Simulations of Two-Dimensional Photon Scanning Tunneling Microscope by Boundary Integral Equation Method: p-polarization

Tanaka, Kazuo; Tanaka, Masahiro; Katayama, Kiyofumi

doi:10.1007/s10043-999-0249-3

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…(1) can also be directly derived by Green's theorem. 15,17,[19][20][21] The Green's functions G 2 , the singular solution of the Helmholtz equation of medium 2, satisfies…”

Section: Integral Presentationsmentioning

confidence: 99%

“…(15) with (18), and Eq. (16) with (19), a set of integral equations of the total field of the exterior ⍀ 1 is obtained as 1 2…”

Section: Surface Integral Equationsmentioning

confidence: 99%

“…(11) and (20), as the governing equations for the two unknowns ͑H z , E t ͒ on the enclosed surface S; this method has been used in some studies. 15,17,[19][20][21] In principle, the two methods should be equivalent. However, for the numerical viewpoint, using Eqs.…”

Section: Surface Integral Equationsmentioning

confidence: 99%

“…With these equations, the normal displacement, the tangential electric field, and the tangential magnetic field on the boundary are solved simultaneously. As compared with other BEM studies 15,17,[19][20][21] of the TM mode, our approach calculates these physical components directly, instead of the tangential magnetic field and its normal gradient. In addition, this approach, based on the Stratton-Chu formulation, can be extended straightforward to a 3D problem, unlike the other BEM that uses Debye potentials.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of surface plasmon resonance of metallic nanoparticles by the boundary-element method

Liaw

2006

J. Opt. Soc. Am. A

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A set of new surface integral equations (Fredholm equations of the second kind) has been systematically derived from the Stratton-Chu formulation of Maxwell's equations for a two-dimensional TM mode to investigate the interactions of an incident electromagnetic wave with nanostructures, especially metals. With these equations, the surface components (the tangential magnetic field, the normal displacement, and the tangential electric field) on the boundary are solved simultaneously by the boundary-element method numerically. For nanometer-sized structures (e.g., dimension of 10 nm), our numerical results show that surface plasmon resonance causes a strong near-field enhancement of the electric field within a shallow region close to the interface of metal and dielectric. In addition, the corresponding pattern of the far-field scattering cross section is like a dipole. For the submicrometer-sized cases (dimension of several hundreds of nanometers), the numerical results indicate the existence of a standing wave on the backside surface of metals. This phenomenon could be caused by two surface plasmon waves that creep along the contour of metals clockwise and counterclockwise, respectively, and interfere with each other.

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“…(1) can also be directly derived by Green's theorem. 15,17,[19][20][21] The Green's functions G 2 , the singular solution of the Helmholtz equation of medium 2, satisfies…”

Section: Integral Presentationsmentioning

confidence: 99%

“…(15) with (18), and Eq. (16) with (19), a set of integral equations of the total field of the exterior ⍀ 1 is obtained as 1 2…”

Section: Surface Integral Equationsmentioning

confidence: 99%