메뉴 건너뛰기




Volumn 146, Issue 2, 1998, Pages 603-626

Numerical solution of optimal design problems for binary gratings

Author keywords

Diffraction by periodic structures; Generalized fem with minimal pollution; Gradient formulae; Helmholtz equation; Nonlocal boundary conditions; Optimal design; Transmission problems

Indexed keywords

DIFFRACTION EFFICIENCY; DIFFRACTION GRATINGS; FINITE ELEMENT METHOD; GRADIENT METHODS; HELMHOLTZ EQUATION; OPTIMAL SYSTEMS; THERMAL GRADIENTS;

EID: 0032209646     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6071     Document Type: Article
Times cited : (40)

References (27)
  • 1
    • 0003923946 scopus 로고
    • Electromagnetic theory of gratings
    • Springer-Verlag, Berlin
    • 1. R. Petit (Ed.), Electromagnetic Theory of Gratings, Topics in Current Physics, Vol. 22 (Springer-Verlag, Berlin, 1980).
    • (1980) Topics in Current Physics , vol.22
    • Petit, R.1
  • 2
    • 0019586874 scopus 로고
    • Rigorous coupled-wave analysis of planar-grating diffraction
    • 2. M. G. Moharam and T. K. Gaylord, Rigorous coupled-wave analysis of planar-grating diffraction, J. Opt. Soc. Am. 71, 811 (1981).
    • (1981) J. Opt. Soc. Am. , vol.71 , pp. 811
    • Moharam, M.G.1    Gaylord, T.K.2
  • 4
    • 0028743599 scopus 로고
    • Differential theory of gratings: Extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm
    • 4. F. Montiel and M. Nevière, Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm, J. Opt. Soc. Am. A 11, 1321 (1994).
    • (1994) J. Opt. Soc. Am. A , vol.11 , pp. 1321
    • Montiel, F.1    Nevière, M.2
  • 5
    • 0001007539 scopus 로고
    • The integral method for coated gratings: Computational cost
    • 5. A. Pomp, The integral method for coated gratings: computational cost, J. Mod. Opt. 38, 109 (1991).
    • (1991) J. Mod. Opt. , vol.38 , pp. 109
    • Pomp, A.1
  • 6
    • 0000343624 scopus 로고    scopus 로고
    • Highly improved convergence of the coupled-wave method for TM polarization
    • 6. P. Lalanne and G. M. Morris, Highly improved convergence of the coupled-wave method for TM polarization, J. Opt. Soc. Am. A 13, 779 (1996).
    • (1996) J. Opt. Soc. Am. A , vol.13 , pp. 779
    • Lalanne, P.1    Morris, G.M.2
  • 7
    • 0002127645 scopus 로고    scopus 로고
    • Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings
    • 7. L. Li, Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings, J. Opt. Soc. Am. A 13, 1024 (1996).
    • (1996) J. Opt. Soc. Am. A , vol.13 , pp. 1024
    • Li, L.1
  • 8
    • 0027610033 scopus 로고
    • Numerical solution of diffraction problems: A method of variation of boundaries
    • 8. O. P. Bruno and F. Reitich, Numerical solution of diffraction problems: a method of variation of boundaries, J. Opt. Soc. Amer. A 10, 1168 (1993).
    • (1993) J. Opt. Soc. Amer. A , vol.10 , pp. 1168
    • Bruno, O.P.1    Reitich, F.2
  • 9
    • 0028407804 scopus 로고
    • Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem
    • 9. A.-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem, Math. Methods Appl. Sci. 17, 305 (1994).
    • (1994) Math. Methods Appl. Sci. , vol.17 , pp. 305
    • Bonnet-Bendhia, A.-S.1    Starling, F.2
  • 10
    • 0029304592 scopus 로고
    • Mathematical studies in rigorous grating theory
    • 10. G. Bao, D. C. Dobson, and J. A. Cox, Mathematical studies in rigorous grating theory, J. Opt. Soc. Amer. A 12, 1029 (1995).
    • (1995) J. Opt. Soc. Amer. A , vol.12 , pp. 1029
    • Bao, G.1    Dobson, D.C.2    Cox, J.A.3
  • 11
    • 0000028035 scopus 로고
    • A variational method for electromagnetic diffraction in biperiodic structures
    • 11. D. C. Dobson, A variational method for electromagnetic diffraction in biperiodic structures, Model. Math. Anal. Numer. 28, 419 (1994).
    • (1994) Model. Math. Anal. Numer. , vol.28 , pp. 419
    • Dobson, D.C.1
  • 12
    • 84975630427 scopus 로고
    • Mathematical modeling for diffractive optics
    • 12. D. C. Dobson and J. A. Cox, Mathematical modeling for diffractive optics, Proc. SPIE CR49, 32 (1994).
    • (1994) Proc. SPIE , vol.CR49 , pp. 32
    • Dobson, D.C.1    Cox, J.A.2
  • 13
    • 0000497724 scopus 로고
    • Finite element approximation of time harmonic waves in periodic structures
    • 13. G. Bao, Finite element approximation of time harmonic waves in periodic structures, SIAM J. Numer. Anal. 32, 1155 (1995).
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1155
    • Bao, G.1
  • 14
    • 0030493887 scopus 로고    scopus 로고
    • Numerical analysis of diffraction by periodic structures: TM polarization
    • 14. G. Bao, Numerical analysis of diffraction by periodic structures: TM polarization, Numer. Math. 75, 1 (1996).
    • (1996) Numer. Math. , vol.75 , pp. 1
    • Bao, G.1
  • 15
    • 85189847706 scopus 로고    scopus 로고
    • Diffraction in periodic structures and optimal design of binary gratings. I. Direct problems and gradient formulas
    • in press
    • 15. J. Elschner and G. Schmidt, Diffraction in periodic structures and optimal design of binary gratings. I. Direct problems and gradient formulas, Math. Methods Appl. Sci., in press.
    • Math. Methods Appl. Sci.
    • Elschner, J.1    Schmidt, G.2
  • 16
    • 0031365078 scopus 로고    scopus 로고
    • Photolithography simulation on nonplanar substrate using the finite-element method with absorbing boundary conditions
    • 16. I. H. Park, H. K. Oh, and S. B. Hyun, Photolithography simulation on nonplanar substrate using the finite-element method with absorbing boundary conditions, Proc. SPIE 3051, 578 (1997).
    • (1997) Proc. SPIE , vol.3051 , pp. 578
    • Park, I.H.1    Oh, H.K.2    Hyun, S.B.3
  • 17
    • 0001136150 scopus 로고
    • Optimal design of periodic antireflective structures for the Helmholtz equation
    • 17. D. C. Dobson, Optimal design of periodic antireflective structures for the Helmholtz equation, Eur. J. Appl. Math. 4, 321 (1993).
    • (1993) Eur. J. Appl. Math. , vol.4 , pp. 321
    • Dobson, D.C.1
  • 18
    • 0026383914 scopus 로고
    • Inverse grating diffraction problems
    • 18. T. Jaaskelainen and M. Kuittinen, Inverse grating diffraction problems, Proc. SPIE 1574, 272 (1991).
    • (1991) Proc. SPIE , vol.1574 , pp. 272
    • Jaaskelainen, T.1    Kuittinen, M.2
  • 19
    • 84975624368 scopus 로고
    • Parametric optimization of multilevel diffractive optical elements by electromagnetic theory
    • 19. E. Noponen, J. Turunen, and A. Vasara, Parametric optimization of multilevel diffractive optical elements by electromagnetic theory, Appl. Opt. 31, 5910 (1992).
    • (1992) Appl. Opt. , vol.31 , pp. 5910
    • Noponen, E.1    Turunen, J.2    Vasara, A.3
  • 20
    • 0010018282 scopus 로고    scopus 로고
    • Subwavelength gratings optimized for broadband quarter-wave plates
    • 20. H. Kikuta, Y. Ohira, and K. Iwata, Subwavelength gratings optimized for broadband quarter-wave plates, Proc. SPIE 2873, 218 (1996).
    • (1996) Proc. SPIE , vol.2873 , pp. 218
    • Kikuta, H.1    Ohira, Y.2    Iwata, K.3
  • 21
    • 0029487468 scopus 로고
    • A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
    • 21. I. Babuška, F. Ihlenburg, E. Paik, and S. Sauter, A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution, Comp. Methods Appl. Mech. Eng. 128, 325 (1995).
    • (1995) Comp. Methods Appl. Mech. Eng. , vol.128 , pp. 325
    • Babuška, I.1    Ihlenburg, F.2    Paik, E.3    Sauter, S.4
  • 23
    • 0000350889 scopus 로고
    • On accuracy conditions for the numerical computation of waves
    • 23. A. Bayliss, C. I. Goldstein, and E. Turkel, On accuracy conditions for the numerical computation of waves, J. Comput. Phys. 59, 396 (1985).
    • (1985) J. Comput. Phys. , vol.59 , pp. 396
    • Bayliss, A.1    Goldstein, C.I.2    Turkel, E.3
  • 24
    • 0029239896 scopus 로고
    • A Galerkin least-squares finite element method for the twodimensional Helmholtz equation
    • 24. L. J. Thompson and P. M. Pinsky, A Galerkin least-squares finite element method for the twodimensional Helmholtz equation, Int. J. Numer. Methods Eng. 38, 371 (1995).
    • (1995) Int. J. Numer. Methods Eng. , vol.38 , pp. 371
    • Thompson, L.J.1    Pinsky, P.M.2
  • 25
    • 0001254041 scopus 로고    scopus 로고
    • Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers
    • 25. I. Babuška and S. Sauter, Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers, SIAM J. Numer. Anal. 34, 2392 (1997).
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2392
    • Babuška, I.1    Sauter, S.2
  • 26
    • 0031382539 scopus 로고    scopus 로고
    • A comparison between rigorous light scattering methods
    • 26. M. Davidson, B. Kleemann, and J. Bischoff, A comparison between rigorous light scattering methods, Proc. SPIE 3051, 606 (1997).
    • (1997) Proc. SPIE , vol.3051 , pp. 606
    • Davidson, M.1    Kleemann, B.2    Bischoff, J.3
  • 27
    • 0025795819 scopus 로고
    • Linearity of coherence probe metrology: Simulation and experiment
    • 27. M. Davidson, K. Monahan, and R. Monteverde, Linearity of coherence probe metrology: simulation and experiment, Proc. SPIE 1464, 155 (1991).
    • (1991) Proc. SPIE , vol.1464 , pp. 155
    • Davidson, M.1    Monahan, K.2    Monteverde, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.