Optical waveguides – Having nonlinear property
Reexamination Certificate
2002-04-22
2004-03-02
Healy, Brian (Department: 1712)
Optical waveguides
Having nonlinear property
C385S129000, C385S130000, C385S131000, C385S141000
Reexamination Certificate
active
06701048
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to the field of photonic crystals and their applications in optics and microwave technology. More specifically, the invention relates to nonreciprocal magnetic photonic crystals, including magnetic multilayered structures, with magnetic constituent being a gyrotropic material with appreciable Faraday rotation.
2. Description of the Prior Art
Photonic crystals comprise various spatially periodic structures composed of the constituents each of which is practically lossless for electromagnetic radiation in the frequency range of interest. As a consequence of spatial periodicity, the electromagnetic frequency spectrum of photonic crystals develops a band-gap structure similar to that of electrons in semiconductors and metals. The existence of forbidden frequency gaps (stop-bands) in the electromagnetic spectrum forms the basis for the majority of photonic crystals applications in optics and microwave technology. Additional practically important feature of photonic crystals that has been utilized in a number of optical and microwave solid-state devices is the possibility to engineer photonic crystals with prescribed dispersion. This feature allows to control the direction and speed of electromagnetic wave propagation through composite media.
Another category of optical and microwave solid-state devices that can be seen as a prior art to the present invention, comprises various nonreciprocal devices and circuit elements. Some examples are presented by microwave and optical isolators, gyrators, rotators, nonreciprocal phase shifters, etc. Nonreciprocal solid-sate devices based on the effect of Faraday rotation in magnetic media are widely used in microwave and optics.
Nonreciprocal Magnetic Photonic Crystals
In gyrotropic photonic crystals, wave propagation can display additional features, utilization of which forms the basis of the present invention. In particular, in gyrotropic photonic crystals, electromagnetic waves propagating in two opposite directions may display strong asymmetry
&ohgr;(
k
)≠&ohgr;(−
k
), (1)
as shown in FIG.
2
.
The present invention utilizes the strong spectral asymmetry (1) of the bulk electromagnetic waves in gyrotropic photonic crystals. Unlike the case of surface electromagnetic waves, the spectral asymmetry of the bulk waves is prohibited by symmetry in all nonmagnetic and most magnetic photonic crystals. The strong spectral asymmetry though of the bulk waves has been shown to exist in gyrotropic photonic crystals with some special space arrangement of the constituents (A. Figotin and I. Vitebskiy, Phys. Rev. E, 2001). It can be achieved by proper space arrangement of its constitutive components. The spectral asymmetry by no means occurs automatically in any gyrotropic photonic crystal. Quite the opposite, only special periodic arrays of the gyrotropic and other components can produce the effect. For this reason, all magnetic photonic crystals considered in previous art, have perfectly symmetric bulk dispersion relations. The search for periodic arrays yielding strongly asymmetric dispersion relations constitutes an important part of the design.
Strong spectral asymmetry may result in the phenomenon of unidirectional wave propagation, which forms the physical basis of the present invention. Consider a plane wave propagating through a gyrotropic photonic crystal along the Z direction, so that both the wave group velocity u=∂&ohgr;/∂k and the wave vector k are parallel to Z. Suppose that the electromagnetic dispersion relation is asymmetric, and that one of the spectral branches &ohgr;(k) develops a stationary inflection point at k=k
1
and &ohgr;=&OHgr; as shown in
FIG. 3
At
k=k
1
: ∂&ohgr;/∂k=
0; ∂
2
&ohgr;/∂k
2
=0; and ∂
3
&ohgr;/∂k
3
≠0 (2)
There are exactly two bulk electromagnetic modes associated with the frequency &OHgr;, with the corresponding wave numbers being k
1
and k
2
. Observe that only one of the two waves can transfer the energy, namely the one with k=k
2
and the group velocity u(k
2
)>0. Indeed, the backward wave with k=k
1
has zero group velocity u(k
1
)=0 and does not propagate through the medium. Because of this property, we call the mode related to k=k
1
the frozen mode, while a gyrotropic photonic crystal supporting the frozen mode is referred to as a unidirectional gyrotropic photonic crystal.
At first sight, the unidirectional photonic crystal would act similarly to a common microwave or optical isolator, transmitting radiation of the frequency &OHgr; only in one of the two opposite directions. But in fact, there is an important difference. An isolator simply eliminates (usually, absorbs or deflects) the wave propagating in the undesired direction, whereas the unidirectional photonic crystal, being transparent for electromagnetic wave propagating in one direction, freezes and accumulates the radiation of the same frequency &OHgr; propagating in the opposite direction, as shown in
FIGS. 10 and 11
. This quality is critical for the present invention and its applications.
The fact that not only the group velocity u of the backward wave vanishes at &ohgr;=&OHgr;, but so does its derivative ∂u/∂k, enhances the property of unidirectionality preventing the frozen wave packet from spreading.
The property of unidirectionality only exists for k∥Z, &ohgr;=&OHgr;, where Z is the direction of unidirectionality, and &OHgr; is the frozen mode frequency. This means that for directions of wave propagation different from Z and/or for the wave frequencies different from &OHgr;, the effect of unidirectionality disappears.
The present invention utilizes the property of electromagnetic unidirectionality in several proposed microwave and optical devices.
In summary, we present the list of the basic terms and definitions we refer to when describing the invention.
A gyrotropic photonic crystal:
is a composite periodic array of two or more constituents each of which does not substantially absorb the energy of ac electromagnetic field in the frequency range of interest. At least one of the constituents must display Faraday rotation. The preferred embodiment of gyrotropic photonic crystals is a periodic magnetic stack, examples of which are shown in
FIGS. 5 and 7
. In real devices, the total number of the elementary fragments constituting photonic crystal may vary within a wide range starting from just a few.
Bulk spectral asymmetry:
is the property of a homogeneous or periodic composite medium to support an asymmetric dispersion relation &ohgr;(k)≠&ohgr;(−k) as explained in
FIG. 2
or
3
. When applied to real systems of finite dimensions, the term spectral asymmetry means the spectral asymmetry of the infinite periodic structure built up of the same primitive fragments as the finite one.
A unidirectional photonic crystal:
is a photonic crystal that transmits electromagnetic waves of a certain frequency &OHgr; propagating in a certain direction Z and, at the same time, it freezes the radiation of the same frequency &OHgr; propagating in the opposite direction, as shown in
FIGS. 3 and 11
. The frozen wave (mode) is defined as the one having zero or negligible group velocity U, together with its derivative ∂u/∂k. The frequency &OHgr; is referred to as the frozen mode frequency. The direction Z is referred to as the direction of unidirectionality.
A unidirectional slab:
is a fragment of a unidirectional photonic crystal bounded by a pair of plane parallel faces, as shown in
FIGS. 10 and 11
. This device transmits electromagnetic wave packet with k∥Z and the frequency &ohgr; close to &OHgr; only in one of the two opposite directions along the Z axis, this direction is designated with the arrow
2
in
FIGS. 10 and 11
. The slab faces are perpendicular to the Z-direction associated with the frozen mode, unless otherwise is specifically qualified.
A tunable photonic crystal:
is
Figotin Alexander
Vitebskiy Ilya
Dawes Daniel L.
Healy Brian
Myers Dawes Andras & Sherman LLP
The Regents of the University of California
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