EPSILON-NEAR-ZERO (ENZ) AND

MU-NEAR-ZERO (MNZ) MATERIALS

S A RA H N A H A R C H O W D H U RYPURDUE UNIVERSITY

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Applications

Basics

Design ENZ MaterialsLumped circuit elements

Decoupling Direction emission Tunneling

Supercoupling of ENZ ENZ Field concentration Supercoupling of MNZ

Photonic wires Optical switching Antennas

OUTLINE

Basics

Basics

Q/A session

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HOW?

How can this be achieved?

Some materials show nearzero index of refraction atcertain frequency bands

By matching the resonances in series-parallel circuit of aDNG metamaterial, the propagation constant as a function offrequency continuously passes through zero index with anon-zero slope with non-zero group speed in its transitionfrom DNG to DPG

Dielectric with arrays of metal

inclusions

DNG

Ziolkowski, R. W., and C.-Y. Cheng (2004), Lumped element models of double negative metamaterial-based transmission lines, Radio Sci., 39, RS2017

• L-C configuration for a DPGmedium, β > 0 (𝛽 = 𝜔√𝜀𝜇)

• C-L configuration of a DNGmedium, β < 0

DNG

DPG

At matched cut-off frequencies, when the series-parallel lumped circuit unit cell is

small (∆𝑧 < λ) and

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• a structure composed of a periodic mesh of metallic thinwires, when its characteristic dimensions (period, section ofthe wires) are small in comparison to the wavelength, behaves asa homogenous material with low plasma frequency

Near-zero refractive index materials

• At 𝜔 = 𝜔,, wave number, k=0• Wavelength, λ = ∞, 𝜗=∞• Group velocity is finite• This behavior corresponds to plasmon

resonance, where ε ~ 0 or/and µ ~ 0• Varying effective impedance, we can

achieve particular group speed at 𝜔 =𝜔,

Near-zero metamaterials

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Near-zero refractive index

materials

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Properties of ENZ and MNZ materials

1. Light manipulation occurs withartificially designed metamaterialstructure

2. ENZ and MNZ materials have near zeroparameters (ε ~ 0 or/and μ ~ 0)

3. Refractive index, n=√εμ ≈ 04. Low wave number (due to n≈ 0) and

hence no phase variation inside themedium

5. Static like character even whendynamically oscillating

Decoupling of electric and magnetic fields

∇ × E = iωμH ∇ × E = 0

∇ × H = −iωεE ∇ × H = 0Decoupling even at non-zero frequency

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ENZ and MNZ materials for direction emission

• Let us consider a point source inside a low refractive index metamaterial• Incidence on top slab coming from a source inside the slab of metamaterial• For low n, the refracted ray is nearly normal to the slab• The second figure assumes that light is dispersing in all directions• Experimental work has been done with Cu wires• Can be used as directional antennas

Stefan Enoch, Gérard Tayeb, Pierre Sabouroux, Nicolas Guérin, and Patrick Vincent, A Metamaterial for Directive Emission Phys. Rev. Lett. 89, 213902 7

Tunneling through distorted channels

Mário Silveirinha and Nader Engheta, Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using ε-Near-Zero Materials Phys. Rev. Lett. 97, 157403 (2006)

Motivation: Since thewavelength of radiation insidethe ENZ material is extremelylarge, the wave must be able topropagate inside the ENZmaterial with no relevantreflection losses at abrupt bendsor junctions

• Since refractive index is low, phase variation is slow• Wave fronts are radiated in parallel to the ENZ

material interface

Equations

Inside ENZ, 𝛻Hz vanishesOutside,

Using Boundary conditions of matched magnetic fields

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Tunneling through distorted channels

Liberal, I. & Engheta, N. Near-zero refractive index photonics. Nature Photonics 11, 149–158 (2017)

a1 ≈ a2 Relative permeability≈0Cross-sectional area or width

small

Outcome:As the ENZ channel becomes increasingly narrower, the reflectancedecreases more

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Supercoupling and squeezing of wave energy

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• Interaction with electromagnetic waves is independent of the granularity or lattice arrangement of the specific material and the channel size or shape

• Confining EM field in very small subwavelength air cavity with enormous field enhancement

• For U-shaped tunneling, Ap = (L1 + L2)a + Lach

For ENZ material, its reflectivity only depends on the volume, independent of the geometry

and transverse cross section

Silveirinha, M. G. & Engheta, N. Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials. Phys. Rev. B 76, 245109 (2007)

• When EM wave is squeezed, fieldis highly enhanced

• Magnetic field is constant• The electric field is such that at

the boundary it depends onach/a1

• Electric field amplified by afactor of a/ach

• Magnetic field nearly constantwhen losses are moderate

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ENZ Field concentration and confinement

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MNZ Supercoupling, field concentration and confinement

Marcos, J. S., Silveirinha, M. G. & Engheta, N. µ-near-zero supercoupling. Phys. Rev. B 91, 195112 (2015)

• parallel plate waveguide can be modeled as a transmission line with C and L

• η0d0 = η1d1

1. For ENZ, both electric field and power are compressed into the channel2. Phase constant3. They are independent of bending due to ‘supercoupling’4. Supercoupling basically emerges from the combination of a constant transverse magnetic field,

produced by the enlargement of the wavelength in ENZ media, and the associated reduction of the magnetic flux induced by narrowing the channel, which, in turn, imposes a zero circulation ofthe electric field and enforces full transmission

5. For MNZ medium, tunneling will be observed if the height of the channel is substantially increased6. EMNZ acts like an electromagnetic ‘point’, thus seemingly ‘directly connecting’ the input and output

ports and enabling full transmission 13

Tunneling

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BOUNDARY EFFECTS AND LIGHT TRAPPING

(D-DOT WIRES)

• Layered metamaterial board with effective epsilon-near-zero (ENZ) property, over which nanocircuit traces may be carved out

• A metamaterial substrate that may be formed by alternating thin layers of epsilon-positive Si3N4 and epsilon-negative Ag

• The carved loop, filled with air, is surrounded by an effective ENZ substrate

• This prevents leakage of displacement current.

• As a result, Jd is confined within the air groove,

• This is analogous to optical nanowire• An ENZ material surrounding a lumped

nanocircuit element would indeed “insulate” the element from the unwanted coupling with other neighboring elements

Alù, A. & Engheta, N. All optical metamaterial circuit board at the nanoscale. Phys. Rev. Lett. 103, 143902 (2009)M. G. Silveirinha, A. Alu`, J. Li, and N. Engheta, J. Appl. Phys. 103, 064305 (2008)

Requisite?Ø Silicon based circuit parametersØ Problem with proper couplingØ Leakage current

If we could confine the current?

Design a nanoinsulatorusing ENZ

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Metatronics

• Light, not charge, plays the role ofinformation carrier, with small(subwavelength) components playingthe roles of lumped circuit elements

• Positive permittivity represents acapacitor; negative permittivity aninductor, while loss represents aresistor.

• The photonic wires are fabricated onepitaxially grown highly dopedsemiconducting layers, which serve asthe plasmonic material base for thehybrid waveguide geometry

• Can work in the optical domain

Liu, R., Roberts, C. M., Zhong, Y., Podolskiy, V. A. & Wasserman, D. Epsilon-near-zero photonics wires. ACS Photon. 3, 1045–1052 (2016)

“Photonic wire” is a cylindrical waveguide with deeply subwavelength cross section that is formed by a core with ENZ surrounded to bounds the displacement current flow

Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths

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Oxygen-Deprived AZO Thin Films

• Optical switching at ENZ regime• Operating in this regime (i.e. n<1) produces larger

absolute changes in the reflection for a fixedchange in the refractive index

• Traditional materials can not achieve this attelecom wavelengths

• AZO has large intrinsic carrier concentration toenable ENZ properties at the technologicallyimportant telecommunication wavelengths (whichenhances the optical/electrical tunability

N. Kinsey, C. DeVault, J. Kim, M. Ferrera, V. M. Shalaev, and A. Boltasseva. Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths Optica Vol. 2, Issue 7, pp. 616-622 (2015)

Extremely convergent microlenses (EMNZ Lens antennas)

17Navarro-Cía, M., Beruete, M., Campillo, I. & Sorolla, M. Enhanced lens by ε and µ near-zero metamaterial boosted by extraordinary optical transmission. Phys. Rev. B 83, 115112 (2011)

§ EMNZ to transform isotropic source into plane-wave like beam with low ohmic losses

§ EMNZ gives an enhancement of directivity at 5.24 nm

EPSILON-NEAR-ZERO (ENZ)

ANDMU-NEAR-ZERO

(MNZ) MATERIALS

TAKEAWAYSAcknowledge

ment

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Materials

FeaturesBasicStructure

Applications

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