Waves in Gradient Metamaterials

Shvartsburg, A. B.; Maradudin, A. A.

doi:10.1142/8649

Cited by 75 publications

(62 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The non‐local dispersion of TE‐polarized surface wave, determined by the profile

W_{2} true(z true)

(5) can be examined by analogy with the approach, used above for the

W_{1} true(z true)

profile. Substituting the expressions (1) to the Maxwell equations and presenting the generating function

normalΨ

, unlike (2), in a form

Ψ = \frac{B f true(z true)}{\sqrt{W_{2} true(z true)}} \exp true[i true(k_{y} y - ω t true) true]

we obtain again the equation, similar to (9), governing the function f , but distinguished from (9) by the another values of coefficients and dimensionless variable:

\frac{d^{2} f}{d ξ^{2}} + \frac{1}{ξ} \frac{d f}{d ξ} + true(- q^{2} - \frac{m^{2}}{ξ^{2}} true) f = 0

q^{2} = {(\frac{ω L}{c})}^{2} true(n^{2} - n_{v}^{2} true); n^{2} \geq n_{v}^{2}; m^{2} = \frac{1}{4} true(1 - \frac{ω^{2}}{{normalΩ}^{2}} true); ξ = 1 + \frac{z}{L}

…”

Section: Narrow Band Spectra Of Surface Te‐polarized Wavesmentioning

confidence: 99%

“…Localization of traveling waves in the subsurface dielectric layer is stipulated by non‐local dispersion, formed by the gradient of

ϵ true(z true)

. This dispersion depends upon the scales of spatially heterogeneous distribution of dielectric permittivity, which are shown below to determine some characteristic frequency of the gradient medium, possessing neither free carriers nor plasma frequency.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Surface Electromagnetic Waves on the Interfaces of Gradient Dielectric Media: Visible Spectral Range

Shvartsburg

Silin

Nesterov

2019

Physica Status Solidi (b)

View full text Add to dashboard Cite

This paper is devoted to a peculiar branch of surface electromagnetic waves, belonging to the visible spectral range. Contrary to the well known surface waves, supported by the sharp boundary of solid plasma in metals and semiconductors, the waves discussed here are shown a gradient interface of non‐conducting gradient dielectric without free carriers. The subsurface layer of this dielectric is characterized by the gradual decrease of dielectric permittivity ϵbold-italictrue(bold-italiczbold-italictrue) in the direction z, normal to the boundary z = 0, saturated in the depth of medium. Unlike the traditional condition ϵ<0, the field's localization near the interface of the dielectric is determined by another condition: grad ϵ<0, meanwhile ϵ<0. Spectra of surface modes are determined by the non‐local dispersion, stipulated by the spatial distribution ϵbold-italictrue(bold-italiczbold-italictrue). The spatial structure of surface wave fields is examined by means of two different exactly solvable models ϵbold-italictrue(bold-italiczbold-italictrue). The broadband and wide band spectral ranges of visible surface waves illustrating the sensitivity of their spectra to the fine details of distribution ϵbold-italictrue(bold-italiczbold-italictrue), presented by these models, are considered.

show abstract

“…The non‐local dispersion of TE‐polarized surface wave, determined by the profile

W_{2} true(z true)

(5) can be examined by analogy with the approach, used above for the

W_{1} true(z true)

profile. Substituting the expressions (1) to the Maxwell equations and presenting the generating function

normalΨ

, unlike (2), in a form

Ψ = \frac{B f true(z true)}{\sqrt{W_{2} true(z true)}} \exp true[i true(k_{y} y - ω t true) true]

we obtain again the equation, similar to (9), governing the function f , but distinguished from (9) by the another values of coefficients and dimensionless variable:

\frac{d^{2} f}{d ξ^{2}} + \frac{1}{ξ} \frac{d f}{d ξ} + true(- q^{2} - \frac{m^{2}}{ξ^{2}} true) f = 0

q^{2} = {(\frac{ω L}{c})}^{2} true(n^{2} - n_{v}^{2} true); n^{2} \geq n_{v}^{2}; m^{2} = \frac{1}{4} true(1 - \frac{ω^{2}}{{normalΩ}^{2}} true); ξ = 1 + \frac{z}{L}

…”

Section: Narrow Band Spectra Of Surface Te‐polarized Wavesmentioning

confidence: 99%

“…Localization of traveling waves in the subsurface dielectric layer is stipulated by non‐local dispersion, formed by the gradient of

ϵ true(z true)

Section: Introductionmentioning

confidence: 99%

Surface Electromagnetic Waves on the Interfaces of Gradient Dielectric Media: Visible Spectral Range

Shvartsburg

Silin

Nesterov

2019

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

“…Currently wave propagation in materials with variable index of refraction has become of importance in many fields including sound propagation in the ocean and metamaterials. 3 Perhaps the first to study propagation with variable index of refraction was Rayleigh, who addressed the propagation of light in the atmosphere. 4 Of particular relevance to our considerations are references.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion for rays in a Snell's law medium

Ben-Benjamin

Cohen

2015

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

The equations of motion for a ray in a Snell's law medium with a varying index of refraction are derived. A stratified medium is considered. Explicit expressions are given for the velocity and acceleration components of the ray. These are derived directly from Snell's law. It is further shown that the propagation of a ray can be modeled in terms of Newtonian-like equations of motion and that momentum is conserved along the interface. It is shown that Snell's law follows from this conservation law. Properties of the motion are studied and an example is given.

show abstract

“…13 Formation of gradient all-dielectric nanostructures with the prescribed spatial distributions of refractive index n for the controlled reflectance and transmittance of wave flows is now a challenging task, important for several problems of nanophotonics. 14 Gradient nanostructures, fabricated from the dielectrics without free carriers, possess the strong nonlocal heterogeneity-induced dispersion, determined by the shape, gradient, and curvature of refractive index inside this structure, controlled by the technology of fabrication. 15 The attention is given below to the controlled distribution of refractive index n(z) along the direction z across the plate gradient dielectric nanofilm.…”

Section: Introductionmentioning

confidence: 99%

Artificial dispersion of all-dielectric gradient nanostructures: Frequency-selective interfaces and tunneling-assisted broadband antireflection coatings

Shkatula¹,

Volpian²,

Shvartsburg

et al. 2015

Journal of Applied Physics

View full text Add to dashboard Cite

The non-locality of optical properties of gradient dielectric nanofilms, stipulated by smooth spatial distributions of refractive index, is shown to create the peculiar plasma-like dispersion of non-polar dielectric films, determined by the shapes and sizes of these distributions. Gradient all-dielectric nanostructures, characterized by the artificial heterogeneity-induced nonlocal dispersion and providing the broadband antireflection tunneling regime of energy transport in the visible and infrared ranges, are designed and tested. The wave energy flow in these structures is supported due to interference of evanescent and antievanescent modes formed by the non-Fresnel reflections of these modes on the discontinuities of gradient of refractive index on the boundaries of adjacent nanofilms. The transmittance spectra of these structures in the visible and infrared ranges, characterized by strong dispersion nearby the red edge of visible range, almost constant high transmittance in the near infrared range and weak dependence of tunneling energy flow upon the multilayer structure thickness, are calculated; the experimental verifications of these effects are presented. The perspectives to use the tunneling of light in gradient media for reconsideration of Hartman paradox are shown. Potential of periodical gradient all-dielectric nanostructures for optimized design of optical dispersive elements and broadband antireflection coatings for the visible and IR spectral range, respectively, is discussed.

show abstract

Waves in Gradient Metamaterials

Cited by 75 publications

References 0 publications

Surface Electromagnetic Waves on the Interfaces of Gradient Dielectric Media: Visible Spectral Range

Surface Electromagnetic Waves on the Interfaces of Gradient Dielectric Media: Visible Spectral Range

Equations of motion for rays in a Snell's law medium

Artificial dispersion of all-dielectric gradient nanostructures: Frequency-selective interfaces and tunneling-assisted broadband antireflection coatings

Contact Info

Product

Resources

About