Prof. Ya Yan Lu
Department of Mathematics
City University of Hong Kong
Tat Chee Avenue, Kowloon, Hong Kong
Office: Room Y6513, Academic Building 1, City University of Hong Kong
Telephone: (852) 3442 7436
Fax: (852) 3442 0250
E-mail: mayylu@cityu.edu.hk
Teaching:
- Course materials for
MA3513
Elementary Numerical Methods can be found here.
- Course materials for MA3514
Numerical Methods for Differential Equations can be found here.
- Course materials for MA4528
Introduction to Dynamical Systems and Chaos can be found here.
- Course materials
for MA6606
Computational Linear Algebra can be found here.
- Course materials
for MA6618
Mathematical Methods for Electromagnetic and Optical Waves
can be found
here.
Research Interest:
Prof. Lu works on numerical methods and mathematical modeling of photonic structures, including
optical waveguides, photonic crystals, diffraction gratings,
plasmonics, and nonlinear optics. Some
information can be found in his research
projects.
Recent publications:
- Amgad Abdrabou and Ya Yan Lu,
Exceptional points of resonant states on a periodic slab,
Physical Review A,
Vol. 97, Article 063822, June 2018.
- Lijun Yuan and Ya Yan Lu,
Bound states in the continuum on periodic structures surrounded by
strong resonances,
Physical Review A, Vol. 97, Article 043828, April 2018.
- Zhen Hu and Ya Yan Lu,
Resonances and bound states in the continuum on periodic arrays
of slightly noncircular cylinders,
Journal of Physics B: Atomic, Molecular and Optical Physics,
Vol. 51, Article 035402, 2018.
- Zhen Hu, Junshan Lin, Ya Yan Lu, and Sang-Hyun Oh,
Fast vertical mode expansion method for the simulation of
extraordinary terahertz field enhancement in an annular nanogap,
Journal of the Optical Society of America B,
Vol. 35, No. 1, pp. 30-38, Jan. 2018.
- Wangtao Lu, Ya Yan Lu, and Jianliang
Qian,
Perfectly-matched-layer boundary integral equation method for
wave scattering in a layered medium,
SIAM Journal on Applied Mathematics,
Vol. 78, No. 1, pp. 246-265, 2018.
- Lijun Yuan and Ya Yan Lu,
Bound states in the continuum on periodic structures:
perturbation theory and robustness,
Optics Letters,
Vol. 42, No. 21, pp. 4490-4493, Nov. 2017.
- Zhen Hu and Ya Yan Lu,
Propagating bound states in the continuum at the surface of a photonic crystal,
Journal of the Optical Society of America B,
Vol. 34, No. 9, pp. 1878-1883, Sept. 2017.
- Lijun Yuan and Ya Yan Lu,
Robust iterative method for nonlinear Helmholtz equation,
Journal of Computational Physics,
Vol. 343, pp. 1-9, Aug. 2017.
- Hualiang Shi, Ya Yan Lu, and Qiang Du,
Calculating corner singularities by boundary integral equations,
Journal of the Optical Society of America A,
Vol. 34, No. 6, pp. 961-966, June 2017.
- Lijun Yuan and Ya Yan Lu,
Propagating Bloch modes above the lightline on a periodic array of cylinders,
Journal of Physics B: Atomic, Molecular and Optical Physics,
Vol. 50, No. 5, Art. 05LT01, March 2017.
- Lijun Yuan and Ya Yan Lu,
Strong resonances on periodic arrays of cylinders and optical
bistability with weak incident waves,
Physical Review A,
Vol. 95, No. 2, Art. 023834, Feb. 2017.
- Zhen Hu and Ya Yan Lu,
Sensitivity analysis for photonic crystal microcavities,
Journal of the Optical Society of America B,
Vol. 33, No. 9, pp. 1897-1905, Sept. 2016.
- Lijun Yuan and Ya Yan Lu,
Diffraction of plane waves by a periodic array of nonlinear circular cylinders,
Physical Review A,
Vol. 94, No. 1, Article 013852, July 2016.
- Hualiang Shi, Xun Lu and Ya Yan Lu,
Vertical mode expansion method for numerical modeling of biperiodic structures,
Journal of the Optical Society of America A,
Vol. 33, No. 5, pp. 836-844, May 2016.
- Xun Lu and Ya Yan Lu,
Efficient method for analyzing multiple circular cylindrical
nanoparticles on a substrate,
Journal of Optics,
Vol. 18, Art. 055604, May 2016.
- Xun Lu and Ya Yan Lu,
Analyzing bull's eye structures by a vertical mode expansion method with rotational symmetry,
Journal of the
Optical Society of America B, Vol. 32, No. 11,
pp. 2294-2298, Nov. 2015.
- Y. M. Wu and Ya Yan Lu, Efficient operator marching
method for analyzing crossed arrays of cylinders,
Communications in Computational Physics,
Vol. 18, No. 5, pp. 1461-1481, Nov. 2015.
- Lijun Yuan and Ya Yan Lu,
Nonlinear standing waves on a periodic array of circular cylinders,
Optics Express, Vol.
23, No. 16, pp. 20636-20646, August 2015.
- Hualiang Shi and
Ya Yan Lu, Efficient vertical mode
expansion method for scattering by arbitrary layered cylindrical
structures, Optics Express, Vol.
23, No. 11, pp. 14618-14629, June 2015.
- Zhen Hu and Ya Yan Lu, Standing waves on
two-dimensional periodic dielectric waveguides, Journal of Optics,
Vol. 17, No. 6,
Art. 065601, June 2015.
- Zhen Hu and Ya
Yan Lu, Efficient numerical modeling
of photonic crystal heterostructure devices,
Journal of Lightwave Technology, Vol.
33, No. 10, pp. 2012-2018, May 2015.
- Dawei Song and
Ya Yan Lu, Analyzing leaky waveguide
modes by pseudospectral modal method, IEEE Photonics Technology Letters, Vol. 27, No. 9, pp.
955-958, May 2015.
- Hualiang Shi and
Ya Yan Lu, Vertical mode
expansion method for analyzing elliptic cylindrical objects in a layered
background, Journal of the
Optical Society of America A, Vol. 32, pp. 630-636, Apr. 2015.
- Zhen Hu and Ya
Yan Lu, Second order sensitivity
analysis for a photonic crystal waveguide bend,
Journal of the Optical Society of America B. Vol.
32, pp. 69-75, Jan. 2015.
- Lijun Yuan and
Ya Yan Lu, Bilateral symmetry breaking
in nonlinear circular cylinders, Optics Express, Vol. 22, No. 24, pp. 30128-30136, Dec.
2014.
- Zhen Hu and Ya
Yan Lu, Compact wavelength
demultiplexer via photonic crystal multimode resonators,
Journal of the Optical Society of America B. Vol.
31, pp. 2330-2333, Oct. 2014.
- Wangtao Lu and
Ya Yan Lu, Efficient high order
waveguide mode solvers based on boundary integral equations,
Journal of Computational Physics, Vol.
272, pp. 507-525, Sept. 2014.
- Lijun Yuan and
Ya Yan Lu, Mode reduction for
efficient modeling of photonic crystal slab structures,
Journal of Lightwave Technology, Vol.
32, No. 13, pp. 2340-2344, July 2014.
- Dawei Song and
Ya Yan Lu, Pseudospectral modal method for
computing optical waveguide modes, Journal of Lightwave Technology, Vol. 32, No. 8, pp.
1624-1630, April 2014.
- Yuexia Huang and
Ya Yan Lu, Efficient method for
lasing eigenvalue problems of periodic structures,
Journal of Modern Optics, Vol. 61,
No. 5, pp. 390-396, 2014.
- 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.
- 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.
-
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Zhen Hu and Ya
Yan Lu, Improved bends for two-dimensional
photonic crystal waveguides , Optics
Communications, Vol. 284, pp. 2812-2816, June 2011.
- 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.
-
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
-
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.
-
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
-
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.
-
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.
- 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.
- 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.
- 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.
-
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.
- Ya Yan Lu, Minimizing the discrete reflectivity of
perfectly matched layers, IEEE
Photonics Technology Letters, Vol. 18, No. 3, pp. 487-489,
Feb. 2006.
Useful Links:
- Academic Calendar.
- SIAM: Society for Industrial and Applied
Mathematics.
- AMS: American Mathematics Society.
- OSA: Optical Society of America.
- LEOS: IEEE Photonics Society.