EMNZ metamaterial configured into a waveguide having a length that is less than or equal to 0.1 of a wavelength
An epsilon-and-mu-near-zero (EMNZ) metamaterial. The EMNZ metamaterial includes a waveguide. A length l of the waveguide satisfies a length condition according to l≤0.1λ, where λ is an operating wavelength of the EMNZ metamaterial. The EMNZ metamaterial further includes a magneto-dielectric material deposited on a lower wall of the waveguide. The waveguide includes an impedance surface placed on the magneto-dielectric material.
1. An epsilon-and-mu-near-zero (EMNZ) metamaterial, comprising:
a waveguide, a length l of the waveguide satisfying a condition according to l≤0.1λ, where λ is an operating wavelength of the EMNZ metamaterial, the waveguide comprising one of a rectangular waveguide and a parallel-plate waveguide;
a magneto-dielectric material deposited on a lower wall of the waveguide;
a graphene monolayer placed on the magneto-dielectric material, the graphene monolayer attached to a left sidewall of the rectangular waveguide and a right sidewall of the rectangular waveguide; and
a dielectric spacer coated on the graphene monolayer and attached to an upper wall of the waveguide, wherein:
a thickness h of the dielectric spacer satisfies a condition according to
h
≤
λ
4
;
a permittivity of the dielectric spacer is equal to a permittivity ϵ of the magneto-dielectric material; and
a permeability of the dielectric spacer is equal to a permeability μ of the magneto-dielectric material;
wherein a cutoff frequency f c of the EMNZ metamaterial is configured to be adjusted by adjusting a chemical potential μ c of the graphene monolayer according to an operation defined by:
f
c
=
1
4
a
μϵ
eff
where:
α is a distance between the upper wall and a lower wall of the waveguide, and
ϵ eff is an effective permittivity of the magneto-dielectric material and the graphene monolayer, where ϵ eff =ϵ(1−165√{square root over (a)}μ c ).
2. An epsilon-and-mu-near-zero (EMNZ) metamaterial, comprising a waveguide, a length l of the waveguide satisfying a length condition according to l≤0.1λ, where λ is an operating wavelength of the EMNZ metamaterial.
3. The EMNZ metamaterial of claim 2 , wherein the waveguide comprises one of a rectangular waveguide and a parallel-plate waveguide.
4. The EMNZ metamaterial of claim 3 , further comprising a magneto-dielectric material deposited on a lower wall of the waveguide.
5. The EMNZ metamaterial of claim 4 , wherein the waveguide further comprises an impedance surface placed on the magneto-dielectric material.
6. The EMNZ metamaterial of claim 5 , wherein the impedance surface comprises a tunable impedance surface comprising a tunable conductivity.
7. The EMNZ metamaterial of claim 6 , wherein the tunable impedance surface comprises a graphene monolayer.
8. The EMNZ metamaterial of claim 7 , wherein a dielectric spacer is coated on the graphene monolayer and attached to an upper wall of the waveguide, a thickness h of the dielectric spacer satisfying a thickness condition according to
h
≤
λ
4
,
a permittivity of the dielectric spacer equal to a permittivity ϵ of the magneto-dielectric material and a permeability of the dielectric spacer equal to a permeability μ of the magneto-dielectric material.
9. The EMNZ metamaterial of claim 7 , wherein the graphene monolayer is attached to a left sidewall of the rectangular waveguide and a right sidewall of the rectangular waveguide.
10. The EMNZ metamaterial of claim 7 , wherein a cutoff frequency f c of the EMNZ metamaterial is configured to be adjusted by adjusting a chemical potential μ c of the graphene monolayer.
11. The EMNZ metamaterial of claim 10 , wherein the cutoff frequency f c is configured to be adjusted according to an operation defined by:
f
c
=
1
4
a
μϵ
eff
where:
α is a distance between an upper wall and the lower wall of the waveguide, μ is the permeability of the magneto-dielectric material and
ϵ eff is an effective permittivity of the magneto-dielectric material and the graphene monolayer, where ϵ eff =ϵ(1−165√{square root over (α)}μ c ).
12. A method for adjusting a cutoff frequency f c of an epsilon-and-mu-near-zero (EMNZ) metamaterial, the EMNZ metamaterial comprising a waveguide, the method comprising designing the waveguide by determining a length l of the waveguide based on a length condition defined by l≤0.1λ, where λ is an operating wavelength of the EMNZ metamaterial.
13. The method of claim 12 , wherein designing the waveguide comprises designing one of a rectangular waveguide and a parallel-plate waveguide.
14. The method of claim 13 , further comprising depositing a magneto-dielectric material on a lower wall of the waveguide.
15. The method of claim 14 , further comprising placing an impedance surface on the magneto-dielectric material.
16. The method of claim 15 , wherein placing the impedance surface on the magneto-dielectric material comprises placing a tunable impedance surface on the magneto-dielectric material, the tunable impedance surface comprising a tunable conductivity.
17. The method of claim 15 , wherein placing the tunable impedance surface on the magneto-dielectric material comprises placing a graphene monolayer on the magneto-dielectric material as the tunable impedance surface.
18. The method of claim 17 , wherein placing the graphene monolayer on the magneto-dielectric material further comprises:
coating a dielectric spacer on the graphene monolayer, comprising determining a thickness h of the dielectric spacer based on a thickness condition defined by
h
≤
λ
4
;
and
attaching the dielectric spacer to an upper wall of the waveguide;
wherein a permittivity of the dielectric spacer equals a permittivity ϵ of the magneto-dielectric material and a permeability of the dielectric spacer equals a permeability μ of the magneto-dielectric material.
19. The method of claim 17 , wherein placing the graphene monolayer further comprises:
attaching the graphene monolayer to a left sidewall of the rectangular waveguide; and
attaching the graphene monolayer to a right sidewall of the rectangular waveguide.
20. The method of claim 17 , further comprising adjusting a cutoff frequency f c by adjusting a chemical potential μ c of the graphene monolayer according to an operation defined by:
f
c
=
1
4
a
μϵ
eff
where:
α is a distance between an upper wall and the lower wall of the waveguide, μ is the permeability of the magneto-dielectric material and
ϵ eff is an effective permittivity of the magneto-dielectric material and the graphene monolayer, where ϵ eff =ϵ(1-165√{square root over (α)}μ c ).