Abstract

Anisotropic fibers of the depressed-cladding type are analyzed by employing an iterative perturbation technique in a simple and straightforward way. An analytic expression is obtained for calculating the leaky-mode losses of an anisotropic depressed-cladding fiber. Numerical results show that such fibers possess much higher losses than those predicted earlier for a step-index model and hence are more advantageous for use in achieving single-polarization, single-mode operation.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Ruhl, A. W. Snyder, IEEE J. Lightwave Technol. LT-2, 284 (1984).
    [CrossRef]
  2. A. W. Snyder, F. Ruhl, J. Opt. Soc. Am. 73, 1165 (1983).
    [CrossRef]

1984 (1)

F. Ruhl, A. W. Snyder, IEEE J. Lightwave Technol. LT-2, 284 (1984).
[CrossRef]

1983 (1)

Ruhl, F.

F. Ruhl, A. W. Snyder, IEEE J. Lightwave Technol. LT-2, 284 (1984).
[CrossRef]

A. W. Snyder, F. Ruhl, J. Opt. Soc. Am. 73, 1165 (1983).
[CrossRef]

Snyder, A. W.

F. Ruhl, A. W. Snyder, IEEE J. Lightwave Technol. LT-2, 284 (1984).
[CrossRef]

A. W. Snyder, F. Ruhl, J. Opt. Soc. Am. 73, 1165 (1983).
[CrossRef]

IEEE J. Lightwave Technol. (1)

F. Ruhl, A. W. Snyder, IEEE J. Lightwave Technol. LT-2, 284 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Index profile of a depressed-cladding anisotropic fiber.

Fig. 2
Fig. 2

(a) Leaky-mode losses versus wavelength for depressed-cladding anisotropic fibers. Curve I: δyx = δyz = 0.0018. Curve II: δyx, = δyz = 0.0015. Curve III: δyx = δyz = 0.0012. (b) Leaky-mode losses versus δyz for depressed-cladding anisotropic fibers.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

{ t 2 + k 2 n x 2 - β 2 } e x = 2 δ x z 2 e x x 2 + 2 δ y z 2 e y x y ,
{ t 2 + k 2 n y 2 - β 2 } e y = 2 δ x z 2 e x x y + 2 δ y z 2 e y y 2 ,
e 0 y y = { J 0 ( u p ) J 0 ( u ) p < 1 C 0 I 0 ( v p ) + D 0 k 0 ( v p ) 1 < p < d F 0 K 0 ( w p ) K 0 ( w d ) p > d ,
e 0 x y = 0 ,
u = a { k 2 n 1 y 2 - β y 2 } 1 / 2 v = a { β y 2 - k 2 n 2 y 2 } 1 / 2 , w = a { β y 2 - k 2 n 3 y 2 } 1 / 2 , C 0 = K 0 ( v ) [ k ^ 0 ( v ) - J ^ 0 ( u ) ] , D 0 = I 0 ( v ) [ I ^ 0 ( v ) + J ^ 0 ( u ) ] , F 0 = C 0 I 0 ( v d ) + D 0 K 0 ( v d ) , J ^ n ( x ) = x J 1 ( x ) J n ( x ) , I ^ n ( x ) = x I 1 ( x ) I n ( x ) , K ^ n ( x ) = x K 1 ( x ) K n ( x ) , H ^ n ( i ) ( x ) = x H 1 ( i ) ( x ) H n ( i ) ( x ) ,
I 0 ( v ) K 0 ( v d ) K ^ 0 ( w d ) - K ^ 0 ( v d ) K ^ 0 ( w d ) + I ^ 0 ( v d ) = I 0 ( v d ) K 0 ( v ) J ^ 0 ( u ) - K ^ 0 ( v ) J ^ 0 ( u ) + I ^ 0 ( v ) .
{ t 2 + k 2 n x 2 - β y 2 } e 1 x y = 2 δ y z 2 e 0 y y x y ,
{ t 2 + k 2 n y 2 - β y 2 } e 1 y y = 2 δ y z 2 e 0 y y y 2 ,
e 1 y y = { - δ y z 2 u p J 1 ( u p ) J 0 ( u ) + A 01 J 0 ( u p ) J 0 ( u ) + [ - δ y z 2 u p J 3 ( u p ) J 0 ( u ) + A 04 J 2 ( u p ) J 2 ( u ) ] cos 2 θ , p < 1 - J y z 2 v p [ - C 0 I 1 ( v p ) + D 0 K 1 ( v p ) ] + A 01 [ C 0 I 0 ( v p ) + D 0 K 0 ( v p ) ] + { δ y z 2 v p [ - C 0 I 3 ( v p ) + D 0 K 3 ( v p ) ] } + C 02 I 2 ( v p ) + D 02 K 2 ( v p ) ] cos 2 θ , 1 < p < d , - δ y z 2 F 0 w p K 1 ( w p ) K 0 ( w d ) + A 01 F 0 K 0 ( w p ) K 0 ( w d ) + { δ y z 2 F 0 w p K 3 ( w p ) K 0 ( w d ) + F 02 K 2 ( w p ) K 2 ( w d ) } cos 2 θ , p > d
e 1 x y = { [ 1 2 k 2 a 2 n x 2 δ y z δ y x u 2 J 2 ( u p ) J 0 ( u ) + A 21 J 2 ( u x p ) J 2 ( u x ) ] s i n 2 θ , p < 1 [ 1 2 k 2 a 2 n x 2 δ y z δ y x v 2 { C 0 I 2 ( v p ) + D 0 K 2 ( v p ) } + C 21 I 2 ( v x p ) + D 21 K 2 ( v x p ) ] sin 2 θ , 1 < p < d [ 1 2 k 2 a 2 n x 2 δ y z δ y x w 2 F 0 K 2 ( w p ) K 0 ( w d ) + F 21 K 2 ( w x p ) K 2 ( w x d ) ] sin 2 θ , p > d
e 1 x y = { [ 1 2 k 2 a 2 n x 2 δ y z δ y x u 2 J 2 ( u p ) J 0 ( u ) + A 22 J 2 ( u x p ) J 2 ( u x ) ] sin 2 θ , p < 1 [ 1 2 k 2 a 2 n x 2 δ y z δ y x v 2 { C 0 I 2 ( v p ) + D 0 K 2 ( v p ) } + C 22 I 2 ( v x p ) + D 22 K 2 ( v x p ) ] sin 2 θ , 1 < p < d [ 1 2 k 2 a 2 n x 2 δ y z δ y x F 0 w 2 K 2 ( w p ) K 0 ( w d ) + F 22 H 2 ( 2 ) ( Q P ) H 2 ( 2 ) ( Q d ) ] sin 2 θ , p > d
e 1 x y = { [ 1 2 k 2 a 2 n x 2 δ y z δ y x u 2 J 2 ( u p ) J 0 ( u ) + A 23 J 2 ( u x p ) J 2 ( u x ) ] sin 2 θ , p < 1 [ 1 2 k 2 a 2 n x 2 δ y z δ y x v 2 { C 0 I 2 ( v p ) + D 0 K 2 ( v p ) } + C 23 H 2 ( 1 ) ( s p ) + D 23 H 2 ( 2 ) ( s p ) ] sin 2 θ , 1 < p < d [ 1 2 k 2 a 2 n x 2 δ y z δ y x F 0 w 2 K 2 ( w p ) K 0 ( w d ) + F 23 H 2 ( 2 ) ( Q P ) H 2 ( 2 ) ( Q d ) ] sin 2 θ p > d
α = Δ P / 2 P ,
p = β z a 2 2 w μ v 2 [ V 1 2 J 1 2 ( u ) J 0 2 ( u ) + d 2 V 2 2 F 0 2 K 1 2 ( w d ) K 0 2 ( w d ) ]
Δ P = lim r l ½ ( e × h * ) · r ^ d l .
α = | F 22 H 2 ( 2 ) ( θ d ) | 2 v 2 ( 1 + n x 2 n z 2 + Q 2 β y 2 a 2 n x 4 n z 4 ) 2 β y z a 2 [ V 1 2 J 1 2 ( u ) J 0 2 ( u ) + d 2 V 2 2 F 0 2 K 1 2 ( w d ) K 0 2 ( w d ) ] ,             k n 2 x < β y < k n 3 x , F 22 = { 1 2 k 2 a 2 n x 2 δ y z δ y x 1 D D 2 { F 0 V 2 2 D D 2 - h 1 V 1 2 + h 3 F 0 V 2 2 [ I 2 ( v x d ) K 2 ( v x ) a 22 + I 2 ( v x ) K 2 ( v x d ) a 12 ] } , n y n 2 1 k 2 a 2 n y 2 1 D D 2 { V 1 2 - 1 d F 0 V 2 2 [ I 2 ( v x d ) K 2 ( v x ) a 22 + K 2 ( v x d ) a 12 I 2 ( v x ) ] } , n y = n 2 , D D 2 = - I 2 ( v x ) K 2 ( v x d ) a 12 a 42 + K 2 ( v x ) a 22 a 32 I 2 ( v x d ) , a 12 = I ^ 2 ( v x ) - J ^ 2 ( u x ) , a 22 = K ^ 2 ( v x ) + J ^ 2 ( u x ) , a 32 = I ^ 2 ( v x d ) - H ^ 2 ( θ d ) , a 42 = K ^ 2 ( v x d ) + H ^ 2 ( 2 ) ( θ d ) , h 1 = J ^ 2 ( u x ) + J ^ 0 ( u ) , h 3 = K ^ 0 ( w d ) + H ^ 2 ( 2 ) ( θ d ) , V 1 2 = a 2 k 2 [ n 1 y 2 - n 2 y 2 ] , V 2 2 = a 2 k 2 [ n 3 y 2 - n 2 y 2 ] ,
α = | F 23 H 2 ( 2 ) ( θ d ) | 2 v 2 ( 1 + n x 2 n z 2 + Q 2 β y 2 a 2 n x 4 n z 4 ) 2 β y z a 2 [ V 1 2 J 1 2 ( u ) J 0 2 ( u ) + d 2 V 2 2 F 0 2 K 1 2 ( w d ) K 0 2 ( w d ) ] ,             β y < k n 2 x < k n 3 x , F 23 = { - 1 2 k 2 a 2 n x 2 δ y z δ y x 1 D D 3 { j 4 z h 1 V 1 2 - F 0 V 2 2 D D 3 + h 3 F 0 V 2 2 [ H 2 ( 1 ) ( s d ) ( H 2 ( 2 ) ( s ) a 23 - H 2 ( 1 ) ( s ) H 2 ( 2 ) ( s d ) ( a 13 ] } , n y n z 1 k 2 a 2 n y 2 1 D D 3 { j 4 z V 1 2 + 1 d F 0 V 2 2 [ H 2 ( 1 ) ( s d ) H 2 ( 2 ) ( s ) a 23 - H 2 ( 1 ) ( s ) H 2 ( 2 ) ( s d ) a 13 ] } , n y = n z D D 3 = H ^ 2 ( 1 ) ( s ) H 2 ( 2 ) ( s d ) a 13 a 43 - H 2 ( 2 ) ( s ) H 2 ( 1 ) ( s d ) a 33 a 23 a 13 = H ^ 2 ( 1 ) ( s ) - J ^ 2 ( u x ) ,             a 23 = H ^ 2 ( 2 ) ( s ) - J ^ 2 ( u x ) , a 33 = H ^ 2 ( 1 ) ( s d ) - H ^ 2 ( 2 ) ( θ d ) , a 43 = H ^ 2 ( 2 ) ( s d ) - H ^ 2 ( 2 ) ( θ d ) .

Metrics