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Waveguiding losses of micro-structured fibres—plane wave method revisited

Optical and Quantum Electronics volume 39, Article number: 469 (2007) Cite this article

Abstract

We present a numerical method for the analysis of translationally invariant systems with anisotropic and dispersive electric and magnetic properties. This material model enables us to calculate the mode structure of photonic devices such as photonic crystal fibres (PCF) containing inclusions with anisotropic, conducting, magnetic, or negative index materials. The method is based on the popular plane wave (PWM) discretisation scheme applied to the generalised vectorial transmission line equations. The analysis is focused on the calculation of radiation losses. For this purpose we consider a uniaxial perfectly matched layer (UPML) termination of the otherwise periodic system. We asses the accuracy of the method and the properties of spurious modes created inside the UPML.

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References

  • Antkowiak M., Kotyński R., Nasilowski T., Lesiak P., Wojcik J., Urbanczyk W., Berghmans F., Thienpont H. (2005). Phase and group modal birefringence of triple-defect photonic crystal fibres. J. Opt. A: Pure Appl. Opt. 7: 763–766

    Article  ADS  Google Scholar 

  • Bjarklev A., Jes B., Bjarklev A.S. (2003). Photonic Crystals Fibers. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Campbell S., McPhedran R.C., de Sterke C.M., Botten L.C. (2004). Differential multipole method for microstructured optical fibers. J. Opt. Soc. Am. B 21: 1919–1928

    ADS  Google Scholar 

  • Cucinotta A., Selleri S., Vincetti L., Zoboli M. (2002). Holey fiber analysis through the finite-element method. IEEE Photon. Technol. Lett. 14: 1530–1532

    Article  ADS  Google Scholar 

  • Dems M., Kotyński R., Panajotov K. (2005). Plane Wave Admittance Mehtod— a novel approach for determining the electromagnetic modes in photonic structures. Opt. Express. 13: 3196–3207

    Article  ADS  Google Scholar 

  • Ferrando A., Silvestre E., Miret J.J., Andres P., Andres M.V. (1999). Full-vector analysis of a realistic photonic crystal fiber. Opt. Lett. 24: 276–278

    ADS  Google Scholar 

  • Hochman A., Leviatan Y. (2005). Calculation of confinement losses in photonic crystal fibers by use of a source-model technique. J. Opt. Soc. Am. B 22: 474–480

    Article  ADS  Google Scholar 

  • Hochman A., Leviatan Y. (2005). Modal dynamics in hollow-core photonic-crystal fibers with elliptical veins. Opt. Express 13: 6193–6201

    Article  ADS  Google Scholar 

  • Issa N., Poladian L. (2003). Vector wave expansion method for leaky modes of microstructured optical fibers. IEEE J. Lightwave Technol. 21: 1005–1012

    Article  ADS  Google Scholar 

  • Johnson S.G., Joannopoulos J.D. (2001). Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8: 173–190

    ADS  Article  Google Scholar 

  • Kotyński R., Antkowiak M., Berghmans F., Theinpont H., Panajotov K. (2005). Photonic crystal fibers with material anisotropy. Opt. Quant. Electron. 37: 253–264

    Article  Google Scholar 

  • Knight J.C, Broeng J., Birks T.A., Russell P.St.J. (1998). Photonic band gap guidance in optical fibers. Science 283: 1476–1478

    Article  Google Scholar 

  • Monro T.M., Richardson D.J., Broderick N.G.R., Bennett P.J. (2000). Modelling large air fraction holey optical fibers. IEEE J. Lightwave Technol. 18: 50–56

    Article  ADS  Google Scholar 

  • Panajotov K., Kotyński R., Camarena M., Thienpont H. (2005). Modeling of the polarization behavior of elliptical surface-relief VCSELs. Opt. Quant. Electron. 37: 241–252

    Article  Google Scholar 

  • Pottage J.M., David, Bird, Hedley T.D., Knight J.C., Birks T.A., Russell P.St.J., Roberts P.J. (2003). Robust photonic band gaps for hollow core guidance in PCF made from high index glass. Opt. Express 11: 2854–2861

    ADS  Article  Google Scholar 

  • Ouyang G., Xu Y., Yariv A. (2002). Theoretical study on dispersion compensation in air-core Bragg fibers. Opt. Express 10: 899–908

    ADS  Google Scholar 

  • Russell P. (2003). Photonic Crystal Fibers. Science 299: 358–362

    Article  ADS  Google Scholar 

  • Saitoh K., Koshiba M. (2001). Full-vectorial finite element beam propagation method with perfectly matched layers for anistropic optical waveguides. IEEE J. Lightwave Technol. 19: 405–413

    Article  ADS  Google Scholar 

  • Sauvan C., Lalanne P., Hugonin J.P. (2004). Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory. Opt. Quant. Electron. 36: 271–284

    Article  Google Scholar 

  • Sozuer H.S., Haus W., Inguva R. (1992). Photonic bands: Convergence problems with the plane-wave method. Phys. Rev. B 45: 13962–13972

    Article  ADS  Google Scholar 

  • Szpulak M., Urbanczyk W., Serebryannikov E., Zheltikov A., Hochman A., Leviatan Y., Kotyński R., Panajotov K. (2006). Comparison of different methods for rigorous modeling of photonic crystal fibers. Opt. Express 14: 5699–5714

    Article  ADS  Google Scholar 

  • White T.P.,Kuhlmey B.T., McPhedran R. C., Maystre D., Renversez G., de Sterke C.M, Botten L.C. (2002). Multipole method for microstructured optical fibers. I. Formaulation. J. Opt. Soc. Am. B 19: 2322–2330

    ADS  Article  Google Scholar 

  • Zhu Z., Brown T.G. (2001). Analysis of the space filling modes of photonic crystal fibers. Opt. Express 8: 547–554

    ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Warsaw University, Pasteura 7, Warsaw, 02-093, Poland

    Rafał Kotyński

  2. Institute of Physics, Technical University of Łódź, Wólczańska 219, Lodz, 93-005, Poland

    Maciej Dems

  3. Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Krassimir Panajotov

  4. Institute of Solid State Physics, 72 Tzarigradsko Chaussee Blvd., Sofia, 1784, Bulgaria

    Krassimir Panajotov

Authors
  1. Rafał Kotyński
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  2. Maciej Dems
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  3. Krassimir Panajotov
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Correspondence to Rafał Kotyński.

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Kotyński, R., Dems, M. & Panajotov, K. Waveguiding losses of micro-structured fibres—plane wave method revisited. Opt Quant Electron 39, 469 (2007). https://doi.org/10.1007/s11082-007-9092-6

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  • DOI: https://doi.org/10.1007/s11082-007-9092-6

Keywords

  • Plane wave method
  • Perfectly matched layer
  • Photonic crystal fibres
  • Radiation losses
  • Anisotropy
  • Magnetic material