AAWSAP DIRD High Frequency Gravitational Wave Communications April 6 2010
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Defense
Intelligence
Reference
Document
Acquisition Threat Support
6 April 2010
ICOD : 1 December 2009
DIA-08- 1004-005
High-Frequency Gravitational
Wave Communications
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High-Frequency Gravitational Wave Communications
Prepared by:
Acquisition Support Division (DW0-3)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Author:
AAP Person 77
Administrative Note
COPYRIGHT WARNING: Further dissemi nation of the photographs in this publication is not author ized .
This product is one in a series of advanced technology reports produced in FY 2009
under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace
Weapon System Applications (AAWSA Pro ram. Comments or uestions pertaining to
this document should be addressed t AAP Person 1 AAWSA Program
Manager, Defense Intelligence Agency, ATTN: CLAR/ DWO-3, Bldg 6000, Washington,
DC 20340-5100.
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Contents
Summary......................... .......... .... ...... ........ .......... ...... .......... ................ ........ ......... . v
1.0 Introduction .. .................................. ................................................................. 1
1.1 Introduction .................... ........ .... .... .. .... .... .. ........ .. ....................................... 1
1.2 Definition of High-Frequency Gravitational Waves ....................................... 1
2.0 HFGW Communications .................................................................................... 2
2.1 HFGW Generators (Transmitters) .... ........ .... .. .. ............................................. 2
2.1 .1 HFGW Generator Concepts ..... .. ................ ............................................. 2
2.1 .2 Alternative Approaches ........ .......... .. ...... ........... .................................... 6
2. 1.3 Piezoelectric Approach .......................................................................... 6
2.1.4 Infrared-Excited Molecules Approach .................................................... 7
2.2 HFGW Detectors (Receivers) ...................................................................... 12
2.2.1 Alternative Approaches ....................................................................... 12
2.2.2 Concept (Li-Effect) .............................................................................. 14
2.2.3 Quantum Back-Action Limit ................................................................. 16
2.2.4 Li-Baker HFGW Detector...................................................................... 20
3.0 Operational Concerns ..................................................................................... 22
3.1 Link Budget ................................................................................................ 22
3.1.1 Signal-to-Noise Ratio .......................................................................... 22
3.1.2 Link Budget Considerations ................................................................. 23
3.2 Bandwidth .................................................................................................. 25
3.3 Frequency and Time Standard .................................................................... 25
3.3.1 Improvements Accruing from a HFGW Time Standard ......................... 27
3.3.2 Search Space Improvement Accruing From HFGW FTS ........................ 28
3.3.3 The Impact of Phase Noise Improvements on Phase Shift Encoding ... 29
3.3.4 The Impact of Frequency Noise Improvements on FDMA and FHSS..... 30
3.4 Possible Future Upgrades to the FTS Devices ............................................. 30
3.4.1 Propagating Signals From Optical Lattice Clocks for Timing ................ 31
3.4.2 In Navigating and Mapping Interplanetary Geoids .............................. 31
4.0 Future Potential ............................................................................................. 32
4.1 Developmental Roadmap ............................................................................ 32
4.2 HFGW Communications Predictions to 2050 ............................................... 33
4.3 Interplanetary Navigation and Geoid Mapping to 2050 .............................. 34
4.4 Other Possible HFGW Applications ............................................................. 36
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4.5 2050 and Beyond ........................ .. ............................................................. 37
5.0 Acknowledgements ........................................................................................ 37
6.0 References ..................................................................................................... 37
Appendix A: Nomenclature ................................................................................... 44
Appendix B: Li-Baker HFGW Detector ................................................................... 45
Appendix C: Perturbative Photon Fluxes Generated By High-Frequency
Gravitational Waves and Their Physical Effects .................................... 52
Figures
Figure 1. Communication Link Block Diagram ........................................................ 2
Figure 2. Change in Centrifugal Force of Orbiting Masses, Afct, Replaced by Change
in Tangential Force, '1ft, to Achieve HFGW Radiation ............................... 3
Figure 3. Circular Resonator Geometry Using Infrared Excitation .......................... 8
Figure 4. Radiation Pattern Calculated by Landau and Lifshitz (1975) ................... 8
Figure 5. GW Flux Growth Analogous to Stack of N Orbital Planes ......................... 9
Figure 6. Stack of Circular-Wave-Guide Plates With Typical Molecule Jerks, Af's ... 9
Figure 7. Omni-Directional Nature of the HFGW Radiation Pattern ....................... 10
Figure 8. Predicted Relic GW Energy Density as a Function of Frequency ............. 11
Figure 9. Birmingham University HFGW Detector ................................................. 13
Figure 10. INFN Genoa HFGW Detector ................................................................ 13
Figure 11. The National Astronomical Observatory of Japan 100 MHz Detector ... 14
Figure 12. Detection Photons Sent to Locations that are Less Affected by Noise .. 15
Figure 13. Quantum Back Action as a Mechanism for Creating the Standard
Quantum Limit ..................................................................................... 17
Figure 14. Schematic of Ultra-Sensitive HFGW Detector....................................... 21
Figure 15. Fractal Membrane Component of Li-Baker Detector Exhibited in Planar
Form .................................................................................................... 21
Figure 16. Conceptual SNR Fill Factors: Signal and Noise Components ................ 23
Figure 17. A Block Diagram of a Typical Link Budget............................................ 24
Figure 18. A Proposed Near Earth Distribution of Frequency Time Standard........ 26
Figure 19. HFGW Supplemented Remote Terminal Design .................................... 27
Figure 20. Acquisition Search Space Improvement Accruing From HFGW FTS ...... 28
Figure 21. The Impact of Phase Noise Improvements on Phase Shift Encoding ... 29
Figure 22. The Impact of Frequency Noise Improvements on FDMA and FHSS ..... 30
Figure 23. The Earth's Associated Lagrangian Points ........................................... 31
Figure 24. HFGW Com Space Application Development Roadmap, Estimated
Timeline .............................................................................................. 32
Figure 25. A GW Pair on Earth as Used by a Lunar Mission ................................... 34
Figure 26. A GW Pair on Earth and on the Moon, as Used by a Mission to Mars .... 35
Figure 27. A GW Pair on Earth and on Mars for an Outer Planetary Reference
Pair...................................................................................................... 35
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High-Frequency Gravitational Wave Communications
Summary
• Fourteen laboratory high-frequency gravitational wave (HFGW) generators
(or transmitter s) have been proposed in the past 45 years in peer-reviewed
journal articles.
• The most promising laboratory HFGW generators are those that utilize very
large numbers of sub-microscopic radiation elements.
• The Piezoelectric Approach to HFGW generation is best for the proof- of
concept test and the proposed IR-excited Molecules Approach i s best for an
oper ational communications HFGW transmitter.
• Ten different HFGW detectors (or receivers) have been proposed since
1978 and reported in peer-reviewed journal articles.
• Several different HFGW receivers can be utilized for communication, but the
proposed Li-Baker detector (plans & specification development in Appendix
B) shows the most promise (underlying concept in Appendix C). The Li
effect, upon which the Li-Baker detector is based, is not so new that it is
untested in the literature. At least nine peer-reviewed research publications
concerning the theory have appeared following the initial peer-reviewed
article by Li, Tang and Zhao (1992).
• Because HFGW communications are carried on an extremely narrow beam
directly through the Earth, there is a very low probability of interception.
• Theoretical results confirm that the Li-Baker detector is photon-signal
limited, not quantum-noise limited-that is, the Standard Quantum Limit is
so low that a properly designed Li-Baker detector can have sufficient
sensitivity to observe HFGWs of amplitude A:::;$ 10- 32 m/m.
• Utilizing the IR-excited Molecules HFGW generator approach and the Li
Baker detector, the theoretical information-transfer rate over 7,000 km of
distance, beamed directly through the Earth, is about 1.9 x 10 6 bits per
second.
• A means of propagating a Frequency Time Standard may be one viable
early low-bandwidth application for HFGW communications.
• HFGW sources on the Earth, the Moon, and Mars may act as reference
standards for interplanetary navigation, with the advantage that they
cannot be shielded or shadowed by planetary masses. Plasma interference
seen at planetary entry would be eliminated, and precise charting of
Lagrangian points would be possible.
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1.0 Introduction
1.1 INTRODUCTION
Of the applications of high-frequency gravitational waves (HFGWs), communication
appears to be the most important and most immediate. Gravitational waves have a
very low cross section for absorption by normal matter, so high-frequency waves could,
in principle, carry significant information content with effectively no absorption unlike
electromagnetic (EM) waves. Multi-channel HFGW communications can be both point
to -point (for example, to deeply submerged submarines) and point-to-multipoint, like
cell phones. HFGWs pass through all ordinary material things without attenuation and
represent the ultimate wireless system. One could communicate directly t hrough t he
Earth from Moscow in Russia to Caracas in Venezuela-without the need for fiber optic
cables, microwave relays, or satellite transponders. Antennas, cables, and phone lines
would be things of the past. A timing standard alone, provided by HFGW stations
around the globe, could result in a multi-billion dollar savings in conventional telecom
systems over ten years, according to the recent analysis of Harper and Stephenson
(2007). The communication and navigation needs of future magneto hydrodynamic
(MHD) aerospace vehicles, such as the MHD aerodyne (www.mhdprospects.com), which
is high in electromagnetic interference, similar to plasma interference seen at reentry,
would be another possible applications area for HFGW communications.
1.2 DEFINITION OF HIGH-FREQUENCY GRAVITATIONAL WAVES
Visualize the luffing of a sail as a sailboat comes about or tacks. The waves in the sail's
fabric are similar in many ways to gravitational waves (GWs), but instead of sailcloth
fabric, gravitational waves move through a "fabric" of space. Einstein called this fabric
the "space-time continuum" in his 1915 work known as General Relativity (GR).
Although his theory is very sophisticated, the concept is relatively simple. This fabric is
four-dimensional: it has the three usual dimensions of space-east-west, north-south,
and up-down -plus the fourth dimension of time. Here is an example: we define a
location on this "fabric" (Einstein, 1916) as 5th Street and Third Avenue on the fourth
floor at 9 AM. No one can see this "fabric," just as no one can see wind, sound, or
gravity. Nevertheless, those elements are real, and so is this "fabric." If one could
generate ripples in this space-time fabric, many applications would become available.
Much like radio waves can be used to transmit information through space, gravitational
waves could be used to perform analogous functions. Gravitational waves are the
subject of extensive current research, which so far has focused on low frequencies.
High-frequency gravitational waves, as defined by physicists Doug lass and Braginsky
(1979), are gravitational waves having frequencies higher than 100 kHz. Low-frequency
gravitational waves (LFGWs), such as those detectable by interferometric GW detectors
(for example, the Laser Interferometer Gravitat ional Observatory, or UGO) are not
applicable to communications due to their very long wavelengths, often thousands of
kilometers in length and, even more importantly, t he inability to generate them
effectively in the laboratory. Furthermore LFGW detectors cannot detect HFGWs
(Shawhan, P. S., 2004).
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2.0 HFGW Communications
Consider the case of a single point-to-point two station fu ll duplex communication
system, as is represented in Figure 1. Such a system is often characterized as a single
data link, and requires two transmitters, one at each end, and two receivers, one at
each end . To avoid self-interference the link in one direction often uses a frequency of
radiation different than the link in the opposite direction.
Full Duplex Communication Link
Using Gravitational Wave Generators and Sensors
Station 1 Station 2
r------------------~ r------------------~
I
GW Generator ' I GW Sensor
'
I
I
I
'' Sianal 1 + Source Noise ,~
I
<01 Xmit 1 I ~
Rcvr 2 (01
-----. I
Additional Link Noise ---~ ►
I
-----.
I
I
I
I
I
I
GW Sensor I
I GW Generator
_, Sianal 2 + Source Noise I
~, '
'
<02 Rcvr 1 r-e+-------Additional_Link
' Noise
I
'' Xmit2 {02
+-- '' '''
+--
''' ',' ___________________
•-------------------· '
Figure 1. Communication Link Block Diagram
If one were to apply the emerging technology of gravitational wave control to such a
link, one wou ld use GW generators for the transmitters on each end, and GW sensors
for the receivers at each end (Stephenson, 2009a). In the example shown in Figure 1,
station 1 would have a GW generator transmitting at a frequency of ro1 and a GW
sensor sensitive to a frequency of CO2, without being sensitive to a frequency of co1.
Likewise, station 2 would have a GW generator transmitting at a frequency of ffi2 and a
GW sensor sensitive to a frequency of ro1 , without being sensitive to a frequency of co2.
This is the minimum functionality required to constitute a communication link. Signal
strengths of the respective GW generators would need to be sufficient to overcome link
loss, coupling losses, and noises sources. Signal to noise considerations and link
budgets are covered in further detail in Section 3.1.
2.1 HFGW GENERATORS (TRANSMITTERS)
2.1.1 HFGW Generator Concepts
Several sources for HFGWs or means for their generation exist. The first generation
means is the same for gravitational waves (GWs) of all frequencies and is based upon
the quadrupole equation first derived by Einstein in 1918. A formulation of the
quadrupole that is easily related to the orbital motion of binary stars or black holes,
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rotating rods, laboratory HFGW generation, and so forth is based upon the "jerk" or
shake of mass (time rate of change of acceleration) and is derived by Baker (2006) as
P = 1.76x1Q-52 (2r.M/6t) 2 W (1)
where Pis the power of the GWs, W; r is the distance between two masses, m; Mis a
change in force, N; over the time interval 6t, s; that is, the jerk or shake of the two
masses, such as the change in centrifugal force vector with time; for example, as
masses move around each other on a circular orbit. Figure 2 describes that situation.
Please recognize, however, that M need NOT be a gravitational force (see Einstein,
1918; Infeld quoted by Weber 1964, p. 97; Grishchuk 1974). Electromagnetic forces
are more than 1035 larger than gravitational forces and should be employed in
laboratory GW generation. As Weber (1964, p. 97) points out: "The non-gravitational
forces play a decisive role in methods for detection and generation of gravitational
waves ... " Equation (1) is also termed "quadrupole formalism" and holds in weak
gravitational fields (well over 100 g's), for speeds of the generator "components" less
than the speed of light and for r less than the GW wavelength. This last restriction may
not really apply. Certainly there would be GW generated for r greater than the GW
wavelength, but the quadrupole formalism might not apply exactly. For very small 6t,
the GW wavelength, AGw = c6t (where c ~ 3x 108 ms-1, the speed of light) is very small
and the GW frequency VGw is high. As a numerical example, r is choosen to be 10 m
(convenient laboratory size, though usually greater than AGw), M = 4x 10 8 N; for
example, the force produced by a large number of piezoelectric resonators and M =
2x 10-10 s; equivalent to about a VGw = 5 GHz jerk or shake frequency so that AGw = 6
cm and P = 2.8x 10-13 W or 0.28 picowatts. Clearly a very small HFGW power is
generated.
GW
GW
A
I
[
A
~~----------8
fct I
___
r
! __ __._f...=Cf"---!Y
I 8
I
l
I I
I
'
GW I
T
GW
Figure 2. Change in Centrifugal Force of Orbiting Masses, dfct, Replaced by Change in Tangential Force,
df,, to Achieve HFGW Radiation
One of the first suggested means for the laboratory generation of HFGWs was the so
called gaser analogous to the laser for light. Simply described (Halpern and Laurent,
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1964), the gaser consists of a long rod of a material and microscopic parts of which can
be excited by a means, such as electromagnetic (EM) radiation, to emit HFGWs. They
utilize linearized theory to treat the interaction of a gravitational field with matter:
"Application is made to the emission ... of gravitons by microscopic systems such as
molecules and nuclei." Grishchuk and Sazhin in early 1974 discussed the emission of
gravitational waves by an electromagnetic cavity. In August of 1974 Chapline, Nuckolls
and Woods suggested the generation of HFGWs by nuclear explosions. In this same
regard Fontana suggested that the problem of efficient generation of HFGWs and pulses
of gravitational radiation might find a reasonably simple solution by employing nuclear
matter (Fontana and Baker, 2006; Fontana and Binder, 2009), especially isomers. A
fissioning isomer not only rotates at extremely high frequency(~ 3.03x10 24 s-1 )
according to the aforementioned references, but is also highly deformed in the first
stages of fission (the nucleus is rotating and made asymmetric "before" fission). Thus
one achieves significant impulsive forces (for example, 3.67x 108 N) acting over
extremely short time spans (for example, 3.3x 10-22 s). Alternatively, a pulsed particle
beam, which could include antimatter, could trigger nuclear reactions and build up a
coherent GW as the particles move through a target mass. The usual difficulty with
HFGWs generated by nuclear reactions is the small dimensions of their nuclear-reaction
volumes-that is, the small moment of inertia and submicroscopic radii of gyration (for
example, 10-16 m) of the nuclear-mass system. Such a difficulty is overcome by utilizing
small clusters of nuclear material, whose nuclear reactions are in synchronization; for
example, through the use of a computer controlled logic system. Such nuclear
energized HFGW generators are currently very theoretical. Braginsky and Rudenko
(1978) discussed the generation of gravitational waves in the laboratory and proposed
a means utilizing small particles In 1981 Romero and Dehnen analyzed the generation
of gravitational radiation in the laboratory also utilizing a linear array of piezoelectric
crystals that will be analyzed in more detail in Section 2.1.3. In 1988 Pinto and Rotoli
presented a paper on the laboratory generation of gravitational waves at the Italian
Conference on General Relativity and Gravitational Physics. Another Italian, Giorgio
Fontana (1998), suggested that the possibil ity of emission of high frequency
gravitational radiation from junction between d-wave and s-wave superconductors.
Kraus (1991) proposed that gravitational-wave communication might be possible in the
IEEE Antennas & Propagation magazine. At the first HFGW Working Group Conference
at the MITRE Corporation in 2003, Grishchuk analyzed electromagnetic generators and
detectors of gravitational waves. At that same Conference Valentin Rudenko presented
a paper on the optimization of parameters of a coupled generator-receiver for a HFGW
Hertz experiment. At the second HFGW Working Group Conference in Austin, Texas, in
2007, Kolosnitsyn and Rudenko presented another paper on the generation and
detection of the high-frequency gravitational radiation in a strong magnetic field. In
2007, and more recently this year, a new type of HFGW generator/detector and mirror
system based on thin, type I superconducting films was proposed by R. Chiao, S.
Minter, and K. Wegter-McNelly (2007; 2009a,b). Therefore it is evident that a number
of devices for the laboratory generation of HFGWs have been proposed including the
aforementioned gaser (as has been mentioned, was first proposed by Halpren and
Laurent in 1964, some 45 years ago) discussed by Fontana and Baker (2003); as well
as an actual laser generator of HFGWs as discussed by Li and Li (2006). Finally a rather
practical laboratory HFGW generator, which may be appropriate for the initial proof-of
concept test, is one utilizing off-the-shelf components such as magnetron energized
piezoelectric crystals or Film Bulk Acoustic Resonators or FBARs has been analyzed in
Woods and Baker, (2005) and Baker, Woods and Li (2006).
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The figure of merit for a HFGW generator is given explicitly by Baker, Woods and Li
(2006). This Figure of merit can be extended by considering other effects since in the
laboratory the force change could not even approach those of the celestial sources. It
would seem that the magnitude of any laboratory generated GWs could be best
increased (1) by utilizing electromagnetic forces rather than gravitational, (2) by
increasing the distance between the gravitational radiators, (3) by increasing the GW
frequency (that is, reducing ~t) and especially ( 4) by developing a large number of in
phase system elements. This last effect enters as the square of the number of
elements, N , as proved using General Relativity analyses by Dehnen and Romero
Borja's analyses (Romero and Dehnen, 1981; Dehnen and Romero, 2003). Such N2
dependence also may be the key to successful laboratory generation of GWs, especially
HFGWs. In that regard, recent proposal by Woods (Woods and Baker, 2009; Black and
Baker, 2009)) propose the use of infrared-energized atomic nuclei, electrons and or
molecules, which have a very large N, contained in a stack of N waveguide rings
(Patents Pending). The distance between GW radiators may be proportional to the GW
wavelength in that it may have a limit that is less than or equal to a GW wavelength.
The wavelength is inversely proportional to the GW frequency. Thus given some value
for the proportional constant, say unity or the distance between radiators equal to one
GW wavelength, the GW frequency cancels out. As already noted it is important to take
advantage of square of the number of in phase elements for useful laboratory HFGW
generation. If the elements are sliced in one dimension (the dimension along the axis of
HFGW generation) in order to increase the number of elements, then the change in
force per element will be inversely proportional to the number of elements. For
example, if the elements are sliced into one hundred separate pieces, then each piece
will have one hundredth of the force of the unsliced element. Essentially, f = ma and it
is assumed that the acceleration of the element was the same after the split as before.
This result also follows Equation (8), page 17 in Baker, Stephenson and Li (2008b) and
if there were 100 splits of an FBAR, then the power to an individual slice, P and its
mass, m would be both one hundredth of their un-split value and the square root of
their product would again be one hundredth. The frequency of the spl it elements may
be a higher value -- but the attendant increase in GW power proportional to the square
of the higher frequency and the decrease in power due to a smaller distance between
tracks (assuming that the distance between tracks is one GW wavelength, which would
be smaller) would cancel and there would be no net effect on HFGW amplitude. It is
concluded, therefore, that in this particular special situation the amplitude of the
generated HFGWs is proportional to the number of in-phase elements, N (not the
square). In any event a large number of elements for a given HFGW-generator length
can be best realized by reducing the size of the individual elements to submicroscopic
size (as discussed in U. S. Patent Number 6,784,591).
In the case of HFGW generation for communications applications, it is important to
relate the amplitude of a GW, A, with the power, P, or more exactly with the GW flux,
FGw, in wm- 2 . For a viable communications link, the HFGW amplitude, A, must be large
enough to be detected at the HFGW receiver. From Appendix B of Baker, Woods and Li
(2006),
A= 1.28x10-18 ( FGw/VGw) 112 m/m (2)
where A has the dimensionless value of spacetime strain or m/m and VGw is the GW
frequency s-1 . Following the proceeding numerical example we will concentrate the
HFGW on a diffraction -limited area of 4x 10-3 m 2 or 0.004 m 2 for a HFGW flux of
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(2.8x1Q· )/(4x1Q· = 7x10· wm · Thus A= 2x1Q·
13 3
)
11 2
.
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. It is an extremely small
HFGW amplitude, but possibly a detectable signal.
2.1.2 Alternative Approaches
There are several alternative approaches to the laboratory generation of HFGWs
developed over the past 45 years as discussed in the preceding Section 2.1.1. They can
be categorized as EM -cavity generated, nuclear-energy generated, superconductor
generated, laser-impact generated and energized microscopic & submicroscopic-particle
generated HFGWs. Of these categories the last category appears to be the most
promising for early deployment in HFGW communications systems. Furthermore, one
embodiment of that category: the Magnetron-energized FBARs generator, utilizing off
the-shelf equipment, would seem the most useful for proof-of-concept tests. For a
practical, operational commun ications system HFGW generator (transmitter) the strong
dependence of HFGW generator's power on the number of radiating elements, N,
recommends a system utilizing molecular elements as suggested by Braginsky and
Rudenko (1978) or using Infrared (IR)-energized pentane molecules in a stack of
circular waveguides as proposed by Woods and Baker (2009). The Magnetron-energized
FBARs and the IR-energized pentane will be considered in the next-following sections.
2.1 .3 Piezoelectric Approach
Let us consider the l.8x 108 cell-phone film bulk acoustic resonators or FBARs, 10,000
Microwave-Magnetron, proof-of-concept laboratory HFGW generator. Assuming a 10 µm
distance or margin between the 100 µm square conventional FBARs, the overall length
of the laboratory generator will be 110 x (10· m) x (l.8x 10 elements) = 19.8 km. It
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will have a total HFGW power of 0.066 W and for a distance out from the last in-line, in
phase FBAR element of one HFGW wavelength (6 .1 cm) it will have a flux of 3.53 wm· 2 ,
yielding a HFGW amplitude there of A= 4.9x 10- 28 m/m. By the way, the inline set of
FBAR elements also produces a more needlelike radiation pattern of HFGWs so that the
flux and resulting A may even be larger. Although the frequencies may be different
analyses (2003), one can extrapolate approximately from the results of Dehnen and
Romero-Borja's analyses in which the ang le of the needle-like radiation pattern is
inversely proportional to the square root of the product of the distance between the
radiators (the width between FBAR bands or tracks) and N. The distance for the system
discussed here is 6.1 cm and for Dehne n's system 0.00001 m, for a factor of 6,100 and
N differs by (1.8x 108 )/(5x 107 ) = 3.6 for a product of 2.2x 104 and the inverse of the
square root is 6.7xl0· 3 . Using the result from Dehnen's paper (Equation (4.51), page
12) of a needle half angle of 1. 7 degrees we would extrapolate to 0.0115 degrees or
very approximately 2x10·4 radians. Since there is no longer the constraint to the use of
rudimentary off-the-shelf components as there was for the proof-of-concept apparatus,
the specially designed submicroscopic elements can be manipulated. First, they will be
staggered into two bands or tracks of 100 rows each or 110 x 100 µm = 1.1 cm wide
bands of FBARs a wavelength or 6.1 cm apart. The rows will be staggered by displacing
adjacent rows in the bands by 1.1 µm. Thus the overall length will be reduced to 198
m. Second, the 100 µm length of each FBAR element can be sl iced, along the direction
of travel of the HFGW build up, into one-hundred 1 µm wide slices (exhibiting 0.1 µm
margins). The staggered row displacements are now reduced to 11 nm. The overall
length will be reduced to about 198 cm. Concentrating the 10 MW power to each of
these 1.1 cm wide bands may prove to be difficult. Thus, as an example, the
continuous-wave Magnetrons will be replaced by a pulsed microwave source having
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one-microsecond-long pulses one second apart. The required average power for each
FBAR band will now be 10 W. As a practical nanotechnology limit, the slice width can be
reduced by two orders of magnitude to 10 nm. This would also require that the row
displacements would be 110 pm (we are now into atomic if not sub-atomic dimensional
changes). The overall length could be reduced to about 2 cm or the ampl itude of the
HFGWs could be increased to A= 4.9x10-26 . In this latter case the average energizing
microwave power applied to each band wou ld need to be increased to 1 kW. A preferred
compromise in this apparent nano-technology limit might be to reduce the HFGWs
generator's length to about 20 cm and increase the HFGW amplitude A to 4x 10-27 m/m.
The complementary approach to optimizing a practical HFGW generator is to increase
the force produced by each element without increasing the required power (that is,
increasing element efficiency). This was initially done using the modern light-weight
piezoelectric FBARs rather than the heavy 10-gram crystals considered by Dehnen and
Romero-Borja that were of 1981 vintage. Special designs of FBAR-like elements for
optimum force-generation efficiency will improve the HFGW generator performance
beyond that for the usual cell-phone FBAR designs. Another approach to element design
is to utilize nano-size lasers whose targets are the force-generating elements (Li and Li,
2006). Utilization of myriads of nano-size lasers would generate high-frequency HFGW
pulses as noted in U. S. Patent Number 6,784,591. Thus there are a number of
opportunities to enhance HFGW generation performance, utilizing special element
designs, either by reducing the generator size or increasing the generated HFGW
ampl itude or both.
2.1.4 Infrared-Excited Molecules Approach
The very theoretical IR-generated HFGWs suggested by Woods and Baker (2009) have
significant promise. If one has a standing wave in a waveguide ring and excites it
properly, then one will have a GW source at its center, as shown in Figure 3. The GW
flux produced at its center is proportional to the n submicroscopic particle pairs (in this
case pentane molecule pairs) in each r ing. There is no n 2 bui ldup, but there is an n
buildup. If one has a stack of N plates of rings, which are excited in sequence at light
speed as a generated, growing as a GW passes by, then one has an nN2 buildup in GW
flux.
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IR monomode waveguide
formed by active material
High power IR source
Position of
focused GW
generated
Figure 3. Circular Resonator Geometry Using Infrared Excitation
Analogous to Figure 2, we see in Figure 4 the radiation pattern for a pair of orbiting
masses.
GW
I
.1
'
GW
Figure 4. Radiation Pattern Calculated by Landau and Lifshitz (1975)
Next consider a number N of such orbit planes stacked one on top of another with the
gravitational-wave (GW) radiation growing flux (Wm-2) proportional to N2 as the GW
moves up the axis of the N orbit planes as in Figure 5.
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The stack of orbital planes are no replaced by a stack of N plates each containing n
molecules in each waveguide ring as exhibited in Figure 6. Now there is a HFGW wave
moving up the axis of the rings (or normal to the waveguide plates) and increasing in
strength according to the product nN2 .
GW GW
Figure 5. GW Flux Growth Analogous to Stack of N Figure 6. Stack of Circular-Wave-Guide Plates
Orbital Planes With Typical Molecule Jerks, df's
One should consider the IR rings in more detail. As calculated, the IR wavelength is
about 2.Sx10· 6 m. The IR waveguide has a cross-sectional area radius of A/4 in order
for it to be a monomode (lowest order mode) so that the phase doesn't change across
the waveguide. Thus the cross-sectional area of each IR ring is n x (2.Sx10·6 m/4 ) 2 =
l.23x 10- 12 m 2 and its diameter is 1.25xl0- 6 m. The volume of each 100-m radius nano
size toroidal ring is 2n x (100) x (1.23x 10-12 ) = 7. 7x 10-12 m 3 . The mass density of
pentane is divided by its molecular mass and that gives the density of jerkable masses
of 6.3x10 28 m· 3 . Thus the number of jerkable mass pairs, n, in a 100 m radius circular
wave guide 2n = (6.3 xl0 28 ) x ( 7.7x 10-12 ) = 4.85x10 17 submicroscopic "particles" or
potentially jerkable masses or n = 2.45 x 10 17 mass pairs. According to Table 1 of
Woods and Baker (2009) for pentane A= 4.62x 10- 16 W. Thus the flux at one meter
distance for all of the mass pairs in a single ring from Equation (8) of Black and Baker
(2009) is n x (0.01146) x P; = 1.29 wm- 2 • It should be recognized that the axes of the
opposite pentane molecules jerk (in response to the EM wave) may not be anti-parallel
and tangential to the circular waveguides. On the other hand, the radiation pattern for
the HFGW exhibits some omni-directional form, as shown in Figure 7, so significant
HFGW radiation will be directed along the axis of the stack of circular waveguides
(normal to the plates) and the HFGW will build up.
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G
Figure 7. Omni-Directional Nature of the HFGW Radiation Pattern
Next consider a more convenient laboratory arrangement for the rings. The ring radius
is reduced to one meter, but set up 100 rings, concentrically (side by side concentric
rings in the same plane or plate) with an average radius of the one meter. The reduced
radius drops the P i by (100) 2 to 4.62x 10-20 , but because of the 100 concentric rings the
n = 4.85x10 17/2 remains the same. Thus the flux for a single "plate" of concentric rings
is only reduced by 10 4 to 1.29x 10- 4 Wm· 2 . Now stack some 10 6 of these 1.25x 10-6 m
thick plates on top of one another. Thus a 1.25 m high stack, barrel or cylinder as
described in Baker (2001) is created. In this case, as shown in Figure 6, N = 106 and
the N2 law can be applied. Thus a HFGW total flux of 1.29x 10 8 wm -2 in a very narrow
beam will be generated by the stack. Of course (as pointed out in Woods and Baker
(2009)) caution needs to be taken on how much power is fed to each ring. One possible
arrangement is to feed the output of one ring to the input of the next. The problem
here is that the source won't have a long enough coherence length, even if the
attenuation of the IR doesn't kill the power after a ring or two. To avoid this, from one
source the available energizing power could be divided equally between all the rings
and fed to them up the stack or cylinder at the speed of light. The practical difficulties
would be how to drive them all in correct phase, but it is a challenge for future research
in the IR-ring approach.
For an operational so,oooA infrared (IR), 12.5 meter long, 10-meter radius (10 4
concentric rings per plate so Pi = 1.29x 10 2 wm- 2 and 107 plates) cylindrical HFGW
generator (Woods and Baker, 2009), the flux at a one-meter distance from the
generator is, according to Table 1 of Black and Baker (2009) for N = 107 , (1.146x 10 12 )
x (1.29x 10 2 ) = 1.48x 10 14 wm·2 (very large, but with a very narrow 2.3x 10-4 radian
half-power-point needle beam). The required generator power can be reduced by
utilizing pulsed HFGWs. Suppose that the distance between the generating or
transmitting device and the detecting or receiving device is a little more than an Earth's
equatorial radius, or~ 7x 106 meters. At this distance, 7,000 km, the flux of the
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received signal, S, is (1.48x10 14 )/(7x10 6 ) 2 = 3 wm ·2 , more than adequate for an
effective communication system.
With this configuration, the width of the needle-like, narrow HFGW beam at the receive
end is (2.3x 10·4 ) x (7x 106 ) = 1.6 km, and multiple HFGW carrier frequencies can be
used, so the signal is very difficult to intercept, and is therefore useful as a low
probability-of-intercept (LPI) signa l, even with widespread adoption of the technology.
From Equation (2) the amplitude A of the HFGW at 7,000 km with the HFGW frequency
(twice the IR frequency of VGw = 1.2x 10 14 s·1 ) given by: A = 1.28x 10-18 (S/vGw )V2 =
1.8x 10-32 (in dimensionless units or m/m), which would be detectable by the currently
designed Li-Baker HFGW detector. Since the exact frequency and phase of the HFGW
signal is known (unlike the stochastic re lic HFGWs, for which the Li-Baker detector was
designed), a much more sensitive, optimized HFGW detector will likely be developed.
As shown in Figure 8, from Grishchuk (2008), there will be negligible relic HFGW noise
at the IR HFGW generator's frequency of 1.2x 10 14 s· 1 and no other cosmic sources at
these frequencies are currently hypothesized. Prior to the proof-of-concept test, one
can assume a noise figure at the Li -Baker detector of 10·8 Wm· 2 .
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2.2 HFGW DETECTORS (RECEIVERS)
2.2.1 Alternative Approaches
One of the first suggested means for the detection of HFGWs concerns electromagnetic
detectors (Braginsky, et al. 1974 and Braginsky and Rudenko, V, 1978). Then
Pegoraro, et al. (1978) suggested the use of tuned resonant chamber HFGW detectors.
Rudenko and Sazhin in 1980 proposed a Laser interferometer as a gravitational wave
detector (somewhat similar to the current Japanese approach). In 1995 Tobar
characterized multi-mode resonant-mass HFGW detectors and three years later in 1998
(Ottaway, et al.) proposed a compact injection-locked Nd :YAG laser for HFGW
detection. And in 1999 Tobar suggested, microwave parametric transducers for the
next generation of resonant-mass gravitational wave HFGW detectors.
In the past few years, HFGW detectors have been fabricated at Birmingham University,
Eng land, INFN Genoa, Italy and in Japan. These types of detectors may be promising
for the detection of the HFGWs in the GHz band (MHz band for the Japanese) in the
future, but currently, their sensitivities are orders of magnitude less than what is
required for the detection of high-frequency re lic gravitational waves (HFRGWs) from
the big bang. Such a detection capability is to be expected, utilizing the Li- Baker
detector (please see Append ix B for Plans & Specifications development). Nevertheless,
all four candidate detectors; plus, possibly, the use of superconductors (Li and Baker,
2007) should be analyzed for possible military applications. The Li-Baker HFGW
detector was invented by R. M L Baker, Jr. of Transportation Sciences Corporation,
Ca lifornia and patented in P. R. China (Baker, 2001). Based upon the theory of Li, Tang
and Zhao (1992) termed the Li-effect, the detect or was proposed by Baker during the
period 1999-2000, a patent for it was filed in 2001, subsequently granted (Baker,
2001), and preliminary details were pub lished later by Baker, Stephenson and Li
(2008a). This detector was conceived to be sensitive to relic HFGWs (HFRGWs) having
amplitudes as sma ll as 10- 32 to 10- 30 .
The Birmingham University HFGW detector measures cha nges in the polarization state
of a microwave beam (indicating the presence of a GW) moving in a waveguide about
one meter across (see Figure 9). Also see Cruise (2000), Ingley and Cruise (2001) and
Cruise and Ingley (2005). It is expected to be sensitive to HFGWs having spacetime
strai ns of A ~ 2 x 10-13 (Hz)·½, where Hz is the GW frequency, and as usual A is a
measure of the strain or fractiona l deformation in the spacetime continuum
(dimension less m/m).
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Figure 9. Birmingham University HFGW Detector
The INFN Genoa HFGW resonant antenna consists of two coupled, superconducting,
spherical, harmonic oscillators a few centimeters in diameter (see Figure 10). The
oscillators are designed to have (when uncoupled) almost equal resonant frequencies.
In theory, the system is expected to have a sensitivity to HFGWs with size (fractional
deformations) of about ~ 2x 10·17 (Hz) ·½ with an expectation to reach a sensitivity of~
2x 10-20 (Hz)·½ (Bernard, Gemme, Parodi, and Picasso (2001); Chincarini and Gemme.
(2003)). As of this date, however, there is no further development of the INFN Genoa
HFGW detector.
Figure 10. INFN Genoa HFGW Detector
The Kawamura 100 MHz HFGW detector has been built by the Astronomical
Observatory of Japan. It consists of two synchronous interferometers exhibiting an
arms length of 75 cm. Please see Figure 11. Its sensitivity is now about 10-16 (Hz)·½
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According to Cruise (2008) of Birmingham University its frequency is limited to 100 MHz
and at higher frequencies its sensitivity diminishes. In the case of the Infrared-excited
molecules approach, on might employ a variant of the Robinson Gravitational Wave
Background Telescope for the receiver or detector (Yoon, et al., 2006). It is a
bolometric large angular scale Cosmic Microwave Background (CMB) polarimeter, but
might possibly be modifiable for direct HFGW detection.
Development of 100MHz GW detectors
at N ational Astronomical Observ atory of
Japan
Two synchronous recycling
interferometers were built!
S y nchronous recy cling Interferometer (Concept: Drever 1983)
Figure 11. The National Astronomical Observatory of Japan 100 MHz Detector
2.2.2 Concept (Li-Effect)
The Li-Effect was first published in 1992 and subsequently, some nine peer-reviewed
papers have been published concerning it including a capstone paper, Li, et al. (2008)
included as Appendix C. The Li-Effect is very different from the classical (inverse)
Gertsenshtein-Effect. With the Li-Effect, a gravitational wave transfers energy to a
separately generated electromagnetic (EM) wave in the presence of a static magnetic
field. That EM wave has the same frequency as the GW and moves in the same
direction. This is the "synchro-resonance condition," in which the EM and GW waves are
synchronized (move in the same direction and have the same frequency) and is unlike
the Gertsenshtein- Effect.
The result of the intersection of the parallel and superimposed EM and GW beams,
according to the Li-Effect, is new EM photons moving off in a direction perpendicular to
the beams and the magnetic field directions. Thus, these new photons occupy a
separate reg ion of space (see Figure 12) that can be made essentially noise-free and
the synchro-resonance EM beam itself (in this case a Gaussian beam) is not sensed
there, so it does not interfere with detection of the photons. This Li-Effect was utilized
by Baker (2001) in the design of the Li-Baker HFGW detector and Chinese Patent
(Baker, 2000) of a device to detect HFGWs, the innovative Li-Baker HFGW Detector.
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:z
Signal (PPF) and Noise (BPF)
have very different physical behavior
PPF > BPF at this end of x-axis
Very Noisy
(BPF)
/
Poynting Vector or
Detection
Photons (PP )
/
/
-✓-----------► Y S
Poynting Vector or
Detection
otons (P F)
..
X
Signal (PPF) and Noise (BP F)
have very different physical behavior
PPF > BPF at this end of x-axis
GW&E
Synchro-Resonant
Figure 12. Detection Photons Sent to Locations That are Less Affected by Noise
The synchro-resonance solution of Einstein's field equations [Li et al. (2008), pp. 411 to
413] is radically different from the Gertsenshtein (1962) effect. The newer Li-Effect
solution utilizes a coupling between EM and gravitational waves (Li, Tang and Zhao,
1992) t hat arises according to the theory of relativity. And a strong static magnetic field
in the y-direction, B, is superimposed upon a GW propagating in the z-direction, as in
the inverse Gertsenshtein effect. However, with the Li-Effect, there is an additional
focused microwave beam ("Gaussian beam") at t he expected frequency, phase and
bandwidth of the HFGWs in the same direction (z) as the GW (as shown in Figure 12).
Unlike the Gertsenshtein effect, a first-order perturbative photon flux (PPF), comprising
the detection photons, will be generated in the x-d irection. Since there is a 90 degree
shift in direction, there is little crosstalk between the PPF and the superimposed EM
wave (Gaussian beam), so the PPF signal can be isolated and distinguished from the
effects of the Gaussian beam, enabling detection of the GW.
Here's how it works:
The perturbative photon flux (PPF), which signals t he detection of a passing
gravitational wave (GW), is generated when the two waves (EM and GW) have the
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same frequency, direction and phase. This situation is termed "synchro-resonance."
These PPF detection photons a are generated as the EM wave propagates along its z
axis path, which is also the path of the GWs, as shown in Figure 12.
The magnetic field is in the y-direction. According to the Li-Effect, the PPF detection
photon flux (also called the "Poynting Vector") moves out along the x-axis in both
directions.
The signal (the PPF) and the noise, or background photon flux (BPF) from the Gaussian
beam have very different physical behaviors. The BPF (background noise photons) are
from the synchro-resonant EM Gaussian beam and move in the z-direction, whereas the
PPF (signal photons) move out in the x-direction along the x-axis.
The PPF signal can be intercepted by electromagnetic-interference-shielded microwave
receivers located on the x-axis (isolated from the synchro-resonance Gaussian EM field,
which is along the z-axis). In addition, isolation is further improved by cooling the
microwave receiver apparatus to greatly reduce thermal noise background (Baker,
Stephenson and Li, 2008a).
The resultant efficiency of detection of HFGWs is very much greater than from the
inverse Gertsenshtein effect, which has been exploited in some previously proposed
HFGW detectors and found to have insufficient sensitivity to HFGWs (Eardley, et al.,
2008). The amplitude of the PPF has space accumulation dependence-that is, it is
proportional to the length of the wave overlap . This is because the GWs (gravitons) and
EM waves (photons) have identical propagation velocities, so that the two waves
overlap synchronously and coherently throughout and their interaction is cumulative
(Boccaletti et al., 1970; Delogi and Mickelson, 1977). This is the synchro-resonant
condition or Li-effect. This means that for maximum signal, the interaction overlap
coupling must be as long as possible . It should be noted that the identification of this
coupling or Li-effect, upon which the Li-Baker HFGW detector is based, is not so new
that it is untested in the literature. At least nine peer-reviewed research publications
concerning the theory have appeared following Li, Tang and Zhao (1992), including
those by Li and Tang (1997), Li et al. (2000), Li, Tang and Sh i (2003), Li and Yang
(2004), Li and Li (2006), Li and Baker (2007), Li, Baker and Fang (2007), Baker,
Stephenson and Li (2008a), and Li et al. (2008).
2.2.3 Quantum Back-Action Limit
The Standard Quantum Limit (SQL) will be introduced and reviewed in this section
(Stephenson, 2009b), and design of the Li-Baker HFGW Detection System will also be
reviewed to understand how the SQL might limit the sensitivity of this new type of GW
detector.
Review of the Standard Quantum Limit
The Standard Quantum Lim it (SQL) is often defined as "The limit on measurement
accuracy at quantum scales due to back-action effects." But what is "back-action"? (See
Kippenberg and Vahala, 2008.) From Clerk (2008) the Heisenberg Uncertainty Principle
is
(&') X (Lip) > fl/2 (3)
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where L1x is the position uncertainty, LJp is the momentum uncertainty, and n is
Planck's reduced constant. Thus measuring x disturbs p, which in turn disturbs future
measurements of x
Llx(dt) = Llx(O) + dt[L1p(O)/m] (4)
where Llx(O) is the initial position uncertainty is, Llp(O) is the initial momentum
uncertainty, dt is the time of the future measurement, and m is the mass of the system
under measurement. E/c2 may be substituted for mass in an energy only system. This
is depicted in Figure 13.
To summarize, the quantum effects of measurements on future measurements is
quantum back action. Therefore the Standard Quantum Limit defines the lower
sensitivity limit for all measurement instruments, including gravitational-wave
detectors, according to the Heisenberg uncertainty principle. Detectors cannot avoid
quantum back action, however the use of higher energies in the detection process can
change the relative scale and impact of back action, and the use of squeezed states can
shift the relative distribution of back action into states not involved in measurement.
TIME t= 0 TIME t= dt
Quantum Back Action:
x dt) measurement affected
l1Y, earlier x(O) measurement
"A---+----,'• :
I
I \
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I I
ox dt) ---.: ~I I
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which drives up Ap(O) Therefore ApjO) drives up Ax(£1t)
Figure 13. Quantum Back Action as a Mechanism for Creating the Standard Quantum Limit
Calculating the Standard Quantum Lim it (SOU
A method for calculating the Standard Quantum Limit (SQL) is introduced in this
section. The calculation of coherent versus stochastic SQL is compared and contrasted.
Important terms of the SQL calculation are described, including the impact of contained
energy levels within the detector on SQL, and the sources of Quality Factor and its
effect on SQL. Calculating the Standard Quantum Limit (SQL)
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Coherent Versus Stochastic SOL
The question under consideration in this paper is whether or not the Li-Baker detector,
Figure 14, is quantum-limited when detecting relic HFGW. In other words, does the
standard quantum limit (SQL) interfere with the sensitivity of the Li-Baker detector
design? The answer will be negative if the SQL is less than 10- 32 m/m. Grishchuk (1977,
2007) has calculated the SQL for GW detectors in general, which for a coherent GW is
hdet = (1/Q)(nwJE/ 12 (5)
and for a stochastic GW is:
(6)
where hdet is the metric (strain) detection limit in m/m, w is the frequency of sensed
gravitational waves (typically around 10 GHz in the Li-Baker detector), Eis the effective
energy contained within the detector cavity summed over the detection averaging time,
and Q is the quality factor or selectivity of the signal over noise.
The SQL depends on the values of these parameters. For the remainder of th is paper,
we will consider the SQL of only the stochastic signal detection case. In the following
subsections the best possible value of the SQL using current technology will be
estimated to determine the fundamental limitations of the Li-Baker detector as now
envisioned.
Impact of Contained Energy Levels on SOL
First attempt to estimate a realistic best case for the energy contained within the
detection process, E. Typically it is expected that for a refrigerated microwave resonant
cavity the best possible electrical quality factor will be around 2nx10 5 . Assuming a "best
efforts" value of 1000 W for the power of the Gaussian beam in a laboratory
installation, the effective tota l RF energy stored in the microwave resonant cavity of the
Li-Baker detector, summed over the system averaging time, is estimated to be given by
(Grishchuk, 2007):
ERF = (10 3 W) x (1000s) x (21tx10 5/21t) = 10 11 ] (7)
over a typical 1000 s averaging time. Both the Li-Baker detector and a detector using
the Gertsenshtein effect use a large static magnetic field B. For the present suggested
outline design for the Li-Baker detector, the nominal value of B = 3 T, so that the
magnetic energy density is given by
(8)
The interaction volume in a practical laboratory-based detector is likely to be a
maximum of around 1 m 3 • So, the effective total stored energy from the Gaussian
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beam is much greater than the stored magnetic field energy, and it follows that E::; ERF
= 10 11 J to a reasonable approximation.
Sources of Quality Factor and Effect on SOL
To calculate the SQL, hdet, we also need the value of the detector quality factor Q (not
the same as the cavity quality factor). Anything that concentrates or enhances the
signal preferentially over noise, in any measurement dimension, can be considered a
contributor to the quality factor Q. The quality factor can therefore be understood as
the "signal selectivity" in each dimension, so that
Qtot = ( Qspatial) (Qt) = QrQsolid angle Qt . (9)
The temporal quality factor in the Li-Baker detector arises from averaging the signal
over time, so that at 10 GHz, Qt= nt;nt = (10 x109 Hz) x 1000s = 10 13 .
There is a contribution to Q arising from the fractal membranes that focus and
concentrate the signal photon energy - but not the background photons - along the
radial dimension. The radial selectivity arising from the general relativity solution, in
conjunction with fractal membranes, is calculated by Li et al. (2008). Their table III
gives Qr= SNRrr=J7cmJ/SNRrr=J.scmJ = 3.4x10 21 .
This is mostly due to the effective Q contribution arising from the synchro-resonance
solution to the Einstein field equations that limit the PPF signal to a radiation pattern in
certain directions, whereas noise is distributed uniformly. By utilizing directional
antennas, the Li-Baker detector can capitalize upon this gain due to the focusing power
of fractal membranes as a contribution to Q in angular space as well. This is calculated
in detail, octant by octant, by Li et al. (2008). Page 24 of Li et al. summarizes this in
terms of angular concentration onto the detector. A non-directional antenna
corresponds roughly to solid angle 21r steradians (one hemisphere), so that the effective
antenna gain is estimated as (Qsolidangle) = 2n sr/10-4 sr = 6.3x104 . Therefore, the
predicted maximum quality factor will be Qtotal = QrQsolidang1eQt = 2.1 x10 39 . This finally
gives the Standard Quantum Limit (SQL) for stochastic GW detection at 10 GHz:
hdet = (1/Q) 11 2cncv/E) 112 = 1.Sxl0- 37 m/m . (10)
Comparison of SOL With Predicted Sensitivity
As noted in the previous section, hdet = 1.Sxl0- 37 m/m represents the lowest possible
GW amplitude detectable by each RF receiver in the Li-Baker HFGW detector, limited by
quantum back-action. An additional (1/ ✓ 2) factor applies if the separate outputs from
the two RF receivers are averaged, rather than used independently for false alarm
reduction, resulting in a minimum hdet = 1.2x10- 37 . Since the predicted best sensitivity
of the Li-Baker detector in its currently proposed configuration is A = 10- 32 m/m, these
results confirm that the Li-Baker Detector is photon-signal limited, not quantum noise
limited; that is, the Standard Quantum Limit is so low that a properly designed Li-Baker
detector can have sufficient sensitivity to observe HFRGW of amplitude A ~ 10-32 m/m.
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2.2.4 Li-Baker HFGW Detector
The detector, shown in Figure 14, has five major components:
1. A Gaussian (focused, with minimal side lobes) microwave beam (GB) is aimed along
the +z-axis at the same frequency as the intended HFGW signa l to be detected (Yariv,
1975), typically in the GHz band, and also aligned in the same direction as the HFGW to
be detected. The microwave transmitter's horn antenna is not shown, but would be
located on the -z-axis.
2. A static magnetic field B, generated by two powerful magnets, typically using
powerful superconductor magnets such as those found in a conventional MRI medical
body scanner, is directed along the y-axis.
3. Two paraboloid-shaped reflectors, which are formed from "fractal membranes" (Wen
eta/., 2002; Zhou eta/., 2003; Hou eta/., 2005), are located in the y-z pla ne at the
origin of the coordinate system to aim and focus the detection photons at diffraction
limited spot antennas connected to two microwave receivers. These reflectors, shown in
planer form in Figure 15, are segmented (similar to a Fresnel lens) and located back-to
back in the y-z plane. They are thin enough (less t han a centimeter thick in the x
direction) to not block the z-directed Gaussian beam. These microwave reflectors reflect
the x-directed detection photons (PPF} and reject the z-directed Gaussian-beam
photons, which move parallel to the surface of the reflectors in the y-z plane.
4. High-sensitivity sh ielded microwave receivers are located at each end of the x-axis
each about one meter distant from the origin.
5. Interior noise from thermal photon generation is elim inated by cooling the Li-Baker
detection apparatus to below ~ 48 mK (0.048 Kelvin). Thus there are effectively no
thermal photons at 10 GHz. Noise from the interior background photon flux (BPF) from
the EM Gaussian beam is reduced to a negligible level by moving the receivers out to
the side about a meter away from the EM beam and by a series of superconductor or
microwave absorbent baffles to "shade" the receivers. Stray EM resulting from
scattering of particulate matter near the apparatus and possible dielectric dissipation
can be effectively suppressed by evacuating the apparatus to about 7.5x10-7 Torr (a
rather high vacuum). External noise is eliminated by the use of a steel and titanium
cryogenic containment vessel surrounding the low-temperature Li-Baker detection
apparatus.
In summary, several different HFGW receivers can be utilized for communication; but
the proposed Li-Baker detector (plans & specification development in Append ix B)
shows the most promise (detailed underlying concept is derived in the paper included
as Appendix C).
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z
Stainless Steel & Titanium Vacuum /
Cryogenic Containment Vesse l and
Faraday Cage (7 .5(10)A -7 Torr, <480m K)
10 GHz, 10W microwave transmitter
focused at fractal membrane
Sensitivity to HFGW:
A = 10·32 m / m
Figure 14. Schematic of Ultra-Sensitive HFGW Detector
Figure 15. Fractal Membrane Component of Li-Baker Detector Exhibited in Planar Form
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3.0 Operational Concerns
3.1 LINK BUDGET
3.1 . 1 Signal-to-Noise Ratio
Signal-to-noise ratio (SNR) is an im portant figure of merit in communication systems
because it is an indicator of whether or not a transmitted signal will be useful upon
arrive at its destination, the receiver. Without processing gain an SNR > 1 will be
required to maintain a link budget. On the transm itter's end, the signal to noise is
determined by the useful signal that is produced by the transmitter after it is already in
its transm ission mode, such as the GW power at the output of the GW generator
antenna, divided by the RSS (Root Sum Square) of the uncorrelated noise sources
referred to the same spot in the signal chain-that is, output referred noise equivalent
power (NEP). This signal to noise ratio is represented by the left hand column in Figure
16.
The components of the transmitter's noise equivalent power may be sorted by the
source of the noise. First, before the signal is converted to GW it is in the rea lm of EM
or photon radiation. Photons themselves make noise, and this component goes as the
square root of the total number of photons. Then there is thermal noise-that is, the
photons generated by blackbody radiation of the transmitter components themselves.
Other electron ic and semiconductor components provid ing the source signal generate
their own photon noise due to carrier activity. All these noise sources are carried along
with the original EM signal and may be converted just as faithfully as if they were
signals should they fall within the transmission bandwidth. All of this is just for the EM
noise component.
The generation process itself may also be a source of noise, and will vary widely
depending upon the generator method used. For example, the generation process noise
created in the GASER would be significantly different than that created in a tuned
resonant EM toroid cavity. Th is of course would be an important consideration in
selecting a generator type.
Finally, it is expected that there are a variety of GW noise sources. Background sources
from space are predicted, in low levels, across the entire frequency spectrum. Also, in a
GW generator situation, pa rasitic vibrations may also have quadrupole moments, such
as the walls of a generation cavity for instance, or an unwanted vibration within a slab
of SC, and these could also generate GW noise.
Then there is link loss to contend with. While it is expected that the attenuation of GW
due to absorption and scatter will be quite low, geometry alone will dictate that a
spherically uniform radiating source will fall off as 1/R2 . This link loss will affect both the
transmitted signal and the transmitted noise.
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Signal to noise ratios (SNR's) at the transmitter and at the receiver
must be calculated to support a communications link design.
Predicted SNR Predicted SNR
Components at Link Components at
the Transmitter Loss the Receiver
------
GW
r
Signal
GW
Sourc
Noise
Xmit
Signal
1/R2
Loss
GW Antenna
& Receiver
Noise
Noise
i EM to GW/'-,--------- - -
conversion \ EM Receiver - -.....i---- - - - - - - 1~
GW to EM
Conversion
EM Source
Noise Noise Noise
Noise
Figure 16. Conceptual SNR Fill Factors: Signal and Noise Components
In the receiver all these same noise sources are duplicated in reverse, as shown on the
right had side of Figure 16. Referring power now to the input, there will be a received
power, and the created by the receiver that was not created at the transmitter, also GW
to EM conversion noise, and EM receiver noise of the same types as received
propagated transm it noise. Added to this will be GW noise admitted or outlined for
transmitters. When all these noise components are referred the input of the receiver,
the total NEP, wh ich is the RSS of all the noise components, must be less than the
signal present at the input of the rece iver to qualify as a useful link.
A few comments are in order regarding the "Q-factor" of the receiver. One way to
increase Q is to narrow bandwidth . However, this has lim ited va lue. At some point,
shrinking the bandwidth will shrink the signal received as quickly as the noise received,
and some receiver noise components remain constant, resulting in a net drop in SNR.
Another way to increase Q is to arbitrary increase sample times of the signal. This
technique will, relatively speaking, shrink receiver end noise components as referred to
the input of the receiver, but it will not have any impact of the noise generated at the
transmitter. Therefore in this case the SNR will approach a constant. However, both of
these approaches for improving sensitivity will have an adverse effect on the
information capacity of the channel, which is important for a communication
application .
3.1.2 Link Budget Considerations
Now consider the signal side of the commun ication cha llenge. The central question is,
How do we close the link? That is, how much signal is necessary at the input of a
commun ication channel to have a usefu l signal at the other end? These questions may
be answered, qualitatively in this case, by considering the terms of the expression in
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Figure 17. In general, an EM signal Si will be used to actuate some type of GW
generation device, and this device will have a conversion efficiency of µeg, which
represents the ratio of power of the EM input signal to power of the GW signal
generated. Not all of the GW generated will be constructively used to radiate in the
desired direction; some of the GW power will be lost to destructive interference, and
some will not be radiated through the antenna aperture. Thus the transmitter will have
a less than unity radiated power efficiency, Rx.
An end-to-end power link budget from the transmitter to the receiver
must be also calculated to support a communications link design.
Transmitter Terms Receiver Terms
A Link
r --.. Loss r ~
isi M~eg 1G~1
I
jI GW
T
GW GW
Rr ---- µge E~ So
I I
I
Input EM/GW Radiated
I
Propagation Receiver
GW/EM
I
Output
Signal Xmit Ant. Losses Antenna
Conversion : Conversion Signal
Power (Transmission Power
Power Efficiency Efficiency Power
Efficiency Factor) Efficiency
Figu re 17. A Block Diagram of a Typical Link Budget
Then there will be propagation link loss, or transmission loss, T, which will be t he
antenna pattern integrated across the solid angle of t he receiver antenna aperture as
seen from t he source. The receiver may have an GW anten na t hat aids in foc using an
otherwise wider solid angle into a narrower detection aperture, and if t his is true, then
there will be an efficiency associated with this receiver antenna, designated here as Rr .
At the receiver's detector, there is another conversion factor to account for, the
conversion efficiency of GW signa l power to EM signa l power µ 9e, which would be much
less than unity, except that the Q factor enters the equation as a component of µ 9 e. Of
course Q may also impact the bandwidth range over which the signa l is collected, Ll to
L2. There is also a hidden integral here which occurs over the sample time, which is
understood.
Al l of these terms will have to be defined and well understood before a communication
system can be successfully designed. Many of these parameters have been predicted
for the components reviewed in prior sections, however, they will not be verified until a
successful experiment can be performed.
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3.2 BANDWIDTH
An estimate of the bandwidth that a HFGW transglobal communication system might
achieve, after a proof-of-concept test is successfully completed, based on a technical
paper by Black and Baker (2009), is as follows: for a 50,000..&. infrared (IR), 12.5 meter
long,10-meter radius {10 4 concentric rings per plate so P; = l.29x 10 2 wm ·2 and 10 7
plates) cylindrical HFGW generator (Woods and Baker, 2009), the flux at a one-meter
distance from the generator is, according to Table 1 for N = 10 7 , (1.146x 10 12 ) x
(1.29x10 2 ) = 1.48x10 14 wm·2 (very large, and with a very narrow 2.3x10-4 radian
half-power point needle beam). The required generator power can be reduced by
utilizing pulsed HFGWs. Suppose that t he distance between the generating or
transmitting device and the detecting or receiving device is a little more than an Earth's
equatorial radius, or~ 7x 10 6 meters. At this distance, 7000 km, the flux of the
received signal, S, is (1.48x10 14)/(7x10 6 ) 2 = 3 wm ·2, more t han adequate for an
effective communication system.
With this configuration, the width of the need le-like, narrow HFGW beam at the receive
end is (2.3x 10·4) x (7x 106 ) = 1.6 km, and multiple HFGW carrier frequencies can be
used, so the signal is very difficult to intercept, and is therefore useful as a low
probability-of-intercept (LPI) signa l, even with widespread adoption of the technology.
From Equation (2), derived in the Appendix of Baker, Stephenson and Li (2008a), the
amplitude A of the HFGW at 7,000 km with the HFGW frequency (twice the IR
frequency of VGw = l.2x 10 14 s· 1) given by: A = l.28x 10- 18 S½/VGw = l.8x 10-32 (in
dimensionless units or m/m), which would be detectable by the currently designed Li
Baker HFGW detector. Since the exact frequency and phase of the HFGW signal is
known (unlike big-bang relic HFGWs, for which the detector was designed), a much
more sensitive, optimized HFGW detector will likely be developed.
Grishchuk (2008) indicates that there will be negligible relic HFGW noise at the IR
HFGW generator's frequency of l.2x 10 14 s· 1 and no other cosmic sources at these
frequencies are currently hypothesized. Prior to the proof-of-concept test, we will
assume a noise figure at the Li-Baker detector of 10·8 wm -2 .
Usin g C.E. Shannon's classical equation (1948), the maximum rate of information
transfer, C, is given by:
C = Blog2(l+S/N) (3A)
C = Blog2(1+3.0/10·8) ~ 1.9x 106 bps (3B)
The bandwidth, B, here is arbitrarily taken to be 100 kHz for a future advanced system .
The necessity for large temporal Q factors, (Qt ~10 9), currently precludes bandwidths
larger than a few Hz for early systems, but the use of coherent signals will represent an
easing of sensitivity requirements significantly, improving bandwidth. Note that it is
based on a single carrier chopping frequency, whereas in practice, one can spread the
information over an entire band of HFGW frequencies.
3.3 FREQUENCY AND TIME STANDARD
The
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