Defense Intelligence Reference Document High-Frequency Gravitational Wave Communications

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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 ti.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 split 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 = 1.28x 10-18 ( FGw/VGw)½ m/m
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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