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Rotation angle optimization of the polarization eigenmodes for detection of weak mode coupling in birefringent waveguides

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Abstract

White light interferometry has been adopted to measure distributed polarization coupling in high-birefringence waveguides. Since the coupling mode is weak compared to the exciting mode, the contrast ratio of the interferogram is very low. This will increase the difficulty of direct detection of the polarization coupling intensity. By rotating the angle between the polarization eigenmodes and the principal axis of the linear polarizer from 45° to 85°, the contrast ratio of the interferogram can be improved more than 10 times. As a result, the measurement sensitivity can be improved more than 100 times.

©2002 Optical Society of America

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Figures (3)

Fig. 1
Fig. 1 Structure of the white light interferometer
Fig. 2
Fig. 2 Relationship between the normalized minimum detectable h-parameter and the rotation angle
Fig. 3
Fig. 3 Relationship between the relative measurement error and the rotation angle

Equations (27)

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E x 0 = A e ( t ) exp ( i φ 0 )
E y 0 = A c ( t ) exp ( i φ 0 ) ,
E x 1 = A e ( t ) exp { i ( φ 0 + k x l ) } = A e ( t ) exp { i ( φ 0 + k 0 n x l ) }
E y 1 = A c ( t ) exp { i ( φ 0 + k y l ) } = A c ( t ) exp { i ( φ 0 + k 0 n x l + k Δ n b l ) } ,
E xy 0 = A e ( t ) exp [ i ( φ 0 + Δ φ 1 + k x l ) ] cos α + A c ( t ) exp [ i ( φ 0 + Δ φ 1 + k y l ) ] sin α ,
E xy 1 = E xy 2
= 2 2 { A e ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k x l ) ] cos α + A c ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k y l ) ] sin α }
E xyr 1 = 1 2 { A e ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k x l + k 0 δ 0 + k 0 Δ s ) ] cos α
+ A c ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k y l + k 0 δ 0 + k 0 Δ s ) ] sin α } ,
E xyr 2 = 1 2 { A e ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k x l + k 0 δ 0 ) ] cos α
+ A c ( t ) exp [ i ( φ 0 + Δ φ 1 + Δ φ 2 + k y l + k 0 δ 0 ) ] sin α }
E int = E xyr 1 + E xyr 2 .
I tatal = R 0 E int · E int * = I 1 + I 2 + I 3 + I 4 + I 5 ,
I 1 = 1 4 R 0 [ A e 2 ( t ) + A c 2 ( t ) ] · 2 cos 2 α
I 2 = 1 4 R 0 A e ( t ) A c ( t ) cos ( k 0 Δ n b l k 0 Δ s ) sin ( 2 α )
I 3 = 1 4 R 0 [ A e 2 ( t ) + A c 2 ( t ) ] cos ( k 0 Δ s ) · 2 cos 2 α .
I 4 = 1 4 R 0 2 A e ( t ) A c ( t ) cos ( k 0 Δ n b l ) sin ( 2 α )
I 5 = 1 4 R 0 A e ( t ) A c ( t ) cos ( k 0 Δ n b l + k 0 Δ s ) sin ( 2 α )
I total I 1 + I 2 ,
h = I c I e = E y 0 · E y 0 * E x 0 · E x 0 * = A c 2 ( t ) A e 2 ( t ) ,
I 2 I 1 = A e ( t ) A c ( t ) cos ( k 0 Δ n b l k 0 Δ s ) sin ( 2 α ) A e 2 ( t ) + A c 2 ( t ) · 2 cos 2 α ,
h 1 2 f ( k 0 Δ n b l k 0 Δ s ) tan α
h ( l ) max l ( I 2 I 1 ) 2 cot 2 α , Δ n b l Δ s L c
R ( l ) = 2 I 2 , max I 1 + I 2 , max ,
2 h 1 / 2 ( l ) tan α
h min R min 2 4 cos 2 α .
Err = cot 2 ( α ) cot 2 ( α + Δ α ) cot 2 ( α + Δ α ) .
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