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Access via FulcrumVariational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface. I.
| dc.contributor.author | Meecham, William Coryell | en_US |
| dc.date.accessioned | 2010-05-06T21:43:18Z | |
| dc.date.available | 2010-05-06T21:43:18Z | |
| dc.date.issued | 1956-04 | en_US |
| dc.identifier.citation | Meecham, W. C. (1956). "Variational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface. I.." Journal of Applied Physics 27(4): 361-367. <http://hdl.handle.net/2027.42/70157> | en_US |
| dc.identifier.uri | https://hdl.handle.net/2027.42/70157 | |
| dc.description.abstract | A variational method is presented which is used to calculate the energy appearing in the various diffracted orders set up when a plane wave is incident upon a periodic reflecting surface. Either the first or the second boundary condition can be so treated. A sample problem is worked showing that if the average absolute slope of the reflecting surface is small (segments of surface with large slope may be included) and if the displacement of the surface is not large compared with the wavelength of the incident radiation, the formulation gives results correct to within a few percent. The calculation shows the existence of Wood anomalies; these are discussed in the paper. | en_US |
| dc.format.extent | 3102 bytes | |
| dc.format.extent | 584388 bytes | |
| dc.format.mimetype | text/plain | |
| dc.format.mimetype | application/pdf | |
| dc.publisher | The American Institute of Physics | en_US |
| dc.rights | © The American Institute of Physics | en_US |
| dc.title | Variational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface. I. | en_US |
| dc.type | Article | en_US |
| dc.subject.hlbsecondlevel | Physics | en_US |
| dc.subject.hlbtoplevel | Science | en_US |
| dc.description.peerreviewed | Peer Reviewed | en_US |
| dc.contributor.affiliationum | Physics Department, University of Michigan, Ann Arbor, Michigan | en_US |
| dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70157/2/JAPIAU-27-4-361-1.pdf | |
| dc.identifier.doi | 10.1063/1.1722378 | en_US |
| dc.identifier.source | Journal of Applied Physics | en_US |
| dc.identifier.citedreference | B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens’ Principle (Oxford University Press, New York, 1950), second edition, Chap. II. | en_US |
| dc.identifier.citedreference | Lord Rayleigh, Proc. Roy. Soc. (London) A79, 399 (1907). | en_US |
| dc.identifier.citedreference | V. Twersky, J. Acoust. Soc. Am. 22, 539 (1950). | en_US |
| dc.identifier.citedreference | C. Eckart, J. Acoust. Soc. Am. 25, 566 (1953). | en_US |
| dc.identifier.citedreference | L. M. Brekhovskikh, Zhur. Exspi. Teort. Fiz. 23, 275 (1952). Translated by G. N. Goss, U.S. Navy Electronics Laboratory, San Diego, California. | en_US |
| dc.identifier.citedreference | E. Trefftz, Math. Ann. 100, 503 (1928). | en_US |
| dc.identifier.citedreference | One could use the same method to treat problems where the boundary condition is of the form [Aϕ+B(∂ϕ/∂n)]z−ζ(x) = 0[Aϕ+B(∂ϕ∕∂n)]z−ζ(x)=0 where A and B may be functions of x or, in fact, the more general problem where one is given two different media separated by a periodic surface and is asked to find the reflected and the transmitted fields. | en_US |
| dc.identifier.citedreference | Lord Rayleigh, Theory of Sound (Dover Publications, New York, 1945), second edition, Vol. II, p. 89. | en_US |
| dc.identifier.citedreference | U. Fano, Phys. Rev. 51, 288 (1937). | en_US |
| dc.identifier.citedreference | K. Artmann, Z. Physik 119, 529 (1942). | en_US |
| dc.identifier.citedreference | B. A. Lippmann, J. Opt. Soc. Am. 43, 408 (1953). | en_US |
| dc.identifier.citedreference | Baker and Copson, see reference 1, Chaps. I and II | en_US |
| dc.identifier.citedreference | B. A. Lippmann and A. Oppenheim, Technical Research Group, 56 West 45 Street, New York 36. Final Report on Contract No. AF18 (600)‐954. | en_US |
| dc.identifier.citedreference | Setting ϕτNPϕτNP [of Eq. (13)] equal to zero is equivalent to assuming that this is possible. | en_US |
| dc.identifier.citedreference | For a reference concerning representations in terms of systems of functions see R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience Publishers, Inc., New York, 1953), Vol. I, Chap. II, Sees. 2 and 3. | en_US |
| dc.identifier.citedreference | See reference 8, Vol. 2, Sec. 294. | en_US |
| dc.identifier.citedreference | R. W. Wood, Phil. Mag. 4, 396 (1902). | en_US |
| dc.identifier.citedreference | Lord Rayleigh, Phil. Mag. 14, 60 (1907). | en_US |
| dc.identifier.citedreference | C. H. Palmer, Jr., J. Opt. Soc. Am. 42, 268 (1952). | en_US |
| dc.owningcollname | Physics, Department of |
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