Abstract
For a (d + 1)-dimensional photonic crystal with a linear defect strip (waveguide), we calculate real intervals containing spectrum of the associated spectral problem. If such an interval falls completely into a spectral gap of the unperturbed problem (without defect), this will prove the existence of additional spectrum induced by the waveguide.
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References
P. Kuchment, B. Ong, On guided waves in photonic crystal waveguides, Waves in periodic and random media, South Hadley, MA (2002), 105–115, Contemp. Math. 339, Amer. Math. Soc., Providence, RI, 2003.
P.D. Hislop, I.M. Sigal, Introduction to spectral theory with applications to Schrödinger operators, Springer, New York, Berlin, Heidelberg, 1996.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Malcolm Brown, B., Hoang, V., Plum, M., Wood, I.G. (2008). On Spectral Bounds for Photonic Crystal Waveguides. In: Bandle, C., Losonczi, L., Gilányi, A., Páles, Z., Plum, M. (eds) Inequalities and Applications. International Series of Numerical Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8773-0_3
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DOI: https://doi.org/10.1007/978-3-7643-8773-0_3
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