Abstract

Nearest-neighbor coupled-mode theory is a powerful framework to describe electromagnetic-wave propagation in multicore fibers, but it lacks precision as the separation between cores decreases. We use abstract symmetries to study a ring of evenly distributed identical cores around a central core, a common configuration used in telecommunications and sensing. We find its normal modes and their effective propagation constants while including the effect of all high-order inter-core couplings. Finite element simulations support our results to good agreement. Only two of these effective modes involve fields in all the cores. These two modes display opposite-sign phase configurations between the fields in the external cores and the central core. These two modes still appear in the limit where the external cores become a continuous ring. Our results might help improve predictions for crosstalk in telecommunications or precision in sensing applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

D. J. Nodal Stevens, B. Jaramillo Ávila, and B. M. Rodríguez-Lara, “Necklaces of PT-symmetric dimers,” Photonics Res. 6(5), A31 (2018).
[Crossref]

B. M. Rodríguez-Lara, R. El-Ganainy, and J. Guerrero, “Symmetry in optics and photonics: a group theory approach,” Sci. Bull. 63(4), 244–251 (2018).
[Crossref]

2017 (3)

H. Choi, M. Park, D. S. Elliott, and K. Oh, “Optomechanical measurement of the Abraham force in an adiabatic liquid-core optical-fiber waveguide,” Phys. Rev. A 95(5), 053817 (2017).
[Crossref]

I. Chekhovskoy, M. Sorokina, A. Rubenchik, and M. Fedoruk, “Spatiotemporal multiplexing based on hexagonal multicore optical fibres,” Quantum Electron. 47(12), 1150–1153 (2017).
[Crossref]

D. A. May-Arrioja and J. R. Guzman-Sepulveda, “Highly sensitive fiber optic refractive index sensor using multicore coupled structures,” J. Lightwave Technol. 35(13), 2695–2701 (2017).
[Crossref]

2016 (2)

Z. Zhao, M. A. Soto, M. Tang, and L. Thévenaz, “Distributed shape sensing using Brillouin scattering in multi-core fibers,” Opt. Express 24(22), 25211 (2016).
[Crossref]

J. D. Huerta Morales, J. Guerrero, S. López-Aguayo, and B. M. Rodríguez-Lara, “Revisiting the optical PT-symmetric dimer,” Symmetry 8(9), 83 (2016).
[Crossref]

2015 (4)

2013 (3)

S. O. Arık and J. M. Kahn, “Coupled-core multi-core fibers for spatial multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

A. M. Rubenchik, E. V. Tkachenko, M. P. Fedoruk, and S. K. Turitsyn, “Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core,” Opt. Lett. 38(20), 4232–4235 (2013).
[Crossref]

2012 (2)

2011 (2)

2010 (1)

2009 (1)

2006 (1)

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(06), 1739–1752 (2006).
[Crossref]

2004 (1)

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: The existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107(5), 13 (2004).
[Crossref]

2000 (1)

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36(12), 1438–1444 (2000).
[Crossref]

1996 (1)

R. Vance, “Matrix Lie group-theoretic design of coupled linear optical waveguide devices,” SIAM J. Appl. Math. 56(3), 765–782 (1996).
[Crossref]

1994 (1)

1991 (2)

C. Schmidt-Hattenberger, U. Trutschel, R. Muschall, and F. Lederer, “Envelope description of an optical fibre array with circularly distributed multiple cores,” Opt. Commun. 82(5–6), 461–465 (1991).
[Crossref]

D. B. Mortimore and J. W. Arkwright, “Monolithic wavelength-flattened 1 × 7 single-mode fused fiber couplers: theory, fabrication, and analysis,” Appl. Opt. 30(6), 650–659 (1991).
[Crossref]

1988 (2)

N. Kishi and E. Yamashita, “A simple coupled-mode analysis method for multiple-core optical fiber and coupled dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 36(12), 1861–1868 (1988).
[Crossref]

A. W. Snyder and A. Ankiewicz, “Optical fiber couplers-optimum solution for unequal cores,” J. Lightwave Technol. 6(3), 463–474 (1988).
[Crossref]

1986 (1)

N. Kishi, E. Yamashita, and K. Atsuki, “Modal and coupling field analysis of optical fibers with circularly distributed multiple cores and a central core,” J. Lightwave Technol. 4(8), 991–996 (1986).
[Crossref]

1985 (1)

E. Yamashita, S. Ozeki, and K. Atsuki, “Modal analysis method for optical fibers with symmetrically distributed multiple cores,” J. Lightwave Technol. 3(2), 341–346 (1985).
[Crossref]

1972 (1)

Abe, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-pb/s (12 sdm/222 wdm/456 gb/s) crosstalk-managed transmission with 91.4-b/s/hz aggregate spectral efficiency,” in Eur. Conf. Exhib. Opt. Commun., (2012), p. Th.3.C.1.

Amma, Y.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Ankiewicz, A.

A. W. Snyder and A. Ankiewicz, “Optical fiber couplers-optimum solution for unequal cores,” J. Lightwave Technol. 6(3), 463–474 (1988).
[Crossref]

Antonio-Lopez, J. E.

Arik, S. O.

S. O. Arık and J. M. Kahn, “Coupled-core multi-core fibers for spatial multiplexing,” IEEE Photonics Technol. Lett. 25(21), 2054–2057 (2013).
[Crossref]

Arkwright, J. W.

Atsuki, K.

N. Kishi, E. Yamashita, and K. Atsuki, “Modal and coupling field analysis of optical fibers with circularly distributed multiple cores and a central core,” J. Lightwave Technol. 4(8), 991–996 (1986).
[Crossref]

E. Yamashita, S. Ozeki, and K. Atsuki, “Modal analysis method for optical fibers with symmetrically distributed multiple cores,” J. Lightwave Technol. 3(2), 341–346 (1985).
[Crossref]

Bai, N.

Chan, F. Y. M.

Chekhovskoy, I.

I. Chekhovskoy, M. Sorokina, A. Rubenchik, and M. Fedoruk, “Spatiotemporal multiplexing based on hexagonal multicore optical fibres,” Quantum Electron. 47(12), 1150–1153 (2017).
[Crossref]

Choi, H.

H. Choi, M. Park, D. S. Elliott, and K. Oh, “Optomechanical measurement of the Abraham force in an adiabatic liquid-core optical-fiber waveguide,” Phys. Rev. A 95(5), 053817 (2017).
[Crossref]

Christodoulides, D. N.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(06), 1739–1752 (2006).
[Crossref]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: The existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107(5), 13 (2004).
[Crossref]

Chung, Y.

Correa, R. A.

Cui, L.

Da Ros, F.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Danicic, A.

Dimarcello, F. V.

Droulias, S.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(06), 1739–1752 (2006).
[Crossref]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: The existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107(5), 13 (2004).
[Crossref]

Dutta, M.

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36(12), 1438–1444 (2000).
[Crossref]

Efremidis, N. K.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(06), 1739–1752 (2006).
[Crossref]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: The existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107(5), 13 (2004).
[Crossref]

El-Ganainy, R.

B. M. Rodríguez-Lara, R. El-Ganainy, and J. Guerrero, “Symmetry in optics and photonics: a group theory approach,” Sci. Bull. 63(4), 244–251 (2018).
[Crossref]

Elliott, D. S.

H. Choi, M. Park, D. S. Elliott, and K. Oh, “Optomechanical measurement of the Abraham force in an adiabatic liquid-core optical-fiber waveguide,” Phys. Rev. A 95(5), 053817 (2017).
[Crossref]

Fedoruk, M.

I. Chekhovskoy, M. Sorokina, A. Rubenchik, and M. Fedoruk, “Spatiotemporal multiplexing based on hexagonal multicore optical fibres,” Quantum Electron. 47(12), 1150–1153 (2017).
[Crossref]

Fedoruk, M. P.

Fini, J. M.

Fishteyn, M.

Galili, M.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Goto, Y.

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-pb/s (12 sdm/222 wdm/456 gb/s) crosstalk-managed transmission with 91.4-b/s/hz aggregate spectral efficiency,” in Eur. Conf. Exhib. Opt. Commun., (2012), p. Th.3.C.1.

Guan, N.

K. Takenaga, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “Reduction of crosstalk by quasi-homogeneous solid multi-core fiber,” Opt. Fiber Commun. (OFC), collocated Natl. Fiber Opt. Eng. Conf. 2010 Conf. on (OFC/NFOEC) pp. 35–37 (2010).

Guan, P.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Guerrero, J.

B. M. Rodríguez-Lara, R. El-Ganainy, and J. Guerrero, “Symmetry in optics and photonics: a group theory approach,” Sci. Bull. 63(4), 244–251 (2018).
[Crossref]

J. D. Huerta Morales, J. Guerrero, S. López-Aguayo, and B. M. Rodríguez-Lara, “Revisiting the optical PT-symmetric dimer,” Symmetry 8(9), 83 (2016).
[Crossref]

B. M. Rodríguez-Lara and J. Guerrero, “Optical finite representation of the Lorentz group,” Opt. Lett. 40(23), 5682 (2015).
[Crossref]

Guzman-Sepulveda, J. R.

D. A. May-Arrioja and J. R. Guzman-Sepulveda, “Highly sensitive fiber optic refractive index sensor using multicore coupled structures,” J. Lightwave Technol. 35(13), 2695–2701 (2017).
[Crossref]

D. A. May-Arrioja and J. R. Guzman-Sepulveda, “Fiber optic sensors based on multicore structures,” in Fiber Optic Sensors: Current Status and Future Possibilities, I. R. Matias, S. Ikezawa, and J. Corres, eds. (Springer International Publishing, 2017), pp. 347–371.

Hadzievski, L.

Hizanidis, K.

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Localized modes in a circular array of coupled nonlinear optical waveguides,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(06), 1739–1752 (2006).
[Crossref]

K. Hizanidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, “Centrally coupled circular array of optical waveguides: The existence of stable steady-state continuous waves and breathing modes,” Phys. Scr. T107(5), 13 (2004).
[Crossref]

Hossain, M. A.

M. A. Hossain and S. P. Majumder, “Performance analysis of crosstalk due to inter-core coupling in a heterogeneous multi-core optical fiber communication system,” in 2017 IEEE Int. Conf. Telecomm. Photon. (ICTP), (IEEE, 2017), pp. 142–146.

Hu, H.

H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. Porto da Silva, M. Nooruzzaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E. Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, and L. K. Oxenløwe, “Single-source chip-based frequency comb enabling extreme parallel data transmission,” Nat. Photonics 12(8), 469–473 (2018).
[Crossref]

Huang, W.-P.

Hudgings, J.

J. Hudgings, L. Molter, and M. Dutta, “Design and modeling of passive optical switches and power dividers using non-planar coupled fiber arrays,” IEEE J. Quantum Electron. 36(12), 1438–1444 (2000).
[Crossref]

Huerta Morales, J. D.

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Figures (3)

Fig. 1.
Fig. 1. (a) Array of $n$ identical cores distributed in a circle of radius $R$ around a, possibly-different, central core. The cores in the circle have radius $r_e$ and the central core has radius $r_c$. (b)–(d) show the array when the circle has five, six, and seven cores respectively.
Fig. 2.
Fig. 2. (a)–(g) Comparison of analytic coupled-mode theory (small light orange dots) versus numerical finite element (large dark green dots) normal modes for a multicore fiber composed by seven identical cores; fiber parameters can be found in the text. (a)–(e) Normal modes that do not mix with the central core and (f)–(g) modes that mix with the central core. The propagation constants associated to the normal modes shown in (f) and (g) are $\lambda _{+}$ and $\lambda _{-}$, respectively. In these figures, the horizontal axis is the core number, where $c$ labels the central core and the vertical axis is the real part of the average electric field in each core. Figures (h) and (i) display the real part of the electric field in a cross-section of the waveguide, where the electric field is normalized to its maximum value in the array, for normal modes associated to $\lambda _{+}$ and $\lambda _{-}$, in that order.
Fig. 3.
Fig. 3. Mode profiles for the multicore structure with a continuous ring around a central core with parameters identical to those in Fig. 2.

Equations (11)

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i d d z E ( z ) = M E ( z ) ,
[ M ] p , q = { g k q = p + n k , k = 1 , 2 , , n 1 2 , g k q = p + k , k = 1 , 2 , , n 2 , β q = p , g k p = q + k , k = 1 , 2 , , n 2 , g k p = q + n k , k = 1 , 2 , , n 1 2 .
[ F ] p , q = 1 n e i 2 π n ( p 1 ) ( q 1 ) .
λ j = β + { 2 k = 1 m 1 { g k cos [ π m ( j 1 ) k ] } + g m ( 1 ) j 1 , n = 2 m , 2 k = 1 m { g k cos [ 2 π 2 m + 1 ( j 1 ) k ] } , n = 2 m + 1.
u j = F e ^ j ,
M c = ( M g c g c g c g c β c ) .
D c = ( λ 1 0 0 g c n 0 λ 2 0 0 0 0 λ n 0 g c n 0 0 β c ) .
λ ± = ( λ 1 + β c ± ( λ 1 β c ) 2 + 4 g c 2 n , ) / 2 , λ 2 , , λ n ,
v + = ( u 1 0 ) cos θ + ( 0 n 1 ) sin θ , v = ( u 1 0 ) sin θ + ( 0 n 1 ) cos θ ,
tan θ = 2 n g c λ 1 β c + ( λ 1 β c ) 2 + 4 n g c 2 ,
λ ( R , ± ) = 1 2 ( β R + β c ± ( β R β c ) 2 + 4 g R 2 ) ,

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