US 2026/0099644 A1Published application

Systems and methods for evaluating devices exhibiting near-zero scattering utilizing negative index metamaterials and/or negative kerr coefficient materials

AssigneeThe Penn State Research Foundation

InventorTaoufik Meklachi

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Abstract

Embodiments can relate to systems and methods for developing a structure exhibiting near-zero wave scattering. The technique can involve receiving a number (n) of layers for the structure, each layer comprising a material, receiving a susceptibility coefficient (η) for one or more layers, receiving a wave number (k) for an optical wave or acoustic wave that will be propagated through one or more layers, receiving an electric field measurement (u) to be applied to one or more layers, receiving a refractive index coefficient (ηk) for one or more layers; and/or receiving a Kerr coefficient (β) for one or more layers. The technique can involve solving near-zero wave scattering equation to optimize parameters related to one or more materials for the structure and/or parameters related to geometric dimensions for the structure.

Claims14

Dependent claims

A system for developing a structure exhibiting near-zero wave scattering, the system comprising:

a processor in operative association with a memory, the memory having instructions stored thereon that when executed by the processor will cause the processor to:
receive a number (n) of layers for the structure, each layer comprising a material;
receive a susceptibility coefficient (η) for one or more layers;
receive a wave number (k) for an optical wave or acoustic wave that will be propagated through one or more layers;
receive an electric field measurement (u) to be applied to one or more layers;
receive a refractive index coefficient (ηk) for one or more layers;
and/or
receive a Kerr coefficient (β) for one or more layers;
solve one or more of the following equations:
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
=
0
;
∑
k
=
1
n
η
0
k
⁢
U
k
=
0
;
η
in
0
⁢
U
in
+
η
out
0
⁢
U
out
+
β
in
0
⁢
U
in
⁢
β
+
β
out
0
⁢
U
out
⁢
β
=
0
;
η
eff
≈
η
⁢
U
0
+
β
⁢
U
1
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
+
β
k
⁢
U
k
β
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
U
0
;
λ
h
=
λ
0
-
i
⁢
λ
0
5
2
4
⁢
π
⁢
U
0
[
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
]
⁢
h
+
𝒪
⁡
(
h
2
)
;
wherein:
η0 is a susceptibility coefficient for a homogeneous layer with constant susceptibility;
β0 is a Kerr coefficient for a homogenous layer within a constant electric field;
ηeff is an effective susceptibility coefficient for the structure, wherein ηeff captures a combined contribution of each η for each layer of the structure;
and
λ is resonance of a layer;
generate an output based on solving the one or more equations, the output including:
η for one or more layers;
a range of k values for the structure;
a range of u for one or more layers;
ηk for one or more layers;
β for one or more layers;
ηeff for the structure;
λ for one or more layers;
and/or
Δλ for the structure.

197 more elements

A system for evaluating a structure for a nonlinear optical component or a nonlinear acoustic component, the structure comprising plural layers of material, the system comprising:

a processor in operative association with a memory, the memory having instructions stored thereon that when executed by the processor will cause the processor to:
receive a parameter related to one or more materials for the structure;
receive a geometric dimension related to one or more layers of the structure;
generate an output that is a determination that, or a prediction of whether, the structure will exhibit near-zero wave scattering, the determination or prediction based on solving one or more of the following equations:
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
=
0
;
∑
k
=
1
n
η
0
k
⁢
U
k
=
0
;
η
in
0
⁢
U
in
+
η
out
0
⁢
U
out
+
β
in
0
⁢
U
in
⁢
β
+
β
out
0
⁢
U
out
⁢
β
=
0
;
η
eff
≈
η
⁢
U
0
+
β
⁢
U
1
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
+
β
k
⁢
U
k
β
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
U
0
;
λ
h
=
λ
0
-
i
⁢
λ
0
5
2
4
⁢
π
⁢
U
0
[
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
]
⁢
h
+
𝒪
⁡
(
h
2
)
;
wherein:
n=the number of layers of the structure;
η=susceptibility coefficient for a layer;
k=a wave number for an optical wave or acoustic wave that will be propagated through the structure;
u=an electric field measurement to be applied to the structure;
ηk=a refractive index coefficient for a layer;
β=a Kerr coefficient for a layer;
η0 is a susceptibility coefficient for a homogeneous layer with constant susceptibility;
β0 is a Kerr coefficient for a homogenous layer within a constant electric field;
ηeff is an effective susceptibility coefficient for the structure, wherein ηeff captures a combined contribution of each η for each layer of the structure;
and
λ is resonance of a layer.

188 more elements

A method for developing a structure exhibiting near-zero wave scattering, the method comprising:

receiving a number (n) of layers for the structure, each layer comprising a material;
receiving a susceptibility coefficient (i) for one or more layers;
receiving a wave number (k) for an optical wave or acoustic wave that will be propagated through one or more layers;
receiving an electric field measurement (u) to be applied to one or more layers;
receiving a refractive index coefficient (ηk) for one or more layers;
and/or
receiving a Kerr coefficient (β) for one or more layers;
solving one or more of the following equations:
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
=
0
;
∑
k
=
1
n
η
0
k
⁢
U
k
=
0
;
η
in
0
⁢
U
in
+
η
out
0
⁢
U
out
+
β
in
0
⁢
U
in
⁢
β
+
β
out
0
⁢
U
out
⁢
β
=
0
;
η
eff
≈
η
⁢
U
0
+
β
⁢
U
1
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
+
β
k
⁢
U
k
β
U
0
;
η
eff
=
∑
k
=
1
n
⁢
η
k
⁢
U
k
U
0
;
λ
h
=
λ
0
-
i
⁢
λ
0
5
2
4
⁢
π
⁢
U
0
[
∑
k
=
1
n
η
0
k
⁢
U
k
+
β
0
k
⁢
U
k
β
]
⁢
h
+
𝒪
⁡
(
h
2
)
;
wherein:
η0 is a susceptibility coefficient for a homogeneous layer with constant susceptibility;
β0 is a Kerr coefficient for a homogenous layer within a constant electric field;
ηeff is an effective susceptibility coefficient for the structure, wherein ηeff captures a combined contribution of each η for each layer of the structure;
and
λ is resonance of a layer;
determining or predicting based on solving the one or more equations:
η for one or more layers;
a range of k values for the structure;
a range of u for one or more layers;
ηk for one or more layers;
β for one or more layers;
ηeff for the structure;
λ for one or more layers;
and/or
Δλ for the structure.

196 more elements

Dependencies are inferred from the claim text.