Abstract

A novel supercell overlapping method is developed to analyze the photonic crystal fibers (PCFs). The electric field is decomposed using the localized Hermite-Gaussian functions, and the dielectric constant of the PCF missing the central air hole is considered as the sum of two different periodic dielectric structures of virtual perfect photonic crystals (PCs). The structures of both virtual PCs are expanded in cosine functions. From the wave equations and the orthonormality of Hermite-Gaussian functions,the propagation characteristics of the PCF, such as the mode field distribution,the effective area, the birefringence, and the dispersion properties, are obtained. There are fewer computations, and all the elements of the eigenvalue equation are analytical. We are convinced that this novel method is accurate and efficient due to the numerical calculation processes and its results.

© 2004 IEEE

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J. Lightwave Technol. (9)

T. M. Monro, D. J. Richardson, N. G. R. Broderick and P. J. Bennett, "Modeling large air fraction holey optical fibers", J. Lightwave Technol., vol. 18, pp. 50-56, 2000.

T. M. Monro, D. J. Richardson, N. G. R. Broderick and P. J. Bennett, "Holey optical fibers: An efficient modal model", J. Lightwave Technol., vol. 17, pp. 1093-1102, 1999.

D. Mogilevtsev, T. A. Birks and P. S. Russell, "Localized function method for modeling defect mode in 2-D photonic crystal", J. Lightwave Technol., vol. 17, pp. 2078-2081, 1999.

M. Koshiba, Y. Tsuji and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits", J. Lightwave Technol., vol. 18, pp. 102-109, 2000.

K. M. Lo, R. C. McPhedran, I. M. Bassett and G. W. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders", J. Lightwave Technol., vol. 12, pp. 396-410, 1994.

M. J. Steel and R. M. Osgood, "Polarization and dispersive properties of elliptical-hole photonic crystal fibers", J. Lightwave Technol., vol. 19, pp. 495-503, 2001.

C. D. Poole, N. S. Bergano, R. E. Wagner and H. J. Schulte, "Polarization dispersion and principal states in a 147-km undersea lightwave cable", J. Lightwave Technol., vol. 6, pp. 1185-1190, 1988.

G. J. Foschini and C. D. Poole, "Statistical theory o polarization dispersion in single mode fibers", J. Lightwave Technol., vol. 9, pp. 1439-1456, 1991.

L. P. Shen, W. P. Huang and S. S. Jian, "Design of photonic crystal fibers for dispersion-related applications", J. Lightwave Technol., vol. 21, pp. 1644-1651, 2003.

Opt. Express (7)

Opt. Lett. (5)

Other (21)

T. P. White, R. C. McPhedran, C. M. de Sterke and L. C. Botten, "Multipole method for efficient microstructured optical fiber calculations", in QELS2001,, JTuC6,. pp. 123-124.

R. Guobin, L. Shuqin, W. Zhi and J. Shuisheng, "Study on dispersion properties of photonic crystal fiber by effective-index model", ACTA Optica Sinica, to be published.

A. Ferrando, E. Silvestre, J. J. Miret and P. Andres, "Vector description of higher-order modes in photonic crystal fibers", J. Opt. Soc. Amer. A, vol. 17, pp. 1333-1340, 2000.

M. Koshiba, "Full vector analysis of photonic crystal fibers using the finite elelment method", in IEICE Electron, vol. 4, 2002, E85-C,. pp. 881-888.

F. Brechet, J. Marcou, D. Pagnoux and P. Roy, "Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method", Opt. Fiber Technol., vol. 6, pp. 181-191, 2000.

T. A. Birks, D. Mogilevtsev, J. C. Knight, P. S. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan and J. C. Fajardo, "The analogy between photonic crystal fibers and step index fibers", in OFC'98,, FG4,. pp. 114-116.

J. Broeng, D. Mogilevstev, S. E. Barkou and A. Bjarklev, "Photonic crystal fibers: A new class of optical waveguides", Opt. Fiber Technol., vol. 5, pp. 305-330, 1999.

S. E. Barkou, J. Broeng and A. Bjarklev, "Dispersion properties of photonic bandgap guiding fibers", in OFC'98,, FG5,. pp. 117-119.

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals: Molding The Flow Of Light, New York: Princeton Univ. Press, 1995.

J. M. Dudley and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers", IEEE J. Select. Topics Quantum Electron., vol. 8, pp. 651-659, 2002.

N. A. Mortensen, J. R. Folken, P. M. W. Skovgaard and J. Broeng, "Numerical aperture of single-mode photonic crystal fibers", IEEE Photon. Technol. Lett., vol. 14, pp. 1094-1096, 2002.

J. Broeng, D. Mogilevtsev, S. E. B. Libori and A. Bjarklev, "Polarization-preserving holey fibers", in OFC'2001,, MA1.3,. pp. 6-7.

R. B. Dyott, Elliptical Fiber Waveguides, Boston, MA: Artech House, 1995.

C. A. De Francisco, B. V. Borges and M. A. Romero, "A semivectorial iterative finite-difference method to model photonic crystal fibers", in SBMO/IEEE MTT-S IMOC, 2001, pp. 407-409.

C. Kim and J. O'Brien, "Maximization of transmission at branches in photonic crystal waveguides", in OFC2002,, ThK6,. pp. 471-472.

L. P. Shen, C. L. Xu and W. P. Huang, "Modal characteristics of index-guiding photonic crystal fibers: A comparison between scalar and vector analysis", Modal characteristics of index-guiding photonic crystal fibers: A comparison between scalar and vector analysis,

A. W. Snyder and J. D. Love, Optical Waveguide Theory, New York: Chapman and Hall, 1983.

I. S. Gradshtein and I. M. Ryzhik, Tables Of Integrals, Series and Products, New York: Academic, 1994.

I. Kimel and L. R. Elias, "Relations between hermite and laguerre gaussian modes", IEEE J. Quantum Electron., vol. 29, pp. 2562 -2567, 1993.

W. Zhi, R. Guobin, L. Shuqin, L. Weijun and J. Shuisheng, "The mode characteristics of the photonic crystal fibers", ACTA Optica Sinica, to be published.

R. G. Bin, W. Zhi, L. S. Qin and S. S. Jian, "Study on dispersion properties of photonic crystal fiber by effective-index model", in Proc. OECC'2003,.

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