1. (with W. Wu) Error estimates of the generalized difference
methods for 2nd order hyperbolic equations,
Acta. Sci. Natur. Univ. Jilin
2. (with W.W. Symes)
A trace theorem for solutions of linear
partial differential equations,
Math. Meth. in the Appl. Sci.
3. (with W.W. Symes) Trace regularity for a second order
hyperbolic equation with nonsmooth coefficients,
J. of Math. Anal. Appl.
4. Time like trace regularity of the wave equation, Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, ed. by R. Kleinman, T. Angell, D. Colton, F. Santosa, and I. Stakgold, SIAM, Philadelphia, 20-29, 1993.
5. (with D. Dobson) Nonlinear optics in periodic diffraction structures, Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, ed. by R. Kleinman, T. Angell, D. Colton, F. Santosa, and I. Stakgold, SIAM, Philadelphia, 30-38, 1993.
6. A uniqueness theorem for an inverse problem in periodic
diffractive optics, Inverse Problems
7. (with D. Dobson) Second harmonic generation in
nonlinear optical films,
J. Math. Phys.
8. (with D. Dobson, J.A. Cox) Mathematical issues in the electromagnetic theory of gratings, in Diffractive Optics: Design, Fabrication and Applications, Technical Digest, Optical Society of American, Vol. 11 (1994), 8-11.
9. (with W.W. Symes) Time like trace regularity of the
wave equation with a nonsmooth principal part,
SIAM J. Math. Anal.
10. (with D. Dobson, J.A. Cox) Mathematical studies in the rigorous
grating theory,
J. Opt. Soc. Am.
11. An inverse diffraction problem in periodic structures, Proceedings of Third International Conference on Mathematical and Numerical Aspects of Wave Propagation, Ed. by G. Cohen, SIAM, Philadelphia, 694-704, 1995.
12. Finite element approximation of time harmonic waves in periodic structures, SIAM J. Numer. Anal., Vol. 32, No. 4 (1995), 1155-1169.
13. (with A. Friedman) Inverse problems for scattering by
periodic structures,
Arch. Rat. Mech. Anal.
14. (with D. Dobson) Diffractive optics in nonlinear media with
periodic structure, Euro. J. Appl. Math.
15. Inverse problems in partial differential equations, in ``Numerical Methods in Applied Sciences'', ed. by W. Cai, Z. Shi, C-W. Shu, and J. Xu, Science Press, New York, 20-38, 1996.
16. (with W.W. Symes) Computation of pseudo-differential operators
, SIAM J. Sci. Comput.
17. (with W.W. Symes) On the sensitivity of solutions of hyperbolic
equations to the coefficients,
Comm. in P.D.E.
18. Numerical analysis of diffraction by periodic structures:
TM polarization, Numer. Math.
19. (with Y. Chen) A nonlinear grating problem in diffractive optics, SIAM J. Math. Anal., Vol. 28, No. 2 (1997), 322-337.
20. Variational approximation of Maxwell's equations in biperiodic structures, SIAM J. Appl. Math., Vol. 57, No. 2 (1997), 364-381.
21. (with Z. Zhou) Inverse diffraction by a doubly periodic structure, C.R. Acad. Sci., Paris, t 324, Serie I (1997), 627-632.
22. (with W.W. Symes) Regularity of an inverse problem in wave propagation, in ``Inverse Problems of Wave Propagation and Diffraction'', Springer Lecture Notes in Phys., ed. by G. Chavent and P. Sabatier, Springer-Verlag, 226-235, 1997.
23. Smoothness between coefficients and boundary values for the wave equation, SIAM J. Math. Anal., Vol. 29, No. 2 (1998), 380-394.
24. Mathematical modeling of nonlinear diffractive optics, J. Dynamical Systems and Differential Equations, Special Issue, Vol. 1, 89-99, 1998.
25. Diffraction by a periodic surface, in the Proceedings of Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Ed. by J. DeSanto, SIAM, Philadelphia, 476-478, 1998.
26. Mathematical modeling of diffractive gratings, in Diffractive Optics: Design, Fabrication and Applications, Technical Digest Series, Optical Society of American, Vol. 10 (1998), 4-6.
27. On the relation between the coefficients and solutions for
a diffraction problem,
Inverse Problems
28. Inverse diffraction by a periodic perfect conductor with several measurements, in Inverse Problems in Engineering, Theory and Practice, Ed. by D. Delaunay, Y. Jarny, K.A. Woodbury, ASME, 297-303, 1998.
29. (with H. Ammari) Analysis of the diffraction by periodic chiral
structures, C.R. Acad. Sci., Paris, t.
30. (with Z. Zhou) An inverse problem for scattering by a doubly
periodic structure, Trans. Ameri. Math. Soc.
31. (with H. Ammari) Une etude mathematique de la
localisation d'une tumeur cancereuse dans
le cerveau humain,
C.R. Acad. Sci., Paris, t.
32. Direct and inverse diffraction by periodic structures, in the Proceedings of International Conference on Nonlinear PDE and Applications, Ed. By B. Guo, World Scientific, 1-7, 1998.
33. (with D. Dobson) Modeling and optimal design of diffractive
optical structures,
Survey on Industrial Math.
34. (with H. Ammari and K. Hamdache) The effect of thin coatings on
second harmonic generation, Electronic. J. Diff. Eq., Vol.
35. (with H. Ammari) Identification of cracks by boundary
measurements at low frequencies, Inverse Problems
36. (with H. Yang) A least-squares finite element analysis of diffraction problems, SIAM J. Numer. Anal., Vol. 37, No. 2 (2000), 665-682.
37. (with H. Ammari) Scattering by a subwavelength object
embedded in a periodic structure, C.R. Acad. Sci., Paris,
t.
38. (with Y. Chen and F. Ma) Regularity and stability for the scattering map of a linearized inverse medium problem, J. Math. Anal. Appl., Vol. 247, No. 1 (2000), 255-271.
39. (with D. Dobson) On the scattering by a biperiodic structure, Proc. Amer. Math. Soc. 128 (2000), 2715-2723.
40. (with T. Van) Modeling of the evanescent energy in optical fibers, J. Comput. Phys., Vol. 161, No. 2 (2000), 700-717.
41. (with H. Ammari, T. Van, and A. Wood) Scattering from electromagnetic cavities, in the Proceedings of Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, ed. by A. Bermudez, D. Gomez, C. Hazard, P. Joly, and J. E. Roberts, SIAM, Philadelphia, 211-215, 2000.
42. (with H. Ammari) Modeling of near-field optics, in the Proceedings of Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, ed. by A. Bermudez, D. Gomez, C. Hazard, P. Joly, and J. E. Roberts,SIAM, Philadelphia, 445-449, 2000.
43. (with H. Ammari and A. Wood) An integral equation method for the electromagnetic scattering from cavities, Math. Meth. in the Appl. Sci., Vol. 23 (2000), 1057-1072.
44. (with Y. Cao and H. Yang) Numerical solution of diffraction problems by a least-squares finite element method, Math. Meth. in the Appl. Sci., Vol. 23 (2000), 1073-1092.
45. Modeling of micro diffractive optics, in the Proceedings of the International Conf. on Diff. Eqns. Comput. & Simulations, ed. by P. Bates, K. Lu and D. Xu, World Scientific Publishing, 1-8, 2000.
46. (with X. Fang, W. Tan, and T. Van) Evanescent energy in square and circular fibers, J. Math. Chem., v. 27, no. 4 (2000), 12-19.
47. (with D. Dobson) Variational methods for diffractive optics modeling, in ``Mathematical Modeling in Optical Science'', ed. by G. Bao, L. Cowsar, and W. Masters, SIAM Frontiers in Appl. Math., SIAM, Philadelphia, 37-70, 2001.
48. (with L. Cowsar and W. Masters) Preface to the Mathematical Modeling in Optical Science, in ``Mathematical Modeling in Optical Science'', ed. by G. Bao, L. Cowsar, and W. Masters, SIAM Frontiers in Appl. Math., SIAM, Philadelphia, 2001.
49. (with H. Ammari) Analysis of the scattering map of a linearized inverse medium problem for electromagnetic waves, Inverse Problems 17 (2001), 219-234.
50. (with E. Bonnetier) Optimal design of periodic diffractive structures, Appl. Math. Optim. 43 (2001), 103-116.
51. (with G. Li) Optimal design in nonlinear optics, in ``Encyclopedia of Optimization'', ed. by P. M. Pardalos and C. A. Floudas, Kluwer Academic Pub., Dordrecht, Vol IV, 2001, 147-153.
52. On modeling and design problems in micro diffractive optics, International Series of Numer. Math., Vol 139 (2001), 19-30.
53. (with H. Ammari) Mathematical modeling of near-field optics, J. Math. Anal. Appl. 265 (2002), 430-446.
54. (with D. Dobson and K. Ramdani) A constraint on the maximum reflectance of rapidly oscillating dielectric gratings, SIAM J. Control. Opt., Vol. 40, No 6 (2002), 1858-1866.
55. Preface to the Special Issue on Modeling and Computation of Optics and Electromagnetics, Adv. in Comput. Math. 16 (2002), 97-98.
56. (with H. Ammari) Maxwell's equations in a perturbed periodic structure, Adv. Comput. Math. 16 (2002), 99-112.
57. (with H. Ammari and J. Fleming) An inverse source problem for Maxwell's equations in megnetoencephalography, SIAM J. Appl. Math. 62 (2002), 1369-1382.
58. (with K. Ramdani) Resonant frequencies for diffraction gratings, Appl. Math. Lett. 16 (2002), 755-760.
59. (with H. Ammari and A. Wood) Analysis of the electromagnetic scattering from a cavity, Japan J. Indust. Appl. Math. 19 (2002), 301-310.
60. (with H. Ammari and K. Hamdache) Analysis of thin coatings on nonlinear diffraction gratings, Nonlinear Analysis: Series B Real World Appl. 3(4) (2002), 485-502.
61. (with H. Ammari and A. Wood) A cavity problem for Maxwell's equations, Meth. Appl. Anal. 9 (2002), 249-260.
62. (with K. Huang and G. Schmidt) Optimal design of nonlinear diffraction gratings, J. Comput. Phys. 184 (2003), 106-121.
63. (with H. Ammari) Maxwell's equations in periodic chiral structures, Math. Nachr. 251 (2003), 3-18.
64. (with G. W. Wei and S. Zhao) Local spectral time-domain method for electromagnetic wave propagation, Optics Lett., 28(7) (2003), 513-515.
65. Inverse and optimal design problems in diffractive optics, in ``Recent Developments in Theories & Numerics'', Proceedings of the International Conf. on Inverse Problems, ed. by Y. Hon, M. Yamamoto, J. Cheng, and J. Lee, World Sci., Hong Kong, 37-46, 2003.
66. (with A. Minut and Z. Zhou) Maxwell's equations in nonlinear biperiodic structures Proceedings of Sixth International Conference on Mathematical and Computational Aspects of Wave Propagation, ed. by G. Cohen, E. Heikkola, P. Joly, and P. Neittaanmaki, Springer, Berlin, 406-411, 2003.
67. (with K. Huang) Optimal design of waveguide-grating resonances Proceedings of Sixth International Conference on Mathematical and Computational Aspects of Wave Propagation, ed. by G. Cohen, E. Heikkola, P. Joly, and P. Neittaanmaki, Springer, Berlin, 830-835, 2003.
68. (with Z. Zhou) On nonlinear Maxwell's equations from second harmonic generation, Proceedings of the 3rd International ISAAC Congress, ed. by H. Begehr, R. Gilbert, and M. Wong, 1097-1106, 2003.
69. (with J. Liu and H.-C. Wei) Recursive linearization of an inverse medium problem, Proceedings of the 3rd International ISAAC Congress, ed. by H. Begehr, R. Gilbert, and M. Wong, 1423-1436, 2003.
70. (with A. Minut and Z. Zhou) $L^p$ estimates for Maxwell's equations in stratified media, C. R. Acad. Sci., Paris, 337 (2003), 365-370.
71. (with J. Liu) Numerical solution of inverse scattering problems with multi-experimental limited aperture data, SIAM J. Sci. Comput., Vol 25, No 3 (2003), 1102-1117.
72. (with K. Huang) Optimal design of guided mode grating resonance filters, IEEE Photonic Tech. Lett., Vol 16, No. 1 (2004), 141-143.
73. (with G. W. Wei and S. Zhao) Numerical solution of the Helmholtz equation with high wave number, Int. J. Numer. Meth. Engng., 59 (2004), 389-408.
74. (with P. Li) Inverse medium scattering for three-dimensional time harmonic Maxewll's equations, Inverse Problems, Vol. 20 (2) (2004), L1 - L7.
75. Recent mathematical studies in the modeling of optics and electromagnetics, Comput. Math., Vol. 22 (2) (2004), 148-155.
76. Recent mathematical studies of diffractive optics, Math. Modelling in Physics, Engineering and Cognitive Sciences. Vol. 7, . Proceedings of the Conference on Mathematical Modelling of Wave Phenomena, Ed. by B. Nilsson, Vaxjo Univ. Press., 23-28, 2004.
77. (with J. Liu) Accurate computation of the electromagnetic scattering from a cavity, Proceedings of 3rd International Workshop on Scientific Computing and Applications, ed. by Y. Lu, W. Sun, and T. Tang, Sci. Press, Beijing, 45-54, 2004.
78. (with G. W. Wei and S. Zhao) A new algorithm for solving the Helmholtz equation with high wavenumbers, Proceedings of 3rd International Workshop on Scientific Computing and Applications, ed. by Y. Lu, W. Sun, and T. Tang, Sci. Press, Beijing, 55-67, 2004.
79. The mathematics of diffractive optics, Proceedings of ICCM2001, ed. by C. Lin, L. Yang, and S. T. Yau, International Press, MA, 555-567, 2004.
80. (with A. Zhou) Analysis of finite dimensional approximations to a class of partial differential equations, Math. Meth. Appl. Sci., 27 (2004), 2055-2066.
81. (with Z. Chen and H. Wu) Adaptive finite element method for diffraction gratings, J. Opt. Soc. Amer. A, Vol. 22, No. 6 (2005), 1106-1114.
82. (with K. Huang) Computational design for guided-mode grating resonances, J. Opt. Soc. Amer. A, Vol. 22, No. 7 (2005), 1408-1413.
83. (with P. Li) Inverse medium scattering problems for electromagnetic waves, SIAM J. Appl. Math., Vol. 65, No. 6 (2005), 2049-2066.
84. (with P. Li) Inverse medium scattering for the Helmholtz equation at fixed frequency, Inverse Problems 21 (2005), 1621-1644.
85. (with H. Wu) Convergence analysis of the perfectly matched layer problems for time-harmonic Maxwell's equations, SIAM J. Numer. Anal., Vol. 43, No. 5 (2005), 2121-2143.
86. (with W. Zhang) An improved mode matching method for large cavities, IEEE Antennas and Wireless Propagation Letters, Vol. 4 (2005), 393-396.
87. (with W. Sun) A fast algorithm for the electromagnetic scattering from a large cavity, SIAM J. Sci. Comput., SIAM J. Sci. Comput., Vol. 27, No. 2 (2005), 553-574.
88. (with Y. Li and H. Wu) Numerical solution of nonlinear diffraction problems, J. Comput. Appl. Math. 190 (2006), 170-189.
89. (with P. Li) Computational inverse medium problems at fixed frequency, in "Advances in Applied and Computational Mathematics", ed. by F. Liu, Z. Nashed, G. N'Guerekata, D. Pokrajac and Z. Qiao, Nova Science, Publishers, (2006), 1-9.
90. (with P. Li) Numerical solution of inverse scattering for near-field optics, Optics Lett., Vol. 32, Issue 11 (2007), 1465-1467.
91. (with P. Li) Inverse medium scattering problems in near-field optics, J. Comput. Math., Vol. 25, No. 3 (2007), 252-265.
92. (with S. Hou and P. Li) Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm, J. Comput. Phys. 227 (2007), 755-762.
93. (with A. Minut and Z. Zhou) L^p estimates for Maxwell's equations with source term, Comm. in P.D.E. 32 (2007), 1449-1471.
94. (with S. Hou and P. Li) Recent studies on inverse medium scattering problems, Lecture Notes in Computational Science and Engineering 59 (2007), ed. by H. Ammari, 165-186.
95. (with H. Ammari) Coupling of finite element and boundary element methods for the scattering by periodic chiral structures, J. Comput. Math., Vol. 26, No. 3 (2008), 261-283.
96. (with Y. Sun, H. Ajiki) Computational modeling of optical response from excitons in a nano optical medium, Comm. Comput. Phys, 4 (2008), 1051-1068.
97. (with Y. Li and Z. Zhou) L^p estimates of time-harmonic Maxwell's equations in a bounded domain, J. Diff. Eq. 245 (2008), 3674-3686.
98. (with K. Yun) On the stability of an inverse problem for the wave equation, Inverse Problems 25 (2009), 045003, 7pp.
99. (with P. Li) Numerical solution of an inverse medium scattering problem for Maxwell's equations at fixed frequency J. Comput. Phys. 228(2009), 4638-4648.
100. (with Y. Sun) Modeling and computation of the scattering by a nano optical medium, Contemp. Math. 494 (2009), 27-41.
101. (with Y. Sun) Optical polariton modes in a nanoscale semiconductor, Optics Lett., Vol. 34, No. 21 (2009), 3436-3438.
102. (with P. Li and H. Wu) An adaptive edge element method with perfectly matched absorbing layers for wave scattering by periodic structures, Math. Comp. 79(2010), 1-34.
103. (with F. Triki) Error estimates for the recursive linearization for solving inverse medium problems, J. Comput. Math., 28(6) (2010), 725-744.
104. (with J. Lin and F. Triki) A multi-frequency inverse source problem, J. Diff. Eqn. 249(12) (2010), 3443-3465.
105. (with S-N Chow, P. Li, and H-M Zhou) Numerical solution of an inverse medium scattering problem with a stochastic source, Inverse Problems, 26 (2010), 7-29.
106. (with Z. Xu ) A numerical scheme for nonlinear Helmholtz equation in nonlinear optics, J. Opt. Soc. Amer. A. 27(11) (2010), 2347-2353.
107. (with L. Dou, T. Ehlers, P. Li, Y. Wang, and Z. Xu) Quantifying tectonic and geomorphic interpretations of thermochronometer data: The reconstruction of mountain surface. Comm. Comput. Phys., 9(1) (2011), 129-146.
108. (with H. Zhang and J. Zou) Unique determination of periodic polyhedral structures by scattered electromagnetic fields, Trans. Amer. Math. Soc. 363 (2011), 4527-4551.
109. (with Z. Xu, J. Yuan) Continuation finite element simulation of second harmonic generation in photonic crystals, Comm. Comput. Phys., 10 (2011), 57-69.
110. (with J. Gao, and P. Li) Analysis of direct and inverse problems for electromagnetics scattering from cavities, Numer. Math. Theor. Meth. Appl., 4 (2011), 335-358.
111. (with J. Lin and F. Triki) Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data, Contemp. Math., AMS, 548 (2011), 45-60.
112. (with J. Lin) Imaging of local surface displacement on an infinite ground plane: the multiple frequency case, SIAM J. Appl. Math., 71 (2011),1733-1752.
113. (with J. Lin and F. Triki) An inverse source problem with multiple frequency data, C. R. Math. Acad. Sci. Paris 349 (2011), 855-859.
114. (with P. Li and H. Wu) A computational inverse diffraction grating problem, J. Opt. Soc. Am. A., Vol. 29, No. 4 (2012), 394-399.
115. (with J. Gao, J. Lin, and W. Zhang) Mode matching for the electromagnetic scattering from three dimensional large cavities, IEEE Trans. Antennas & Wave Propagation, Vol. 60? No. 4 ?2012??1-7.
116. (with K. Yun, and Z. Zhou) Stability of the scattering from a large electromagnetic cavity in two dimensions, SIAM J. Math. Anal. 44(1) (2012), 383-404.
117. (with X. Xu) An inverse diffusivity problem for the helium production-diffusion equation, Inverse Problems 28 (2012) 085002 (15pp).
118. (with G. Hu, and D. Liu) A h-adaptive FEM solver for the calculations of the electronic structures, J. Comput. Phys., 231 (2012), 4967-4979.
119. (with G. Hu, and D. Liu) Numerical solution of the Kohn-Sham equation by finite element methods with an adaptive mesh redistribution technique, J. Sci. Comput., DOI 10.1007/s10915-012-9636-1, 2012.
120. (with J. Lin) Imaging of reflective surfaces by near-field optics, Optics Lett., 37(24)(2012), 5027-9. doi: 10.1364/OL.37.005027.
121. (with T. Ehlers, and P. Li) Radiogenic source identification for the helium production-diffusion equation, Comm. Comput. Phys., 14 (1) (2013), 1-20.
122. (with J. Qian, L. Ying, and H. Zhang) A convergent multiscale Gaussian-beam parametrix for wave equations, Comm. in P.DE., 38(2013), 92-134.
123. (with P. Li, and J. Lv) Reconstruction of perfectly reflecting gratings from intensity data, J. Opt. Soc. Am. A., Vol. 30 (3)(2013), 293-299.
124. (with Y. Wang) Optimal design of antireflection coatings with different metrics, J. Opt. Soc. Am. A 30 (2013), 656-662.
125. (with X. Xu) An inverse random source problem in quantifying the elastic modulus of nano-materials, Inverse Problems, 29 (1)(2013), 015006.
126. (with S-N Chow, P. Li, and H-M Zhou) An inverse random source problem for the Helmholtz equation in one dimension, Math. Comp., to appear.
127. (with H. Zhang, and J. Zou) Unique determination of periodic polyhedral structures by scattered electromagnetic fields Part II: The resonance case, Trans. Amer. Math. Soc., to appear.
128. (with J. Lin) Near-field imaging of the surface displacement on an infinite ground plane, Inverse Problems and Imaging, to appear.
129. (with G. Hu, D. Liu, and S. Luo) Multiphysical modeling and multiscale computation of nano-optical responses, Contemp. Math., AMS, to appear.
130. (with D. Liu, and S. Luo) A multiscale method for optical responses of nano structures, SIAM J. Appl. Math., to appear.
1. (edit with L. Cowsar and W. Masters) Mathematical Modeling in Optical Science, the SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 333 pages, 2001.
2. (edit) Modeling and Computation of Optics and Electromagnetics, Special Issue, Advances in Computational Mathematics, Vol. 16 (2002).
3. (edit) Mathematics and Computation of Optics and Electromagnetics, Special Issue, Comm. in Comput. Phys., Vol. 1, No. 6, 2006.
4. (edit with Z. Chen, Z.-C. Shi, and B. Zhang) Recent Mathematical and Computational Developments of Maxwell's Equations Special Issue, J. Comput. Math., Vol. 25, No. 3, 2007.