Grazing-angle scattering of electromagnetic waves in gratings with varying mean parameters: grating eigenmodes

A highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. This pattern is shown to exist in the geometry of grazing-angle scattering (GAS), that is when the scattered wave (+1 diffracted order) in the slab propagates almost parallel to the slab (grating) boundaries. The predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. Their physical explanation is associated with resonant generation of a completely new type of eigenmodes in a thick slab with a periodic grating. These new slab eigenmodes are generically related to the grating; they do not exist if the grating amplitude is zero. The field structure of these eigenmodes and their dependence on structural and wave parameters is analysed. The results are extended to the case of GAS of guided modes in a slab with a periodic groove array of small corrugation amplitude and small variations in the mean thickness of the slab at the array boundaries.Comment: 16 pages, 6 figure

Jacob Goodman & Co.- R. H. Walker, November 4, 1927

Correspondence: Letter from Jacob Goodman, Jacob Goodman & Co., New York, New York to Rosa G. Holmes Walker, Jacksonville, Florida requesting mortgage payment and interest on mortgage payment

Jacob Goodman & Co.- R. H. Walker, February 9, 1928

Correspondence: From J.D. Goodman, Jacob Goodman & Co., New York, New York to Rosa G. Holmes Walker, Jacksonville, Florida, letter regarding mortgage paymen

Receipt, J.D. Goodman - Rosie H. Walker

Receipt: Proof of payment received on account of the principal of third mortgages on property #206 West 122nd St., New York City

Jacob Goodman & Co.- R. H. Walker, October 18, 1927

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Jacob Goodman & Co.- R. H. Walker, May 4, 1928

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Bill: Invoice and payment documentation for third mortgage for property 206 W. 122nd St, New York City. Date: May 1, 192

Jacob Goodman & Co.- R. H. Walker, May 31, 1927

Correspondence: Letters from Jacob Goodman, Jacob Goodman & Co., New York, New York to Rosa G. Holmes Walker, Jacksonville, Florida regarding property 206 West 122nd Street, New York City

Jacob Goodman & Co.- R. H. Walker, February 4, 1928

Correspondence: From J.D. Goodman, Jacob Goodman & Co., New York, New York to Rosa G. Holmes Walker, Jacksonville, Florida, the letter is in response to Mrs. Walker\u27s letter regarding selling property on 206 West 122nd Street, New York City