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Approximate analysis of planar photonic bandgap waveguides: a simple semi-analytical method

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Abstract

A semi-analytical approximate method, Vopt, is applied to a planar photonic bandgap (PBG) waveguide and a coupler configuration. The variational process of the Vopt method presents simple effective index analysis of the complex two dimensional (2-D) structures. The Vopt method expresses the refractive index profile of the 2-D structure as two 1-D refractive index profiles and obtains the optimized indices for the two structures iteratively. The Vopt method separates the planar PBG waveguide into an effective multilayer waveguide confining optical field in the lateral direction and a 1-D Bragg reflector that gives characteristic reflection/transmission spectra. The results obtained by the Vopt method show good agreement with the numerical results of the finite difference time domain analysis. The present analysis is helpful in understanding the optical properties of such complex waveguides and can be used as starting approximation for optimizing the structures for various applications.

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References

  • Adibi, A., Xu, Y., Lee, R.K., Yariv, A., Scherer, A.: Properties of the slab modes in photonic crystal optical waveguides. J. Lightwave Technol. 18, 1554–1564 (2000)

    Article  ADS  Google Scholar 

  • Adibi, A., Xu, Y., Lee, R.K., Yariv, A., Scherer, A.: Guiding mechanism in dielectic-core photonic-crystal optical waveguides. Phys. Rev. B 64, 033308 (2001a)

  • Adibi, A., Xu, Y., Lee, R.K., Loncar, M., Yariv, A., Scherer, A.: Role of distributed Bragg reflection in photonic-crystal optical waveguides. Phys. Rev. B 64, 041102 (2001b)

  • Benisty, H., Lalanne, P., Olivier, S., Rattier, M., Weisbuch, C., Smith, C.J.M., Krauss, T.F., Jouanin, C., Cassagne, D.: Finite-depth and intrinsic losses in vertically etched two-dimensional photonic crystals. Opt. Quantum Electron. 34, 205–215 (2002)

    Article  Google Scholar 

  • Bindal, P., Sharma, A.: Modelling of photonic crystal waveguides: a simple and accurate approach. Opt. Quantum Electron. 42, 435–446 (2011)

    Article  Google Scholar 

  • Chiang, K.S.: Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Opt. Quantum Electron. 26, S113–S134 (1994)

    Article  Google Scholar 

  • Ferrini, R., Houdre, R., Benisty, H., Qiu, M., Moosburger, J.: Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant. J. Opt. Soc. Am. B 20, 469–478 (2003)

    Article  ADS  Google Scholar 

  • Ferrini, R., Berrier, A., Dunbar, L.A., Houdre, R., Mulot, M., Anand, S., Rossi, Sd, Talneau, A.: Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide. Appl. Phys. Lett. 85, 3998–4000 (2004)

    Article  ADS  Google Scholar 

  • Hammer, M., Ivanova, O.V.: Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment. Opt. Quantum Electron. 41, 267–283 (2009)

    Article  Google Scholar 

  • Joannopoulos, J.D., Villeneuve, P.R., Fan, S.: Photonic crystals: putting a new twist on light. Nature 386, 143–149 (1997)

    Article  ADS  Google Scholar 

  • Johnson, S.G., Villeneuve, P.R., Fan, S., Joannopoulos, J.D.: Linear waveguides in photonic-crystal slabs. Phys. Rev. B 62, 8212–8222 (2000)

    Article  ADS  Google Scholar 

  • Knox, R.M., Toulios, P.P.: Integrated circuits for the millimeter through optical frequency range. In: Fox, J. (ed.) Proceedings of the Symposium on Submillimeter Waves, pp. 497–516. Polytechnic Press, Brooklyn (1970)

  • Lalanne, P., Benisty, H.: Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis. J. Appl. Phys. 89, 1512–1514 (2001)

    Article  ADS  Google Scholar 

  • Vassallo, C.: Optical Waveguide Concepts, pp. 40–44. Elsevier, Amsterdam (1991)

  • Yang, L., Motohisa, J., Fukui, T.: Suggested procedure for the use of the effective-index method for high-index-contrast photonic crystal slabs. Opt. Eng. 44, 078002 (2005)

    Google Scholar 

  • Yariv, A., Yeh, P.: Photonics: Optical Electronics in Modern Communications, pp. 555–558. Oxford University Press, New York (2007)

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Acknowledgments

One of the authors (Kanchan Gehlot) would like to thank the Council of Scientific and Industrial Research (CSIR), India, for providing Senior Research Fellowship.

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  1. Department of Physics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Kanchan Gehlot & Anurag Sharma

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  1. Kanchan Gehlot
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  2. Anurag Sharma
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Correspondence to Anurag Sharma.

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Gehlot, K., Sharma, A. Approximate analysis of planar photonic bandgap waveguides: a simple semi-analytical method. Opt Quant Electron 46, 455–464 (2014). https://doi.org/10.1007/s11082-014-9873-7

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  • DOI: https://doi.org/10.1007/s11082-014-9873-7

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