Ukrainian Journal of Physical Optics 
Home page
 
 

Other articles 

in this issue
Supermodes of a double-ring fibre array with symmetric coupling
Download this article

Alexeyev C. N., Fadeyeva T. A., Boklag N. A. and Yavorsky M. A.

We study the structure of supermodes of a double-ring array of identical evanescently coupled single-mode fibres with the same coupling constant, which describes interaction between the fibres. We ob-tain the expressions for normal modes of such an array and the spectrum of their propagation con-stants. We show that these supermodes are represented by symmetric and antisymmetric combinations of supermodes of a single-ring circular array.

Keywords: fibre array, circular array, double-ring array

PACS: 42.81Q; 42.81Qb
UDC: 535.32
Ukr. J. Phys. Opt. 12 83-88 doi: 10.3116/16091833/12/2/83/2011
Received: 01.03.2011

Анотація. Досліджено структуру супермод двокільцевого джгута ідентичних, радіаційно зв’язаних одномодових волокон з однаковим значенням константи зв’язку, що описує взаємодію між волокнами. Отримано вираз для нормальних мод цього джгута і спектр констант поширення. Показано, що його супермоди можна представити симетричною та антисиметричною ком-бінацією супермод однокільцевого круглого джгута..
REFERENCES
  1. Jones A L, 1965. Coupling of optical fibers and scattering in fibers. J. Opt. Soc. Amer. 55: 261–269. doi:10.1364/JOSA.55.000261
  2. Szameit A, Pertsch T, Dreisow F, Nolte S and Tünnermann A, 2007. Light evolution in arbitrary two-dimensional waveguide arrays. Phys. Rev. A. 75: 053814. doi:10.1103/PhysRevA.75.053814
  3. Efremidis N K, Zhang P, Chen Z, Christodoulides D N, Rüter C E and Kip D, 2010. Wave propa-gation in waveguide arrays with alternating positive and negative couplings. Phys. Rev. A. 81: 053817. doi:10.1103/PhysRevA.81.053817
  4. Patra K C, Srivastava S and Sharma E K, 2010. Power exchange in strongly coupled diffused channel waveguide arrays: an analytical approach. J. Opt. 12: 08550. doi:10.1088/2040-8978/12/8/085501
  5. Christodulides DN, Lederer F, Silberberg Y, 2003. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature. 424: 817–823. doi:10.1038/nature01936PMid:12917695
  6. Longhi S, 2009. Discrete diffraction and shape-invariant beams in optical waveguide arrays. Phys. Rev. A. 79: 033847. doi:10.1103/PhysRevA.79.033847
  7. Longhi S, 2009. Rectification of light refraction in curved waveguide arrays. Opt. Lett. 34: 458–460. doi:10.1364/OL.34.000458 PMid:19373340
  8. Kartashov Y V, Malomed B A, Vysloukh V A and Torner L, 2009. Stabilization of multibeam necklace solitons in circular arrays with spatially modulated nonlinearity. Phys. Rev. A. 80: 053816. doi:10.1103/PhysRevA.80.053816
  9. Setzpfandt F, Sukhorukov A A, Neshev D N, Schiek R, Kivshar Y S and Pertsch T, 2010. Phase transitions of nonlinear waves in quadratic waveguide arrays. Phys. Rev. Lett. 105: 233905. doi:10.1103/PhysRevLett.105.233905 PMid:21231464
  10. Longhi S, 2009. Polychromatic optical Bloch oscillations. Opt. Lett. 34: 2174–2176. doi:10.1364/OL.34.002174 PMid:19823539
  11. Thompson C, Vemuri G and Agarwal G S, 2010. Anderson localization with second quantized fields in a coupled array of waveguides. Phys. Rev. A. 82: 053805. doi:10.1103/PhysRevA.82.053805
  12. Khomeriki R, 2010. Nonlinear Landau-Zener tunneling in coupled waveguide arrays. Phys. Rev. A. 82: 013839. doi:10.1103/PhysRevA.82.013839
  13. Wang X, Fu J, Liu X and Tong L-M, 2009. Subwavelength focusing by a micro/nanofiber array. J. Opt. Soc. Amer. A. 26: 1827–1833. doi:10.1364/JOSAA.26.001827
  14. Snyder A W, 1972. Coupled-mode theory for optical fibers. J. Opt. Soc. Amer. 62: 1267–1277. doi:10.1364/JOSA.62.001267
  15. Snyder A W and Love J D, Optical waveguide theory. London, New York: Chapman and Hall (1985). 
  16. Longhi S, 2007. Light transfer control and diffraction management in circular fibre waveguide arrays. J. Phys. B. 40: 4477. doi:10.1088/0953-4075/40/23/008
  17. Kurti R S, Halterman K, Shori R K and Wardlaw M J, 2009. Discrete cylindrical vector beam generation from an array of optical fibers. Opt. Express. 17: 13982–13988. doi:10.1364/OE.17.013982 PMid:19654806
  18. Yu Y F, Fu Y H, Zhang X M, Liu A Q, Bourouina T, Mei T, Shen Z X and Tsai D P, 2010. Pure angular momentum generator using a ring resonator. Opt. Express. 18: 21651–21662. doi:10.1364/OE.18.021651 PMid:20941064
  19. Alexeyev C N, Volyar A V and Yavorsky M A, 2009. Linear azimuthons in circular fiber arrays and optical angular momentum of discrete optical vortices. Phys. Rev. A. 80: 063821. doi:10.1103/PhysRevA.80.063821
  20. Alexeyev C N, Alexeyev A N, Boklag N A and Yavorsky M A, 2009. Effect of the spin-orbit interaction on polarization conversion in coupled waveguides. J. Opt. A: Pure Appl. Opt. 11: 125404. doi:10.1088/1464-4258/11/12/125404
  21. Alexeyev C N, Boklag N A and Yavorsky M A, 2010. Higher order modes of coupled optical fibres. J. Opt. 12: 115704. doi:10.1088/2040-8978/12/11/115704
  22. Davydov A S, Quantum mechanics. Oxford: Pergamon (1976). 
  23. Alexeyev C N, Boklag N A, Fadeyeva T A and Yavorsky M A, 2010. Tunnelling of orbital angular momentum in parallel optical waveguides. J. Opt. 13 (in press). 
(c) Ukrainian Journal of Physical Optics