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Local-field and effective-background effects in coupled integrated photonic waveguide systems

Anastasiia Sheveleva, Mathieu Leonardo, Christophe Finot, and Pierre Colman*

  • Laboratoire Interdisciplinaire Carnot de Bourgogne UMR CNRS 6303, Université Bourgogne–Franche-Comté, 9 Avenue Savary, 21000 Dijon, France

  • *Corresponding author: pierre.colman@u-bourgogne.fr
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Phys. Rev. A 107, 063502 – Published 1 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.063502

Abstract

The coupling constant between two nearby waveguides is usually predicted using formulas derived from the perturbative theory applied to the electromagnetic Maxwell equations. These formulas, however, fail to provide any reliable estimate when the index contrast between the core of the waveguide and its cladding becomes large. We demonstrate in this paper that a good accuracy can be retrieved if the local field effect is taken into account. Moreover, we show that in case of structured and inhomogeneous cladding, an effective background index must be taken into account so that the local field effect correction remains accurate. This theoretical study is the occasion for physics-oriented discussions regarding the impact of the substrate on the interwaveguide coupling constant.

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References (69)

  1. N. C. Harris, J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, Linear programmable nanophotonic processors, Optica 5, 1623 (2018).
  2. X. Yi, T. X. H. Huang, and R. Minasian, Tunable and reconfigurable photonic signal processor with programmable all-optical complex coefficients, IEEE Trans. Microwave Theory Tech. 58, 3088 (2010).
  3. W.-P. Huang, Coupled-mode theory for optical waveguides: An overview, J. Opt. Soc. Am. A 11, 963 (1994).
  4. A. Yulin, D. V. Skryabin, and A. Vladimirov, Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion, Opt. Express 14, 12347 (2006).
  5. I. Babushkin, A. Husakou, J. Herrmann, and Y. S. Kivshar, Frequency-selective self-trapping and supercontinuum generation in arrays of coupled nonlinear waveguides, Opt. Express 15, 11978 (2007).
  6. A. Joushaghani, R. Iyer, J. K. S. Poon, J. S. Aitchison, C. M. de Sterke, J. Wan, and M. M. Dignam, Quasi-Bloch Oscillations in Curved Coupled Optical Waveguides, Phys. Rev. Lett. 103, 143903 (2009).
  7. Y. Lahini, E. Frumker, Y. Silberberg, S. Droulias, K. Hizanidis, R. Morandotti, and D. N. Christodoulides, Discrete X-Wave Formation in Nonlinear Waveguide Arrays, Phys. Rev. Lett. 98, 023901 (2007).
  8. S. Longhi, Quantum-optical analogies using photonic structures, Laser and Photon. Rev. 3, 243 (2009).
  9. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Observation of Dynamic Localization in Periodically Curved Waveguide Arrays, Phys. Rev. Lett. 96, 243901 (2006).
  10. G. Lenz, I. Talanina, and C. M. de Sterke, Bloch Oscillations in an Array of Curved Optical Waveguides, Phys. Rev. Lett. 83, 963 (1999).
  11. N. Chiodo, G. D. Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, and U. Morgner, Imaging of Bloch oscillations in erbium-doped curved waveguide arrays, Opt. Lett. 31, 1651 (2006).
  12. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Theory of coupled optical PT-symmetric structures, Opt. Lett. 32, 2632 (2007).
  13. N. K. Efremidis, Topological photonic Su-Schrieffer-Heeger-type coupler, Phys. Rev. A 104, 053531 (2021).
  14. N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, Observation of optical Shockley-like surface states in photonic superlattices, Opt. Lett. 34, 1633 (2009).
  15. J. T. Young, C. Wei, C. R. Menyuk, and J. Hu, Mode coupling at avoided crossings in slab waveguides with comparison to optical fibers: Tutorial, J. Opt. Soc. Am. B 38, F104 (2021).
  16. Y. Liu, C. Wu, X. Qiang, J. Wu, X. Yang, and P. Xu, Evanescent-wave coupling phase-matching for ultrawidely tunable frequency conversion in silicon-waveguide chips, Opt. Express 27, 28866 (2019).
  17. B. Liu, H. Yu, Z. Yuan Li, and L. Tong, Phase-matched second-harmonic generation in coupled nonlinear optical waveguides, J. Opt. Soc. Am. B 36, 2650 (2019).
  18. A. Hardy and W. Streifer, Coupled mode theory of parallel waveguides, J. Lightwave Technol. 3, 1135 (1985).
  19. H. Haus, W. Huang, S. Kawakami, and N. Whitaker, Coupled-mode theory of optical waveguides, J. Lightwave Technol. 5, 16 (1987).
  20. J. Ding, J. Lin, and Y. Sun, Calculation of coupling length for spatial waveguides using planar waveguides, Optik 126, 4319 (2015).
  21. M. Kuznetsov, Expressions for the coupling coefficient of a rectangular-waveguide directional coupler, Opt. Lett. 8, 499 (1983).
  22. S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators, Nat. Commun. 8, 372 (2017).
  23. N. Kohli, S. Srivastava, and E. K. Sharma, Orthogonal solutions for asymmetric strongly coupled waveguide arrays: An elegant, analytical approach, J. Opt. Soc. Am. B 31, 2871 (2014).
  24. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Perturbation theory for Maxwell's equations with shifting material boundaries, Phys. Rev. E 65, 066611 (2002).
  25. M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, and Y. Fink, Analysis of general geometric scaling perturbations in a transmitting waveguide: Fundamental connection between polarization-mode dispersion and group-velocity dispersion, J. Opt. Soc. Am. B 19, 2867 (2002).
  26. M. Skorobogatiy, S. Jacobs, S. Johnson, and Y. Fink, Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates, Opt. Express 10, 1227 (2002).
  27. E. Marcatili, Improved coupled-mode equations for dielectric guides, IEEE J. Quantum Electron. 22, 988 (1986).
  28. S. Ghadirli, K. Thyagarajan, and A. Kumar, Band stop filter characteristics of non identical waveguides directional couplers; A comparison of three methods, Opt. Commun. 84, 144 (1991).
  29. K. Okamoto, Coupled mode theory, in Fundamentals of Optical Waveguides (Elsevier, New York, 2006), pp. 159–207.
  30. P.-R. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures, Phys. Rev. E 79, 065601(R) (2009).
  31. X. C. Tong, Silicon-on-insulator waveguides, in Advanced Materials for Integrated Optical Waveguides (Springer International Publishing, Cham, 2013), pp. 253–287.
  32. H. Yıldırım, Dispersion parameters and nonlinear optical properties of silicon nitride rib waveguides, Opt. Commun. 284, 2031 (2011).
  33. J. Wang, Z. Yao, and A. W. Poon, Silicon-nitride-based integrated optofluidic biochemical sensors using a coupled-resonator optical waveguide, Front. Mater. 2 (2015), doi: 10.3389/fmats.2015.00034.
  34. K. Hammani, L. Markey, M. Lamy, B. Kibler, J. Arocas, J. Fatome, A. Dereux, J.-C. Weeber, and C. Finot, Octave spanning supercontinuum in titanium dioxide waveguides, Appl. Sci. 8, 543 (2018).
  35. J.-C. Weeber, K. Hammani, G. C. des Francs, A. Bouhelier, J. Arocas, A. Kumar, F. Eloi, S. Buil, X. Quélin, J.-P. Hermier, M. Nasilowski, and B. Dubertret, Colloidal quantum dot integrated light sources for plasmon mediated photonic waveguide excitation, ACS Photonics 3, 844 (2016).
  36. M. Belt, M. L. Davenport, J. E. Bowers, and D. J. Blumenthal, Ultra-low-loss Ta2O5-core/SiO2-clad planar waveguides on Si substrates, Optica 4, 532 (2017).
  37. S. G. Johnsonand J. D. Joannopoulos, Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis, Opt. Express 8, 173 (2001).
  38. A. W. Snyderand J. D. Love, Green's function methods, in Optical Waveguide Theory (Springer, New York, 1983), pp. 656–665.
  39. L. Ramunnoand S. Hughes, Disorder-induced resonance shifts in high-index-contrast photonic crystal nanocavities, Phys. Rev. B 79, 161303(R) (2009).
  40. A. Yaghjian, Electric dyadic greens functions in the source region, Proc. IEEE 68, 248 (1980).
  41. O. J. F. Martinand N. B. Piller, Electromagnetic scattering in polarizable backgrounds, Phys. Rev. E 58, 3909 (1998).
  42. S. G. Johnson, M. L. Povinelli, M. Soljačić, A. Karalis, S. Jacobs, and J. D. Joannopoulos, Roughness losses and volume-current methods in photonic-crystal waveguides, Appl. Phys. B 81, 283 (2005).
  43. P. V. Rysselberghe, Remarks concerning the Clausius-Mossotti law, J. Phys. Chem. 36, 1152 (1932).
  44. C. Böttcher, Theory of Electric Polarization (Elsevier, New York, 1973).
  45. V. A. Markel, Introduction to the Maxwell Garnett approximation: Tutorial, J. Opt. Soc. Am. A 33, 1244 (2016).
  46. M. B. Doost, W. Langbein, and E. A. Muljarov, Resonant state expansion applied to two-dimensional open optical systems, Phys. Rev. A 87, 043827 (2013).
  47. S. V. Lobanov, W. Langbein, and E. A. Muljarov, Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes, Phys. Rev. A 100, 063811 (2019).
  48. J. E. Sipe, Vector k-p approach for photonic band structures, Phys. Rev. E 62, 5672 (2000).
  49. P. Y. Chen, D. J. Bergman, and Y. Sivan, Generalizing Normal Mode Expansion of Electromagnetic Green's Tensor to Open Systems, Phys. Rev. Appl. 11, 044018 (2019).
  50. S. Rao, G. L. Saux, Y. Sivan, and P. Y. Chen, Generalized normal mode expansion method for open and lossy periodic structures, J. Opt. Soc. Am. B 39, 1338 (2022).
  51. P. T. Kristensen, J. R. de Lasson, and N. Gregersen, Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems, Opt. Lett. 39, 6359 (2014).
  52. M. L. Cooper and S. Mookherjea, Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides, Opt. Express 17, 1583 (2009).
  53. M. Pattersonand S. Hughes, Interplay between disorder-induced scattering and local field effects in photonic crystal waveguides, Phys. Rev. B 81, 245321 (2010).
  54. N. Mann, A. Javadi, P. D. García, P. Lodahl, and S. Hughes, Theory and experiments of disorder-induced resonance shifts and mode-edge broadening in deliberately disordered photonic crystal waveguides, Phys. Rev. A 92, 023849 (2015).
  55. V. LeBihan, A. Pillonnet, D. Amans, G. Ledoux, O. Marty, and C. Dujardin, Critical dimension where the macroscopic definition of refractive index can be applied at a nanometric scale, Phys. Rev. B 78, 113405 (2008).
  56. P. Lunnemann and A. F. Koenderink, The local density of optical states of a metasurface, Sci. Rep. 6, 20655 (2016).
  57. M. Patterson, S. Hughes, D. Dalacu, and R. L. Williams, Broadband Purcell factor enhancements in photonic-crystal ridge waveguides, Phys. Rev. B 80, 125307 (2009).
  58. M. Eguchi, Multilayered effective-index analysis of dielectric waveguides with complicated microstructures, J. Opt. Soc. Am. B 28, 2478 (2011).
  59. N. Mann, S. Combrié, P. Colman, M. Patterson, A. D. Rossi, and S. Hughes, Reducing disorder-induced losses for slow light photonic crystal waveguides through Bloch mode engineering, Opt. Lett. 38, 4244 (2013).
  60. K. S. Chiang, Performance of the effective-index method for the analysis of dielectric waveguides, Opt. Lett. 16, 714 (1991).
  61. T. A. van der Sijs, O. El Gawhary, and H. P. Urbach, Electromagnetic scattering beyond the weak regime: Solving the problem of divergent Born perturbation series by Padé approximants, Phys. Rev. Res. 2, 013308 (2020).
  62. O. J. F. Martin, A. Dereux, and C. Girard, Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape, J. Opt. Soc. Am. A 11, 1073 (1994).
  63. A. Udupiand S. K. Madhava, Plasmonic coupler and multiplexer/demultiplexer based on nano-groove-arrays, Plasmonics 16, 1685 (2021).
  64. P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures, Phys. Rev. B 68, 125404 (2003).
  65. P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, Light interaction with photonic and plasmonic resonances, Laser Photonics Rev. 12, 1700113 (2018).
  66. C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Theory of the Spontaneous Optical Emission of Nanosize Photonic and Plasmon Resonators, Phys. Rev. Lett. 110, 237401 (2013).
  67. M. B. Mia, S. Z. Ahmed, I. Ahmed, Y. J. Lee, M. Qi, and S. Kim, Exceptional coupling in photonic anisotropic metamaterials for extremely low waveguide crosstalk, Optica 7, 881 (2020).
  68. L. C. Andreaniand D. Gerace, Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method, Phys. Rev. B 73, 235114 (2006).
  69. J. Jensenand O. Sigmund, Topology optimization for nano-photonics, Laser Photon. Rev. 5, 308 (2011).

Outline

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Phys. Rev. A 107, 063502– Published 1 June, 2023
  • Received 12 August 2022
  • Revised 28 February 2023
  • Accepted 4 May 2023
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