G. Bao, H. Zhang, and J. Zou, “Unique determination of periodic polyhedral structures by scattered electromagnetic fields,” Trans. Am. Math. Soc. 363, 4527–4551 (2011).

[CrossRef]

G. Bao and P. Li, “Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency,” J. Comput. Phys. 228, 4638–4648 (2009).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math. 65, 2049–2066 (2005).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering for the Helmholtz equation at fixed frequency,” Inverse Probl. 21, 1621–1641 (2005).

[CrossRef]

G. Bao, Z. Chen, and H. Wu, “Adaptive finite element method for diffraction gratings,” J. Opt. Soc. Am. A 22, 1106–1114 (2005).

[CrossRef]

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19, 1195–1211 (2003).

[CrossRef]

G. Bruckner and J. Elschner, “A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,” Inverse Probl. 19, 315–329 (2003).

[CrossRef]

J. Elschner, G. Hsiao, and A. Rathsfeld, “Grating profile reconstruction based on finite elements and optimization techniques,” SIAM J. Appl. Math. 64, 525–545 (2003).

[CrossRef]

Z. Chen and H. Wu, “An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures,” SIAM J. Numer. Anal. 41, 799–826 (2003).

[CrossRef]

F. Hettlich, “Iterative regularization schemes in inverse scattering by periodic structures,” Inverse Probl. 18, 701–714 (2002).

[CrossRef]

G. Bruckner, J. Cheng, and M. Yamamoto, “An inverse problem in diffractive optics: conditional stability,” Inverse Probl. 18, 415–433 (2002).

[CrossRef]

K. Ito and F. Reitich, “A high-order perturbation approach to profile reconstruction: I. perfectly conducting gratings,” Inverse Probl. 15, 1067–1085 (1999).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

D. Dobson, “Optimal shape design of blazed diffraction grating,” Appl. Math. Optim. 40, 61–78 (1999).

[CrossRef]

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. 21, 1297–1342 (1998).

[CrossRef]

J. Elschner and G. Schmidt, “Numerical solution of optimal design problems for binary gratings, J. Comput. Phys. 146, 603–626 (1998).

[CrossRef]

G. Bao and Z. Zhou, “An inverse problem for scattering by a doubly periodic structure,” Trans. Am. Math. Soc. 350, 4089–4103 (1998).

[CrossRef]

Y. Chen, “Inverse scattering via Heisenberg uncertainty principle,” Inverse Probl. 13, 253–282 (1997).

[CrossRef]

F. Hettlich and A. Kirsch, “Schiffer’s theorem in inverse scattering theory for periodic structures,” Inverse Probl. 13, 351–361 (1997).

[CrossRef]

G. Bao and A. Friedman, “Inverse problems for scattering by periodic structure,” Arch. Ration. Mech. Anal. 132, 49–72 (1995).

[CrossRef]

H. Ammari, “Uniqueness theorems for an inverse problem in a doubly periodic structure,” Inverse Probl. 11, 823–833 (1995).

[CrossRef]

G. Bao, D. Dobson, and J. A. Cox, “Mathematical studies in rigorous grating theory,” J. Opt. Soc. Am. A 12, 1029–1042 (1995).

[CrossRef]

A. Kirsch, “Uniqueness theorems in inverse scattering theory for periodic structures,” Inverse Probl. 10, 145–152 (1994).

[CrossRef]

G. Bao, “A unique theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335–340 (1994).

[CrossRef]

J. C. Nédélec and F. Starling, “Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell’s equations,” SIAM J. Math. Anal. 22, 1679–1701 (1991).

[CrossRef]

R. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973).

[CrossRef]

H. Ammari, “Uniqueness theorems for an inverse problem in a doubly periodic structure,” Inverse Probl. 11, 823–833 (1995).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19, 1195–1211 (2003).

[CrossRef]

G. Bao, H. Zhang, and J. Zou, “Unique determination of periodic polyhedral structures by scattered electromagnetic fields,” Trans. Am. Math. Soc. 363, 4527–4551 (2011).

[CrossRef]

G. Bao and P. Li, “Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency,” J. Comput. Phys. 228, 4638–4648 (2009).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering for the Helmholtz equation at fixed frequency,” Inverse Probl. 21, 1621–1641 (2005).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math. 65, 2049–2066 (2005).

[CrossRef]

G. Bao, Z. Chen, and H. Wu, “Adaptive finite element method for diffraction gratings,” J. Opt. Soc. Am. A 22, 1106–1114 (2005).

[CrossRef]

G. Bao and Z. Zhou, “An inverse problem for scattering by a doubly periodic structure,” Trans. Am. Math. Soc. 350, 4089–4103 (1998).

[CrossRef]

G. Bao and A. Friedman, “Inverse problems for scattering by periodic structure,” Arch. Ration. Mech. Anal. 132, 49–72 (1995).

[CrossRef]

G. Bao, D. Dobson, and J. A. Cox, “Mathematical studies in rigorous grating theory,” J. Opt. Soc. Am. A 12, 1029–1042 (1995).

[CrossRef]

G. Bao, “A unique theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335–340 (1994).

[CrossRef]

G. Bruckner and J. Elschner, “A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,” Inverse Probl. 19, 315–329 (2003).

[CrossRef]

G. Bruckner, J. Cheng, and M. Yamamoto, “An inverse problem in diffractive optics: conditional stability,” Inverse Probl. 18, 415–433 (2002).

[CrossRef]

Y. Chen, “Inverse scattering via Heisenberg uncertainty principle,” Inverse Probl. 13, 253–282 (1997).

[CrossRef]

G. Bruckner, J. Cheng, and M. Yamamoto, “An inverse problem in diffractive optics: conditional stability,” Inverse Probl. 18, 415–433 (2002).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

D. Colton and R. Kress, “Inverse Acoustic and Electromagnetic Scattering Theory,” 2nd ed., Vol. 93 of Applied Mathematical Sciences (Springer-Verlag, 1998).

D. Dobson, “Optimal shape design of blazed diffraction grating,” Appl. Math. Optim. 40, 61–78 (1999).

[CrossRef]

G. Bao, D. Dobson, and J. A. Cox, “Mathematical studies in rigorous grating theory,” J. Opt. Soc. Am. A 12, 1029–1042 (1995).

[CrossRef]

D. Dobson, “Optimal design of periodic antireflective structures for the Helmholtz equation,” Eur. J. Appl. Math. 4, 321–340 (1993).

[CrossRef]

G. Bruckner and J. Elschner, “A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,” Inverse Probl. 19, 315–329 (2003).

[CrossRef]

J. Elschner, G. Hsiao, and A. Rathsfeld, “Grating profile reconstruction based on finite elements and optimization techniques,” SIAM J. Appl. Math. 64, 525–545 (2003).

[CrossRef]

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. 21, 1297–1342 (1998).

[CrossRef]

J. Elschner and G. Schmidt, “Numerical solution of optimal design problems for binary gratings, J. Comput. Phys. 146, 603–626 (1998).

[CrossRef]

H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).

G. Bao and A. Friedman, “Inverse problems for scattering by periodic structure,” Arch. Ration. Mech. Anal. 132, 49–72 (1995).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).

F. Hettlich, “Iterative regularization schemes in inverse scattering by periodic structures,” Inverse Probl. 18, 701–714 (2002).

[CrossRef]

F. Hettlich and A. Kirsch, “Schiffer’s theorem in inverse scattering theory for periodic structures,” Inverse Probl. 13, 351–361 (1997).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

J. Elschner, G. Hsiao, and A. Rathsfeld, “Grating profile reconstruction based on finite elements and optimization techniques,” SIAM J. Appl. Math. 64, 525–545 (2003).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

K. Ito and F. Reitich, “A high-order perturbation approach to profile reconstruction: I. perfectly conducting gratings,” Inverse Probl. 15, 1067–1085 (1999).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19, 1195–1211 (2003).

[CrossRef]

F. Hettlich and A. Kirsch, “Schiffer’s theorem in inverse scattering theory for periodic structures,” Inverse Probl. 13, 351–361 (1997).

[CrossRef]

A. Kirsch, “Uniqueness theorems in inverse scattering theory for periodic structures,” Inverse Probl. 10, 145–152 (1994).

[CrossRef]

D. Colton and R. Kress, “Inverse Acoustic and Electromagnetic Scattering Theory,” 2nd ed., Vol. 93 of Applied Mathematical Sciences (Springer-Verlag, 1998).

G. Bao and P. Li, “Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency,” J. Comput. Phys. 228, 4638–4648 (2009).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering for the Helmholtz equation at fixed frequency,” Inverse Probl. 21, 1621–1641 (2005).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math. 65, 2049–2066 (2005).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

R. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973).

[CrossRef]

J. C. Nédélec and F. Starling, “Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell’s equations,” SIAM J. Math. Anal. 22, 1679–1701 (1991).

[CrossRef]

H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).

J. Elschner, G. Hsiao, and A. Rathsfeld, “Grating profile reconstruction based on finite elements and optimization techniques,” SIAM J. Appl. Math. 64, 525–545 (2003).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

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. 21, 1297–1342 (1998).

[CrossRef]

J. Elschner and G. Schmidt, “Numerical solution of optimal design problems for binary gratings, J. Comput. Phys. 146, 603–626 (1998).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

J. C. Nédélec and F. Starling, “Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell’s equations,” SIAM J. Math. Anal. 22, 1679–1701 (1991).

[CrossRef]

G. Bruckner, J. Cheng, and M. Yamamoto, “An inverse problem in diffractive optics: conditional stability,” Inverse Probl. 18, 415–433 (2002).

[CrossRef]

G. Bao, H. Zhang, and J. Zou, “Unique determination of periodic polyhedral structures by scattered electromagnetic fields,” Trans. Am. Math. Soc. 363, 4527–4551 (2011).

[CrossRef]

G. Bao and Z. Zhou, “An inverse problem for scattering by a doubly periodic structure,” Trans. Am. Math. Soc. 350, 4089–4103 (1998).

[CrossRef]

G. Bao, H. Zhang, and J. Zou, “Unique determination of periodic polyhedral structures by scattered electromagnetic fields,” Trans. Am. Math. Soc. 363, 4527–4551 (2011).

[CrossRef]

D. Dobson, “Optimal shape design of blazed diffraction grating,” Appl. Math. Optim. 40, 61–78 (1999).

[CrossRef]

G. Bao and A. Friedman, “Inverse problems for scattering by periodic structure,” Arch. Ration. Mech. Anal. 132, 49–72 (1995).

[CrossRef]

D. Dobson, “Optimal design of periodic antireflective structures for the Helmholtz equation,” Eur. J. Appl. Math. 4, 321–340 (1993).

[CrossRef]

G. Bruckner, J. Cheng, and M. Yamamoto, “An inverse problem in diffractive optics: conditional stability,” Inverse Probl. 18, 415–433 (2002).

[CrossRef]

A. Kirsch, “Uniqueness theorems in inverse scattering theory for periodic structures,” Inverse Probl. 10, 145–152 (1994).

[CrossRef]

G. Bao, “A unique theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335–340 (1994).

[CrossRef]

H. Ammari, “Uniqueness theorems for an inverse problem in a doubly periodic structure,” Inverse Probl. 11, 823–833 (1995).

[CrossRef]

F. Hettlich and A. Kirsch, “Schiffer’s theorem in inverse scattering theory for periodic structures,” Inverse Probl. 13, 351–361 (1997).

[CrossRef]

K. Ito and F. Reitich, “A high-order perturbation approach to profile reconstruction: I. perfectly conducting gratings,” Inverse Probl. 15, 1067–1085 (1999).

[CrossRef]

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19, 1195–1211 (2003).

[CrossRef]

F. Hettlich, “Iterative regularization schemes in inverse scattering by periodic structures,” Inverse Probl. 18, 701–714 (2002).

[CrossRef]

G. Bruckner and J. Elschner, “A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles,” Inverse Probl. 19, 315–329 (2003).

[CrossRef]

Y. Chen, “Inverse scattering via Heisenberg uncertainty principle,” Inverse Probl. 13, 253–282 (1997).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering for the Helmholtz equation at fixed frequency,” Inverse Probl. 21, 1621–1641 (2005).

[CrossRef]

G. Bao and P. Li, “Numerical solution of an inverse medium scattering problem for Maxwell’s equations at fixed frequency,” J. Comput. Phys. 228, 4638–4648 (2009).

[CrossRef]

J. Elschner and G. Schmidt, “Numerical solution of optimal design problems for binary gratings, J. Comput. Phys. 146, 603–626 (1998).

[CrossRef]

J. B. Keller, “Singularities and Rayleigh’s hypothesis for diffraction gratings,” J. Opt. Soc. Am. A 17, 456–457 (2000).

[CrossRef]

G. Bao, Z. Chen, and H. Wu, “Adaptive finite element method for diffraction gratings,” J. Opt. Soc. Am. A 22, 1106–1114 (2005).

[CrossRef]

G. Bao, D. Dobson, and J. A. Cox, “Mathematical studies in rigorous grating theory,” J. Opt. Soc. Am. A 12, 1029–1042 (1995).

[CrossRef]

O. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993).

[CrossRef]

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. 21, 1297–1342 (1998).

[CrossRef]

R. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973).

[CrossRef]

J. Elschner, G. Hsiao, and A. Rathsfeld, “Grating profile reconstruction based on finite elements and optimization techniques,” SIAM J. Appl. Math. 64, 525–545 (2003).

[CrossRef]

G. Bao and P. Li, “Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math. 65, 2049–2066 (2005).

[CrossRef]

H. Ammari, J. Garnier, H. Kang, M. Lim, and K. Solna, “Multistatic imaging of extended targets,” SIAM J. Imaging Sci., to be published.

J. C. Nédélec and F. Starling, “Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell’s equations,” SIAM J. Math. Anal. 22, 1679–1701 (1991).

[CrossRef]

Z. Chen and H. Wu, “An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures,” SIAM J. Numer. Anal. 41, 799–826 (2003).

[CrossRef]

G. Bao and Z. Zhou, “An inverse problem for scattering by a doubly periodic structure,” Trans. Am. Math. Soc. 350, 4089–4103 (1998).

[CrossRef]

G. Bao, H. Zhang, and J. Zou, “Unique determination of periodic polyhedral structures by scattered electromagnetic fields,” Trans. Am. Math. Soc. 363, 4527–4551 (2011).

[CrossRef]

R. Coifman, M. Goldberg, T. Hrycak, M. Israeli, and V. Rokhlin, “An improved operator expansion algorithm for direct and inverse scattering computations,” Waves Random Media 9, 441–457 (1999).

[CrossRef]

H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).

D. Colton and R. Kress, “Inverse Acoustic and Electromagnetic Scattering Theory,” 2nd ed., Vol. 93 of Applied Mathematical Sciences (Springer-Verlag, 1998).

R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).

G. Bao, L. Cowsar, and W. Masters, eds., Mathematical Modeling in Optical Science, Vol. 22 of Frontiers in Applied Mathematics (SIAM, 2001).