Radiation imagery chemistry: process – composition – or product th – Imaging affecting physical property of radiation sensitive... – Making electrical device
Reexamination Certificate
1998-05-28
2001-08-14
Duda, Kathleen (Department: 1756)
Radiation imagery chemistry: process, composition, or product th
Imaging affecting physical property of radiation sensitive...
Making electrical device
C430S320000, C430S329000, C427S124000
Reexamination Certificate
active
06274293
ABSTRACT:
TECHNIAL FIELD OF THE INVENTION
This invention relates to electromagnetic wave filtering devices and methods of manufacturing same, and more particularly to a flexible metallic photonic band gap structure suitable for filtering in the infrared frequency region and a method of manufacturing same.
BACKGROUND OF THE INVENTION
Photonic band gap (PBG) structures are periodic dielectric structures that exhibit frequency regions in which electromagnetic waves cannot propagate. The idea for PBGs was first proposed by Eli Yablonovitch in 1987. The interest in PBGs arises from the fact that photon behavior in a dielectric structure is similar to the behavior of electrons in a semiconductor. The periodic arrangement of atoms in a semiconductor lattice opens up forbidden gaps in the energy band diagram for the electrons. Similarly in PBG structures, the periodic placement of dielectric “atoms” opens up forbidden gaps in the photon energy bands. This analogy can be easily seen in the Schrödinger equation (1) (see below) of a propagating electron wave in a potential, V(r) and equation (2), which is derived from the Maxwell's equations, for the electric field amplitude E(r) propagating a monochromatic electromagnetic wave of frequency &ohgr; in an inhomogeneous but nondispersive dielectric media as shown in the following equations:
{
-
ℏ
2
2
m
∇
2
+
V
(
r
)
}
ψ
(
r
)
=
E
ψ
(
r
)
,
(
1
)
-
∇
2
E
(
r
)
+
∇
(
∇
·
E
(
r
)
)
-
ω
2
c
2
ϵ
fluc
(
r
)
E
(
r
)
=
ϵ
0
ω
2
c
2
E
(
r
)
.
(
2
)
Here, m is the electron rest mass and &psgr;(r) is the scalar wave function in equation (1). In equation (2), the total dielectric is separated as
&egr;(
r
)=&egr;
&ogr;
+&egr;
fluc
(
r
), (3)
where &egr;
o
is the average dielectric constant value and &egr;
fluc
(r) defines the spatially fluctuating part. The latter plays a role analogous to the V(r) in the Schrödinger equation, and the quantity &egr;
o
&ohgr;
2
c
2
is equivalent to the energy eigenvalue E of the Schrödinger equation.
The idea of PBGs has led to the proposal of many novel applications at optical wavelengths, such as thresholdless lasers, single-mode light-emitting-diodes and optical wave guides. In addition, PBGs are already being used in the millimeter and microwave regimes, where the applications include efficient reflectors, antennas, filters, sources and wave guides. They have also found possible applications as infrared filters. As a result, they have been extensively studied in the last few years.
The PBG structures behave as ideal reflectors in the band gap region. Depending on the directional periodicity of these dielectric structures, the band gap may exist in 1-D, 2-D or all the three directions.
One of the unique features of PBG structures is their scaleable characteristic from microwaves to optical frequency. This can be explained better by going back to Maxwell's equations. Equation (2) listed earlier is derived from Maxwell's equations which can be rewritten in a magnetic field vector form as:
∇
×
(
1
ϵ
(
r
)
∇
×
H
(
r
)
)
=
(
ω
c
)
2
H
(
r
)
,
(
4
)
where H(r) is the magnetic field vector. A new dielectric constant is defined,
&egr;′(
r
)=&egr;(
r/s
)=&egr;(
r
′) (5)
where s is some scalar parameter. Basically the dielectric has been compressed or expanded by this scalar value s. Now defining a new variable, r′=sr and ∇′=′/s, equation (4) can be rewritten as:
s
∇
′
×
(
1
ϵ
(
r
′
/
s
)
s
∇
′
×
H
(
r
′
/
s
)
)
=
(
ω
c
)
2
×
H
(
r
′
/
s
)
(
6
)
which can also be written as
∇
′
×
(
1
ϵ
′
(
r
′
)
∇
′
×
H
(
r
′
/
s
)
)
=
(
ω
cs
)
2
×
H
(
r
′
/
s
)
(
7
)
Here, &egr;(r′/s)=&egr;′(r′) and this allows return to the master equation with mode profile H′(r′)=H(r′/s) and frequency &ohgr;′=&ohgr;/s. If the mode profile is studied after changing the length scale by a factor of s, the old mode and its frequency simply needs to be scaled by the same factor. The solution of a problem at one length scale determines the solutions at all other scales.
The modes of photonic crystals can be tested at microwave frequencies with bigger dimension and because of scalability of the structure it is ensured that the electromagnetic properties will not change at optical frequencies with submicron dimensions.
Now studying the effect of change in the dielectric configuration, suppose that a new system has a dielectric constant &egr;′(r)=&egr;(r)/s
2
. Therefore,
∇
×
(
1
s
2
ϵ
′
(
r
)
∇
×
H
(
r
)
)
=
(
ω
c
)
2
×
H
(
r
)
or
,
(
8
)
∇
×
(
1
ϵ
′
(
r
)
∇
×
H
(
r
)
)
=
(
s
ω
c
)
2
×
H
(
r
)
(
9
)
The harmonic modes of the system are unchanged but all the frequencies have been scaled up by a factor of s. For example, if the dielectric constant is multiplied by a factor of ¼, the mode patterns are unchanged but the frequencies are doubled. So, by changing the dielectric constant or changing the dimensions of the structure, the electromagnetic properties can be scaled anywhere from microwave to optical frequencies. Similar to the impurity doping in a semiconductor, localized electromagnetic modes can be created in the band gap region of PBG structures by introducing defects that disturb the periodicity of the structure. This can be achieved by adding extra material to the crystal, which acts like a donor atom of a semiconductor. The defect gives rise to donor modes which have their origin at the bottom of the conduction band. A defect can also be introduced by removing a part of the material, thus creating states similar to the semiconductor behavior with acceptor atoms. Experiments have shown that the acceptor modes, acting like cavities, are of greater importance with their highly localized and single-mode cavity characteristics. In photonic crystals with defects, the transmission spectrum is changed by the presence of a narrow transmission peak within the band gap. Defect peaks with quality factors in the range of 1000-2000 have been experimentally demonstrated.
Much of the PBG research effort up to this point has focused on the use of purely dielectric material to construct the PBG structure. Metallic photonic band gap (MPBG) structures have received relatively little attention due to perceived problems relating to lossiness in the metal components.
However, MPBG structures do have some distinct advantages over their all dielectric counterparts, and these advantages have garnered MPBGs more attention recently. MPBG structures offer the potential of lighter weight, reduced size and lower materials and fabrication costs when compared to all dielectric structures. The use of metal can also lead to fundamentally different PBG characteristics. For an interconnected mesh structure, the stopbands of the MPBG will extend from zero frequency up to some cut-off frequency, which is determined by the periodicity of the structure. Such behavior is in contrast to purely dielectric PBG structures, which typically have stop bands extending over relatively narrow ranges of frequencies. On the other hand, it has also been shown that MPBG structures consisting of isolated metal patches have a band-stop behavior very similar to the all dielectric photonic band gap structures.
As stated above, the idea of photonic band gaps was first proposed by Yablonovitch in 1987. The idea is analogous to the behavior of electrons in a crystal lattice.
Gupta Sandhya
Ho Kai-Ming
McCalmont Jonathan S.
Sigalas Mihail
Tuttle Gary L.
Duda Kathleen
Iowa State University Research Foundation
Leydig,Voit & Mayer,Ltd.
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