Circuits with Light at Nanoscales
Nader Engheta
University of Pennsylvania
Department of Electrical and Systems Engineering
Philadelphia, PA U.S.A.
October 16, 2007
R
R
C
C
C
L
L
L
C
Circuits and Signal Manipulations
d
λ
<<
d λ
;
Can We Have Lumped Circuit
Elements in Optics?
L
C
R
RF
Optics
?
?
?
?
?
A Typical RF Circuit Diagram
http://www.hamcircuits.fsnet.co.uk/AR1500MainCircuit.jpg
From
Optical Wave Interaction with Materials
z
How to model and quantify wave interaction with matter?
1n
E
+
_
Bulk Parameters in Materials
z
Electric Permittivity – Dielectric Function – Epsilon ε
+
-
+
-
+
-
+
-
+
-
+
-
ε
ε
+
o E
D
P
=
= E
z
Magnetic Permeability – Magnetic Response – Mu μ
μ
μ
+
o H
B
M
=
= H
Materials & Metamaterials
rε
rμ
0
0
r
rε
μ
<
>
0
0
r
rε
μ
>
<
0
0
r
rε
μ
>
>
0
0
r
rε
μ
<
<
inc
E
inc
E
inc
E
inc
E
p
int
E
ext -dipole
E
+++
+ ++
− −−
− − −
+++
− − −
r
r
n
ε μ
=
Optical Fields in Nanoparticles
z
1
1
k a <<
inc
E
inc
H
2a
sphere
Z
ext dipole
Z
−
imp
I
(
)
2
imp
o
inc
I
j
a E
ω ε ε π
=
−
ε
inc
E
inc
E
inc
E
inc
E
int
E
ext-dipole
E
Engheta, et al., Phys. Rev. Lett. 95, 095504 (2005)
0
∇× ≅
E
0
∇⋅D =
i
t
ωε
∂
→ −
∂
D
E
Lumped Circuit Elements with Light
RF
Optics
E
H
a
λ
<<
( )
Re
0
ε >
C
( )
Re
0
ε <
E
H
L
( )
Im
0
ε ≠
E
H
R
Engheta, Science, 317, 1698 (2007)
Optical Lumped “Nanoinsulator”
z
r
ε
?
shield
ε
=
?
shield
ε
=
/
cond shield
shield
σ
=
J
E
Shield
σ
= 0
RF
1
2
0
n
n
D
D
=
=
Epsilon-Near-Zero (ENZ)
Materials as Nano-Insulator
Shield
i
t
ωε
∂
→ −
∂
D
E = 0
ε shield = 0
Optics
L
C
Silveirinha, Alu, Li, and Engheta, arXiv:cond-mat/0703600 (2007)
How about “Wire”?
http://www.hamcircuits.fsnet.co.uk/AR1500MainCircuit.jpg
From
Optical “Wire”
z
L
C
RF L-C
0
r
ε >
0
r
ε <
?
contact
ε
=
?
contact
ε
=
/
cond contact
contact
σ
=
J
E
contact
σ
∞
=
RF
V =
d
Δ
Δ
E
contact
i
t
ωε
∂
→ −
∂
D
E
ε
∞
contact =
Optics
n
E ; 0
V
Δ
; 0
Alu and Engheta, Optics Express, 15, 13773 (2007)
Optical “Wire”
Alu and Engheta, Optics Express, 15, 13773 (2007)
Optical “Wire”
Amplitude of Elong
Phase of Elong
Optical Nanomodule: