Analysis of optical characteristics of holey photonic crystal devices with the extended coupled-mode formalism

  • Elena Smith
  • Vladislav ShteemanEmail author
  • Amos A. Hardy


Presented here is a new approach for analysis of the so-called holey photonic crystals—a class of electro-optical components, in which periodicity of air holes in dielectric media is used for confinement of light. This class includes several kinds of microstructured fibers, semiconductor lasers etc. Accurate evaluation of optical characteristics of those devices is usually a complicated problem due to the large dimensions and the fine structure of their refractive index distribution. Furthermore, usually, only numerical solutions for this class of optical components are available. The overwhelming majority of the physical models, suitable for analysis of holey photonic devices, proceed from the “natural” assumption: the devices are considered as arrays of air holes, surrounded by dielectric material. In this work we propose another model. Namely, we treat them as arrays of dielectric spots (waveguides), embedded in the air (cladding material). This model allows utilization of the extended coupled-mode theory (a relatively new approach designed for analysis of infinite arrays of coupled waveguides and previously considered inapplicable to holey optical components) for calculations of the latter. In this sense, we present a new method for analysis of holey photonic crystals. On the one hand, our method allows analytical evaluation of some optical characteristics of holey optical components (such as the number of photonic bands and bandwidth). On the other hand, accurate numerical computation of the photonic band structure of the holey photonic devices, incorporating a large number of holes, can be done with this technique on a timescale of several minutes.


Holey photonic crystals Photonic crystal fibers Semiconductor lasers Extended coupled-mode theory Photonic band structure 



Vladislav Shteeman would like to thank Nir Shteeman for his help and support.


  1. Doerr, C., Kogelnik, H.: Dielectric waveguide theory. IEEE J. Lightwave Technol. 26(9), 1176–1187 (2008)ADSCrossRefGoogle Scholar
  2. Giladi, L., Smith, E., Shteeman, V., Kapon, E., Hardy, A.A.: Coupled-mode analysis of holey photonic crystals. In: Proceedings of the IEEEI 2014, 2014 IEEE 28th Convention of Electrical and Electronics Engineers in Israel (English), pp. 1–5 (2014)Google Scholar
  3. Hardy, A.A., Kapon, E.: Coupled-mode formulations for parallel-laser resonators with application to vertical-cavity semiconductor-laser arrays. IEEE J. Quantum Electron. 32, 966–971 (1996)ADSCrossRefGoogle Scholar
  4. Hardy, A.A., Streifer, W.: Coupled mode solutions of multiwaveguide systems. IEEE J. Quantum Electron. 22(4), 528–534 (1986)ADSCrossRefGoogle Scholar
  5. Hardy, A.A., Streifer, W., Osinski, M.: Coupled mode equations for multiwaveguide systems in isotropic or anisotropic media. Opt. Lett. 11(11), 742–744 (1986)ADSCrossRefGoogle Scholar
  6. Hertel, P.: Lectures on Theoretical Physics. Dielectric Waveguides. University of Osnabruck, Osnabrück (2004)Google Scholar
  7. Kittel, C.: Quantum theory of Solids. Wiley, Hoboken (1963)zbMATHGoogle Scholar
  8. Knight, J., Birks, T., Russell, P.: Photonic band gap guidance in optical fibers. Science 282, 1476–1478 (1998)CrossRefGoogle Scholar
  9. Sakoda, K.: Optical Properties of Photonic Crystals. Springer, Berlin (2001)CrossRefGoogle Scholar
  10. Shteeman, V., Boiko, D., Kapon, E., Hardy, A.A.: Extension of coupled mode analysis to periodic large arrays of identical waveguides for photonic crystals applications. IEEE J. Quantum Electron. 43(3), 215–224 (2007)ADSCrossRefGoogle Scholar
  11. Shteeman, V., Nusinsky, I., Kapon, E., Hardy, A.A.: Extension of coupled mode analysis to infinite photonic superlattices. IEEE J. Quantum Electron. 44(8), 826–833 (2008)ADSCrossRefGoogle Scholar
  12. Snyder, A.: Coupled-mode theory for optical fibers. J. Opt. Soc. Am. 62(11), 1267–1277 (1972)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringORT Braude College of EngineeringKarmielIsrael
  2. 2.Department of Electrical Engineering – Physical ElectronicsTel Aviv UniversityRamat AvivIsrael

Personalised recommendations