# Electromagnetic Field Enhancement in Small Gaps: A Rigorous Mathematical Theory

@article{Lin2015ElectromagneticFE, title={Electromagnetic Field Enhancement in Small Gaps: A Rigorous Mathematical Theory}, author={Junshan Lin and Fernando Reitich}, journal={SIAM J. Appl. Math.}, year={2015}, volume={75}, pages={2290-2310} }

This paper is concerned with the field enhancement when an electromagnetic wave passes through subwavelength metallic gaps. We focus on a particular configuration when there is extreme scale difference between the wavelength of the incident wave, the thickness of metal films, and the size of gap apertures. Based upon a rigorous study of the perfect electrical conductor model for the transverse magnetic ploarization, we show that enormous electric field enhancement occurs inside the gap if the…

## 15 Citations

### Electromagnetic field enhancement in a subwavelength rectangular open cavity

- PhysicsPartial Differential Equations and Applications
- 2021

Consider the transverse magnetic polarization of the electromagnetic scattering of a plane wave by a perfectly conducting plane surface, which contains a two-dimensional subwavelength rectangular…

### Scattering and Field Enhancement of a Perfect Conducting Narrow Slit

- PhysicsSIAM J. Appl. Math.
- 2017

It is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement, and the field enhancement at nonresonant frequencies in the quasi-static regime is investigated.

### Field enhancement and saturation of millimeter waves inside a metallic nanogap.

- PhysicsOptics express
- 2014

The millimeter electromagnetic waves passing through a metal nanogap is investigated to show that the electric field enhancement inside the gap saturates as the gap size approaches zero, and the ultimate enhancement strength is inversely proportional to the thickness of the metal film.

### A Mathematical Theory for Fano Resonance in a Periodic Array of Narrow Slits

- PhysicsSIAM J. Appl. Math.
- 2020

It is proved that the Fano-type anomalies occurs for the transmission of energy through the slab, and it is shown that the field enhancement is of order $1/(\kappa\varepsilon)$, which is stronger than Fabry-Perot resonance.

### Fano resonance for a periodic array of perfectly conducting narrow slits

- Physics
- 2019

This work concerns resonant scattering by a perfectly conducting slab with periodically arranged subwavelength slits, with two slits per period. There are two classes of resonances, corresponding to…

### Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits.

- PhysicsOptics express
- 2020

This paper performs computations of a single nanoslit using the hybridizable discontinuous Galerkin method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals, which enables the efficient simulation of the slit while accounting for the nonlocal interactions between electrons and the incident light.

### Scattering resonances for a three-dimensional subwavelength hole

- PhysicsPartial Differential Equations and Applications
- 2021

This work aims to investigate scattering resonances and the field amplification at resonant frequencies for a subwavelength hole of width ε embedded in a sound hard slab. We apply the integral…

### Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits

- Physics
- 2020

: With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. The plasmonic response in these extreme-scale gaps is…

### An integral equation method for numerical computation of scattering resonances in a narrow metallic slit

- MathematicsJ. Comput. Phys.
- 2019

### Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures

- PhysicsIMA Journal of Applied Mathematics
- 2020

We derive the formulas for the resonance frequencies and their sensitivity when the nano-slit structures are used in the detection of thin layers. For a thin layer with a thickness of $H$ deposited…

## References

SHOWING 1-10 OF 17 REFERENCES

### Field enhancement and saturation of millimeter waves inside a metallic nanogap.

- PhysicsOptics express
- 2014

The millimeter electromagnetic waves passing through a metal nanogap is investigated to show that the electric field enhancement inside the gap saturates as the gap size approaches zero, and the ultimate enhancement strength is inversely proportional to the thickness of the metal film.

### Resonant transmission of microwaves through a narrow metallic slit.

- PhysicsPhysical review letters
- 2002

Strong resonant transmission of microwave radiation through a very narrow (much less than the radiation wavelength) metallic slit is recorded. The results show that a set of resonant self-coupled…

### Light passing through subwavelength apertures

- Physics
- 2010

This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical…

### Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit

- Physics
- 2009

The effect of a tiny gap in a metal substrate on incident terahertz radiation in the regime where the gap's dimensions are smaller than the metal's skin-depth are investigated. The results and…

### Extraordinary optical transmission through sub-wavelength hole arrays

- PhysicsNature
- 1998

The desire to use and control photons in a manner analogous to the control of electrons in solids has inspired great interest in such topics as the localization of light, microcavity quantum…

### Optical resonance in a narrow slit in a thick metallic screen.

- PhysicsPhysical review letters
- 2001

Spectral transmission from a periodic array of such slits features the same peaks with a high increase in their magnitude, confirming that a grating acts as an amplifier of those resonances.

### Transmission and diffraction properties of a narrow slit in a perfect metal

- Physics
- 2010

By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width.…

### Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electromagnetic waves.

- PhysicsNature communications
- 2013

A new patterning technology based on atomic layer deposition and simple adhesive-tape-based planarization is introduced, which creates vertically oriented gaps in opaque metal films along the entire contour of a millimetre-sized pattern.

### Imaging of Local Surface Displacement on an Infinite Ground Plane: The Multiple Frequency Case

- MathematicsSIAM J. Appl. Math.
- 2011

By using multiple frequency data to image the profile of the surface displacement, a stable and accurate reconstruction method is presented and an integral equation approach is introduced for the solution of the forward scattering problem.

### Integral equation methods in scattering theory

- Mathematics
- 1983

Preface to the Classics Edition Preface Symbols 1. The Riesz-Fredholm theory for compact operators 2. Regularity properties of surface potentials 3. Boundary-value problems for the scalar Helmholtz…