x and y components of the field at a particular point in space.
The effect of transmission through an optical device is modeled by multiplying the
input field vector by a complex two-by-two device matrix to obtain an output field
vector.
The matrix representation of an unknown device can be found by measuring three
output Jones vectors in response to three known stimulus polarizations. Calculation
of the matrix is simplest when the stimuli are linear polarizations oriented at 0, 45,
and 90 degrees (Fig. 1), but any three distinct stimuli may be used. The matrix
calculated in this manner is related to the true Jones matrix by a multiplicative
complex constant c. The magnitude of this constant can be calculated from intensities measured with the device removed from the optical path, but the phase is
relatively difficult to calculate, requiring a stable interferometric measurement.
Fortunately, measurements of many characteristics such as PMD do not require
determination of this constant.
?
?
?
X1
Y2
X2
Y2
X3
Y3
k1 =
k3 =
X1
Y1
k2 =
X3
Y3
M=c
k4 =
k1k4
k2
k4
1
X2
Y2
k3 – k2
k1 – k3
Fig. 1. Measurement of the Jones matrix requires application of three known states of polarization. Output electric field descriptions and ratios kx are complex quantities. The Jones
matrix M is found to within a complex constant c, whose phase represents the absolute
propagation delay and is not required for PMD measurements.
)&++ &,+ !$+) &%%+!% + +.& ')!%!'# *++*
& '&#)!1+!&% )+ & )&++!&% !* +)$!% 0 + !)%+!# )&,' #0
'&#)!1+!&% !*')*!&% -+&) !* ')&#0 + $&*+
!%+,!+!-#0 $%!%,# )')*%++!&% & ,* !+ !*
!% !% + *$ )# + )3!$%*!&%# *' * + &!%)2 *' ) !* -+&) &)!!%+* + + %+) & + &!%)2 *' ) % '&!%+* +&.) + ')!%!'# *++ &
'&#)!1+!&% &,+ . ! + &,+',+ *++* & '&#)!1+!&%
)&++ !% &,%+)#&".!* *%* .!+ !%)*!% + ),)0 .#++3") &,)%#
s()
()
()
Principal State
of Polarization
#+!&%* !' +.% + '&#)!1+!&% !*')*!&% -+&) % + &,+',+ *++ & '&#)!1+!&% &% + &!%)2 *' ) -0 #!% * &.* + '+ & + &,+',+ '&#)!1+!&% * + &'+!#
)(,%0 %* &,+',+ '+ !* '')&/!$+ &-) *$##
)% & )(,%0 * !),#) ) %)+ 0 )&++!&% &,+ + '&#)!1+!&% !*')*!&% -+&) -+&) '&!%+* !% + !)+!&% &
&% ')!%!'# *++ & '&#)!1+!&% % *&% ')!%!'# *++ &
'&#)!1+!&% !* #&+ !$+)!##0 &''&*!+ &% + *' )
#%+ & !* + !)%+!# )&,' #0 % + &,+',+
*++ & '&#)!1+!&% !* /')** * + )3!$%*!&%# -3
+&) &$'&* & %&)$#!1 +&"* ')$+)* #&+!%
+ *++ & '&#)!1+!&% &% + *' ) + )&++!&% &,+ + ')!%!'# *++* & '&#)!1+!&% % .)!++% * )&**
')&,+ )#+!&% * × % + $&*+ %)# * !* ,%+!&% & + &'+!# )(,%0 % *&$ &'+!# &$'&%%+* *, * !*&#+&)* % .-3
,! $&,#+&)* &)!!%+* !% )0*+#* &) .-,!*
+ )&, . ! #! + ')&'+* .!+ !)%+ )&,' #0*
&) !)%+ '&#)!1+!&%* * + &'+!# )(,%0 +)%*3
$!++ + )&, + * &$'&%%+* !* -)! )$!%* !/
!% &)!%++!&% . !# $! + -)0 *#! +#0 * )*,#+ &
)&$+! !*')*!&% !% '&#)!1+!&% $& -!*
*, * + * !% . ! !* **%+!##0 !%'%%+ & ) *'!##0 *!$'# +& *)! % +& $*,) % ')+!,3
#) + !)%+!# )&,' #0 !* &%*+%+ &-) +!$ % %
,)+#0 )+)!1 * ." ,%+!&% & )(,%0
, -!* % ,*,# * *+%)* ,* + !) )3
+)!*+!* % /'+ +& )$!% *+# )&$ &% +!$
% #&+!&% +& + %/+
&)% *!%#3$& !)* !- -)0 #&. #-# & #&#
!))!%% !% !+!&% +& #&. ')&'+!&% #&** ,+ + +* & *$## #&# !))!%%* #&% + !) % 3
,$,#+ +& ,* *!%!!%+ + )&, !) $%0
"!#&$+)* #&% !))!%% !* ')&')+0 & !#+)!
*)!!% + !)% !% + !%/* & ))+!&% &) !3
)%+ '&#)!1+!&%* &# !))!%% !% !) % ,* 0 -!+!&%* )&$ ')+ !),#) *0$$+)0 & + !) &) &) 0 *0$$+)!# *+)** !% + &) )!&% &.!%
+& + $%,+,)!% ')&** %* !% + !) &) +$')3
+,) )!%+* +)*** % % .!+ +$')+,) %
.!+ +!$ * + #** % + *,))&,%!% # )#/ #3
!% +& !))!%% #&% + !) #%+ + + -&#-*
 Hewlett-Packard Company 1995
The Poincaré sphere is a graphical tool in real, three-dimensional space that allows
convenient description of polarized signals and of polarization transformations
caused by propagation through devices. Any state of polarization can be uniquely
represented by a point on or within a unit sphere centered on a rectangular (x,y,z)
coordinate system. The coordinates of the point are the three normalized Stokes
parameters describing the state of polarization. Partially polarized light can be
considered a combination of purely polarized light of intensity IP and unpolarized
light of intensity IU.
Right Circular
–45 Linear
Vertical
The degree of polarization IP/(IP + IU) corresponding to a point is the distance of
that point from the coordinate origin, and can vary from zero at the origin (unpolarized light) to unity at the sphere surface (completely polarized light). Points close
together on the sphere represent polarizations that are similar, in the sense that
the interferometric contrast between two polarizations is related to the distance
between the corresponding two points on the sphere.
Orthogonal polarizations with zero interferometric contrast are located diametrically
opposite on the sphere. As shown in Fig. 1, linear polarizations are located on the
equator. Circular states are located at the poles, with intermediate elliptical states
continuously distributed between the equator and the poles. Right-hand and lefthand elliptical states occupy the northern and southern hemispheres, respectively.
Because a state of polarization is represented by a point, a continuous evolution of
polarization can be represented as a continuous path on the Poincaré sphere. For
example, the evolution of polarization for light traveling through a waveplate or
birefringent crystal is represented by a circular arc about an axis drawn through
the two points representing the eigenmodes of the medium. (Eigenmodes are
polarizations that propagate unchanged through the medium.) A path can also
record the polarization history of a signal, for example in response to changing
strain applied to a birefringent fiber.
Horizontal
+45 Linear
Left Circular
The real, three-dimensional space of the Poincaré sphere surface is closely linked
to the complex, two-dimensional space of Jones vectors (see page 28). Most
physical ideas can be expressed in either context, the mathematical links between
the two spaces having previously been established for dealing with angular momentum. The graphical Poincaré description allows for a more intuitive approach
to polarization mathematics.
Fig 1. Points displayed on the surface of the Poincaré sphere represent the polarized portion
of a lightwave. Linear polarizations are located on the equator. Circular states are located at
the poles, with intermediate elliptical states continuously distributed between the equator
and the poles. Right-hand and left-hand elliptical states occupy the northern and southern
hemispheres, respectively. Example states are shown ascending the front of the sphere.
(/+ -#& "#, "/#(+ %, -( &,.+% -"- #, .'-#(' ( (-" +*.'2 ' -#& ,( -"- ,--#,-#% )#6
-.+ (&, -" &(,- ))+()+#- /#0 ( (+ -"
,2,-& ,#!'+
,--#,-#% &(% 0"' ,/+% %('! #+ ,-#(', + ('6
-'- -" 1)- /%. ( # +'-#% !+(.) %2 (+
-" ('-'-#(' #, !#/' 2 -" +((- ,.& ( ,*.+, ( -"
1)- /%., (+ -" ,-#(', -"- #,
-#% ,--#,-#% &(% ( ", ' /%()
+(& -" ,#, ( .&.%- %(% #+ +#'!', ' ",
' 1)+#&'-%%2 (' #+&
" ( -" 1 2 ' 3 (&)(''-, ( -" )(%+#3-#(' #,6
)+,#(' /-(+ (+ %('! #+ (%%(0, '(+&% #,-+#.-#('
0#-" 3+( &' , +,.%- -" (+#'--#(' ( #, .'# (+&%2
#,-+#.- ' -" #,-+#.-#(' ( -" # +'-#% !+(.)
%2 Dt jj #, )+()(+-#('% -( Dt1)Dt a "#, #,
( -' %% 10%% #,-+#.-#(' ., #- #, -" ,& ,
-" 10%% #,-+#.-#(' ( &(%.%+ ,) (+ !, #'
-"+&% *.#%#+#.& " #,-+#.-#(' ", ' 1)- /%.
hDti ( a p
" ,--#,-#% -"(+2 )+#-, ' 1)+#&'-, (' #+&
-"- -" # +'-#% !+(.) %2 #,-+#.-#(' &,.+ - )+-#.%+ +*.'2 (/+ %('! )+#( ( -#& #, #'-#%
-( -" #,-+#.-#(' &,.+ - (' -#& (/+ %+! +'!
( +*.'2 "#, - %%(0, ,--#,-#, +)+,'-#'! ,%(0
-#& /+#-#(', -( &,.+ /+2 *.#$%2 2 !-"+#'!
- (/+ 0# +*.'2 +'! , '(-"+ +,.%- ( -"
 Hewlett-Packard Company 1995
5544
hDti 5544
hDti hDti-(-%
5555
, (',*.' hDti-(-% !+(0, )+()(+-#('%%2 -( -"
,*.+ +((- ( -" #+ %'!-" ' -" ( %('! #+
#, ,)# # #' .'#-, ( ),$& 0#-" -" .'+,-'#'! -"-" (+#'--#(' ( #, .'# (+&%2 #,-+#.- ' ('-+,- -"
( ,"(+- ,-#(' ( #+ (+ ( #+ &'. -.+
0#-" (',#,-'- #+ +#'!' (/+ #-, %'!-" #, ,)# # #'
.'#-, ( ),$& ., #- !+(0, )+()(+-#('%%2 -( -" #+
%'!-" ' -" (+#'--#(' ( #, .'+,-(( -( #1
+%-#/ -( -" )"2,#% (+#'--#(' ( -" #+ #' (&6
)(''-, #, -2)#%%2 '(- ,--#,-#% #' (+#!#' ' #, ,#&)%2
,)# # #' ),
0( )(%+#3-#(' &(, + -+',&#-- -"+(.!" /#
1"##-#'! ,#!'# #'- " (+#'! -( #-, (0' )",
%2 ' !+(.) %2 0#'! -( -" .'*.% !+(.) %2,
)+()!-#(' -"+(.!" ,." /# 0#%% "'! -" &.-.%
-&)(+% ("+' -0' -" -0( )(%+#3-#(' &(,
+.+2 0%--6$+ (.+'%
Broadband
Light-Emitting
Diode
Linear
Polarizer
White Light
Source or
Broadband
LED
Linear
Polarizer
DUT
Linear
Polarizer
HP 71450A
Optical
Spectrum
Analyzer
(a)
45
–60
Moving
Mirror
DUT
Linear
Polarizer
Linear
Polarizer
Beam
Splitter
Linear
Polarizer
Photodiode
90
Optical Power (dBm)
0
–70
–80
1100
Fixed Mirror
(a)
Wavelength (nm)
1700
(b)
$ 130$+$,2 -% 31(,& 5 4$*$,&2' 1" ,,(,& 712$+
!*-") #( &0 + ! $ 130$+$,2 -% :)+ 1.--* -% 1(,&*$:+-#$
%(!$0 31(,& 5'(2$ *(&'2 1-30"$
Fringe Visibility
+323 **7 "-'$0$,2 !$ +1 ,$ +(00-0 " , !$ 1" ,,$# (,
.-1(2(-, "0$ 2(,& #(%%$0$,2( * #$* 7 !$25$$, 2'$ 25- -0:
2'-&-, * .-* 0(8 2(-,1 5'("' 0$ 0$"-+!(,$# ,# #(0$"2$#
2'0-3&' 2'$ #$4("$ 3,#$0 2$12 '$, .'-2-"300$,2 (1
+$ 130$# 1 %3,"2(-, -% 2'$ #(%%$0$,2( * (,2$0%$0-+$2$0
#$* 7 "-'$0$,2 %0(,&$1 " , !$ -!1$04$# -,*7 5'$, 2'(1 #(%:
%$0$,2( * #$* 7 (1 "-+.$,1 2$# !7 2'$ #(%%$0$,2( * &0-3.
#$* 7 -% 2'$ (& ! 1'-51 2'$ $,4$*-.$ -% 2'$
"-'$0$,2 %0(,&$1 +$ 130$# 1 %3,"2(-, -% #$* 7
–2
–1
0
1
Differential Delay (ps)
2
(b)
$ 130$+$,2 -% 31(,& (,2$0%$0-+$207 ,2$0%$0$,"$
%0(,&$1 0$ #$2$"2$# -,*7 5'$, 2'$ #(%%$0$,2( * &0-3. #$* 7 !$25$$,
-02'-&-, **7 .-* 0(8$# (,.32 12 2$1 (1 "-+.$,1 2$# !7 2'$ #(%%$0$,:
2( * &0-3. #$* 7 -% 2'$ ! $ 130$+$,2 -% :)+ 1.--*$#
%(!$0
()$5(1$ 2'$ 25- 3,$/3 * .' 1$ #$* 71 *$ # 2- %0$/3$,"7
#$.$,#$,2 -32.32 12 2$ -% .-* 0(8 2(-, (, 0$1.-,1$ 2- %(6$#
(,.32 12 2$ -% .-* 0(8 2(-, '$1$ .'71(" * "' 0 "2$0(12("1
+ )$ .-11(!*$ 4 0($27 -% +$ 130$+$,2 +$2'-#1 ,
(,2$0%$0-+$20(" +$2'-# +$ 130$1 2'$ $%%$"2 -% -,
+323 * "-'$0$,"$ ,# 5 4$*$,&2' 1" ,,(,& +$2'-#
+$ 130$1 2'$ $%%$"2 -% 2'0-3&' 4 0( 2(-,1 -% 2'$ -32.32
12 2$ -% .-* 0(8 2(-, -, 20 ,1+(11(-, 2'0-3&' %(6$# , :
*78$0 +$2'-# #$4$*-.$# !7 $5*$22: ") 0# " *"3* 2$1
2'$ #(%%$0$,2( * &0-3. #$* 7 ,# .0(,"(. * 12 2$1 -% .-* 0(8 :
2(-, 1 %3,"2(-, -% %0$/3$,"7 !7 , *78(,& -,$1 + 20(6$1
+$ 130$# 2 1$/3$,"$ -% -.2(" * %0$/3$,"($1 -12 -%
2'$ 2$"',(/3$1 "300$,2*7 31$# 2- +$ 130$ 0$ 1(+(* 0 (,
.0(,"(.*$ 2- -,$ -% 2'$1$ 2'0$$ +$2'-#1
!*-") #( &0 + -% 2'$ *-5:"-'$0$,"$ (,2$0%$0-+$20("
+$2'-# (1 1'-5, (, (& -**(+ 2$# *(&'2 %0-+ !0- #:
! ,# *(&'2:$+(22(,& #(-#$ (1 .-* 0(8$# ,# 1.*(2 (,2- 25-
$!03 07 $5*$22: ") 0# -30, *
'$ 5 4$*$,&2' 1" ,,(,& +$2'-# *1- " **$# 2'$ %(6$#
, *78$0 +$2'-# (1 1'-5, 1"'$+ 2(" **7 (, (& ,# " ,
!$ 11$+!*$# 31(,& $/3(.+$,2 %-3,# (, + ,7 -.2("1 * !-0 :
2-0($1 5(2'-32 1.$"( *(8$# $/3(.+$,2 %-0 +$ 130$+$,2
-* 0(8$# !0- #! ,# *(&'2 (1 #(0$"2$# 2'0-3&' 2'$ (, 2'$ " 31$1 2'$ -32.32 12 2$ -% .-* 0(8 2(-, 2- 20 "$
-32 , (00$&3* 0 . 2' -, 2'$ -(," 09 1.'$0$ 5'$, +$ 130$#
1 %3,"2(-, -% -.2(" * %0$/3$,"7 1 5 1 1'-5, (, (& 7 +$ 130(,& 2'$ -.2(" * .-5$0 20 ,1+(22$# 2'0-3&' , -32:
.32 , *78$0 1 %3,"2(-, -% -.2(" * %0$/3$,"7 (& ! 5$
$%%$"2(4$*7 +$ 130$ -,$ #(+$,1(-, -% 2'$ 2'0$$:#(+$,1(-, *
. 2' -, 2'$ 1.'$0$ *$ #(,& 2- 0(..*$1 (, 2'$ 1.$"20 * #$,1(27
+$ 130$# !7 2'$ -.2(" * 1.$"203+ , *78$0 '$ 4$0 &$
#(%%$0$,2( * &0-3. #$* 7 -4$0 2'$ +$ 130$# %0$/3$,"7 1. , (1
.0-.-02(-, * 2- 2'$ ,3+!$0 -% 1.$"20 * #$,1(27 $620$+
5(2'(, 2'$ 1. ,
-,$1 + 20(6 $(&$, , *71(1 (1 ! 1$# 3.-, -,$1 + 20(6$1
+$ 130$# 2 1$/3$,"$ -% -.2(" * %0$/3$,"($1 31(,& 2'$ *(&'25 4$ .-* 0(8 2(-, , *78$0 ,# 2'$ ,#
23, !*$ * 1$0 1-30"$1 1 1'-5, 1"'$+ 2(" **7 (,
(& 2 $ "' %0$/3$,"7 -,$1 + 20(6 ) (1 +$ 130$# !7
12(+3* 2(,& 2'$ 5(2' 2'0$$ ""30 2$*7 ),-5, 12 2$1 -%
.-* 0(8 2(-, ,# +$ 130(,& 2'$ 0$1.-,1$ 12 2$ -% .-* 0(8 2(-,
2 2'$ -32.32 '$ + 20(6 .0-#3"2 ) ) 0$4$ *1
2'$ "' ,&$ (, 2'$ .-* 0(8 2(-, 20 ,1%-0+ 2(-, " 31$# !7 2'$
"' ,&$ (, %0$/3$,"7 5'("' (, 2'(1 " 1$ (1 0-2 2(-, !-32 '$ $(&$,4$"2-01 -% ) ) 7($*# 2'$ -0($,2 2(-, -% ,#
 Hewlett-Packard Company 1995
)& "#*-*5: 50 .&"463& 5)& '3&26&/$: %&1&/%&/$& 0' $"/ #& )&-1'6- */ %*"(/04*/( *54 1):4*$"- 03*(*/4 #65 */ &7"?
-6"5*/( " )*()-: .0%&?$061-&% %&7*$& 46$) "4 " -0/( '*#&3
0/-: 5)& "7&3"(& %*''&3&/5*"- (3061 %&-": *4 4*(/*'*$"/5 )*4
3"*4&4 5)& 26&45*0/ 0' )08 .6$) %"5" .645 #& $0--&$5&% #&?
'03& " 3&-*"#-& &45*."5& 0' 5)& "7&3"(& %*''&3&/5*"- (3061
%&-": hDti *4 0#5"*/&% -- 5)3&& 0' 5)&4& 5&$)/*26&4 ("5)&3
%"5" 07&3 " 3"/(& 0' '3&26&/$*&4 "/% -"3(&3 '3&26&/$: 03
8"7&-&/(5) 41"/4 (&/&3"--: 3&46-5 */ .03& 3&-*"#-& &45*."5&4
0' hDti
HP 8509B Lightwave Polarization Analyzer
Polarization
State Generator
Fast
Polarimeter
HP 8168A
Tunable
Laser
Source
0 60 120
Polarization Filters
)& */5&3'&30.&53*$ "/% 0/&4 ."53*9 .&5)0%4 #05) $"/ (*7&
"/ */%*$"5*0/ 0' 8)&/ 46''*$*&/5 %"5" )"4 #&&/ $0--&$5&% #:
$0.1"3*/( .&"463&% %"5" 50 $637&4 5)&03&5*$"--: 13&%*$5&%
#: 5)& 45"5*45*$"- .0%&- /5&3'&30.&53: .&"463&4 %"5" 8&
&91&$5 50 #& /03."--: %*453*#65&% 40 5)& .&"463&% %"5" *4
$0.1"3&% 50 " "644*"/ $637& 50 "44&44 5)& &45*."5& 0' hDti
*( " 4)084 " (00% '*5 *(&/"/"-:4*4 .&"463&4 5)& ."(/*?
56%& jj 8)*$) 8& &91&$5 50 '0--08 " "98&-- %*453*#65*0/
)& $637& 0' %*''&3&/5*"- (3061 %&-": 7&3464 8"7&-&/(5) *4
'*345 $0/7&35&% */50 " )*450(3". 4)08*/( 5)& /6.#&3 0' .&"?
463&.&/54 7&3464 %*''&3&/5*"- (3061 %&-": "/% 5)&/ 5)& )*4?
50(3". *4 $0.1"3&% 50 " "98&-- $637& *( # 4)084 "
(00% '*5
Fiber or
Device
Under Test
(a)
Differential Group Delay (ps)
0.7
0.00
1460
1560
Wavelength (nm)
(b)
&"463&.&/5 0' 64*/( 0/&4 ."53*9 &*(&/"/"-:4*4
" :45&. #-0$, %*"(3". # &"463&.&/5 0' " ?,. =)*()?
4*/(-&?.0%& '*#&3
5)& &*(&/7"-6&4 ρ "/% ρ
0' ,) *
, :*&-% 5)& %*''&3&/5*"(3061 %&-": 5)306() 5)& 3&-"5*0/
Dt + << +
3(ǒρ>>>>
ρ
Ǔ
Dw
8)&3& 3( *4 5)& "3(6.&/5 '6/$5*0/ 5)& "3(6.&/5 0' " $0.?
1-&9 /6.#&3 *4 *54 10-"3 "/(-& 5)"5 *4 3( g&*b b 5&1?
1*/( 1"*38*4& 5)306() 5)& 4&26&/$& 0' ."53*9&4 , 8& 0#?
5"*/ #05) 13*/$*1"- 45"5&4 0' 10-"3*;"5*0/ "/% 5)& %*''&3&/5*"(3061 %&-": "4 " '6/$5*0/ 0' 015*$"- '3&26&/$: *( #
!)&/ 5)& '3&26&/$: 41"/ *4 /05 46''*$*&/5 50 130%6$& " 46''*?
$*&/5-: (00% '*5 50 5)& &91&$5&% $637& /&8 %"5" $"/ #& $0-?
-&$5&% #: 8"*5*/( '03 5)& 1):4*$"- 1301&35*&4 0' 5)& '*#&3 50
$)"/(& "446.*/( 5)"5 5)& 4".& 45"5*45*$"- .0%&- 3&."*/4
7"-*% / 5)& -"#03"503: 5)& $)"3"$5&3*45*$4 0' " 4100-&% '*#&3
"3& .&"463&% "("*/ "'5&3 5)& '*#&3 5&.1&3"563& *4 $)"/(&% #:
" '&8 %&(3&&4 8)*-& " %&1-0:&% '*#&3 .645 #& .&"463&%
"("*/ "'5&3 4&7&3"- )0634 )"7& &-"14&% 6-5*1-& .&"463&?
.&/54 07&3 5)& 4".& '3&26&/$: 41"/ "--08 $0--&$5*0/ 0' "
4&5 0' %"5" 5)"5 "$$63"5&-: 13&%*$54 hDti "4 3&'-&$5&% #: "
(00% '*5 50 5)& &91&$5&% $637&
)& -*()58"7& 10-"3*;"5*0/ "/"-:;&3 %*4$644&% 0/
1"(& 1307*%&4 580 "650."5&% .&5)0%4 '03 .&"463&.&/5
0' 5)& 0/&4 ."53*9 &*(&/"/"-:4*4 "/% 5)3&&?50,&4?
1"3".&5&3 8"7&-&/(5) 4$"//*/( .&5)0%4 *( 05) .",&
64& 0' 5)& 56/"#-& -"4&3 4063$&4 )&
0.025
50
0.015
Counts
Fringe Visibility
0.02
0.01
25
0.005
0
0
–3
–2
(a)
–1
0
1
Differential Group Delay (ps)
2
3
0
0.5
1.0
Differential Group Delay (ps)
1.5
(b)
" )& 4.005) $637& 4)084 5)& &91&$5&% /03."- %*453*#65*0/ 0' 5)& %"5" .&"463&% 64*/( 5)& */5&3'&30.&53*$ .&5)0% / 5)*4 $"4&
5)& .&"463&% %"5" +"((&% -*/& *4 " '"*3-: (00% '*5 # *(&/"/"-:4*4 .&"463&4 5)& ."(/*56%& jj 8)*$) *4 &91&$5&% 50 '0--08 " "98&-%*453*#65*0/ 4.005) $637& &3& 5)& .&"463&% %"5" )*450(3". *4 " (00% '*5
 Hewlett-Packard Company 1995
&#36"3: &8-&55?"$,"3% 063/"-
! !
With the advent of the lightwave polarimeter, engineers in the fields of high-speed
telecommunications, cable TV distribution, optical sensing, optical recording, and
materials science can characterize polarization phenomena with the ease and graphical simplicity of the common oscilloscope. Supplemented by an optical source, a
polarization state generator, and comprehensive measurement software, the polarimeter becomes a polarization analyzer, producing comprehensive measurements of
both optical signals and two-port optical devices.
The HP 8509B lightwave polarization analyzer consists of an optical unit and a
66-MHz HP Vectra PC. The main display window, shown in Fig. 1, conveniently
displays the polarization parameters of an optical signal and provides access to
commonly used controls. The Measurements menu provides access to a variety of
integrated measurement solutions addressing polarization-mode dispersion
(PMD), polarization dependent loss, the Jones matrix, and optimization of optical
launch into polarization maintaining fiber. The Display menu allows customization
of the display window and the System menu enables the user to reconfigure system operating parameters, optimize performance at a particular wavelength, and
automatically check the functional integrity of the instrument.
The heart of the HP 8509A/B is a high-speed polarimeter (see Fig. 4a in the accompanying article). A passive optical assembly (see cover) divides the optical signal into
four beams and passes each beam through polarization filters to photodiode detectors. Autoranging amplifiers and 16-bit ADCs complete the circuitry. A series of
calibration coefficients are determined at manufacture and stored in UV-PROM. The
instrument interpolates among these coefficients to provide operation from 1200 to
1600 nm. Parallel filtering and detection combined with high-speed conversion and
computation result in a measurement rate of 3000 polarization states per second.
A second optical assembly inserts three polarizing filters in the optical source path
to allow measurement of the Jones matrix. The Jones matrix eigenanalysis PMD
measurement method is based upon Jones matrixes (see page 28) measured at a
series of wavelengths. Polarization dependent loss is also derived from the Jones
matrix. In addition, the user can use external polarizers to define a physical reference frame, analytically removing the birefringence and polarization dependent
loss of components between the polarizer and the polarimeter receiver. Once
defined, the reference frame allows the measurement of absolute polarization
state at a point far from the instrument itself.
Fig. 1. Main measurement window of the
HP 8509B lightwave polarization analyzer.
Displays of average power and degree of
polarization (DOP), along with elliptical and
Poincaré sphere displays, fully characterize
the polarization state of a lightwave. Shown
on the sphere are the loci of output polarization states of a polarization maintaining fiber
as the fiber is gently stretched. Red traces are
on the front of the sphere, blue on the back.
Different circles correspond to different states
at the input of the fiber. The circles converge
to points when polarized light is launched
entirely on the fast or slow axes of the fiber.
8#7'-'/)5* 4%#//+/) .'5*0& &'5'3.+/'4 5*3'' 7#-6'4
(30. %*#/)'4 +/ 065165 10-#3+;#5+0/ #4 0$4'37'& #-0/) 5*'
5*3'' #9'4 0( 5*' 0+/%#3< 41*'3' 5*'/ #7'3#)'4 5*'4' 3'=
46-54 50 1307+&' # 4+/)-' 7#-6' 0( 5*#5 +4 .6%* -'44 &'=
1'/&'/5 0/ -#6/%* %0/&+5+0/ 5*#/ %0/7'/5+0/#- +.1-'.'/5#=
5+0/4 0( 8#7'-'/)5* 4%#//+/) *' .'#463'& /03.#-+;'&
50,'4 1#3#.'5'34 #3' +/&'1'/&'/5 0( 4+)/#- 108'3 #/& #3'
5*'3'(03' +..6/' 50 015+%#- 4+)/#- -'7'- %*#/)'4 #--08+/) #
$'55'3 .'#463'.'/5 50 $' &'3+7'& (30. # 4+/)-' 8#7'-'/)5*
48''1 '%#64' 5*' 8#7'-'/)5* 4%#//+/) .'5*0& &0'4 /05
3'26+3' 5*' +/5'3/#- 5*3''=45#5' 10-#3+;'3 5*' .'5*0& +4 #-40
#7#+-#$-' 0/ 5*' *' 015+%#- 41'%536. #/#-:;'3
8+5* 15+0/
+/5'3/#- 8*+5' -+)*5 4063%' +4 # 108'3(6- (06/&#5+0/
(03 53#&+5+0/#- 8#7'-'/)5* 4%#//+/) .'#463'.'/54
'$36#3: '8-'55=#%,#3& 063/#-
*' +/5'3('30.'53+% .'5*0& 0( .'#463'.'/5 +4 #7#+-=
#$-' (03 %'35#+/ #11-+%#5+0/4 7+# 5*' 13'%+4+0/
3'(-'%50.'5'3
*' #65*034 8+4* 50 5*#/, 3') +$$0/4 6/%#/ 63-':
+%*#3& --'/ +,' #35 #/& '(( #6- (03 5*' &'7'-01.'/5
0( 5*' 03+)+/#- 40(58#3' 0( 5*' -+)*58#7' 10-#3=
+;#5+0/ #/#-:;'3 #/& +,' +5;1#53+%, (03 3'%'/5 '/*#/%'=
.'/54 0)'3 6/)'3.#/ #/&: +/) 0/ 3011'3 #/& +.
.+5* (03 5*' &'4+)/ 0( 5*' 10-#3+.'5'3 3'%'+7'3 3'& #8=
40/ #/& #55 -'+/ (03 %+3%6+5 &'4+)/ 6+4 '3/#/&'; (03
07'3#-- 130&6%5 &'4+)/ #/& +. "#3/'-- #/& 7#/ #..'3
(03 %0/53+$65+0/4 50 5*' .'%*#/+%#- &'4+)/ !' #3' #-40
)3#5'(6- 50 #33: *06 (03 +.1035#/5 '/*#/%'.'/54 +/ 5*'
 Hewlett-Packard Company 1995
" 31/0;>)=763)91A);165 )5)3@A-9 ,1:73)@ 6.
763)91A);165C46,- ,1:7-9:165
" 4-):<9-4-5; 9-:<3;: %065-: 4);91? -1/-5)5)3@:1:
4-;06, .69-/96<5, 4-):<9-:
,1..-9-5;1)3 /96<7 ,-3)@ ): ) .<5+;165 6. >)=-3-5/;0 %0;09--C$;62-:7)9)4-;-9 >)=-C
3-5/;0 :+)5515/ 4-;06, *)+2C
/96<5, 1: -50)5+-, *@ )5)3@AC
15/ ;09-- 9-:765:-: 796,<+-, *@
) :15/3- >)=-3-5/;0 :>--7
,-:1/5 )5, ;6 ")4-3) "1;+0-9 )93 $0<*-9; #6/-9 '65/
)+2 <79- </6 &1.1)5 )5, $;-=- ->;65 .69 ;0-19 :;965/
:<7769;
695 )5, '63. "-9/)465 $ -9/)56 "663- )5, # ')/5-9 B5=-:;1/);165 6.
763)91A);165 ,1:7-9:165 15 365/ 3-5/;0: 6. :15/3-C46,- .1*-9 <:15/
4<3;1C365/1;<,15)3 46,- 3):-9: !
&63 %C 77 C
"663- '15;-9: )5, )/-3 B@5)41+)3 -8<);165 .69
763)91A);165 ,1:7-9:165 &63 77 C
6:+0151 )5, "663- B$;);1:;1+)3 ;0-69@ 6. 763)91A);165
,1:7-9:165 15 :15/3-C46,- .1*-9: !
&63 %C 77 C
6+01A<21 ( )41019) )5, ')2)*)@):01 B"63)91:);165
46,- ,1:7-9:165 4-):<9-4-5;: 15 365/ :15/3-C46,- .1*-9: "
&63 77 C
1:15 C" &65 ,-9 '-1, )5, C" "-33)<? B"63)91A);165 46,,1:7-9:165 6. :069; )5, 365/ :15/3-C46,- .1*-9: "
! &63 %C 77 C
)5, 9-.-9-5+-:
;0-9-15
"663- )5, )=15 B"63)91A);165C46,- ,1:7-9:165 4-)C
:<9-4-5;: *):-, 65 ;9)5:41::165 :7-+;9) ;096</0 ) 763)91A-9
! &63 %C
77 C
 Hewlett-Packard Company 1995
-..5-9 B<;64);-, 4-):<9-4-5; 6. 763)91A);165 46,- ,1:C
7-9:165 <:15/ 65-: 4);91? -1/-5)5)3@:1: !
&63 77 C
-..5-9 B++<9);- )<;64);-, 4-):<9-4-5; 6. ,1..-9-5;1)3
/96<7 ,-3)@ ,1:7-9:165 )5, 7915+17)3 :;);- =)91);165 <:15/ 65-:
4);91? -1/-5)5)3@:1: ! &63 77
C
-..5-9 B;;6:-+65,C9-:63<;165 4-):<9-4-5; 6. 763)91A);165
46,- ,1:7-9:165 15 :069; :-+;165: 6. 67;1+)3 .1*-9 &63
77 C
)1:-5*)+0-9 -+2-3 # )05 )5, "6;; B%<5)*3- ):-9
$6<9+-: .69 !7;1+)3 4731.1-9 %-:;15/ " &63
56 -*9<)9@ 77 C
# 65-: B 5-> +)3+<3<: .69 ;0- ;9-);4-5; 6. 67;1+)3 :@:;-4:
& ?7-914-5;)3 ,-;-9415);165 6. ;0- 4);91? ! &63 77 C
)13-@ )5, # $;1473- B!7;1+)3 $7-+;9<4 5)3@A-9: >1;0
1/0 @5)41+ #)5/- )5, ?+-33-5; 57<; $-5:1;1=1;@ "
&63 56 -+-4*-9 77 C
66:;-9 06< )9; $ 1.:<, )5, # #)>:65
B-:1/5 6. ) "9-+1:165 !7;1+)3 6>C60-9-5+- #-.3-+;64-;-9
" &63 56 -*9<)9@ 77 C
-*9<)9@ ->3-;;C")+2)9, 6<95)3