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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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
Bjarklev A., Jes B., Bjarklev A.S. (2003). Photonic Crystals Fibers. Kluwer Academic Publishers, Boston
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
Cucinotta A., Selleri S., Vincetti L., Zoboli M. (2002). Holey fiber analysis through the finite-element method. IEEE Photon. Technol. Lett. 14: 1530–1532
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
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
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
Hochman A., Leviatan Y. (2005). Modal dynamics in hollow-core photonic-crystal fibers with elliptical veins. Opt. Express 13: 6193–6201
Issa N., Poladian L. (2003). Vector wave expansion method for leaky modes of microstructured optical fibers. IEEE J. Lightwave Technol. 21: 1005–1012
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
Kotyński R., Antkowiak M., Berghmans F., Theinpont H., Panajotov K. (2005). Photonic crystal fibers with material anisotropy. Opt. Quant. Electron. 37: 253–264
Knight J.C, Broeng J., Birks T.A., Russell P.St.J. (1998). Photonic band gap guidance in optical fibers. Science 283: 1476–1478
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
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
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
Ouyang G., Xu Y., Yariv A. (2002). Theoretical study on dispersion compensation in air-core Bragg fibers. Opt. Express 10: 899–908
Russell P. (2003). Photonic Crystal Fibers. Science 299: 358–362
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
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
Sozuer H.S., Haus W., Inguva R. (1992). Photonic bands: Convergence problems with the plane-wave method. Phys. Rev. B 45: 13962–13972
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
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
Zhu Z., Brown T.G. (2001). Analysis of the space filling modes of photonic crystal fibers. Opt. Express 8: 547–554
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Kotyński, R., Dems, M. & Panajotov, K. Waveguiding losses of micro-structured fibres—plane wave method revisited. Opt Quant Electron 39, 469–479 (2007). https://doi.org/10.1007/s11082-007-9092-6
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DOI: https://doi.org/10.1007/s11082-007-9092-6