NanophotonicsAtilla Ozgur Cakmak, PhD

Unit 3Lecture 37: Metamaterials-Part4

Outline

• Hyperbolic Metamaterials

• Near-zero index Metamaterials

• Applications• Non-linear optics

• Absorbers

• Cloaking

A couple of words…

In this lecture, we will touch two more very important concepts in the field of metamaterials; namely hyperbolic metamaterials and near-zero index metamaterials. Hyperbolic metamaterials is another example for which negative refraction can be sustained without the need for a strict magnetic resonance. Near-zero index nanophotonics opens up many new areas of study. We will focus on wavefront shaping and tunneling. We will conclude by discussing the application fields; non-linear optics, absorbers and cloaking devices.

Suggested readings: “Fundamentals and Applications of Nanophotonics” by D. de Ceglia, J. W. Haus, N. M. Litchinister, A. Sarangan, M. Scalora, J. Sun, M. A. Vincenti Ch. 9

Hyperbolic Metamaterials

• Normally, the materials we treat in the simulations are assumed to be isotropic. However, the materials might be anisotropic or can even have bianisotropic properties (we saw this in chiral metamaterials).

Hyperbolic Metamaterials

• In the end, the electric flux density (D) and E-field are not parallel to each other in such materials.

Hyperbolic Metamaterials

0 0 0

0 0 0

( , ) (1 ) ( , ) ( ) ( , )

( , ) (1 ) ( , ) ( ) ( , )

ee

mm

D r t E r t j H r t

B r t H r t j E r t

uur r ur r uur r

ur r uur r ur r

Non-chiral κ=0 chiral κ≠0

Reciprocal χ=0 Isotropic/anisotropic medium

Pasteur medium

Non-reciprocal χ≠0 Tellegen medium General bi-isotropic medium

Hyperbolic Metamaterials

2 22( )x z

zz xx

k k

c

0 0 0 0

0 0 , 0 0

0 0 0 0

xx xx

yy yy

zz zz

How about strong anisotropy? Can it bring negative refraction as well? The answer is yes (a). We still have positive permittivity and permeability in (a). In (b), we have negative εxx only, εzz is positive, permeability is also positive.

Isofrequency circles become elliptical for anisotropic materials. We can attain negative refraction for correct incident angle and frequency.

Hyperbolic Metamaterials

a, Layered metal–dielectric structure; b, hyperlens; c, multilayer fishnet; d, nanorod arrays; e, arrays of metal–dielectric nanopyramids; f, graphene metamaterials.

A. Poddubny et al. Nature Photonics vol. 7, 948-957 (2013)

Hyperbolic Metamaterials• 8.1 um-thick multilayered structure composed of interleaved Al0.48In0.52As/In0.53Ga0.47As on an InP

substrate. This multilayered structure enables strong anisotropic permittivity: InGaAs plasma resonance

that gives a negative εxx in the infrared range. Meanwhile, the εzz at the corresponding frequency is positive (a in the previous slide). A metamaterial of silver nanowire arrays in an anodic aluminum oxide (AAO) matrix (d in previous slide). The metamaterial with a wire diameter of 60 nm and a center-to-

center distance of 110 nm exhibited an anisotropic permittivity. εzz, parallel to the silver nanowire, is described by the Drude model with a plasma frequency and εxx, perpendicular to the nanowire, exhibits a resonant behavior (due to localized surface plasmon polaritions) accompanied by a strong dispersion and a very large imaginary part.

• Similar properties could also be shown with a negative permeability as in the case of the fishnet structures (c in previous slide).

• In the mid-infrared and terahertz regions, the hyperbolic regime can be attained in conventional homogeneous materials, such as bismuth and triglycine sulphate. The plasma frequency of bismuth differs depending on whether the electric field is polarized along or perpendicular to the trigonal axis. For frequencies lying between these two plasma frequencies (corresponding to wavelengths in the range 53–62 μm), bismuth is expected to behave as a hyperbolic medium. Natural graphite is known to exhibit hyperbolic dispersion in the ultraviolet region. A true graphene-based hyperbolic metamaterial in which the graphene sheets are separated by slabs of the dielectric host has been theoretically proposed. This structure has hyperbolic dispersion curves for TM-polarized waves at terahertz frequencies. (f in previous slide)

Hyperbolic Metamaterials

A. Poddubny et al. Nature Photonics vol. 7, 948-957 (2013)

To create a subwavelength object, the word “ON” was inscribed on a 50-nm-thick chrome layer deposited on the inner surface of the hyperlens. The object was illuminated with a laser beam (central wavelength, 365 nm; linewidth, 10 nm). The far-field image was focused onto the image plane by a conventional lens. Using this experimental configuration, a subwavelength resolution of 130 nm was achieved. Recently, an optical hyperlens formed on a semi-spherical substrate has been demonstrated. The structure operates at a wavelength of 410 nm, and it permits two 100-nm-diameter dots separated by a distance of 100 nm to be resolved.

Near-zero index metamaterials

The EM wave inside of the zero-index material is static in the spatial domain (i.e., the phase difference between any two arbitrary points is equal to zero). At the same time, it is dynamic in the time domain, thereby allowing energy transport. As a result, every point within the metamaterial experiences a quasiuniform phase; the shape of the wavefront at the output of such metamaterial depends only on the shape of the exit surfaces of the metamaterials. This property provides great flexibility in the design of the phase patterns of the light beams (c). If the source is inside of the zero-index medium, no matter what the kind of source, then the direction of the output beam will be perpendicular to the surface of the zero-index medium (a and b).

Near-zero index metamaterialsWhen n1=0, then θ2=0 no matter what the value of θ1is. That means if there is a point source in the material with zero refractive index, the refracted wave would be a plane wave perpendicular to the interface.

For dispersive media, around a suitable frequency, a zero refractive index can be achieved in metamaterials.

This idea can be used to generate beams and beam steering devices, as well as concentratorsn1 ≈ 0 n2 = 1

FDTD Simulation

point source

n1 ≈ 0 n2 = 1

Point Source

Near-zero index metamaterials

Fundamental block => cutwire pairs

LH RH

Between LH and RH domains, there should be a range for which the effective refractive index becomes zero.

Near-zero index metamaterials

monopole

0n

Monopole Only

Monopole + MTM

As we are cascading the layers, we have no phase accumulation! (around 15.3 GHz)

@15.3 GHz

Near-zero index metamaterials

Tunneling through distorted channels

One can understand this effect more simply by noting that if a near-zero permittivity /

permeability dramatically increases/decreases the medium impedance ( ) , this

action can be compensated structurally by narrowing/widening the channel, thus

maintaining the impedance-matched device. EMNZ is independent of physical

deformations. The tunneling occurs regardless of the obstacles in the channel.

I. Liberal and N. Engheta, Nature Photonics vol. 11, 149-158 (2017)

Non-linear opticsThe nonlinear properties of conventional materials are limited by the properties of

naturally existing materials that are determined by their constituent components. The

rapidly growing field of metamaterials opens up unprecedented opportunities to

overcome those limitations. Recently, there have been several reports related to wave-

mixing in metamaterials using the second-order nonlinearity. In addition to second-order

nonlinearities, there has been continued interest in third-order nonlinearities.

(1) (2) 2 (3) 3

0 ( ...)P E E E

In natural materials, nonlinear optical response conventionally depends on the intensity

of the electric field and is described only by the nonlinear properties of dielectric

permittivity, whereas the nonlinear magnetic response is neglected. It was shown that

metamaterials can also turn on a nonlinear magnetic response.

Non-linear optics

Examples of metamaterials where local field enhancement is used to boost nonlinear processes. T-shaped pairs of elongated nanoparticles and polarization-specific second-harmonic enhancement. Fabricated nanorod “forests.” Emergence of the nonlinear response upon hybridization of nanoparticles with transparent conducting oxides.

Internal structural changeConceptual representation of a magnetoelasticmetamaterial. The layers of electromagnetic resonators can be displaced due to the electromagnetic forces, induced between the element, providing a nonlinear feedback via mutual interaction in the lattice.

M. Lapine et al. Rev. Mod. Phys. vol. 86, 1093 (2014)

Non-linear optics

(a) Schematic of the fishnet metamaterial structure infiltrated with nematic liquid crystal. (b) Scanning electron microscope image (top view) of the fabricated fishnet metamaterials. (c) Side view of the liquid-crystal cell. – electrically controlled optical nonlinearity.

(a) The direction of energy flows and wave vectors of fundamental frequency and second harmonic waves in a slab of metamaterial and amplitudes of the corresponding waves h1,2. (b), (c) Plasmonic nanoparticles arranged in a periodic lattice with different symmetries give substantially different second-harmonic generation.M. Lapine et al. Rev. Mod. Phys. vol. 86, 1093 (2014)

1 22 : Phase mismatchk k k

AbsorbersStealth technology has been traditionally the deriving force of the perfect absorbers.

High absorbance in wide bandwidth is always sought.

https://www.wired.com/2011/06/stealth-tech-obsolete/

Absorbers2 1 1 2

1 2 2 1

2 1

1 2 2 1

cos cos

cos cos

2 cos

cos cos

r

i

t

i

Er

E

Et

E

If we go back to Fresnel coefficients for reflection and transmission, we see that for

general conditions, they are given as shown above. We had derived them much earlier.

0 1,22 1

1,2

1 2 0 1,2

2 1

2 2 1

2 1

2 1

, @Normal incidencer

i

Er

E

R r

In order to have the reflection to be zero, permittivity and permeability of the medium

must be equal for the light coming from air. This is assuming that we have enough

thickness of the metamaterial.

Absorbers

air

metal

air

metal

MTM

We have a chance to manipulate the impedance of the surface with the thickness of the

MTM and the constituent parameters. If we say that our MTM has the following

parameters:

Absorbers

For a thickness of 10um of MTM layer, the peak of the absorption is centered around

1THz, which happens to be the resonance frequency of the permittivity and permeability.

The reflection critically drops around this frequency. We have good amount of losses

around 1THz to sustain perfect absorption.

Absorbers

In this case, the design provides two absorption bands due to plasmonic action and magnetic polariton resonance (a) and (b) on right hand side for the magnetic fields.

J. Kim et al. Scientific Reports vol. 7, 6740 (2017)

Absorbers

J. Y. Rhee et al. J. Electromagnetic Waves Applications vol. 28, 1541-1580 (2014)

Structure [(a) and (b)] and spectral response [(c), (d) and (e)] of a dual-band THz MM absorber.

(a) Geometry of the sample d and h denote thethicknesses of the Al2O3 dielectric layer and the gold film, respectively. a is the lattice constant. (b) Top-view SEM image of the fabricated optical MM absorber. Measured (c) and simulated (d) absorbance spectra.

Absorbers

Upper panel: Diagram of the sawtooth anisotropic MM thin-film absorber. Lower panel: (a) Absorption spectra for the sawtoothabsorber with number of periods N=20 (thick line) and the effective homogeneous sawtooth structure that is shown in the inset (thin line). (b) Angular absorption spectrum of the sawtoothfilm in the upper panel; the line represents the efficiency contour with 0.9. J. Y. Rhee et al. J. Electromagnetic Waves Applications vol. 28, 1541-1580 (2014)

(a) Diagram of the optimized Au-based structure. (b) Top left: Top view of one unit cell of the design. Bottom left: FESEM image of a unit cell of the fabricated structure. (c) Simulation and measurements under unpolarized illumination at normal incidence. The average Au thicknesses of the Au nanostructures determined by atomic force microscopy measurements were 10, 11, and 12 nm. (d) Simulation and measurements for Pd-based absorbers with Pdnanostructure thicknesses of 30 and 40 nm under unpolarized illumination at normal incidence.

Absorbers

Polarization-dependent light absorbers based on metallic gratings and trapezoid arrays. (a) Schematic representation of a three-layer MIM system with the top layer patterned as metallic gratings of width w. (b) Schematic representation of trapezoid array. (c) SEM images of metallic gratings. (d) Schematic representation of the unit cell of a single trapezoid, width varying from 40 to 120 over 300 nm. (e) Measured extinction spectrum for the 60- and 120-nm wire gratings and trapezoid arrays for TM polarization (inset). (f) Measured extinction spectrum for TE polarization (inset). (g) and (h) Simulated extinction spectrum for TM and TE polarizations.

(upper panel) Geometry and schematic of the broadband absorber design. The absorber consists of an array of magnetic resonators placed on top of a thin dielectric. (lower panel) Numerical and experimental data of absorption derived from scattering parameters. The blue dotted line corresponds to the performance of only gold SRR layer.

J. Y. Rhee et al. J. Electromagnetic Waves Applications vol. 28, 1541-1580 (2014)

Functional cloaking device !

CloakingThe first question: Can we make an

object transparent?Or in more scientific terms, can we reduce the total scattering cross

section of an object with a metamaterial cover?Subwavelength Inclusions

CloakingA General Recipe for Perfect Invisibility

in the Geometrical Optics Regime

Cloaking

2 2

2 2 2

2

2 2 2

2

2 2 2

2

0 0

, ,

, ,

,

u v w u v wu u u u

u u

u u u u u u

u

v

w

Q Q Q Q Q Q

Q Q

E Q E H Q H

x y zQ

u u u

x y zQ

v v v

x y zQ

w w w

B H D E

L

L

Coordinate Transformation

u(x,y,z), v(x,y,z), w(x,y,z)

Controlling Electromagnetic Fields

Cloaking

Maxwell’s equations are invariant to coordinate transformations;

only the components of the tensors (ε and ) are scaled by certain factors,

becoming both spatially varying and anisotropic.

Controlling Electromagnetic Fields

Plan: Concealment by cloaking theobject with a metamaterial that willdeflect the rays and guide them aroundthe object.

1) Anisotropy needed: The space is compressed anisotropically.

(Therefore, does not violate the uniqueness theory)

2) Very large tensor values, ε and required.

3) Achieved only at a single frequency.

J. B. Pendry et al., Science vol. 312, pp. 1780 (2006)

CloakingMetamaterial Electromagnetic Cloak at

Microwave Frequencies

A coordinate transformation

based cloak design

Implementation of a 2D cloaking of a conducting cylinder

Cloaking

D. Schurig et al., Science vol. 314, pp. 977 (2006)

Metamaterial Electromagnetic Cloak at Microwave Frequencies

Cloaking

Simulated time-dependent steady state electric field patterns. [D. Schurig et al., Science vol. 314 p. 977 (2006)]

Bare cylinder Cloaked cylinder (exact parameters)

CloakingHFSS simulations at 3 GHz for cloaked object (mesh of PEC rods) with and without the cloak

P. Alitalo, O. Luukkonen, L. Jylhä, J. Venermo, S.A. Tretyakov, Transmission-line networks cloaking objects from electromagnetic fields, IEEE Trans. Antennas Propagation, vol. 56, 2, 416-424, 2008.

Cloaking

zzarb

abr

,,

2

, ,r r

z z

r a r

r r a

b r a

b a r

A coordinate transformation

based cloak design at

optical frequencies

W. Cai et al., Nature Photon. vol. 1, pp. 224 (2007)

Cloaking

Optical Cloaking with Metamaterials

Non-magnetic cloak with wire stripes stackedinto a dielectric host media

W. Cai et al., Nature Photon. vol. 1, pp. 224 (2007)

Cloaking

Simulations of the magnetic-field mapping around the cloaked object with TM

illumination at λ=632.8 nm.

Optical Cloaking with Metamaterials

CloakingHiding Under the Carpet: A New Strategy for Cloaking

• Instead of a complete cloak, a cloak to mimic a flat ground plane.• By choosing a suitable coordinate transform, the anisotropy of the cloak can be minimized.• Reduced losses and a step closer to a broadband cloaking.• Works in a background dielectric.• The cloak made out of only metamaterials with electric resonating elements.

Cloaking

In the presence of the cloak:The incident wave launched at 45o is reflected atthe same angle. The field outside the cloakresembles the field as if we only have a flatground plane.

In the absence of the cloak:The incident wave launched at 45o is deflectedand split into two different angles at around 38o

and 53o.

J. Li et al., Phys. Rev. Lett. vol. 101, 203901 (2008)

Hiding Under the Carpet: A New Strategy for Cloaking

CloakingHiding under the carpet in the

microwave regime

1) Gradually change the refractive index around the object 2) Restore the reflected beam3) Reduce the anisotropy and the losses due to the cloak4) Broadened bandwidth

CloakingMeasured field mapping (E-field)

A) Collimated beam incident on the ground plane at 14 GHz

B) Collimated beam incident on the perturbation at 14 GHz

C) Collimated beam incident on the ground plane cloaked perturbation at 14 GHz

F) Collimated beam incident on the ground plane cloaked perturbation at 16 GHz

E) Collimated beam incident on the ground plane cloaked perturbation at 15 GHz

D) Collimated beam incident on the ground plane cloaked perturbation at 13 GHz

J. Li et al., Phys. Rev. Lett. vol. 101, 203901 (2008)

Cloaking

Full dielectric cloak by Ebbesen et al.

Cloaking

COMSOL simulation by an homogeneous layer-by-layer structure.The cloak comprises 7 levels.

Each layer displays the effective parameters initially computed by the field-Summation (FS) method for each individual BST rod.

Ab-initio Layer by layer

CloakingAn optical cloak made of dielectrics

Hiding under the carpet in the

optical domain

Cloaking

1) Avoids singularities2) Makes use of non-resonant elements (conventional dielectrics)3) Offers low losses and broadband4) Fabricated on a SOI wafer with a 250 nm Si layer on 3 um SiO2 slab

Ion beam milling through the Si layer

The carpet cloak design that transforms a mirror with a bump

into a virtually flat mirror!

An optical cloak made of dielectrics

J. Valentine and J. Li et al., Nature Mater. vol. 8, pp. 568 (2009)

CloakingThe measured performance of the cloak over a wavelength range: 1400 nm – 1800 nm

The intensity profile of the “scattered” field along the screen

with a cloakMaintains the original Gaussian Beam profile

without a cloakThe curved surface

scatters the incident beaminto three seperate lobes

J. Valentine and J. Li et al., Nature Mater. vol. 8, pp. 568 (2009)

CloakingSilicon Nanostructure cloak operating at

optical frequencies

CloakingSilicon Nanostructure cloak operating at

optical frequencies

A deformed mirror distorts the image.The cloaking device corrects the distorted image so that

the observer can no longer identify the deformationin the mirror.

L. H. Gabrielli et al., Nature Photon. vol. 3, pp. 461 (2009)

CloakingSilicon Nanostructure cloak operating at

optical frequenciesSimulations

Output Images from the Fabricated Device

Flat mirror Deformed mirrorDeformed mirror covered with

the cloaking device

L. H. Gabrielli et al., Nature Photon. vol. 3, pp. 461 (2009)