Photonic crystals: modal theory of pc optical fibers and numerical application
by
B. Kuhlmey
Institut Fresnel
Coauthors: D. Maystre, G. Renversez

Since the publication of the original ideas of Yablonovitch and John in 1987 [1, 2], photonic crystals have been the subject of many theoretical and experimental studies. In the recent years, it appeared that one of the most interesting practical applications of photonic crystals could be the fabrication of a new kind of optical fiber: the photonic crystal (pc) fiber. This kind of fiber is made of air holes pierced in a silica fiber.

Recent experimental works have demonstrated the feasibility of making such fibers using the traditional two steps process: fabrication of a fiber preform then drawing of this using a high temperature furnace in a tower setup [3]. Waveguidance in these structures has been shown [4] and very interesting properties have been predicted, for instance the possibility of making single mode fibers at any wavelength or the ability of some of these fibers to concentrate the light power inside the holes.

The attempts at modeling propagation of light in such structures have generally used classical methods like plane wave methods. These methods provide the location of band gaps but, since they use approximations like super-cell representation, they are unable to compute some of the most important features of an optical fiber like radiation losses. The aim of the communication is to describe a rigorous electromagnetic theory of pc fibers of infinite length, which can predict all the performances of these structures. This work has been undertaken in collaboration with the group of R.C. McPhedran and L.C. Botten in the School of Physics of the University of Sydney.

Our theory is inspired by the method developed in our laboratory in the frame of photonic crystal theory [5]. Closely linked theories have been developed almost at the same time and independently by other research groups, in particular in Australia [6]. The first step of the method is to elaborate a theory of scattering of a photonic crystal fiber in conical (off-plane) mounting. As in [5], this theory is based on the use of the scattering matrices of the holes pierced in silica and on the translation properties of Fourier-Bessel functions. In addition, the notion of generalized scattering matrix is employed for the external boundary of the silica fiber. The solution leads to the inversion of a linear system of equations. The second step of the method is to find homogeneous solutions of this scattering problem. It leads to the search for poles of the determinant of the scattering matrix associated to the whole optical fiber.

Examples of numerical results will be given. The losses of pc fibers, which cannot be calculated using the supercell representation, will be analysed as a function of the parameters of the fiber. The influence of a cladding surrounding the fiber will be studied.

References

[1] E. Yablonovitch, Phys. Rev. Letters, 58 (1987) pp. 2059-2062.

[2] S. John, Phys. Rev. Letters, 58 (1987) p. 2486-2489.

[3] A. Bjarklev, Optical fiber amplifiers: design and system applications, Artech House, 1993.

[4] J.C. Knight, J. Broeng, T.A. Birks and P.St Russel, Science, 262 (1998) p. 1476-1478.

[5] D. Felbacq, G. Tayeb, D. Maystre, J. Opt. Soc. Am. A, 11, 9 (1994) p. 2526-2538.

[6] N. A. Nicorovici, R. C. MC Phedran and L. C. Botten, Phys. Rev. E 52 (1985) p. 1135-1145

Date received: April 18, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-02.