Calculating corner singularities by boundary integral equations
Update: 2018-02-24 09:20:34      Author: yangjuan@csrc.ac.cn

Electromagnetic fields around metallic nanoparticles and in subwavelength apertures or slits of metallic films are often many orders of magnitude more intense than the incident wave. Strong near-fields of well-designed plasmonic structures have important applications in biological and chemical sensing, and can be used to enhance nonlinear optical effects, quantum optical effects, Raman scattering and other emission processes. The local field enhancement in plasmonic structures is the result of localized surface plasmon resonances, but geometric features such as corners and edges (see the geometric illustrations in Figures) also strongly influence the near-fields. 

To analyze the local field enhancement phenomenon and to study the numerous applications, it is clearly important to calculate the near-fields accurately near sharp corners and edges where electromagnetic fields exhibit singularities and tend to infinity. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically.

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Recently, CSRC postdoc Hualiang Shi, under the joint supervision of Professors Yayan Lu and Qiang Du used a boundary integral equation method to compute electromagnetic fields near sharp edges. They constructed the leading terms in asymptotic expansions based on numerical solutions. The numerically found singularity exponents agree well with the exact values in all the test cases presented in their work, indicating that the numerical solutions are accurate. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes.

 

References:

Hualiang Shi, Ya Yan Lu, and Qiang Du, Calculating corner singularities by boundary integral equations, Journal of the Optical Society of America A, 34(6), pp. 961-966, (2017)

https://doi.org/10.1364/JOSAA.34.000961




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