A. Malcolm and D. P. Nicholls, “A boundary perturbation method for recovering interface shapes in layered media,” Inverse Probl. 27, 095009 (2011).

[CrossRef]

A. Malcolm and D. P. Nicholls, “A field expansions method for scattering by periodic multilayered media,” J. Acoust. Soc. Am. 129, 1783–1793 (2011).

[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]

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]

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).

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]

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

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

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]

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]

G.-Q. Zhang, “Integrated solutions of ordinary differential equation system and two-point boundary value problems. I. Integrated solution method,” J. Comp. Math. 3, 245–254 (1981).

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

[CrossRef]

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

[CrossRef]

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. 2, 377–396 (2013).

G. Bao, P. Li, and J. Lv, “Numerical solution of an inverse diffraction grating problem from phaseless data,” J. Opt. Soc. Am. A 30, 293–299 (2013).

[CrossRef]

G. Bao, P. Li, and H. Wu, “A computational inverse diffraction grating problem,” J. Opt. Soc. Am. A 29, 394–399 (2012).

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

G. Bao and P. Li, “Near-field imaging of infinite rough surfaces,” SIAM J. Appl. Math. (to be published).

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]

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

[CrossRef]

D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College, 2003).

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

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

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,” Euro. J. Appl. Math. 4, 321–340 (1993).

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).

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).

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

[CrossRef]

N. García and M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).

[CrossRef]

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]

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).

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 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]

G. Bao, P. Li, and J. Lv, “Numerical solution of an inverse diffraction grating problem from phaseless data,” J. Opt. Soc. Am. A 30, 293–299 (2013).

[CrossRef]

G. Bao, P. Li, and H. Wu, “A computational inverse diffraction grating problem,” J. Opt. Soc. Am. A 29, 394–399 (2012).

[CrossRef]

P. Li and J. Shen, “Analysis of the scattering by an unbounded rough surface,” Math. Methods Appl. Sci. 35, 2166–2184 (2012).

G. Bao and P. Li, “Near-field imaging of infinite rough surfaces,” SIAM J. Appl. Math. (to be published).

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. 2, 377–396 (2013).

A. Malcolm and D. P. Nicholls, “A boundary perturbation method for recovering interface shapes in layered media,” Inverse Probl. 27, 095009 (2011).

[CrossRef]

A. Malcolm and D. P. Nicholls, “A field expansions method for scattering by periodic multilayered media,” J. Acoust. Soc. Am. 129, 1783–1793 (2011).

[CrossRef]

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

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]

A. Malcolm and D. P. Nicholls, “A field expansions method for scattering by periodic multilayered media,” J. Acoust. Soc. Am. 129, 1783–1793 (2011).

[CrossRef]

A. Malcolm and D. P. Nicholls, “A boundary perturbation method for recovering interface shapes in layered media,” Inverse Probl. 27, 095009 (2011).

[CrossRef]

D. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: cancellations, conditioning, and convergence,” J. Opt. Soc. Am. A 21, 590–605 (2004).

[CrossRef]

D. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: improved algorithms,” J. Opt. Soc. Am. A 21, 606–621 (2004).

[CrossRef]

N. García and M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).

[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).

D. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: improved algorithms,” J. Opt. Soc. Am. A 21, 606–621 (2004).

[CrossRef]

D. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: cancellations, conditioning, and convergence,” J. Opt. Soc. Am. A 21, 590–605 (2004).

[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]

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

[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).

P. Li and J. Shen, “Analysis of the scattering by an unbounded rough surface,” Math. Methods Appl. Sci. 35, 2166–2184 (2012).

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. Bao, P. Li, and H. Wu, “A computational inverse diffraction grating problem,” J. Opt. Soc. Am. A 29, 394–399 (2012).

[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]

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

[CrossRef]

G.-Q. Zhang, “Integrated solutions of ordinary differential equation system and two-point boundary value problems. I. Integrated solution method,” J. Comp. Math. 3, 245–254 (1981).

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).

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,” Euro. J. Appl. Math. 4, 321–340 (1993).

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]

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]

A. Malcolm and D. P. Nicholls, “A boundary perturbation method for recovering interface shapes in layered media,” Inverse Probl. 27, 095009 (2011).

[CrossRef]

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. 2, 377–396 (2013).

A. Malcolm and D. P. Nicholls, “A field expansions method for scattering by periodic multilayered media,” J. Acoust. Soc. Am. 129, 1783–1793 (2011).

[CrossRef]

G.-Q. Zhang, “Integrated solutions of ordinary differential equation system and two-point boundary value problems. I. Integrated solution method,” J. Comp. Math. 3, 245–254 (1981).

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

[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]

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. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: cancellations, conditioning, and convergence,” J. Opt. Soc. Am. A 21, 590–605 (2004).

[CrossRef]

D. P. Nicholls and F. Reitich, “Shape deformations in rough surface scattering: improved algorithms,” J. Opt. Soc. Am. A 21, 606–621 (2004).

[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, P. Li, and H. Wu, “A computational inverse diffraction grating problem,” J. Opt. Soc. Am. A 29, 394–399 (2012).

[CrossRef]

G. Bao, P. Li, and J. Lv, “Numerical solution of an inverse diffraction grating problem from phaseless data,” J. Opt. Soc. Am. A 30, 293–299 (2013).

[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).

P. Li and J. Shen, “Analysis of the scattering by an unbounded rough surface,” Math. Methods Appl. Sci. 35, 2166–2184 (2012).

N. García and M. Nieto-Vesperinas, “Near-field optics inverse-scattering reconstruction of reflective surfaces,” Opt. Lett. 24, 2090–2092 (1993).

[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).

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]

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

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980).

G. Bao and P. Li, “Near-field imaging of infinite rough surfaces,” SIAM J. Appl. Math. (to be published).

D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College, 2003).