Abstract

The vector modal patterns of anisotropic fiber couplers composed of nonidentical cores with nonaligned optical axes are presented. The four normal modes have different propagation constants with the corresponding electrical-field vectors pointing in different directions.

© 1989 Optical Society of America

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References

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  1. D. J. Michell, A. W. Snyder, “Modes of nonlinear couplers—building blocks for physical insight,” submitted to Opt. Lett.
  2. A. W. Snyder, A. Stevenson, IEEE J. Lightwave Technol. LT-6, 450 (1988).
    [CrossRef]
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 18 and 21.

1988 (1)

A. W. Snyder, A. Stevenson, IEEE J. Lightwave Technol. LT-6, 450 (1988).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 18 and 21.

Michell, D. J.

D. J. Michell, A. W. Snyder, “Modes of nonlinear couplers—building blocks for physical insight,” submitted to Opt. Lett.

Snyder, A. W.

A. W. Snyder, A. Stevenson, IEEE J. Lightwave Technol. LT-6, 450 (1988).
[CrossRef]

D. J. Michell, A. W. Snyder, “Modes of nonlinear couplers—building blocks for physical insight,” submitted to Opt. Lett.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 18 and 21.

Stevenson, A.

A. W. Snyder, A. Stevenson, IEEE J. Lightwave Technol. LT-6, 450 (1988).
[CrossRef]

IEEE J. Lightwave Technol. (1)

A. W. Snyder, A. Stevenson, IEEE J. Lightwave Technol. LT-6, 450 (1988).
[CrossRef]

Other (2)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 18 and 21.

D. J. Michell, A. W. Snyder, “Modes of nonlinear couplers—building blocks for physical insight,” submitted to Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Cross section of a birefringent coupler consisting of two nonidentical anisotropic cores embedded in an infinite isotropic cladding. The coupler in (a) is equivalent to the one in (b) because of negligible form birefringence.2

Fig. 2
Fig. 2

Modal field polarizations for the four normal modes of anisotropic couplers composed of nonidentical cores for various Q and Δβ values. (a) Δβ ≪ 1, (b) Δβ = cos θ, and (c) Δβ ≫ 1. The vectors represent the polarization directions of electrical-field vectors within each core region.

Fig. 3
Fig. 3

Propagation constants for each normal mode of the anisotropic coupler consisting of nonidentical cores against the birefringence parameter Q for a tilt angle of (a) θ = 0 and (b) θ 0, where β = (βα1 + βα2 + βb1 + βα2)/4.

Equations (7)

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e j = N j [ ( a ˆ 1 + α j b ˆ 1 ) ψ 1 + η j ( a ˆ 2 + γ j b ˆ ) ψ 2 ] ,
β j = β a 1 + β a 2 + β b 1 + β b 2 4 ± C [ Q 2 ± 2 Q ( Δ β 2 + cos 2 θ ) 1 / 2 + Δ β 2 + 1 ] 1 / 2 ,
d a j d z = i [ β aj a j + C cos θ a 3 j + ( 1 ) j C sin θ b 3 j ] ,
d b j d z = i [ β bj b j + ( 1 ) 3 j C sin θ a 3 j + C cos θ b 3 j ] .
[ e 1 , e 2 , e 3 , e 4 ] = [ a 1 , b 1 , a 2 , b 2 ] [ T ] ,
[ T ] = [ N 1 N 2 N 3 N 4 α 1 N 1 α 2 N 2 α 3 N 3 α 4 N 4 η 1 N 1 η 2 N 2 η 3 N 3 η 4 N 4 γ 1 η 1 N 1 γ 2 η 2 N 2 γ 3 η 3 N 3 γ 4 η 4 N 4 ]
[ a 1 ( z ) b 1 ( z ) a 2 ( z ) b 2 ( z ) ] = [ T ] [ e j β 1 z 0 0 0 0 e j β 2 z 0 0 0 0 e j β 3 z 0 0 0 0 e j β 4 z ] × [ T ] [ a 1 ( 0 ) b 1 ( 0 ) a 2 ( 0 ) b 2 ( 0 ) ] ,

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