Abstract

All optical fibers, including single-mode, multimode, and multicore fibers, exhibit some degree of birefringence, either purposely, such as in polarization-maintaining fibers, or inadvertently due to material or fabrication imperfections. Finding a low-complexity method to accurately calculate the modal characteristics of elliptical fibers has been a long-standing problem. We present a novel accurate perturbative method that avoids the difficulties associated with the traditional Mathieu function treatment. The method is also applicable to a broader class of oscillating systems with elliptical geometry.

© 2017 Optical Society of America

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References

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2015 (1)

2013 (2)

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, J. Lightwave Technol. 31, 398 (2013).
[Crossref]

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

2012 (1)

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

2001 (3)

D. Frenkel and R. Portugal, J. Phys. A 34, 3541 (2001).
[Crossref]

M. van den Broek and F. M. Peeters, Physica E 11, 345 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

1999 (1)

M. Schneider and J. Marquardt, IEEE Trans. Microw. Theory Tech. 47, 513 (1999).
[Crossref]

1989 (1)

1987 (1)

J. Wang and S. She, Opt. Commun. 64, 297 (1987).
[Crossref]

1981 (1)

J. Sakai and T. Kimura, IEEE J. Quantum Electron. 17, 1041 (1981).
[Crossref]

1979 (2)

M. J. Adams, D. N. Payne, and C. M. Ragdale, Electron. Lett. 15, 298 (1979).
[Crossref]

J. D. Love, R. A. Sammut, and A. W. Snyder, Electron. Lett. 15, 615 (1979).
[Crossref]

1978 (2)

1972 (1)

W. O. Schlosser, Bell Syst. Tech. J. 51, 487 (1972).
[Crossref]

1962 (1)

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[Crossref]

Adams, M. J.

M. J. Adams, D. N. Payne, and C. M. Ragdale, Electron. Lett. 15, 298 (1979).
[Crossref]

Agrawal, G. P.

S. Mumtaz, R.-J. Essiambre, and G. P. Agrawal, J. Lightwave Technol. 31, 398 (2013).
[Crossref]

A. J. Antikainen, R. Essiambre, and G. P. Agrawal, Conference on Lasers and Electro-Optics, San José, California, 2017, paper JTu5A.81.

G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).

Antikainen, A. J.

A. J. Antikainen, R. Essiambre, and G. P. Agrawal, Conference on Lasers and Electro-Optics, San José, California, 2017, paper JTu5A.81.

Bibby, M. M.

M. M. Bibby and A. F. Peterson, Accurate Computation of Mathieu Functions (Morgan & Claypool, 2013).

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Chávez-Cerda, S.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Chen, Z.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Cvijetic, N.

Dyott, R. B.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).

Essiambre, R.

A. J. Antikainen, R. Essiambre, and G. P. Agrawal, Conference on Lasers and Electro-Optics, San José, California, 2017, paper JTu5A.81.

Essiambre, R.-J.

Fickler, R.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

French, W. G.

Frenkel, D.

D. Frenkel and R. Portugal, J. Phys. A 34, 3541 (2001).
[Crossref]

Gutiérrez-Vega, J. C.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Hu, Y.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Ip, E.

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Kanonakis, K.

Kimura, T.

J. Sakai and T. Kimura, IEEE J. Quantum Electron. 17, 1041 (1981).
[Crossref]

Krenn, M.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

Kumar, A.

Li, M.-J.

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Liñares, J.

Love, J. D.

J. D. Love, R. A. Sammut, and A. W. Snyder, Electron. Lett. 15, 615 (1979).
[Crossref]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

Marquardt, J.

M. Schneider and J. Marquardt, IEEE Trans. Microw. Theory Tech. 47, 513 (1999).
[Crossref]

Milione, G.

Montero, C.

Morandotti, R.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Moreno, V.

Mumtaz, S.

New, G. H. C.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Payne, D. N.

M. J. Adams, D. N. Payne, and C. M. Ragdale, Electron. Lett. 15, 298 (1979).
[Crossref]

Peeters, F. M.

M. van den Broek and F. M. Peeters, Physica E 11, 345 (2001).
[Crossref]

Peng, G.

Peterson, A. F.

M. M. Bibby and A. F. Peterson, Accurate Computation of Mathieu Functions (Morgan & Claypool, 2013).

Plick, W. N.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

Portugal, R.

D. Frenkel and R. Portugal, J. Phys. A 34, 3541 (2001).
[Crossref]

Prieto, X.

Ragdale, C. M.

M. J. Adams, D. N. Payne, and C. M. Ragdale, Electron. Lett. 15, 298 (1979).
[Crossref]

Ramaswamy, V.

Ramelow, S.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

Ramírez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Rodríguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Sakai, J.

J. Sakai and T. Kimura, IEEE J. Quantum Electron. 17, 1041 (1981).
[Crossref]

Sammut, R. A.

J. D. Love, R. A. Sammut, and A. W. Snyder, Electron. Lett. 15, 615 (1979).
[Crossref]

Schlosser, W. O.

W. O. Schlosser, Bell Syst. Tech. J. 51, 487 (1972).
[Crossref]

Schneider, M.

M. Schneider and J. Marquardt, IEEE Trans. Microw. Theory Tech. 47, 513 (1999).
[Crossref]

She, S.

J. Wang and S. She, Opt. Commun. 64, 297 (1987).
[Crossref]

Snyder, A. W.

J. D. Love, R. A. Sammut, and A. W. Snyder, Electron. Lett. 15, 615 (1979).
[Crossref]

A. W. Snyder and W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
[Crossref]

Standley, R. D.

Stone, J.

Tepichín, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

van den Broek, M.

M. van den Broek and F. M. Peeters, Physica E 11, 345 (2001).
[Crossref]

Varshney, R. K.

Wang, J.

J. Wang and S. She, Opt. Commun. 64, 297 (1987).
[Crossref]

Yeh, C.

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[Crossref]

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Young, W. R.

Zeilinger, A.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

Zhang, P.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Zhang, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

W. O. Schlosser, Bell Syst. Tech. J. 51, 487 (1972).
[Crossref]

Electron. Lett. (2)

J. D. Love, R. A. Sammut, and A. W. Snyder, Electron. Lett. 15, 615 (1979).
[Crossref]

M. J. Adams, D. N. Payne, and C. M. Ragdale, Electron. Lett. 15, 298 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Sakai and T. Kimura, IEEE J. Quantum Electron. 17, 1041 (1981).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

M. Schneider and J. Marquardt, IEEE Trans. Microw. Theory Tech. 47, 513 (1999).
[Crossref]

J. Appl. Phys. (1)

C. Yeh, J. Appl. Phys. 33, 3235 (1962).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Phys. A (1)

D. Frenkel and R. Portugal, J. Phys. A 34, 3541 (2001).
[Crossref]

Opt. Commun. (2)

J. Wang and S. She, Opt. Commun. 64, 297 (1987).
[Crossref]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, Phys. Rev. A 87, 033806 (2013).
[Crossref]

Phys. Rev. Lett. (1)

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

Physica E (1)

M. van den Broek and F. M. Peeters, Physica E 11, 345 (2001).
[Crossref]

Other (5)

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, 1995).

G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).

M. M. Bibby and A. F. Peterson, Accurate Computation of Mathieu Functions (Morgan & Claypool, 2013).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

A. J. Antikainen, R. Essiambre, and G. P. Agrawal, Conference on Lasers and Electro-Optics, San José, California, 2017, paper JTu5A.81.

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Figures (1)

Fig. 1.
Fig. 1.

Predictions for normalized birefringence between the fundamental modes using different methods. n1=1.5, n2=1.49, and the core ellipse axis ratio is d/D=0.9 (after Ref. [3] with corrections [22]).

Equations (16)

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

n(x,y)={n1,(x/a)2+(y/b)21n2,(x/a)2+(y/b)2>1.
[(1+δ)w2+y2+(k2β2)]F(w,y)=0,
F(w,y)=n=0δnFn(w,y),
[w2+y2+(k2β2)]F0(w,y)=0,
[w2+y2+(k2β2)]Fn(w,y)=w2Fn1(w,y),
F0=n=0ansin(nϕ+ϕn)Zn(γr),
F=n=0cnZn(γr)sin(nϕ+ϕn)+δnFn(p)(r,ϕ),
F1(p)=Apr8[Jn+1(pr)Jn1(pr)]sin(nϕ)Apr16[Jn+3(pr)Jn+1(pr)]sin[(n+2)ϕ]Apr16[Jn1(pr)Jn3(pr)]sin[(n2)ϕ],
F1(p)=Aqr8[Kn+1(qr)+Kn1(qr)]sin(nϕ)+Aqr16[Kn+3(qr)+Kn+1(qr)]sin[(n+2)ϕ]+Aqr16[Kn1(qr)+Kn3(qr)]sin[(n2)ϕ],
Fx1jnsn+x2jn+2sn+2+x3jn2sn2+x1δpr8(jn+1jn1)snx1δpr16(jn+3jn+1)sn+2x1δpr16(jn1jn3)sn2
Fx4knsn+x5kn+2sn+2+x6kn2sn2+x4δqr8(kn+1+kn1)sn+x4δqr16(kn+3+kn+1)sn+2+x4δqr16(kn1+kn3)sn2
ET=iβakc2[(bcos2ϕ+asin2ϕ)Ezr+(ab)sinϕcosϕrEzϕ+ωμβ(ab)sinϕcosϕHzr+ωμβacos2ϕ+bsin2ϕrHzϕ]r^+iβakc2[ωμβ(bcos2ϕ+asin2ϕ)Hzrωμβ(ab)sinϕcosϕrHzϕ+(ab)sinϕcosϕEzr+acos2ϕ+bsin2ϕrEzϕ]ϕ^,
HT=iβakc2[(bcos2ϕ+asin2ϕ)Hzr+(ab)sinϕcosϕrHzϕωϵβ(ab)sinϕcosϕEzrωϵβacos2ϕ+bsin2ϕrEzϕ]r^+iβakc2[ωϵβ(bcos2ϕ+asin2ϕ)Ezr+ωϵβ(ab)sinϕ  cosϕrEzϕ+(ab)sinϕcosϕHzr+acos2ϕ+bsin2ϕrHzϕ,]ϕ^,
Et=iμωkc2[b2a22abNsin(2ϕ)ϕHz+βμωNϕEzNarHz],
Ht=iϵωkc2[b2a22abNsin(2ϕ)ϕEzβϵωNϕHzNarEz],
B=DΔβ[1(d/D)2][1(n2/n1)2]3/2,