Macroscopic optical response and photonic bands

We present a general numerical approach for the calculation of the non‐local macroscopic dielectric response of a binary metamaterial made of arbitrary non‐magnetic materials with any geometry. From the spatial dispersion of the permittivity, characterized by its dependence on the wavevector, we obtain the corresponding effective local macroscopic permeability of the metamaterial. We illustrate our computational approach by calculating the permeability of two‐dimensional split‐ring resonators and validate the results through comparison with those of simple models. Our scheme may be further applied to arbitrary geometries. We discuss the limitations of the local permeability approach.

Section: Magnetic Response and Non‐local Dielectric Responsementioning

confidence: 99%

\nabla \times \nabla \times bold-italicE = \frac{4 π i ω}{c^{2}} J_{ex} + \frac{ω^{2}}{c^{2}} \overset{trueˆ}{ϵ} bold-italicE,

where ω is the frequency, c the speed of light, J ex is an external electric current, and

\overset{trueˆ}{ϵ}

is the microscopic dielectric function which takes a characteristic value within the region occupied by each of the materials composing the metamaterial.…”

Section: Non‐local Macroscopic Response Of Metamaterialsmentioning

confidence: 99%

“…, we identify the macroscopic wave operator in terms of the macroscopic dielectric operator

{\overset{trueˆ}{W}}_{M} = true({\overset{trueˆ}{ϵ}}_{normalM} + \frac{1}{q^{2}} \nabla^{2} {\overset{trueˆ}{P}}_{T} true)

from which we can finally obtain

{\overset{trueˆ}{ϵ}}_{M}

. Equations , , and constitute a procedure for the calculation of the macroscopic dielectric response from the microscopic dielectric function …”

Section: Non‐local Macroscopic Response Of Metamaterialsmentioning

confidence: 99%

“…The analogy of the macroscopic wave operator with the Green's function allow us to apply the well‐known Haydock method to recursively generate an orthonormal basis in which our operator

\overset{trueˆ}{B} \overset{trueˆ}{g}

can be expressed as a tridiagonal matrix . Choosing an initial state |0⟩ normalized under the metric

\overset{trueˆ}{g}

\begin{array}{l} center & true| \overset{n + 1}{true} 〉 = \overset{scriptB}{true} \overset{g}{true} true| n 〉 \\ center & = b_{n + 1} true| n + 1 〉 + a_{n} true| n 〉 + b_{n} g_{n} g_{n - 1} true| n - 1 〉, \end{array}

where the Haydock coefficients a n and b n are chosen to satisfy

true(n true| m true) = 〈 n | \overset{trueˆ}{g} | m 〉 = g_{n} δ_{n m} .

…”

Section: Non‐local Macroscopic Response Of Metamaterialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Magnetic Response of Metamaterials

Mochán

2018

Mie Scattering in the Macroscopic Response and the Photonic Bands of Metamaterials

Juárez

Mendoza²,

Mochán³

2020

Herein, a general approach for the numerical calculation of the effective dielectric tensor of metamaterials is presented, and it is shown that the formalism may be used to study metamaterials beyond the long‐wavelength limit. A system composed of high‐refractive‐index cylindrical inclusions is considered, and it is shown that the method reproduces the Mie resonant features and photonic band structure obtained from a multiple scattering approach, hence opening the possibility to study arbitrarily complex geometries for the design of resonance‐based negative refractive metamaterials at optical wavelengths.

Recursive Calculation of the Optical Response of Multicomponent Metamaterials

Mochán

Singla

Juárez³

et al. 2020

A recursive computational procedure is developed to efficiently calculate the macroscopic dielectric function of multicomponent metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the microscopic response of the system might correspond to non‐Hermitian operators, a representation of the microscopic fields and of the response is developed, and an appropriate metric that makes all operators symmetric is introduced. This allows one to use a modified Haydock recursion, introducing complex Haydock coefficients that allow an efficient computation of the macroscopic response and the microscopic fields. The procedure is tested by comparing the results with analytical ones in simple systems and verifying whether they obey a generalized multicomponent Keller's and the Mortola and Steffe's theorems for four‐component metallic and dielectric systems.