United States Patent
5,493,691
Barrett February 20, 1996
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Oscillator-shuttle-circuit (OSC) networks for conditioning energy in higher-order
symmetry algebraic topological forms and RF phase conjugation
Abstract
The present invention provides passive networks which act as the host to
nonlinear and parametric interactions, with energy inputs to said networks
being caused to "bleed off" auxiliary, and time-delayed conditioning
flows resulting in phase modulations to the main input and which achieve, e.g.,
RF phase conjugation with cancellation of the noise modulation after two-way
passage of beams between transmitter and receiver and when used in duplex
arrangements. Also, passive networks for noise reduction in communications
transmission due to conditioning of electromagnetic fields in higher order
group symmetry form. Because a transmitted wave from a network of the present
invention is in higher-order group symmetry form, and fields of such
higher-order symmetry have a low probability of occurrence naturally, then
environmental noise, which is of lower group symmetry form (usually, U(1)
symmetry) and has a high probably of natural occurrence, will be excluded from
a receiver matched to higher-order symmetry waves. Therefore in the case of
communications, less noise will be processed statistically at a receiver
designed for SU(2) or higher group symmetry operation, resulting in enhanced
signal-to-noise. Also disclosed are passive networks for power transmission
resulting in decreased loss in transmission. Higher-order group symmetry
matched "receivers" will have enhanced signal-to-noise reception over
lower-order symmetry receivers, i.e., leakage to ground will be less.
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Inventors: Barrett; Terence W.
(1453 Beulah Rd., Vienna, VA 22182)
Appl. No.: 172211
Filed: December 23, 1993
Current U.S. Class: 455/20; 307/652; 455/41; 455/73; 455/84;
455/283
Intern'l Class: H04B 007/14
Field of Search:
455/39,41,73,20,89,94,343 307/424,652 333/138,156
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References Cited [Referenced By]
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U.S. Patent Documents
3300729 Jan., 1967 Chang 307/424.
3973208 Aug., 1976 Diamond 328/5.
4314373 Feb., 1982 Sellers 455/73.
4317231 Feb., 1982 Maurer et al. 455/330.
5285177 Feb., 1994 Norose 333/176.
Foreign Patent Documents
WO9323907 Nov., 1993 WO.
Primary Examiner: Eisenzopf; Reinhard J.
Assistant Examiner: Nguyen; Lee
Attorney, Agent or Firm: Zegeer; Jim
Claims
What is claimed is:
1. An oscillator-shuttle circuit network for conditioning electromagnetic
signals, comprising:
an RF energy pump source having first and second pump terminals,
an inductor element having first and second end terminals and means connecting
said first and second terminals to said first and second pump terminals,
respectively,
first and second temporary energy storage means, each having an electrical
connection end and an electrical free floating end,
first means for receiving an RF input signal, said first means for receiving an
RF input signal being connected between said electrical connection end and said
first terminal of one of said inductor element, and
second means connected between said electrical connector end of the second of
said temporary storage means and the second end terminal of said inductor
element for transmitting an output signal which is harmonically related to said
RF energy pump signal and said RF input signal.
2. An oscillator-shuttle circuit network for conditioning energy in higher
order algebraic topological forms and RF phase conjugation, comprising:
an RF energy pump source having first and second pump terminals,
an inductor element having first and second end terminals and means connecting
said first and second end terminals to said first and second pump terminals,
respectively,
first and second temporary energy storage means, each having an electrical
connection end and a free floating end,
first means for receiving an input RF signal, said first means for receiving an
input RF signal being connected between said electrical connection end and said
first end terminal, respectively,
second means connected between said electrical connection end of the second of
said temporary storage means and said second end terminal for transmitting an
output signal which is harmonically related to said RF energy pump signal and
said input RF signal.
3. A circuit network for conditioning electromagnetic signals, comprising:
an energy pump source having first and second pump terminals,
a first energy storage element having first and second end terminals and means
connecting said first and second end terminals to said first and second pump
terminals, respectively,
first and second temporary energy storage means, each having an electrical
connection end and an electrical free floating end,
first means for receiving an RF input signal, said first means for receiving an
RF input signal being connected between said electrical connection end and said
first end terminal of said first energy storage element, and
output means connected between said electrical connection end of the second of
said temporary storage means and said second terminal of said first energy
storage element for transmitting an output signal which is harmonically related
to said energy pump signal and said RF input signal.
Description
BACKGROUND OF THE INVENTION
The present invention relates generally to parametrically pumped passive RF
networks with a single source of energy bled from the input to the networks, to
achieve (i) RF phase conjugation of any order; (ii) phase modulation; (iii)
noise reduction in communications channels; and (iv) power transmission loss
reduction.
The present invention is in the spirit of Tesla's outlook on electromagnetics. Tesla's
approach to electrical engineering addresses and accents primarily the
inductive-reactive part of electromagnetic field-matter interactions, rather
than the resistive part. His approach is more comparable with the physics of
nonlinear optics and many-body systems than with that of the single-body
systems of current electrical engineering. The Tesla approach is fundamentally
a nonlinear many-body approach and may be contrasted with the approach of
mainstream electrical engineering, both linear and nonlinear. The nonlinear
aspects of mainstream electrical engineering are based on feedback in the
resistive field, whereas the nonlinearity in Tesla's approach is based on
coupled inductive oscillators using to-and-fro shuttling of energy to and from
isolated capacitative stores through non-circuit elements attached to
conventional circuits. These network arrangements, which are called
oscillator-shuttle-circuit networks herein, or OSC networks (Barrett, 1991),
result in adiabatic nonlinearities in complete oscillator-shuttle-circuit
systems. OSC networks are inductive-reactive with two-way directional line
feedback rather than resistive single-way directional line feedback, the latter
being the mainstream approach to nonlinear devices. The OSC network arrangement
permits a device or network analog of bulk material nonlinear susceptibilities.
The present invention permits 3-wave, 4-wave . . . n-wave mixing using OSC
network devices as the host medium, rather than bulk material as the host
medium. The present invention also permits RF phase conjugation and the
generation of the complex conjugate of an input wave. The interactions of
oscillator-shuttles (OS) and circuits (C) to which they are attached to form
OSC networks are not describable by linear versions of Kirchhoff's and Ohm's
laws. The oscillator shuttles, OSs, of OSC networks are floating grounds which
are functionally independent and not common grounds. Multiple isolated
"floating" grounds for periodic energy storage and removal by oscillator-shuttles
are not describable in the simple monolithic circuit format. The OSC network of
the present invention permits a many-body definition of the internal activity
of device subsystems which act at different phase relations. The OSC network
concept of the present invention is a basis for polyphase systems of energy
transfer.
The OSC networks which implement four-wave mixing are algebraic topological
analogs of quaternionic systems and more complex OSC networks are analogs of
more complex number elements (e.g., Cayley numbers and "beyond Cayley
numbers").
OBJECTS OF THE INVENTION
It is desirable to parametrically pump an input to a host device, antenna,
substance or network, but without an auxiliary energy source to that same
device, antenna, substance or network, other than that bled from the input.
Parametric pumping with a single source of energy system can be contrasted with
methods of prior art for power control, e.g., with (a) relations which require
two or more power sources; (b) parametric pumping (three-wave mixing) in
conventional circuit theory, with pump, signal and idler waves, but which
requires two or more energy sources; (c) three-wave mixing in nonlinear optics,
which requires a nonlinear material to act as host to the interaction; and (d)
conventional harmonic generation, which again requires auxiliary energy sources
other than that bled from the input. For all of these, including a second-order
network of the present invention, the total power flows, W, is given by the
same well-known Manley-Rowe relation: ##EQU1## where k.sub.pT,z, k.sub.sT,z and
k.sub.iT,z are the phases of the pump, signal and idler;
E.sub.pT, E.sub.sT and E.sub.iT are the total transmitted energies, i.e., the
powers, of the pump, signal and idler;
.alpha..sub.p, .alpha..sub.s and .alpha..sub.i are the angles between E.sub.T
(.omega..sub.i) and E.sub.T.perp. (.omega..sub.i).
However, whereas the power, W, is interpreted as an adiabatic invariant of
passive network arrangements in the case of the present invention, it is not so
interpreted in the case of parametric networks of prior art, as such networks
require an additional auxiliary external signal power source, besides that of
the primary. In the case of parametric networks of prior art the Manley-Rowe
relation applies to (i) a conventional circuit and its power source, together
with (ii) an external modulating signal power source. Because of (ii), prior
art describes nonadiabatic and active networks/device, not adiabatic and
passive networks/devices.
It is desirable to generate the complex or phase conjugate of an input wave
which has been subjected to unwanted noise modulation, in order to compensate
for that unwanted modulation. It is also desirable to accomplish this complex
or phase conjugate wave generation as a phase conjugate mirror and by RF phase
conjugate methods by using network arrangements instead of bulk material.
Accordingly, it is an object of the present invention to provide passive
networks, which act as the host to nonlinear and parametric interactions, with
energy inputs to such networks being caused to "bleed off" auxiliary,
and time-delayed conditioning flows resulting in phase modulations to the main
input and which achieve, e.g., RF phase conjugation with cancellation of the
noise modulation after two-way passage of beams between transmitter and
receiver and when used in duplex arrangements.
It is a further object of the present invention to provide passive networks for
noise reduction in communications transmission due to conditioning of electromagnetic
fields in higher order group symmetry form. Because a transmitted wave from a
network of the present invention is in higher-order group symmetry form, and
fields of such higher-order symmetry have a low probability of occurrence
naturally, then environmental noise, which is of lower group symmetry form
(usually, U(1) symmetry), and has a high probability of natural occurrence,
will be excluded from a receiver matched to higher-order symmetry waves.
Therefore in the case of communications, less noise will be processed
statistically at a receiver designed for SU(2) or higher group symmetry
operation, resulting in enhanced signal-to-noise.
It is a further object of the present invention to provide passive networks for
power transmission resulting in decreased loss in transmission. Higher-order
group symmetry matched "receivers" will have enhanced signal-to-noise
reception over lower-order symmetry receivers, i.e., leakage to ground will be
less.
A further object of the present invention is specifically provide procedures
using OSC network RF phase conjugate mirrors for obtaining relatively
noise-free RF communications in Cellular Telephone Communications, Cable
Networks and Satellite-Ground Communications.
SUMMARY
OF THE INVENTION
The OSC network arrangement of the present invention as a method of energy
crafting or conditioning of conducted energy provides a function similar to
that provided by wave guides or other field-matter interactions at optical
energies. OSC network arrangements offer methods to achieve macroscopic or
device nonlinear interactions presently only achieved, with difficulty, in
nonlinear optics with bulk material.
A distinction can be made between the adiabatic nonlinear
oscillator-shuttle-circuit networks addressing the dynamics of the
inductive-reactive field considered here, and nonadiabatic circuits addressing
the resistive field. For example, Chua and coworkers have described many
nonlinearities in physical systems such as, e.g., four linear passive elements
(2 capacitors, 1 inductor and 1 resistor) and one active nonlinear 2-terminal
resistor characterized by a 3 segment piecewise linear voltage-current
characteristic. Such circuits exhibit: bifurcation phenomena, the Hopf
bifurcation, period-doubling cascades, Rossler's spiral and screw type
attractors, periodic windows, the Shilnikov phenomenon, the double scroll and
the boundary crisis. The tunneling current of Josephson-junction circuits can
even be modeled by a non-linear flux-controlled inductor. However, in all these
instances of prior art, (i) the nonlinear resistive elements require an energy
source to a nonlinear resistor, that energy source being external to that of
the primary energy of the circuit, (ii) the resistive field, not the
inductive-reactive field, is the operative medium, and (iii) the physical
operative mechanism is a one-way circuit, not an OSC network with two-way
oscillator shuttles.
The OSC networks of the present invention can be contrasted in other ways with
prior art. Treatments of electrical circuits by the oriented graph approach all
commence with a one-dimensional cell complex (i.e., a graph) with vertices and
branches connecting them, as well as separable loops. Representing the
connectivity relations of an oriented linear graph by a branch-vertex matrix
A=.SIGMA..alpha..sub.ij, the elements have three values of +1, -1, and 0,
depending on whether current is flowing into, out of, or is stationary, at a
particular vertex (i.e., a.sub.ij =(+1,-1,0)). This linear graph representation
does not, however, take into account any representation (resulting from
modulation) which does not conform to the three values given for a.sub.ij,
e.g., when a.sub.ij takes on spinor values, that is, obeys the even subalgebra
of a Clifford algebra, or values representing two-way flows into and from a
vertex, instead of one-way flows.
There are, however, other approaches to circuit analysis of prior art with are
compatible with the approach of the present invention, but which still do not
describe or propose OSC networks. For example, Kron equated circuits with their
tensor representations. Kron's methods were supported by Roth's demonstration
(1955) that network analysis is a practical application of algebraic topology.
Roth (1955a,b) showed that Kirchhoff's current law is the electrical equivalent
of a homology sequence of a linear graph, and that Kirchhoff's voltage law
corresponds to a cohomology sequence, these sequences being related by an
isomorphism corresponding to Ohm's law. The algebraic topology approach of this
prior art was enhanced considerably further by Bolinder who introduced
three-dimensional hyperbolic geometrical transformations to circuit analysis
and showed how partially polarized electromagnetic or optical waves can be
transformed by Clifford Algebra.
However, this prior art does not address passive network conditioning of
network inputs, nor two-way flows to a vertex, even although OSC networks of
the present invention can be described in Clifford algebra terms and the
simplest OSC networks in quaternion algebra, which is the even subalgebra of a
three-dimensional Clifford algebra with Euclidean metric.
Moreover, OSC network arrangements offer network methods to achieve macroscopic
or device nonlinear interactions at RF energies (as opposed to optical
energies) presently only achieved with difficulty, in nonlinear optics and with
bulk material methods.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A, 1B(i), 1B(ii), 1C(i) and 1C(ii) are examples of OSC networks
incorporating the invention,
FIG. 2 represents four-wave mixing,
FIG. 3 represents a phase conjugate mirror,
FIGS. 4A,B represents an OSC device achieving RF three wave mixing or harmonic
wave generation, and
FIGS. 5A, 5B, 5C illustrate further application areas of the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
FIGS. 1A, 1B(i), 1B(ii), 1C(i) and 1C(ii) are examples of OSC networks
incorporating the invention. FIG. 1A is an OSC network with dimension 2.sup.2
(SU(2) group symmetry), the algebraic topology of the electrical flows being
described in quaternionic numbers, to which number associativity and unique
division applies, but commutativity does not. Accordingly, the voltage across
.alpha. times the voltage across .beta. does not equal the voltage across
.beta. times the voltage across .alpha., i.e.,
.alpha..beta..noteq..beta..alpha.. FIGS. 1B(i) and 1B(ii) are OSC networks with
dimension 2.sup.3 (SU3) group symmetry), the algebraic topology of electrical
flows being described in terms of Cayley numbers, to which unique division
applies but associativity and commutativity does not. Accordingly, and
referring to the voltages, .alpha., .beta. and .gamma.:
.alpha..beta..noteq..beta..alpha. and
(.alpha..beta.).gamma..noteq..gamma.(.alpha..beta.). FIGS. 1C(i) and 1C(ii) are
OSC networks with dimension 2.sup.4 (SU(4) group symmetry), the algebraic
topology of the electrical flows being described in numbers which are known as
"beyond Cayley numbers", to which neither associativity nor
commutativity nor unique division applies, and referring to the voltages,
.alpha., .beta. and .gamma.: .alpha..beta..noteq..beta..alpha.;
(.alpha..beta.).gamma..noteq..gamma.(.alpha..beta.); and .alpha.x+.beta.=0, but
x is not unique.
FIG. 2 represents four-wave mixing. The host medium possesses a third-order
nonlinear susceptibility , .chi..sup.3. There is an input beam A4(0), two pump
beams, A1 and A2, and an output beam A3(0). Under conditions of phase
conjugation, A3(0) is the complex or phase conjugate of A4(0).
FIG. 3 represents a phase conjugate mirror. Two beams are represented. The top
beam is greatly modulated before reaching the a second receiver and transmit
system. The bottom returning beam is the phase conjugate of the first beam, but
it is not modulated on the return path. If the second beam were modulated in an
identical fashion to that of the first, the modulation would be canceled by the
modulations effected by the second receiver and transmit system (the phase
conjugate mirror).
FIG. 4A represents an OSC device achieving RF three wave mixing or harmonic
wave generation. C.sub.1 and C.sub.2 are floating grounds or temporary energy
storage locations. L.sub.1, L.sub.2 and L.sub.3 are inductances. The line
including C.sub.1 and L.sub.2 and the line including C.sub.2 and L.sub.3 are
oscillator shuttles and in this embodiment are also receive and transmit
antennas, respectively. The transmitted wave is the frequency harmonic of the
received wave. FIG. 4B represents an OSC device achieving RF four wave mixing
or RF phase conjugation. C.sub.1 and C.sub.2 are floating grounds or temporary
energy storage locations. L.sub.1, L.sub.2, L.sub.3 and L.sub.4 are
inductances. The line including C.sub.1 and L.sub.2 and the line including
C.sub.2 and L.sub.3 are oscillator shuttles and in this embodiment are also
receive and transmit antennas, respectively. The transmitted wave is the
complex or phase conjugate of the received wave.
The operation of an OSC network can be described by a model of prior art used
in nonlinear optics for describing radiation-matter interactions. The model
applies to the present invention because there exists an analogy between the
functioning of OSC networks and coherent coupling between optical modes in a
nonlinear optical wave guide with bulk matter playing host to the nonlinear
interaction.
For example, if no free charge density is present and the medium is isotropic,
the Maxwell's equations are:
.gradient..times.E=-i.omega..mu..sub.0 H, (1)
.gradient..times.H=i.omega.D, (2)
.gradient..multidot.D=0, (3)
.gradient..multidot..mu..sub.0 H=0, (4)
and
D=.epsilon.E. (5)
By setting
.mu..sub.0 H=.gradient..times.A, (6)
introducing this into the first and second Maxwell equations, using the Lorentz
gauge and using various mathematical manipulations shown in Barrett (1991),
gives: the E and H fields for the x-polarized vector potentials: ##EQU2## The
fields for the y-polarized vector potentials are similar.
If impedance changes are introduced into an OSC network, or the network
equivalent of a bulk material nonlinear second-order susceptibility tensor
.chi..sup.(2) due to the electrical control field and the particular modal
conditionings of an OSC network, and if the frequency of the control or signal
field is designated: .omega..sub.2, and that of the pump field is
.omega..sub.p, then the impedance change caused by the signal or control field
is:
.DELTA.Z.sub.real =Z.sub.0 .chi..sup.(2) E(.omega..sub.p)E*(-.omega..sub.2),
(9A)
.DELTA.Z.sub.imaginary =Z.sub.0 .chi..sup.(2) E(.omega..sub.w)E*(.omega..sub.s),
(9B)
where Z, the complex impedance is: ##EQU3## with magnitude: ##EQU4##
With the signal or control field defined:
E(.omega..sub.2,t)=E.sub.s (t)exp[i(.omega..sub.s t-.beta..sub.s t)], (12)
the pump field defined:
E(.omega..sub.p,t)=E.sub.p (t)exp[i(.omega..sub.p t-.beta..sub.p t)], (13)
and these two fields coupled by the OSC network device "nonlinear
susceptibility" host-mechanism, the following changes in the impedance
occur:
.DELTA.Z.sub.real =Z.sub.0 .chi..sup.(2) E*.sub.s (t)exp[i(.omega..sub.p
-.omega..sub.s)t-i(.beta..sub.p -.beta..sub.s)t], (14A)
.DELTA.Z.sub.imaginary =Z.sub.0 .chi..sup.(2) E*.sub.s (t)E.sub.s (t). (14B)
If the network ".chi..sup.(2) " is purely real (inductive), then only
phase changes are produced. If the network ".chi..sup.(2) " has an
imaginary (resistive) component, then power transfer, and even gain, can be
obtained for one of the inputs.
The idler field or output from the OSC network is:
E.sub.i (.omega..sub.i,t)=.vertline.E.sub.s (t).vertline..sup.2 E.sub.p
(t)exp[i(.omega..sub.p -.omega..sub.s)t-i(.beta..sub.p -.beta..sub.s)t], (15)
where ##EQU5## and E.sub.s and Ep are defined by Eq.s (12) and (13). The
three-body interactive system of E.sub.i, E.sub.s and Ep is defined in terms of
the A vector potential: ##EQU6## The quaternionic impedance for an OSC network
is then: ##EQU7## where the subscripts on i.sub.1, i.sub.2 and i.sub.3
distinguish the separate field conditioning of the waveguide-like properties of
the OSC network and the subscripts on R, .omega.L and .omega.C distinguish the
circuit, C, elements from the oscillator-shuttle, OS, elements of the network.
As the waveguide properties of circuits, C, are fundamentally different from
those of oscillator-shuttles, OS, distinguishing the i.sub.x,y (=.sqroot.-1,
x,y=1,2,3 . . . , i.sub.x i.sub.y =-i.sub.y i.sub.x, where i.sub.x anticommutes
with i.sub.y), is a necessary condition for distinguishing the OS and C dynamic
interaction of the OSC network total arrangement.
The distinguishing characteristics of higher order OSC networks are in analogy
with the dimensions of the number system. The dimensionality of the real
numbers is 2.sup.0 ; of complex numbers is 2.sup.1 ; of quaternions is 2.sup.2
; of Cayley numbers is 2.sup.3 ; of "beyond Cayley numbers" is
2.sup.4 ; etc. Each number system has an associated OSC network device analog
with a higher-order "nonlinear susceptibility".
Quaternions are four-dimensional numbers. The algebra of quaternions is the
even subalgebra of a three-dimensional Clifford algebra with Euclidean metric.
A quaternion is defined:
x=x.sub.0 l+x.sub.1 i+x.sub.2 j+x.sub.3 k,
where the scalar multiplication is:
cx=cx.sub.0 l+cx.sub.1 i+cx.sub.2 j+cx.sub.3 k,
and the sum is:
x+y=(x.sub.0 +y.sub.0)l+(x.sub.1 +y.sub.1)i+(x.sub.2 +u.sub.2)j+(x.sub.3
+y.sub.3)k.
The product is:
xy=(x.sub.0 y.sub.0 -x.sub.1 y.sub.1 -x.sub.2 y.sub.2 -x.sub.3
y.sub.3)l+(x.sub.0 y.sub.1 +x.sub.1 y.sub.0 -x.sub.2 y.sub.3 -x.sub.3
y.sub.2)i+(x.sub.0 y.sub.2 +x.sub.2 y.sub.0 +x.sub.3 y.sub.1 -x.sub.1
y.sub.3)j+(x.sub.0 y.sub.3 +x.sub.3 y.sub.0 +x.sub.1 y.sub.2 -x.sub.2 y.sub.1)k
and
i.sup.2 =j.sup.2 =k.sup.2 =-l.sup.2,
li=il=i,
lj=jl=j,
lk=kl=k,
ij=-ji=k,
jk=-kj=i,
ki=-ik=j.
The set of quaternions is a division ring. The set satisfies all the axioms for
a field except the commutative law of multiplication. If
x=E.sub.x exp[i.omega..sub.x t-.beta..sub.y t],
y=E.sub.y exp[i.omega..sub.y t-.beta..sub.y t],
x=x.sub.0 l+x.sub.1 i+x.sub.2 j+x.sub.3 k,
y=y.sub.0 l+y.sub.1 i+y.sub.2 j+y.sub.3 k,
then: ##EQU8##
The OSC network of FIG. 1A performs transformations described by quaternion
algebra with dimension 2.sup.2 (SU(2) group symmetry), to which number
associativity and unique division applies, but commutativity does not apply.
The OSC networks of FIG. 1B perform transformations described by Cayley numbers
of 2.sup.3 dimensions (SU(3) group symmetry), to which unique division applies,
but associativity and commutativity does not apply. The OSC networks of FIG. 1C
performs transformations described by numbers of 2.sup.4 dimensions (SU(4)
group symmetry), to which neither associativity, nor commutativity nor unique
division applies.
Unitary transformations leave the modulus squared of a complex wavefunction
invariant. Unitary groups have a determinant equal to .+-.1. The elements of a
special unitary group, SU(n), have a determinant equal to +1. For the linear
transformation of a complex 2-dimensional vector (u,v): ##EQU9## If the
requirement is that the sum .vertline.u.vertline..sup.2
+.vertline.v.vertline..sup.2 be left invariant under the transformation, and
that the determinant be:
ad-bc=1,
then the transformation matrix must be: ##EQU10## which is the transformation
matrix of SU(2). The SU(2) group, which has 2.sup.2 -1=3 independent
parameters, e.g., the spatial coordinates x, y and z, in which case: ##EQU11##
and the squared distance x.sup.2 +y.sup.2 +z.sup.2 is invariant (Hamermesh,
1959).
In the case of the SU(3) group there are eight Lie group independent generators
as there are eight (3.sup.2 -1) independent parameters in the SU(3) group.
These eight generators can be represented by a set of 3.times.3 hermitian
matrices: ##EQU12## which commute with each other.
Referring now to FIG. 1. The OSC network of FIG. 1A performs transformations
described by the SU(2) group and there are 2.sup.2 -1=3 independent parameters
represented by the .alpha., .beta. and .gamma. inductances. The OSC networks of
FIG. 1B perform transformations described by the SU(3) group and there are
3.sup.2 -1=8 independent parameters represented by the
(.alpha.,.beta.,.gamma.),.alpha.,.beta.,.gamma.,.delta.,.epsilon. inductances,
where the initial three are represented twice due to the embedding of SU(2)
within SU(3). The OSC networks of FIG. 1C perform transformations described by
the SU(4) group and there are 4.sup.2 -1=15 independent parameters represented
by the
((.alpha.,.beta.,.gamma.),.alpha.,.beta.,.gamma.,.delta.,.epsilon.),.alpha
.,.beta.,.gamma.,.delta.,.epsilon.,.phi.,.psi. inductances, where the initial
three inductances are represented three times, and the following two
inductances are represented twice due to the embedding of SU(2) within SU(3),
which are then embedded in SU(4).
EXAMPLE
#1 OF AN OSC NETWORK
A preferred embodiment of an antenna to be used with OSC network devices in a
practical example of an RF phase conjugate mirror is a small loop antenna which
has an inductive reactance. Such antennas are the dual of a short dipole which
has a capacitative reactance. Thus a small loop antenna can be substituted for
the .beta. inductance of the OSC of FIG. 1A, for the .epsilon. or .delta.
inductances of FIG. 1B, and for the .psi. or .epsilon. inductances of FIG. 1C.
Such antennas could be used in either the send or receive operation modes and
the OSC networks function as "active media".
The present invention provides a wave proportional to the complex conjugate of
an input wave by means of OSC networks acting as host to the interaction, i.e.,
network-based four-wave-mixing and at RF frequencies. Prior art has also
achieved four-wave-mixing by means of a nonlinear medium acting as host to the
interaction, i.e., medium-based four-wave-mixing and at optical frequencies.
The four-wave-mixing achieved by prior art is described as follows. The medium
polarization of the electric field is: ##EQU13## where P is the polarization,
and .chi..sup.(1), .chi..sup.(2) and .chi..sup.(3) are the first, second and
third order susceptibilities.
Referring to FIG. 2, the 3rd-order nonlinear polarization
P.sup.(.omega.3=.omega.1+.omega.2-.omega.3) induced by A.sub.4 is described by
(Yariv, 1989): ##EQU14##
The local input waves A.sub.1, A.sub.2 and the information-carrying input wave,
A.sub.4, are described by: ##EQU15## where i=1 or 2 or 4.
The waves 1 and 2 travel in opposition to each other and are phase conjugate so
that:
.phi..sub.1 +.phi..sub.2 =0.
Because of this phase conjugation, A.sub.3 (L)=0, and the returning wave is
##EQU16## i.e., A.sub.3 (0) is proportional to the phase conjugate of the input
wave A.sub.4.
It is an object of the present invention to achieve such interactions, but with
OSC networks, rather than media, acting as host to the interaction, and with
the interacting waves at RF frequencies, rather than optical. A scenario for
the use of such networks is shown in FIG. 3. which represents a phase conjugate
mirror. Two beams are represented. The top beam is greatly modulated before
reaching the second receiver and transmit system. The bottom returning beam is
the phase conjugate of the first beam, but it is not modulated on the return
path. If the second beam were modulated in an identical fashion to that of the
first, the modulation would be canceled by the modulations effected by the
second receiver and transmit system (the phase conjugate mirror).
FIG. 4A represents an OSC device achieving RF three wave mixing or harmonic
wave generation. C.sub.1 and C.sub.2 are floating grounds or temporary energy
storage locations. L.sub.1, L.sub.2 and L.sub.3 are inductances. The line
including C.sub.1 and L.sub.2 and the line including C.sub.2 and L.sub.3 are
oscillator shuttles and in this embodiment are also receive and transmit
antennas, respectively. The transmitted wave is the frequency harmonic of the
received wave. FIG. 4B represents an OSC device achieving RF four wave mixing
or RF phase conjugation. C.sub.1 and C.sub.2 are floating grounds or temporary
energy storage locations. L.sub.1, L.sub.2, L.sub.3 and L.sub.4 are
inductances. The line including C.sub.1 and L.sub.2 and the line including
C.sub.2 and L.sub.3 are oscillator shuttles and in this embodiment are also
receive and transmit antennas, respectively. The transmitted wave is the
complex or phase conjugate of the received wave. FIG. 4B therefore depicts a
preferred embodiment of the OSC network RF phase conjugate mirror.
Further Application Areas of the Present Invention
FIG. 5 addresses cellular telephone communications. In FIG. 5A, the RF
transmissions from an emitter can be phased modulated by multiple reflections
from surfaces 1, 2, 3, and 4. However, if an OSC network retransmits along the
same path linkage the phase conjugate signal, then the returning signal can be
recaptured (FIG. 5C). The linkage between transmitter and receiver can be
probed by fast path-interrogating signals unobserved by the user, so that the
RF phase conjugation is available at both transmitter and receiver. In cable
communications, FIG. 5B, the RF transmissions from an emitter can be subjected
to phase modulation by the cable through which the transmissions take place. In
this FIG. 5C, four lengths of cable are shown, 1, 2, 3 and 4, which have
different phase modulation properties. Again, the linkage between transmitter
and receiver can be probed by fast path-interrogating signals unobserved by the
user, so that RF phase conjugation is available at the receiver.
Two application areas are illustrated in FIGS. 5A, 5B and 5C; RF cellular
telephone communications and cable communications. A third application area is
RF satellite-ground or ground-satellite communications. A fourth application
area is RF satellite-satellite communications. In all these application areas,
the OSC network provides a returning signal which is phase conjugate to the
entering signal. This means that any undesirable phase changes due to the
properties of the medium intervening between transmitter and receiver will be
removed on the return through the medium back to the transmitter, it being
understood that designation of transmitter in a duplex system is arbitrary.
The medium or path between transmitter and receiver can be probed by a known
signal at intervals during the transmission to provide knowledge of the
phase-altering properties of the medium. In the case of moving communications,
e.g., a cellular telephone in an automobile, aircraft, satellite, etc., the
medium or path between transmitter and receiver can be probed at set intervals
commensurate with the rate of change of the medium or path.
While the invention and preferred embodiments thereof have been disclosed and
described, it will be appreciated that other embodiments and adaptations of the
invention will be apparent to those skilled in the art.