메뉴 건너뛰기




Volumn 43, Issue 2, 2001, Pages 103-116

Optimal Design of Periodic Diffractive Structures

Author keywords

Diffractive optics; Generalized Helmholtz equations; Homogenization; Optimal design; Periodic structure

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; DIFFRACTIVE OPTICS; ELECTROMAGNETIC WAVE POLARIZATION; GEOMETRY; MAGNETIC PERMEABILITY; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS; PERMITTIVITY; PROBLEM SOLVING; THEOREM PROVING; TOPOLOGY;

EID: 0000117171     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00245-001-0004-z     Document Type: Article
Times cited : (24)

References (31)
  • 3
    • 0001295889 scopus 로고
    • Optimal design for minimum weight and compliance in plane stress using extremal microstructures
    • G. Allaire and R. V. Kohn, Optimal design for minimum weight and compliance in plane stress using extremal microstructures. European J. Mech. A (Solids). 12(6) (1993), 839-878.
    • (1993) European J. Mech. A (Solids) , vol.12 , Issue.6 , pp. 839-878
    • Allaire, G.1    Kohn, R.V.2
  • 4
    • 0030493887 scopus 로고    scopus 로고
    • Numerical analysis of diffraction by periodic structures: TM polarization
    • G. Bao, Numerical analysis of diffraction by periodic structures: TM polarization, Numer. Math. 75 (1996), 1-16.
    • (1996) Numer. Math. , vol.75 , pp. 1-16
    • Bao, G.1
  • 5
    • 0242698761 scopus 로고    scopus 로고
    • Regularity of an inverse diffraction problem
    • G. Bao, Regularity of an inverse diffraction problem. Inverse Problems 14 (1998), 1-12.
    • (1998) Inverse Problems , vol.14 , pp. 1-12
    • Bao, G.1
  • 6
    • 0029304592 scopus 로고
    • Mathematical studies of rigorous grating theory
    • G. Bao, D. Dobson, and J. A. Cox, Mathematical studies of rigorous grating theory. J. Opt. Soc. Amer. A, 12(5)(1995), 1029-1042.
    • (1995) J. Opt. Soc. Amer. A , vol.12 , Issue.5 , pp. 1029-1042
    • Bao, G.1    Dobson, D.2    Cox, J.A.3
  • 7
    • 21844509885 scopus 로고
    • Inverse problems for scattering by periodic structures
    • G. Bao and A. Friedman, Inverse problems for scattering by periodic structures, Arch. Rat. Mech. Anal. 132 (1995), 49-72.
    • (1995) Arch. Rat. Mech. Anal. , vol.132 , pp. 49-72
    • Bao, G.1    Friedman, A.2
  • 8
    • 0010073023 scopus 로고
    • Relaxation totale d'un problème d'optimisation de plaques
    • E. Bonnetier and C. Conca, Relaxation totale d'un problème d'optimisation de plaques, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 931-936.
    • (1993) C. R. Acad. Sci. Paris Sér. I Math. , vol.317 , pp. 931-936
    • Bonnetier, E.1    Conca, C.2
  • 9
    • 0010191672 scopus 로고
    • Relaxation of a compliance functional for a plate optimization problem
    • ed. by P. G. Ciarlet and E. Sánchez-Palencia, Masson, Paris
    • E. Bonnetier and M. Vogelius, Relaxation of a compliance functional for a plate optimization problem, in Applications of Multiple Scaling in Mechanics, ed. by P. G. Ciarlet and E. Sánchez-Palencia, Masson, Paris, 1987.
    • (1987) Applications of Multiple Scaling in Mechanics
    • Bonnetier, E.1    Vogelius, M.2
  • 10
    • 0004877092 scopus 로고
    • Transmission problem and boundary homogenization
    • R. Brizzi, Transmission problem and boundary homogenization, Rev. Mat. Apl. 15 (1994), 1-16.
    • (1994) Rev. Mat. Apl. , vol.15 , pp. 1-16
    • Brizzi, R.1
  • 11
    • 0039206064 scopus 로고    scopus 로고
    • Boundary homogenization and Neumann boundary value problem
    • R. Brizzi and J. P. Chalot, Boundary homogenization and Neumann boundary value problem. Ricerche Mat. XLVI (1997), 341-387.
    • (1997) Ricerche Mat. , vol.46 , pp. 341-387
    • Brizzi, R.1    Chalot, J.P.2
  • 12
    • 0033330905 scopus 로고    scopus 로고
    • Maximizing band gaps in two-dimensional photonic crystals
    • S. Cox and D. Dobson, Maximizing band gaps in two-dimensional photonic crystals, SIAM J. Appl. Math. 59 (1999), 2108-2120.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 2108-2120
    • Cox, S.1    Dobson, D.2
  • 14
    • 0042841397 scopus 로고
    • Designing periodic structures with specified low frequency scattered far-field data
    • ed. by R. Vichnevetsky, D. Knight, and G. Richter, IMACS, New Brunswick, NJ
    • D. Dobson, Designing periodic structures with specified low frequency scattered far-field data, in Advances in Computer Methods for Partial Differential Equations VII, ed. by R. Vichnevetsky, D. Knight, and G. Richter, IMACS, New Brunswick, NJ, 1992, pp. 224-230.
    • (1992) Advances in Computer Methods for Partial Differential Equations , vol.7 , pp. 224-230
    • Dobson, D.1
  • 15
    • 0001136150 scopus 로고
    • Optimal design of periodic antireflective structures for the Heimholtz equation
    • D. Dobson, Optimal design of periodic antireflective structures for the Heimholtz equation, European J. Appl. Math. 4 (1993), 321-340.
    • (1993) European J. Appl. Math. , vol.4 , pp. 321-340
    • Dobson, D.1
  • 16
    • 0032675274 scopus 로고    scopus 로고
    • Optimal shape design of blazed diffraction gratings
    • D. Dobson, Optimal shape design of blazed diffraction gratings, Appl. Math. Optim. 40 (1999), 61-78.
    • (1999) Appl. Math. Optim. , vol.40 , pp. 61-78
    • Dobson, D.1
  • 18
    • 0022862030 scopus 로고
    • Homogenization and optimal bounds in linear elasticity
    • G. Francfort and F. Murat, Homogenization and optimal bounds in linear elasticity, Arch. Rat. Mech. Anal. 94 (1986), 307-334.
    • (1986) Arch. Rat. Mech. Anal. , vol.94 , pp. 307-334
    • Francfort, G.1    Murat, F.2
  • 21
  • 23
    • 84990623154 scopus 로고
    • Optimal design and relaxation of variational problems I, II, and III
    • R. V. Kohn and G. Strang, Optimal design and relaxation of variational problems I, II, and III, Comm. Pure Appl. Math. 39 (1986), 113-137, 139-182, 353-377.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 113-137
    • Kohn, R.V.1    Strang, G.2
  • 24
    • 0039677529 scopus 로고
    • Thin plates with rapidly varying thickness, and their relation to structural optimization
    • ed. by J. Ericksen et al., Springer-Verlag, New York
    • R. V. Kohn and M. Vogelius, Thin plates with rapidly varying thickness, and their relation to structural optimization, in Homogenization and Effective Moduli of Materials and Media, ed. by J. Ericksen et al., Springer-Verlag, New York, 1986, pp. 126-149.
    • (1986) Homogenization and Effective Moduli of Materials and Media , pp. 126-149
    • Kohn, R.V.1    Vogelius, M.2
  • 25
    • 84971195680 scopus 로고
    • Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
    • K. Lurie and A. Cherkaev, Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 71-87.
    • (1984) Proc. Roy. Soc. Edinburgh Sect. A , vol.99 , pp. 71-87
    • Lurie, K.1    Cherkaev, A.2
  • 26
    • 0001764754 scopus 로고
    • -1,q est compacte pour tout q < 2
    • -1,q est compacte pour tout q < 2, J. Math. Pures Appl. 60 (1981).
    • (1981) J. Math. Pures Appl. , vol.60
    • Murat, F.1
  • 27
    • 0002615068 scopus 로고
    • H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger
    • Mimeographed Notes English translation in ed. by R. V. Kohn, Birkhäuser, Boston
    • F. Murat, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, Mimeographed Notes (1978), English translation in Topics in the Mathematical Modelling of Composite Materials, ed. by R. V. Kohn, Birkhäuser, Boston, 1997.
    • (1978) Topics in the Mathematical Modelling of Composite Materials
    • Murat, F.1
  • 29
    • 0031377667 scopus 로고    scopus 로고
    • Homogenization of rough boundaries and interfaces
    • J. Nevard and J. B. Keller, Homogenization of rough boundaries and interfaces, SIAM J. Appl. Math. 57 (1997), 1660-1686.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1660-1686
    • Nevard, J.1    Keller, J.B.2
  • 30
    • 0002824641 scopus 로고
    • Electromagnetic Theory of Gratings
    • Springer-Verlag, Heidelberg
    • R. Petit, ed., Electromagnetic Theory of Gratings, Topics in Current Physics, Volume 22, Springer-Verlag, Heidelberg, 1980.
    • (1980) Topics in Current Physics , vol.22
    • Petit, R.1
  • 31
    • 0001357333 scopus 로고
    • Estimations fines des coefficients homogénéisés, Ennio de Giorgi colloquium
    • ed. by P. Krée, Pitman, Boston, MA
    • L. Tartar, Estimations fines des coefficients homogénéisés, Ennio de Giorgi colloquium, ed. by P. Krée, Research Notes in Mathematics, Volume 125, Pitman, Boston, MA, 1985, pp. 168-187.
    • (1985) Research Notes in Mathematics , vol.125 , pp. 168-187
    • Tartar, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.