Application "Applications of diffractive optics"

L. Goray, G. Schmidt, Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method, Phys. Rev. E (3), 85 (2012) pp. 036701-1--036701--12.
Abstract

The conical boundary integral equation method has been proposed to calculate the sensitive optical response of 2D photonic band gaps (PBGs), including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2 x 2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only once for a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated.

G. Hu, B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure, Math. Methods Appl. Sci., 34 (2011) pp. 509--519.

F. Lanzara, V. Maz'ya, G. Schmidt, On the fast computation of high dimensional volume potentials, Math. Comp., 80 (2011) pp. 887--904.

F. Lanzara, V.G. Maz'ya, G. Schmidt, Accurate cubature of volume potentials over high-dimensional half-spaces, J. Math. Sci. (N. Y.), 173 (2011) pp. 683--700.

J. Elschner, G. Hu, Inverse scattering of elastic waves by periodic structures: Uniqueness under the third or fourth kind boundary conditions, Methods Appl. Anal., 18 (2011) pp. 215--244.
Abstract

The inverse scattering of a time-harmonic elastic wave by a two-dimensional periodic structure in $R^2$ is investigated. The grating profile is assumed to be a graph given by a piecewise linear function on which the third or fourth kind boundary conditions are satisfied. Via an equivalent variational formulation, existence of quasi-periodic solutions for general Lipschitz grating profiles is proved by applying the Fredholm alternative. However, uniqueness of solution to the direct problem does not hold in general. For the inverse problem, we determine and classify all the unidentifiable grating profiles corresponding to a given incident elastic field, relying on the reflection principle for the Navier equation and the rotational invariance of propagating directions of the total field. Moreover, global uniqueness for the inverse problem is established with a minimal number of incident pressure or shear waves, including the resonance case where a Rayleigh frequency is allowed. The gratings that are unidentifiable by one incident elastic wave provide non-uniqueness examples for appropriately chosen wave number and incident angles.

J. Elschner, G. Hu, Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings, J. Inverse Ill-Posed Probl., 19 (2011) pp. 717--768.
Abstract

We consider the inverse elastic scattering problem of determining a three-dimensional diffraction grating profile from scattered waves measured above the structure. In general, a grating profile cannot be uniquely determined by a single incoming plane wave. We completely characterize and classify the bi-periodic polyhedral structures under the boundary conditions of the third and fourth kinds that cannot be uniquely recovered by only one incident plane wave. Thus we have global uniqueness for a polyhedral grating profile by one incident elastic plane wave if and only if the profile belongs to neither of the unidentifiable classes, which can be explicitly described depending on the incident field and the type of boundary conditions. Our approach is based on the reflection principle for the Navier equation and the reflectional and rotational invariance of the total field.

J. Elschner, G. Hu, Uniqueness in inverse transmission scattering problems for multilayered obstacles, Inverse Probl. Imaging, 5 (2011) pp. 793--813.
Abstract

Assume a time-harmonic electromagnetic wave is scattered by an infinitely long cylindrical conductor surrounded by an unknown piecewise homogenous medium remaining invariant along the cylinder axis. We prove that, in TM mode, the far field patterns for all observation directions at a fixed frequency uniquely determine the unknown surrounding medium as well as the shape of the cylindrical conductor. A similar uniqueness result is obtained for the scattering by multilayered penetrable periodic structures in a piecewise homogenous medium. The periodic interfaces and refractive indices can be uniquely identified from the near field data measured only above (or below) the structure for all quasi-periodic incident waves with a fixed phase-shift. The proofs are based on the singularity of the Green function to a two dimensional elliptic equation with piecewise constant leading coefficients.

G. Schmidt, B.H. Kleemann, Integral equation methods from grating theory to photonics: An overview and new approaches for conical diffraction, J. Modern Opt., 58 (2011) pp. 407--423.

G. Schmidt, Integral equations for conical diffraction by coated gratings, J. Integral Equations Appl., 23 (2011) pp. 71--112.
Abstract

The paper is devoted to integral formulations for the scattering of plane waves by diffraction gratings under oblique incidence. For the case of coated gratings Maxwell's equations can be reduced to a system of four singular integral equations on the piecewise smooth interfaces between different materials. We study analytic properties of the integral operators for periodic diffraction problems and obtain existence and uniqueness results for solutions of the systems corresponding to electromagnetic fields with locally finite energy.

G. Hu, F. Qu, B. Zhang, Direct and inverse problems for electromagnetic scattering by a doubly periodic structure with a partially coated dielectric, Math. Methods Appl. Sci., 33 (2010) pp. 147--156.

S. Chandler-Wilde, J. Elschner, Variational approach in weighted Sobolev spaces to scattering by unbounded rough surface, SIAM J. Math. Anal., 42 (2010) pp. 2554--2580.

L.I. Goray, G. Schmidt, Solving conical diffraction grating problems with integral equations, J. Opt. Soc. Amer. A, 27 (2010) pp. 585--597.
Abstract

Off-plane scattering of time-harmonic plane waves by a diffraction grating with arbitrary conductivity and general border profile is considered in a rigorous electromagnetic formulation. The integral equations for conical diffraction were obtained using the boundary integrals of the single and double layer potentials including the tangential derivative of single layer potentials interpreted as singular integrals. We derive an important formula for the calculation of the absorption in conical diffraction. Some rules which are expedient for the numerical implementation of the theory are presented. The efficiencies and polarization angles compared with those obtained by Lifeng Li for transmission and reflection gratings are in a good agreement. The code developed and tested is found to be accurate and efficient for solving off-plane diffraction problems including high-conductive surfaces, borders with edges, real border profiles, and gratings working at short wavelengths.

H. Gross, J. Richter, A. Rathsfeld, M. Bär, Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry, J. Eur. Opt. Soc. Rapid Publ., 5 (2010) pp. 10053/1--10053/7.

J. Elschner, G. Hu, Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves, Inverse Problems, 26 (2010) pp. 115002/1--115002/23.
Abstract

In this paper, we investigate the inverse problem of recovering a two-dimensional perfectly reflecting diffraction grating from the scattered waves measured above the structure. Inspired by a novel idea developed by Bao, Zhang and Zou [to appear in Trans. Amer. Math. Soc.], we present a complete characterization of the global uniqueness in determining polygonal periodic structures using a minimal number of incident plane waves. The idea in this paper combines the reflection principle for the Helmholtz equation and the dihedral group theory. We characterize all periodic polygonal structures that cannot be identified by one incident plane wave, including the resonance case where a Rayleigh frequency is allowed. Furthermore, we show that those unidentifiable gratings provide non-uniqueness examples for appropriately chosen wave number and incident angles. We also indicate and fix a gap in the proof of the main theorem of Elschner and Yamamoto [Z. Anal. Anwend., 26 (2007), 165-177], and generalize the uniqueness results of that paper.

H. Gross, A. Rathsfeld, F. Scholze, M. Bär, Profile reconstruction in extreme ultraviolet (EUV) scatterometry: Modeling and uncertainty estimates, Meas. Sci. Technol., 20 (2009) pp. 105102/1--105102/11.
Abstract

Scatterometry as a non-imaging indirect optical method in wafer metrology is also relevant to lithography masks designed for Extreme Ultraviolet Lithography, where light with wavelengths in the range of 13 nm is applied. The solution of the inverse problem, i.e. the determination of periodic surface structures regarding critical dimensions (CD) and other profile properties from light diffraction patterns, is incomplete without knowledge of the uncertainties associated with the reconstructed parameters. With decreasing feature sizes of lithography masks, increasing demands on metrology techniques and their uncertainties arise. The numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. For typical EUV masks the ratio period over wave length is so large, that a generalized finite element method has to be used to ensure reliable results with reasonable computational costs. The inverse problem can be formulated as a non-linear operator equation in Euclidean spaces. The operator maps the sought mask parameters to the efficiencies of diffracted plane wave modes. We employ a Gauß-Newton type iterative method to solve this operator equation and end up minimizing the deviation of the measured efficiency or phase shift values from the calculated ones. We apply our reconstruction algorithm for the measurement of a typical EUV mask composed of TaN absorber lines of about 80 nm height, a period of 420 nm resp. 720 nm, and with an underlying MoSi-multilayer stack of 300 nm thickness. Clearly, the uncertainties of the reconstructed geometric parameters essentially depend on the uncertainties of the input data and can be estimated by various methods. We apply a Monte Carlo procedure and an approximative covariance method to evaluate the reconstruction algorithm. Finally, we analyze the influence of uncertainties in the widths of the multilayer stack by the Monte Carlo method.

H. Gross, A. Rathsfeld, Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures, Waves Random Complex Media, 18 (2008) pp. 129--149.

J. Elschner, M. Yamamoto, Uniqueness in determining polygonal periodic structures, Z. Anal. Anwendungen, 26 (2007) pp. 165--177.

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, A. Rathsfeld, Mathematical modelling of indirect measurements in scatterometry, Measurement, 39 (2006) pp. 782--794.

A. Rathsfeld, G. Schmidt, B.H. Kleemann, On a fast integral equation method for diffraction gratings, Commun. Comput. Phys., 1 (2006) pp. 984-1009.

G. Bruckner, J. Elschner, The numerical solution of an inverse periodic transmission problem, Math. Methods Appl. Sci., 28 (2005) pp. 757--778.

J. Elschner, M. Yamamoto, Uniqueness results for an inverse periodic transmission problem, Inverse Problems, 20 (2004) pp. 1841--1852.

G. Bao, K. Huang, G. Schmidt, Optimal design of nonlinear diffraction gratings, J. Comput. Phys., 184 (2003) pp. 106--121.

G. Bruckner, J. Elschner, A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles, Inverse Problems, 19 (2003) pp. 315--329.

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

J. Elschner, G. Schmidt, M. Yamamoto, An inverse problem in periodic diffractive optics: Global uniqueness with a single wavenumber, Inverse Problems, 19 (2003) pp. 779--787.

J. Elschner, G. Schmidt, M. Yamamoto, Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number, J. Inverse Ill-Posed Probl., 11 (2003) pp. 235--244.

J. Elschner, G. Schmidt, Conical diffraction by periodic structures: Variation of interfaces and gradient formulas, Math. Nachr., 252 (2003) pp. 24--42.

G. Schmidt, Boundary integral methods for periodic scattering problems, in: Around the Research of Vladimir Maz'ya II. Partial Differential Equations, A. Laptev, ed., 12 of International Mathematical Series, Springer Science+Business Media, New York [et al.], 2010, pp. 337--363.

H. Gross, F. Scholze, A. Rathsfeld, M. Bär, Evaluation of measurement uncertainties in EUV scatterometry, in: Modeling Aspects in Optical Metrology II, H. Bosse, B. Bodermann, R.M. Silver, eds., 7390 of Proceedings of SPIE, SPIE, 2009, pp. 7390OT/1--7390OT/11.

H. Gross, A. Rathsfeld, M. Bär, Modelling and uncertainty estimates for numerically reconstructed profiles in scatterometry, in: Advanced Mathematical and Computational Tools in Metrology and Testing VIII, F. Pavese, M. Bär, A.B. Forbes, J.M. Linares, C. Perruchet, N.F. Zhang, eds., 78 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 2009, pp. 142--147.

M.-A. Henn, R. Model, M. Bär, M. Wurm, B. Bodermann, A. Rathsfeld, H. Gross, On numerical reconstructions of lithographic masks in DUV scatterometry, in: Modeling Aspects in Optical Metrology II, H. Bosse, B. Bodermann, R.M. Silver, eds., 7390 of Proceedings of SPIE, SPIE, 2009, pp. 7390OQ/1--7390OQ/11.

H. Gross, R. Model, A. Rathsfeld, F. Scholze, M. Wurm, B. Bodermann, M. Bär, Modellbildung, Bestimmung der Messunsicherheit und Validierung für diskrete inverse Probleme am Beispiel der Scatterometrie, in: Sensoren und Messsysteme, 14. Fachtagung Ludwigsburg, 11./12. März 2008, 2011 of VDI-Berichte, VDI, 2008, pp. 337--346.

R. Model, A. Rathsfeld, H. Gross, M. Wurm, B. Bodermann, A scatterometry inverse problem in optical mask metrology, in: 6th International Conference on Inverse Problems in Engineering: Theory and Practice, 15--19 June 2008, Dourdan (Paris), France, 135 of J. Phys.: Conf. Ser., Inst. Phys., 2008, pp. 012071/1--012071/8.

H. Gross, A. Rathsfeld, F. Scholze, M. Bär, U. Dersch, Optimal sets of measurement data for profile reconstruction in scatterometry, in: Modeling Aspects in Optical Metrology, H. Bosse, B. Bodermann, R.M. Silver, eds., 6617 of Proceedings of SPIE, 2007, pp. 66171B/1--66171B/12.

M. Wurm, B. Bodermann, F. Scholze, Ch. Laubis, H. Gross, A. Rathsfeld, Untersuchung zur Eignung der EUV-Scatterometrie zur quantitativen Charakterisierung periodischer Strukturen auf Photolithographiemasken, in: Proc. of the 107th Meeting of DGaO (German Branch of the European Optical Society), June 6--10, 2006, in Weingarten, DGaO-Proceedings, 2006, pp. P74/1--P74/2.

P. DE Bisschop, A. Erdmann, A. Rathsfeld, Simulation of the effect of a resist-surface bound air bubble on imaging in immersion lithography, in: Optical Microlithography XVIII, B.W. Smith, ed., 5754 of Proceedings of SPIE, 2005, pp. 243--253.

G. Bruckner, J. Elschner, M. Yamamoto, An optimization method for the grating profile reconstruction, Proceedings 3rd ISAAC Congress, Berlin, August 20 - 25, 2001, H.G.W. Begehr, R.P. Gilbert, M.W. Wong, eds., II of Progress in Analysis, World Scientific, New Jersey [u.a.], 2003, pp. 1391--1404.

J. Elschner, R. Hinder, G. Schmidt, Direct and inverse problems for diffractive structures --- Optimization of binary gratings, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 293--304.

G. Schmidt, Electromagnetic scattering by periodic structures (in Russian), Proceedings of the International Conference on Differential and Functional Differential Equations, Moscow, Russia, August 11 - 17, 2002, 3 of Sovrem. Probl. Mat. Fund. Naprav., 2003, pp. 113--128.

G. Schmidt, Conical diffraction by multilayer gratings: A recursive integral equations approach, Preprint no. 1601, WIAS, Berlin, 2011.
Abstract, Postscript (410 kByte), PDF (216 kByte)

In this paper we consider an integral equation algorithm to study the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in $R^2$ coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with an arbitrary number of material layers we present the extension of a recursive procedure developed by Maystre for normal incidence, which transforms the problem to a sequence of equations with $2 times 2$ operator matrices on each interface. Necessary and sufficient conditions for the applicability of the algorithm are derived.

G. Hu, Inverse wave scattering by unbounded obstacles: Uniqueness for the two-dimensional Helmholtz equation, Preprint no. 1592, WIAS, Berlin, 2011.
Abstract, Postscript (1205 kByte), PDF (160 kByte)

In this paper we present some uniqueness results on inverse wave scattering by unbounded obstacles for the two-dimensional Helmholtz equation. We prove that an impenetrable one-dimensional rough surface can be uniquely determined by the values of the scattered field taken on a line segment above the surface that correspond to the incident waves generated by a countable number of point sources. For penetrable rough layers in a piecewise constant medium, the refractive indices together with the rough interfaces (on which the TM transmission conditions are imposed) can be uniquely identified using the same measurements and the same incident point source waves. Moreover, a Dirichlet polygonal rough surface can be uniquely determined by a single incident point source wave provided a certain condition is imposed on it.

G. Hu, Direct and inverse scattering of elastic waves by diffraction gratings, 6th International Conference ``Inverse Problems, Control and Shape Optimization'' (PICOF '12), April 2 - 4, 2012, Palaiseau, France, April 4, 2012.

G. Hu, Direct and inverse scattering of elastic waves by diffraction gratings, Workshop 3 ``Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment'', November 21 - 25, 2011, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 24, 2011.

N. Kleemann, Shape derivatives for conical diffraction by non-smooth interfaces, Technische Universität Berlin, Institut für Mathematik, January 6, 2011.

N. Kleemann, Shape derivatives for conical diffraction by non-smooth interfaces, Friedrich-Schiller-Universität Jena, Mathematisches Institut, February 11, 2011.

A. Rathsfeld, On Born approximation for the scattering by rough surfaces, 262. PTB Seminar, EUV Metrology, October 27 - 28, 2011, Physikalisch-Technische Bundesanstalt, Berlin, October 28, 2011.

G. Schmidt, Fast computation of high-dimensional volume potentials, Trilateral Workshop on Separation of Variables and Applications (SVA), September 8 - 10, 2010, La Colle-sur-Loup, France, September 10, 2010.

G. Schmidt, Integral methods for conical diffraction by multi-profile gratings, Annual International Conference ``Days on Diffraction 2010'', June 8 - 11, 2010, St. Petersburg, Russia, June 9, 2010.

G. Schmidt, On the computation of volume potentials over high-dimensional rectangular domains, The First Workshop on Approximate Approximations and Their Applications, December 14 - 15, 2010, University of Liverpool, UK, December 15, 2010.

A. Rathsfeld, Modelling and algorithms for simulation and reconstruction in scatterometry, Workshop on Scatterometry and Ellipsometry on Structured Surfaces, March 18 - 19, 2009, Physikalisch-Technische Bundesanstalt, Department ``Imaging and Wave Optics'', Braunschweig, March 18, 2009.

A. Rathsfeld, Numerical aspects of the scatterometric measurement of periodic surface structures, Conference on Applied Inverse Problems 2009, July 20 - 24, 2009, University of Vienna, Austria, July 21, 2009.

G. Schmidt, Existence and uniqueness of solution for a system of Helmholtz equations, International Conference on Elliptic and Parabolic Equations, November 30 - December 4, 2009, WIAS, December 3, 2009.

A. Rathsfeld, Scatterometry: Inverse problems and optimization of measurements, University of Tokyo, Department of Mathematical Sciences, Japan, March 6, 2008.

G. Schmidt, Integral equations for conical diffraction by coated gratings, Annual International Conference ``Days on Diffraction'', June 3 - 6, 2008, St. Petersburg, Russia, June 3, 2008.

J. Elschner, On uniqueness in inverse scattering by obstacles and diffraction gratings, Conference ``Boundary Elements --- Theory and Applications'' (Beta 2007), May 22 - 24, 2007, Leibniz Universität Hannover, May 22, 2007.

J. Elschner, On uniqueness in inverse scattering with finitely many incident waves, Workshop ``Inverse Problems in Wave Scattering'', March 5 - 9, 2007, Mathematisches Forschungsinstitut Oberwolfach, March 6, 2007.

A. Rathsfeld, Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 20, 2007.

J. Elschner, Inverse problems for diffraction gratings, Waves Meeting, September 21 - 23, 2006, University of Reading, UK, September 22, 2006.

J. Elschner, Variational approach to scattering by unbounded surfaces, 12th Conference on Mathematics of Finite Elements and Applications (MAFELAP 2006), June 13 - 16, 2006, Brunel University, Uxbridge, UK, June 15, 2006.

J. Elschner, Variational approach to scattering by unbounded surfaces, Autumn School ``Analysis of Maxwell's Equations'' (Research Training Group GRK 1294 ``Analysis, Simulation and Design of Nanotechnological Processes''), October 17 - 19, 2006, Universität Karlsruhe, October 18, 2006.

A. Rathsfeld, Inverses Problem, Sensitivitätsanalyse, optimierte Messstrategie, BMBF-Projekttreffen ABBILD, Physikalisch-Technische Bundesanstalt, Berlin, November 13, 2006.

A. Rathsfeld, Sensitivity analysis for scatterometry and reconstruction of periodic grating structures, Physikalisch-Technische Bundesanstalt, Berlin, October 26, 2006.

J. Elschner, Inverse Probleme für optische Gitter, Physikalisch-Technische Bundesanstalt, Berlin, April 13, 2005.

J. Elschner, Inverse problems for diffraction gratings, Inverse Scattering Workshop, University of North Carolina, Charlotte, USA, June 3, 2005.

J. Elschner, Inverse problems for diffraction gratings, University of Delaware, Department of Mathematics, Newark, USA, June 9, 2005.

A. Rathsfeld, Finite elements for the rigorous simulation of time-harmonic waves, 3rd IISB Lithography Simulation Workshop, September 16 - 18, 2005, Pommersfelden, September 16, 2005.

A. Rathsfeld, Integralgleichungsmethode für optische Gitter --- Weiterentwicklung der IESMP, Kick-off Meeting of BMBF Project ``NAOMI'', Carl Zeiss AG, Jena, May 31, 2005.

A. Rathsfeld, Local optimization of polygonal gratings for classical and conical diffraction, Conference ``Diffractive Optics 2005'', Warsaw, Poland, September 3 - 7, 2005.

A. Rathsfeld, Local optimization of polygonal gratings for classical and conical diffraction, WIAS Workshop ``New Trends in Simulation and Control of PDEs'', September 26 - 28, 2005, Berlin, September 26, 2005.

A. Rathsfeld, Optimierung von optischen Gittern mit tt DiPoG-2.1, 2nd Meeting ``Inverses Problem in der Scatterometrie'', Physikalisch-Technische Bundesanstalt, Braunschweig, October 18, 2005.

A. Rathsfeld, Optimization of diffraction gratings with tt DiPoG, sc Matheon MF 1 Workshop ``Optimization Software'', Konrad-Zuse-Zentrum für Informationstechnik Berlin, June 1, 2005.

G. Schmidt, Simulation und Optimierung periodischer diffraktiver Strukturen mit DiPoG, Physikalisch-Technische Bundesanstalt, Berlin, April 13, 2005.

J. Elschner, Direct and inverse problems for the periodic Helmholtz equation I, University of Tokyo, Department of Mathematical Sciences, Japan, February 12, 2004.

J. Elschner, Direct and inverse problems for the periodic Helmholtz equation II, University of Tokyo, Department of Mathematical Sciences, Japan, February 13, 2004.

J. Elschner, Inverse scattering for diffraction gratings, European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), June 24 - 28, 2004, Jyväskylä, Finland, June 26, 2004.

J. Elschner, Inverse scattering of plane waves from periodic surfaces, Chemnitzer Minisymposium 2004 zu Inversen Problemen, Universität Chemnitz, September 23, 2004.

J. Elschner, Recent progress in inverse periodic diffraction problems, Workshop ``Mathematical Analyses and Numerical Methods for Applied Inverse Problems'', January 19 - 21, 2004, University of Tokyo, Japan, January 20, 2004.

A. Rathsfeld, Simulation und Optimierung diffraktiver Strukturen für die Mikrooptik, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, October 22, 2004.

G. Bruckner, J. Elschner, A. Rathsfeld, G. Schmidt, Simulation, optimization and reconstruction of diffractive structures, Conference ``Diffractive Optics 2003'', Oxford, UK, September 17 - 20, 2003.

J. Elschner, Inverse problems for diffraction gratings: Uniqueness results, Meeting ``Inverse Problems in Wave Scattering and Impedance Tomography'', April 20 - 25, 2003, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2003.

J. Elschner, Inverse problems for periodic diffractive structures, Meeting ``Functional Analysis and Partial Differential Equations'', June 2 - 3, 2003, Han-sur-Lesse, Belgium, June 3, 2003.

J. Elschner, On the numerical solution of inverse periodic transmission problems, University of Tokyo, Department of Mathematical Sciences, Japan, August 5, 2003.

G. Hu, B. Zhang, The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure, Preprint no. arXiv:1003.3067, Cornell University Library, arXiv.org, 2010.

J. Elschner, G. Schmidt, M. Yamamoto, An inverse problem in periodic diffractive optics: Global uniqueness with a single wave number, Preprint no. 5, University of Tokyo, Graduate School of Mathematical Sciences, 2003.