Abstract

We propose a simple physical model that predicts the optical properties of a class of microstructured waveguides consisting of high-index inclusions that surround a low-index core. On the basis of this model, it is found that a large regime exists where transmission minima are determined by the geometry of the individual high-index inclusions. The locations of these minima are found to be largely unaffected by the relative position of the inclusions. As a result of this insight the difficult problem of analyzing the properties of complex structures can be reduced to the much simpler problem of analyzing the properties of an individual high-index inclusion in the structure.

© 2003 Optical Society of America

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References

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. Opt. Soc. Am. B

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331-2340 (2002).
[CrossRef]

Appl. Phys. Lett.

M. A. Duguay, Y. Kukubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multiplayer structures,” Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Bell Syst. Tech. J.

D. Marcuse and W. L. Mammel, “Tube waveguide for optical transmission,” Bell Syst. Tech. J. 52, 423-435 (1973).

IEEE J. Quantum Electron.

T. Baba and Y. Kukubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides—numerical results and analytical expressions,” IEEE J. Quantum Electron. QE-28, 1689-1700 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, , “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Prog. Quantum Electron.

T. F. Krauss and R. M. De La Rue, “Photonic crystals at optical wavelengths - past, present and future,” Prog. Quantum Electron. 23, 51-96 (1999).
[CrossRef]

Science

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Other

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2002), pp. 466-468.

M. M. Z. Kharadly and J. E. Lewis, “Properties of dielectric-tube waveguides,” Proc. IEE 116, 214-224 (1969).

J. A. Stratton, Electromagnetic theory (McGraw-Hill, New York, 1941).

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Figures (3)

Fig. 1.
Fig. 1.

Microstructured optical waveguide geometries (n2 > n1 in all three cases).

Fig. 2.
Fig. 2.

(a) Schematic of planar structure (n1=1.4, n2=1.8, d=3.437µm), (b) calculated transmission spectra for planar and ring structure of length L=5cm, (c) analytical modal cutoff condition, and (d) absolute value of the electric field in high index layer (vertical straight lines show the borders of high index layer).

Fig. 3.
Fig. 3.

(a) Transmission spectrum for fundamental mode of MOF shown in the inset (n1=1.44, n2=1.8, d=3.8µm). Straight dashed lines show analytical predictions (from Eq. (2)) for resonant wavelengths. (b) Analytical versus numerical predictions for resonant wavelengths for different d. (c) Longitudinal component of the Poynting vector Sz, and (d) Sz along X axis for two wavelengths. Straight dashed lines show the position of the high-index inclusion.

Equations (2)

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λ m = 2 d m n 2 2 n 1 2 ,
λ m = 2 d n 2 2 n 1 2 m + 1 2 ,

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