Photonic band gap (PBG) structures consisting of alternating layers of two dielectric materials exhibit PBGs—regions of the electromagnetic spectrum where light propagation is forbidden. The edges of these gaps are found from the Kronig–Penney relation. It is shown that the conditions for the band edges can be visualized using the sides and angles of a triangle. It also is shown that the wavelength at the band edges scales with the layer widths. Photon wavelengths at the band edges are found analytically as a function of PBG parameters for the technologically important cases of quarter-wave/half-wave and eighth-wave/half-wave PBG stacks; in a general case, a pedagogically transparent graphical solution is provided.
REFERENCES
1.
J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, N.J., 1995);
A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
2.
Jonathan Goldstein, Daniel Shifflet, and Joseph W. Haus (unpublished).
3.
Frank
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5.
More generally, for TE waves at non-normal incidence, where the angles are found from Snell’s law.
For TM waves, A. Yariv and R. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
6.
See, for example,
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-1
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© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
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