Prof. Ya Yan Lu is interested in computational photonics. More specifically, he has worked on numerical methods for optical waveguides, photonic crystals, diffraction gratings and nonlinear optics. optical waveguides (such as optical fibres) are structures that guide the propagation of light. Photonic crystals are periodic structures that can block light in certain frequency intervals. diffraction gratings are periodic structures on interfaces that have useful reflection properties. These structures are important in applications such as future integrated circuits based on light waves. Efficient numerical methods are important to engineers who design these structures for practical applications.

Research Interests

• Wave Propagation (Optics and Acoustics)
• Scientific Computation

Teaching

• MA3513 Elementary Numerical Methods
• MA3514 Numerical Methods for Differential Equations
• MA4528 Introduction to Dynamical Systems and Chaos.
• MA6606 Computational Linear Algebra
• MA6618 Mathematical Methods for Electromagnetic and Optical Waves

Selected Publications

• W. Lu and Y. Y. Lu, Waveguide mode solver based on Neumann-to-Dirichlet operators and boundary integral equations, Journal of Computational Physics, to appear.
• L. Yuan and Y. Y. 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.
• H Xie, W. Lu and Y. Y. Lu, Complex modes and instability of full-vectorial beam propagation methods, Optics Letters, Vol. 36, pp. 2474–2476, July 2011.
• Y. Wu and Y. Y. 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.
• Z. Hu and Y. Y. Lu, Improved bends for two-dimensional photonic crystal waveguides , Optics Communications, Vol. 284, pp. 2812–2816, June 2011.
• D. Song, L. Yuan and Y. Y. Lu, Fourier-matching pseudospectral modal method for diffraction gratings, Journal of the Optical Society of America A, Vol. 28, pp. 613–620, April 2011.
• J. Yuan and Y. Y. 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.