Abstract
We investigate the reflection of electromagnetic waves from structures charaterized by a spatially varying dielectric permittivity of an almost periodic nature. The reflection from almost periodic structures is compared and contrasted with the reflection from periodic structures. Paradoxically, it is found that almost periodic structures may prove superior to their periodic counterparts when these structures are used as filters.
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References
A.R.Mickelson, D.L.Jaggard: IEEE Trans.AP-27, 34 (1979)
A.R.Mickelson: Ph.D.thesis, California Institute of Technology, Pasadena (1978)
G.Stokes:Mathematics and Physics Papers, Vol. 4 (Cambridge University Press, Cambridge 1904)
R.Bellman, G.Wing:An Introduction to Invariant Imbedding, (John Wiley and Sons, New York 1975)
H.Bohr:Almost Periodic Functions (Chelsea Publishing, New York 1947)
For numerical confirmation of these approximate boundary conditions, see the Appendix of [2]. Experimental confirmation is given in [11]
J.R.Pierce: J. Appl. Phys.25, 179 (1954)
The numerical instability of two-point boundary value problems is well known. See, e.g., [1,4], or H.B.Keller:Two Point Boundary Value Problems (SIAM, Philadeiphia 1976)
A.Neyfeh:Perturbation Methods (John Wiley and Sons, New York 1973)
C.Elachi, D.L.Jaggard, C.Yeh: IEEE Trans.AP-23, 352 (1975)
D.Flanders, H.Kogelnik, R.Schmidt, C.Shank: Appl. Phys. Lett.24, 194 (1974)
See, e.g., D.L.Jaggard, C.Elachi: J. Opt. Soc. Am.66, 674 (1976)
Y.Tikochinsky: Am. J. Phys.45, 1091 (1977)
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The major portion of this work was performed while the author was with the California Institute of Technology, Pasadena, California 91125, USA