Ya Yan Lu

Professor
Department of Mathematics
City University of Hong Kong
Tat Chee Avenue, Kowloon, Hong Kong

Office: Room Y6509, Academic Building 1, City University of Hong Kong
Telephone: (852) 3442 7436
Fax: (852) 3442 0250
E-mail: mayylu@cityu.edu.hk

Teaching:

1. Course materials for MA3513 Elementary Numerical Methods can be found here.
2. Course materials for MA3514 Numerical Methods for Differential Equations can be found here.
3. Course materials for MA4528 Introduction to Dynamical Systems and Chaos can be found here.
4. Course materials for MA6606 Computational Linear Algebra can be found here.
5. Course materials for MA6618 Mathematical Methods for Electromagnetic and Optical Waves can be found here.

Research Interest:

In the last a few years, I have been working on numerical methods and mathematical modeling of photonic structures, including optical waveguides, photonic crystals and diffraction gratings. Optical waveguides (such as optical fibers) are structures that guide the propagation of light and they are the basic building blocks of photonic integrated circuits . Photonic crystals are periodic structures with a period on the scale of the wavelength of the light and they are being explored to design compact photonic circuits. Efficient numerical methods are being developed based on the the so-called Dirichlet-to-Neumann maps. Some information can be found in my research projects.

Recent publications:

1. Dawei Song and Ya Yan Lu, Pseudospectral modal method for computing optical waveguide modes Journal of Lightwave Technology, to appear.
2. Yuexia Huang and Ya Yan Lu, Efficient method for lasing eigenvalue problems of periodic structures Journal of Modern Optics, to appear.
3. Xun Lu, Hualiang Shi, and Ya Yan Lu, Vertical mode expansion method for transmission of light through a single circular hole in a slab, Journal of the Optical Society of America A, Vol. 31, No. 2, pp. 293-300, Feb. 2014.
4. Dawei Song and Ya Yan Lu, Pseudospectral modal method for conical diffraction of gratings, Journal of Modern Optics, Vol. 60, No. 20, pp. 1729-1734, 2013.
5. Jianxin Zhu and Ya Yan Lu, Asymptotic solutions of eigenmodes in slab waveguides terminated by perfectly matched layers, Journal of the Optical Society of America A, Vol. 30, No. 10, pp. 2090-2095, Oct. 2013.
6. Lijun Yuan and Ya Yan Lu, Efficient numerical method for analyzing optical bistability in photonic crystal microcavities, Optics Express, Vol. 21, No. 10, pp. 11952-11964, 2013.
7. Shichang She and Ya Yan Lu, An improved Dirichlet-to-Neumann map method for scattering by circular cylinders on a lattice, Journal of the Optical Society of America A, Vol. 29, No. 9, pp. 1999-2004, 2012.
8. Zhen Hu and Ya Yan Lu, A simple boundary condition for terminating photonic crystal waveguides , Journal of the Optical Society of America B, Vol. 29, No. 6, pp. 1356-1360, June 2012.
9. Wangtao Lu and Ya Yan Lu, Efficient boundary integral equation method for photonic crystal fibers , Journal of Lightwave Technology, Vol. 20, No. 11, pp. 1610-1616, June 2012.
10. Dawei Song and Ya Yan Lu, High order finite difference modal method for diffraction gratings , Journal of Modern Optics, Vol. 59, No. 9, pp. 800-808, May 2012.
11. Wangtao Lu and Ya Yan Lu, High order integral equation method for diffraction gratings , Journal of the Optical Society of America A, Vol. 29, No. 5, pp. 734-740, May 2012.
12. Wangtao Lu and Ya Yan Lu, Waveguide mode solver based on Neumann-to-Dirichlet operators and boundary integral equations , Journal of Computational Physics, Vol. 231, No. 4, pp. 1360-1371, Feb. 2012.
13. Lijun Yuan and Ya Yan Lu, An efficient numerical method for analyzing photonic crystal slab waveguides , Journal of the Optical Society of America B. Vol. 28, pp. 2265-2270, Sept. 2011.
14. Huan Xie, Wangtao Lu and Ya Yan Lu, Complex modes and instability of full-vectorial beam propagation methods , Optics Letters, Vol. 36, pp. 2474-2476, July 2011.
15. Yumao Wu and Ya Yan Lu, Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction , Journal of the Optical Society of America A, Vol. 28, pp. 1191-1196, June 2011.
16. Zhen Hu and Ya Yan Lu, Improved bends for two-dimensional photonic crystal waveguides , Optics Communications, Vol. 284, pp. 2812-2816, June 2011.
17. Dawei Song, Lijun Yuan and Ya Yan Lu, Fourier-matching pseudospectral modal method for diffraction gratings , Journal of the Optical Society of America A, Vol. 28, pp. 613-620, April 2011.
18. Jianhua Yuan and Ya Yan Lu, Dirichlet-to-Neumann map method with boundary cells for photonic crystals devices , Communications in Computational Physics, Vol. 9, No. 1, pp. 113-128, Jan. 2011.
19. Lijun Yuan and Ya Yan Lu, Dirichlet-to-Neumann map method for analyzing hole arrays in a slab , Journal of the Optical Society of America B, Vol. 27, No. 12, pp. 2568-2579, December 2010.
20. Huan Xie and Ya Yan Lu, Improved spherical wave least squares method for analyzing periodic arrays of spheres , Journal of the Optical Society of America A, Vol. 27, No. 6, pp. 1404-1412, June 2010.
21. X. Antoine, Y. Huang and Ya Yan Lu, Computing high-frequency scattered fields by beam propagation methods: a prospective study , Journal of Algorithms & Computational Technology, Vol. 4, No. 2, pp. 147-166, 2010.
22. Shaojie Li and Ya Yan Lu, Efficient method for computing leaky modes in two-dimensional photonic crystal waveguides , Journal of Lightwave Technology, Vol. 28, No. 6, pp. 978-983, March 2010.
23. Shaojie Li and Ya Yan Lu, Accurate multipole analysis for leaky microcavities in two-dimensional photonic crystals , IEEE Photonics Technology Letters, Vol. 22, No. 2, pp. 94-96, Jan. 2010.
24. Zhen Hu and Ya Yan Lu, Efficient numerical method for analyzing coupling structures of photonic crystal waveguides , IEEE Photonics Technology Letters, Vol. 21, No. 23, pp. 1737-1739, Dec. 2009.
25. Shaojie Li and Ya Yan Lu, Efficient method for analyzing leaky cavities in two-dimensional photonic crystals , Journal of the Optical Society of America B, Vol. 26, No. 12, pp. 2427-2433, Dec. 2009.
26. Yumao Wu and Ya Yan Lu, Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method , Journal of the Optical Society of America A, Vol. 26, No. 11, pp. 2444-2451, Nov. 2009.
27. Yumao Wu and Ya Yan Lu, Dirichlet-to-Neumann map method for analyzing crossed arrays of circular cylinders , Journal of the Optical Society of America B, Vol. 26, No. 11, pp. 1984-1993, Nov. 2009.
28. Dawei Song and Ya Yan Lu, Chebyshev collocation Dirichlet-to-Neumann map method for diffraction gratings, Journal of the Optical Society of America A. Vol. 26, No. 9, pp. 1980-1988, Sept. 2009.
29. Huan Xie and Ya Yan Lu, Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps, Journal of the Optical Society of America A. Vol. 26, No. 7, pp. 1606-1614, July 2009.
30. Yumao Wu and Ya Yan Lu, Dirichlet-to-Neumann map method for analyzing periodic arrays of cylinders with oblique incident waves , Journal of the Optical Society of America B. Vol. 26, No. 7, pp. 1442-1449, July 2009.
31. Lijun Yuan and Ya Yan Lu, An efficient numerical method for optical waveguides with holes , Journal of Lightwave Technology. Vol. 27, No. 14, pp. 2557-2562, July 2009.
32. Lijun Yuan and Ya Yan Lu, Analyzing second harmonic generation from arrays of cylinders using Dirichlet-to-Neumann maps , Journal of the Optical Society of America B, Vol. 26, No. 4, pp. 587-594, April 2009.
33. Zhen Hu and Ya Yan Lu, Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices, Optical and Quantum Electronics, Vol. 40, pp. 921-932, 2008.
34. Ya Yan Lu, Computing Dirichlet-to-Neumann maps for numerical simulation of photonic crystal structures , Proceedings of the National Institute for Mathematical Sciences, Vol. 3, No. 9, pp. 65-70, Oct. 2008.
35. Zhen Hu and Ya Yan Lu, Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps , Optics Express, Vol. 16, No. 22, pp. 17383-17399, Oct. 2008.
36. Yumao Wu and Ya Yan Lu, Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice, Journal of the Optical Society of America B, Vol. 25, pp. 1466-1473, No. 9, Sept. 2008.
37. Suhua Wei and Ya Yan Lu, Coordinate stretching for finite difference optical waveguide mode solvers , Optics Communications, Vol. 281, No. 9, pp. 1491-2497, May 2008.
38. Jianhua Yuan, Ya Yan Lu and X. Antoine, Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps, Journal of Computational Physics, Vol. 227, No. 9, pp. 4617-3629, April 2008.
39. Jianxin Zhu and Ya Yan Lu, Asymptotic solutions of the leaky modes and PML modes in a Pekeris waveguide , Wave Motion, Vol. 45, No. 3, pp. 207-216, Jan. 2008.
40. Ya Yan Lu and Jianxin Zhu, Perfectly matched layer for acoustic waveguide modeling --- benchmark calculations and perturbation analysis , CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 3, pp. 235-247, Dec. 2007.
41. Lijun Yuan and Ya Yan Lu, A recursive doubling Dirichlet-to-Neumann map method for periodic waveguides , Journal of Lightwave Technology, Vol. 25, pp. 3649-3656, Nov. 2007.
42. Yuexia Huang, Ya Yan Lu and Shaojie Li, Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps , Journal of the Optical Society of America B, Vol. 24, No. 11, pp. 2860-2867, Nov. 2007.
43. Ya Yan Lu, A fourth order derivative-free operator marching method for Helmholtz equation in waveguides , Journal of Computational Mathematics, Vol. 25, no. 6, pp. 719-729, Nov. 2007.
44. Shaojie Li and Ya Yan Lu, Computing photonic crystal defect modes by Dirichlet-to-Neumann maps , Optics Express, Vol. 15, No. 22, pp. 14454-14466, Oct. 29, 2007.
45. Zhen Hu and Ya Yan Lu, Computing optimal waveguide bends with constant width , Journal of Lightwave Technology, Vol. 25, no. 10, pp. 3161-3167, Oct. 2007.
46. Lijun Yuan and Ya Yan Lu, Dirichlet-to-Neumann map method for second harmonic generation in piecewise uniform waveguides , Journal of the Optical Society of America B, Vol. 24, pp. 2287-2293, Sept. 2007.
47. Shaojie Li and Ya Yan Lu, Multipole Dirichlet-to-Neumann Map method for photonic crystals with complex unit cells , Journal of the Optical Society of America A, Vol. 24, pp. 2438-2442, Aug. 2007.
48. Yuexia Huang and Ya Yan Lu, Modeling photonic crystals with complex unit cells by Dirichlet-to-Neumann maps , Journal of Computational Mathematics, Vol. 25, No. 3, pp. 337-349, May 2007.
49. Jianhua Yuan and Ya Yan Lu, Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice , Optics Communications, Vol. 273, pp. 114-120, May 2007.
50. Jianhua Yuan and Ya Yan Lu, Photonic bandgap calculations using Dirichlet-to-Neumann maps , Journal of the Optical Society of America A, Vol. 23, pp. 3217-3222, Dec. 2006.
51. Ya Yan Lu, Some techniques for computing wave propagation in optical waveguides, Communications in Computational Physics, Vol. 1, No. 6, pp.1056-1075, Dec. 2006.
52. Lijun Yuan and Ya Yan Lu, An efficient bidirectional propagation method based on Dirichlet-to-Neumann maps , IEEE Photonics Technology Letters, Vol. 18, pp. 1967-1969, Sept. 15, 2006.
53. Yuexia Huang and Ya Yan Lu, Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps, Journal of Lightwave Technology, Vol. 24, pp. 3448-3453, Sept. 2006.
54. Jianxin Zhu and Ya Yan Lu, Leaky modes of slab waveguides --- asymptotic solutions, Journal of Lightwave Technology, Vol. 24, No. 3, pp. 1619-1623, March 2006.
55. Ya Yan Lu, Minimizing the discrete reflectivity of perfectly matched layers, IEEE Photonics Technology Letters, Vol. 18, No. 3, pp. 487-489, Feb. 2006.
56. Ya Yan Lu and Jianxin Zhu, Propagating modes in optical waveguides terminated by perfectly matched layers IEEE Photonics Technology Letters, Vol. 17, No. 12, pp. 2601-2603, Dec. 2005.
57. Ya Yan Lu, A Fourth Order Magnus Scheme for Helmholtz Equation, Journal of Computational and Applied Mathematic, Vol. 173, pp. 247-258, 2005.
58. P. K. Kwan and Ya Yan Lu, Computing Optical Bistability in One-dimensional Nonlinear Structures, Optics Communications, Vol. 238, pp. 169-175, Aug. 2004.
59. S. L. Chui and Ya Yan Lu, A Propagator-$\theta$ Beam Propagation Method, IEEE Photonics Technology Letters, Vol. 16, pp. 822-824, March 2004.
60. S. L. Chui and Ya Yan Lu, Wide-Angle Full-Vector Beam Propagation Method Based on an Alternating Direction Implicit Preconditioner, Journal of the Optical Society of America A, Vol. 21, pp. 420-425, March 2004.
61. Jianxin Zhu and Ya Yan Lu, Validity of One-way Models in the Weak Range Dependence Limit, Journal of Computational Acoustics, Vol. 12, No. 1, pp. 55-66, 2004.
62. Ya Yan Lu and Jianxin Zhu, A Local Orthogonal Transform for Acoustic Waveguides with an Internal Interface, Journal of Computational Acoustics, Vol. 12, No. 1, pp. 37-53, 2004.
63. Ya Yan Lu, Computing a Matrix Function for Exponential Integrators, Journal of Computational and Applied Mathematics, Vol. 161, No. 1, pp. 203-216, Dec. 2003.
64. P. L. Ho and Ya Yan Lu, A Mode-Preserving Perfectly Matched Layer for Optical Waveguides, IEEE Photonics Technology Letters, Vol. 15, No. 9, pp. 1234-1236, Sept. 2003.
65. P. L. Ho and Ya Yan Lu, Improving the Beam Propagation Method for TM Polarization , Optical and Quantum Electronics, Vol. 35, No. 4, pp. 507-519, April 2003.
66. Ya Yan Lu and P. L. Ho, Beam Propagation Modeling of Arbitrarily Bent Waveguides , IEEE Photonics Technology Letters, Vol. 14, No. 12, pp. 1698-1700, Dec. 2002.
67. Ya Yan Lu and S. H. Wei, A New Iterative Bidirectional Beam Propagation Method , IEEE Photonics Technology Letters, Vol. 14, No. 11, pp. 1533-1535, Nov. 2002.
68. Ya Yan Lu and P. L. Ho, A Single Scatter Improvement for Beam Propagation Methods , IEEE Photonics Technology Letters, Vol. 14, No. 8, pp. 1103-1105, Aug. 2002.
69. S. H. Wei and Ya Yan Lu, Application of Bi-CGSTAB to Waveguide Discontinuity Problems , IEEE Photonics Technology Letters, Vol. 14, No. 5, pp. 645-647, May, 2002.
70. Ya Yan Lu and P. L. Ho, Beam Propagation Method Using a [(p-1)/p] Pad\'e Approximant of the Propagator , Optics Letters, Vol. 27, No. 9, pp. 683-685, May, 2002.
71. P. L. Ho and Ya Yan Lu, A Bidirectional Beam Propagation Method for Periodic Waveguides , IEEE Photonics Technology Letters, Vol. 14, No. 3, pp. 325-327, March, 2002.
72. P. L. Ho and Ya Yan Lu, A Stable Bidirectional Propagation Method Based on Scattering Operators , IEEE Photonics Technology Letters, Vol 13, No. 12, pp. 1316-1318, Dec. 2001.

Matrix Function Software:

For a number of matrix functions, I have developed numerical methods that are more efficient than the standard methods (e.g. methods based on eigenvalue decomposition). This includes:
1. The square root of a symmetric positive definite matrix. Here is the related paper and the FORTRAN program .
2. Logarithm of a symmetric positive definite matrix. Here is the related paper and the FORTRAN program .
3. Exponential of a symmetric matrix . Here is the related paper and the FORTRAN program .
4. The function [exp(A)-I]/A for a symmetric matrix A . Here is the related paper and the FORTRAN program .