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Volumn 21, Issue 14, 1998, Pages 1297-1342

Diffraction in periodic structures and optimal design of binary gratings. Part I: Direct problems and gradient formulas

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ELECTROMAGNETIC WAVE DIFFRACTION; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; OPTICAL DESIGN; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032164329     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19980925)21:14<1297::AID-MMA997>3.0.CO;2-C     Document Type: Article
Times cited : (88)

References (39)
  • 2
    • 0001855134 scopus 로고
    • Electromagnetic waves in an inhomogeneous medium
    • Abboud, T. and Nedelec, J. C., 'Electromagnetic waves in an inhomogeneous medium', J. Math. Anal. Appl., 164, 40-58 (1992).
    • (1992) J. Math. Anal. Appl. , vol.164 , pp. 40-58
    • Abboud, T.1    Nedelec, J.C.2
  • 3
    • 84971895494 scopus 로고
    • A quasi-periodic boundary value problem for the Laplacian and the continuation of its resolvent
    • Alber, H. D., 'A quasi-periodic boundary value problem for the Laplacian and the continuation of its resolvent', Proc. Roy. Soc. Edinburgh, 82A, 251-272 (1979).
    • (1979) Proc. Roy. Soc. Edinburgh , vol.82 A , pp. 251-272
    • Alber, H.D.1
  • 4
    • 0029487468 scopus 로고
    • A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
    • Babuška, I., Ihlenburg, F., Paik, E. and Sauter, S., 'A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution', Comput. Meth. Appl. Mech. Engng., 128, 325-359 (1995).
    • (1995) Comput. Meth. Appl. Mech. Engng. , vol.128 , pp. 325-359
    • Babuška, I.1    Ihlenburg, F.2    Paik, E.3    Sauter, S.4
  • 5
    • 0001254041 scopus 로고    scopus 로고
    • Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers
    • Babuška, I. and Sauter, S., 'Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers', SIAM J. Numer. Anal., 34, 2392-2423 (1997).
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2392-2423
    • Babuška, I.1    Sauter, S.2
  • 6
    • 0000497724 scopus 로고
    • Finite element approximation of time harmonic waves in periodic structures
    • Bao, G., 'Finite element approximation of time harmonic waves in periodic structures', SIAM J. Numer. Anal., 32, 1155-1169 (1995).
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1155-1169
    • Bao, G.1
  • 7
    • 0030493887 scopus 로고    scopus 로고
    • Numerical analysis of diffraction by periodic structures: TM polarization
    • Bao, G., 'Numerical analysis of diffraction by periodic structures: TM polarization', Numer. Math., 75, 1-16 (1996).
    • (1996) Numer. Math. , vol.75 , pp. 1-16
    • Bao, G.1
  • 8
    • 0029304592 scopus 로고
    • Mathematical studies in rigorous grating theory
    • Bao, G., Dobson, D. C. and Cox, J. A., 'Mathematical studies in rigorous grating theory', J. Opt. Soc. Amer. A, 12, 1029-1042 (1995).
    • (1995) J. Opt. Soc. Amer. A , vol.12 , pp. 1029-1042
    • Bao, G.1    Dobson, D.C.2    Cox, J.A.3
  • 9
    • 0028407804 scopus 로고
    • Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem
    • Bonnet-Bendhia, A. -S. and Starling, F., 'Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem', Math. Meth. in the Appl. Sci., 17, 305-338 (1994).
    • (1994) Math. Meth. in the Appl. Sci. , vol.17 , pp. 305-338
    • Bonnet-Bendhia, A.S.1    Starling, F.2
  • 11
    • 84971145280 scopus 로고
    • Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
    • Bruno, O. P. and Reitich, F., 'Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain', Proc. Roy. Soc. Edinburgh A, 122, 317-340 (1992).
    • (1992) Proc. Roy. Soc. Edinburgh A , vol.122 , pp. 317-340
    • Bruno, O.P.1    Reitich, F.2
  • 12
    • 0027610033 scopus 로고
    • Numerical solution of diffraction problems: A method of variation of boundaries
    • Bruno, O. P. and Reitich, F., 'Numerical solution of diffraction problems: a method of variation of boundaries, J. Opt. Soc. Amer. A, 10, 1168-1175 (1993).
    • (1993) J. Opt. Soc. Amer. A , vol.10 , pp. 1168-1175
    • Bruno, O.P.1    Reitich, F.2
  • 13
    • 84968484411 scopus 로고
    • Maxwell's equation in a periodic structure
    • Chen, X. and Friedman, A. 'Maxwell's equation in a periodic structure', Trans. Amer. Math. Soc., 323, 465-507 (1991).
    • (1991) Trans. Amer. Math. Soc. , vol.323 , pp. 465-507
    • Chen, X.1    Friedman, A.2
  • 14
    • 0003252819 scopus 로고
    • A symmetric method for the coupling of finite elements and boundary elements
    • J. R. Whiteman, ed., Academic Press, London
    • Costabel, M., 'A symmetric method for the coupling of finite elements and boundary elements', in: The Mathematics of Finite Elements and Applications VI J. R. Whiteman, ed.), pp. 281-288, Academic Press, London. 1988.
    • (1988) The Mathematics of Finite Elements and Applications VI , pp. 281-288
    • Costabel, M.1
  • 15
    • 0022028508 scopus 로고
    • A direct boundary integral equation method for transmission problems
    • Costabel, M. and Stephan, E., 'A direct boundary integral equation method for transmission problems', J. Math. Anal. Appl., 106, 367-413 (1985).
    • (1985) J. Math. Anal. Appl. , vol.106 , pp. 367-413
    • Costabel, M.1    Stephan, E.2
  • 16
    • 0031382539 scopus 로고    scopus 로고
    • A comparison between rigorous light scattering methods
    • Davidson, M., Kleemann, B. and Bischoff, J., 'A comparison between rigorous light scattering methods', Proc. SPIE, 3051, 606-619 (1997).
    • (1997) Proc. SPIE , vol.3051 , pp. 606-619
    • Davidson, M.1    Kleemann, B.2    Bischoff, J.3
  • 17
    • 0025795819 scopus 로고
    • Linearity of coherence probe metrology: Simulation and experiment
    • Davidson, M., Monahan, K. and Monteverde, R., 'Linearity of coherence probe metrology: simulation and experiment', Proc. SPIE, 1464, 155-176 (1991).
    • (1991) Proc. SPIE , vol.1464 , pp. 155-176
    • Davidson, M.1    Monahan, K.2    Monteverde, R.3
  • 18
    • 0001136150 scopus 로고
    • Optimal design of periodic antireflective structures for the Helmholtz equation
    • Dobson, D. C., 'Optimal design of periodic antireflective structures for the Helmholtz equation', European J. Appl. Math., 4, 321-340 (1993).
    • (1993) European J. Appl. Math. , vol.4 , pp. 321-340
    • Dobson, D.C.1
  • 19
    • 0000028035 scopus 로고
    • A variational method for electromagnetic diffraction in biperiodic structures
    • Dobson, D. C., 'A variational method for electromagnetic diffraction in biperiodic structures', Model. Math. Anal. Numer., 28, 419-439 (1994).
    • (1994) Model. Math. Anal. Numer. , vol.28 , pp. 419-439
    • Dobson, D.C.1
  • 23
    • 85034292456 scopus 로고    scopus 로고
    • A fast interface solver for the biharmonic Dirichlet problem on polygonal domains
    • to appear
    • Khoromskij, B. N. and Schmidt, G, 'A fast interface solver for the biharmonic Dirichlet problem on polygonal domains', Numer. Math., to appear.
    • Numer. Math.
    • Khoromskij, B.N.1    Schmidt, G.2
  • 24
    • 0002351315 scopus 로고
    • Diffraction by periodic structures
    • L. Pävarinta and E. Somersalo, (eds), Springer, Berlin
    • Kirsch, A., 'Diffraction by periodic structures', in: Proc. Lapland Conf. on Inverse Problems (L. Pävarinta and E. Somersalo, (eds), pp. 87-102, Springer, Berlin, 1993.
    • (1993) Proc. Lapland Conf. on Inverse Problems , pp. 87-102
    • Kirsch, A.1
  • 25
    • 0000309125 scopus 로고
    • Boundary problems for elliptic equations in domains with conical or angular points
    • Kondratiev, V. A., 'Boundary problems for elliptic equations in domains with conical or angular points', Trans. Moscow Math. Soc., 16, 227-313 (1967).
    • (1967) Trans. Moscow Math. Soc. , vol.16 , pp. 227-313
    • Kondratiev, V.A.1
  • 26
    • 0000343624 scopus 로고    scopus 로고
    • Highly improved convergence of the coupled-wave method for TM polarization
    • Lalanne, P. and Morris, G. M., 'Highly improved convergence of the coupled-wave method for TM polarization', J. Opt. Soc. Am. A, 13(4), 779-784 (1996).
    • (1996) J. Opt. Soc. Am. A , vol.13 , Issue.4 , pp. 779-784
    • Lalanne, P.1    Morris, G.M.2
  • 27
    • 0003062370 scopus 로고
    • Régularité de la solution d'un problème de transmission
    • Lemrabet, K. 'Régularité de la solution d'un problème de transmission', J. Math. Pures Appl., 56, 1-38 (1977).
    • (1977) J. Math. Pures Appl. , vol.56 , pp. 1-38
    • Lemrabet, K.1
  • 28
    • 11544293299 scopus 로고    scopus 로고
    • The Sommerfeld problem: Methods, generalizations and frustrations
    • E. Meister, ed., Peter Lang Verlag, Franfurt am Main
    • Lüneburg, E., 'The Sommerfeld problem: Methods, generalizations and frustrations', in: Modern Mathematical Methods in Diffraction Theory and its Application in Engineering (E. Meister, ed.), pp. 145-173, Peter Lang Verlag, Franfurt am Main, 1997.
    • (1997) Modern Mathematical Methods in Diffraction Theory and Its Application in Engineering , pp. 145-173
    • Lüneburg, E.1
  • 30
    • 0001220661 scopus 로고
    • Einige gelöste und ungelöste kanonische Probleme der mathematischen Beugungstheorie
    • Meister, E., 'Einige gelöste und ungelöste kanonische Probleme der mathematischen Beugungstheorie', Expo. Math., 5, 193-237 (1987).
    • (1987) Expo. Math. , vol.5 , pp. 193-237
    • Meister, E.1
  • 31
    • 0040266890 scopus 로고    scopus 로고
    • Modern Wiener-Hopf methods in diffraction theory
    • B. D. Sleeman and R. J. Jarvis, eds
    • Meister, E. and Speck, F.-O., 'Modern Wiener-Hopf methods in diffraction theory, in: Ordinary and Partial Differential Equations. Vol. II (B. D. Sleeman and R. J. Jarvis, eds), pp. 130-171. Pitman Research Notes in Mathematics Vol. 216, 1989.
    • Ordinary and Partial Differential Equations , vol.2 , pp. 130-171
    • Meister, E.1    Speck, F.-O.2
  • 32
    • 11544374731 scopus 로고
    • Meister, E. and Speck, F.-O., 'Modern Wiener-Hopf methods in diffraction theory, in: Ordinary and Partial Differential Equations. Vol. II (B. D. Sleeman and R. J. Jarvis, eds), pp. 130-171. Pitman Research Notes in Mathematics Vol. 216, 1989.
    • (1989) Pitman Research Notes in Mathematics , vol.216
  • 33
    • 0019586874 scopus 로고
    • Rigorous coupled-wave analysis of plane-grating diffraction
    • Moharam, M. G. and Gaylord, T. K., 'Rigorous coupled-wave analysis of plane-grating diffraction', J. Opt. Soc. Am., 71(7) 811-818 (1981).
    • (1981) J. Opt. Soc. Am. , vol.71 , Issue.7 , pp. 811-818
    • Moharam, M.G.1    Gaylord, T.K.2
  • 34
    • 0000502908 scopus 로고
    • Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell equation
    • Nedelec, J. C. and Starling, F., 'Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell equation', SIAM J. Math. Anal., 22, 1679-1701 (1991).
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1679-1701
    • Nedelec, J.C.1    Starling, F.2
  • 35
    • 0001653017 scopus 로고
    • Electromagnetic Theory of Gratings
    • Springer, Berlin
    • Petit, R., ed, Electromagnetic Theory of Gratings, Topics in Current Physics, Vol. 22, Springer, Berlin, 1980.
    • (1980) Topics in Current Physics , vol.22
    • Petit, R.1
  • 36
    • 0001007539 scopus 로고
    • The integral method for coated gratings: Computational cost
    • Pomp, A., The integral method for coated gratings: computational cost', J. Mod. Opt., 38, 109-120 (1991).
    • (1991) J. Mod. Opt. , vol.38 , pp. 109-120
    • Pomp, A.1
  • 38
    • 0031389510 scopus 로고    scopus 로고
    • Fabrication and application of subwavelength gratings
    • Schnabel, B. and Kley, E.-B., 'Fabrication and application of subwavelength gratings, Proc. SPIE, 3008, 233-241 (1997).
    • (1997) Proc. SPIE , vol.3008 , pp. 233-241
    • Schnabel, B.1    Kley, E.-B.2


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