# A lattice model for resonance in open periodic waveguides

@article{Ptitsyna2010ALM, title={A lattice model for resonance in open periodic waveguides}, author={Natalia Ptitsyna and Stephen P. Shipman}, journal={arXiv: Mathematical Physics}, year={2010} }

We present a discrete model of resonant scattering of waves by an open periodic waveguide. The model elucidates a phenomenon common in electromagnetics, in which the interaction of plane waves with embedded guided modes of the waveguide causes sharp transmission anomalies and field amplification. The ambient space is modeled by a planar lattice and the waveguide by a linear periodic lattice coupled to the planar one along a line. We show the existence of standing and traveling guided modes and…

## 7 Citations

### Total Resonant Transmission and Reflection by Periodic Structures

- Geology, PhysicsSIAM J. Appl. Math.
- 2012

For two-dimensional structures, sufficient conditions are established, involving structural symmetry, under which anomalies attain total transmission and total reflection at frequencies separated by an arbitrarily small amount.

### Electromagnetic Resonant Scattering in Layered Media with Fabrication Errors

- Mathematics
- 2017

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure…

### Trapped-mode resonances in a Voigt plasma layer

- Physics
- 2016

This paper examines the resonant transmission of electromagnetic waves around the trapped modes of a magnetized plasma layer. Expressions for the dispersion relation, the evanescent wave coupling and…

### An exactly solvable model for nonlinear resonant scattering

- Mathematics, Physics
- 2012

This work analyses the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering system. These sharp…

### Bound states in the continuum

- Physics
- 2016

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies…

### Guided modes and resonant transmission in periodic structures

- Physics
- 2011

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…

### Resonant electromagnetic scattering in anisotropic layered media

- Physics
- 2013

The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field…

## References

SHOWING 1-10 OF 23 REFERENCES

### Resonant scattering by open periodic waveguides 1

- Physics
- 2010

This article concerns the interaction between guided electromagnetic or acoustic modes of a penetrable periodic planar waveguide and plane waves originating from sources exterior to the waveguide.…

### A Discrete Model for Resonance Near Embedded Bound States

- PhysicsIEEE Photonics Journal
- 2010

We present a discrete model for resonance in periodic dielectric slabs arising from the interaction of electromagnetic plane waves with guided modes at frequencies embedded in the continuum. Two…

### Theory of Periodic Dielect Waveguides

- Physics
- 1975

The propagation of electromagnetic waves along open periodic, dielectric waveguides is formulated here as a rigorous and exact boundary-value problem. The characteristic field solutions are shown to…

### Resonance and Bound States in Photonic Crystal Slabs

- PhysicsSIAM J. Appl. Math.
- 2003

This work analyzes EM resonance in slabs of two-phase dielectric photonic crystal materials using boundary-integral projections for time-harmonic electromagnetic (EM) fields, and presents numerical examples which demonstrate the effects of structural defects on the resonant properties of a crystal slab and surface waves supported by a die...

### Resonant transmission near nonrobust periodic slab modes.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The perturbation of three coincident zeros-those of the dispersion relation for slab modes, the reflection constant, and the transmission constant-is central to calculating transmission anomalies both for lossless dielectric materials and for perfect metals.

### Analysis of guided resonances in photonic crystal slabs

- Physics
- 2002

We present a three-dimensional analysis of guided resonances in photonic crystal slab structures that leads to a new understanding of the complex spectral properties of such systems. Specifically, we…

### Quasiguided modes and optical properties of photonic crystal slabs

- Physics
- 2002

We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab (PCS) of…

### Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem

- Mathematics
- 1994

We consider the two-dimensional scalar problem of the diffraction of a plane wave by an infinite grating of conducting bodies immersed in a periodical dielectric medium. A Fredholm-type formulation…

### OBSERVATION OF LEAKY SLAB MODES IN AN AIR-BRIDGED SEMICONDUCTOR WAVEGUIDE WITH A TWO-DIMENSIONAL PHOTONIC LATTICE

- Physics
- 1997

An air-bridged, 120-nm-thick semiconductor slab with a two-dimensional (2D) square array of through holes on a 480 nm pitch (Λ) was fabricated using selective wet etching techniques. The second order…

### Microscopic theory of the extraordinary optical transmission

- PhysicsNature
- 2008

A microscopic theory of the transmission through subwavelength hole arrays is derived, by considering the elementary processes associated with scattering of surface-plasmon-polariton (SPP) modes by individual one-dimensional chains of subwa wavelength holes, and derives analytical expressions for all the transmission spectrum characteristics.