Project Cyclops, A Design... - Department of Earth and Planetary ...

5. COMMUNICATION BY ELECTROMAGNETIC WAVES
Having decided on electromagnetic waves as the only
likely interstellar communication means, we then must
ask: "Is it possible with reasonable power and antenna
sizes to signal over the enormous distances involved?
and: ls there an optimum region in the spectrum?" The
answers to these questions involve the interplay of a
number of factors that determine the performance of a
communication link. In this chapter we discuss these
factors as they relate to systems from radio through
optical
frequencies.
go = X2 (1)
where the last equality applies if the antenna is circular
and of diameter d.
For a uniformly illuminated circular aperture, the
ratio of gain, g, or intensity, I, at an angle 0 off axis to
the gain, go, or intensity,
Io, on axis is
ANTENNA GAIN AND DIRECTIVITY
We shall use the term antenna to mean any coherent
collector or radiator of electromagnetic waves. At
optical frequencies, antennas take the form of lenses or
concave mirrors that focus the received energy from
distant point sources into diffraction-limited spots in an
image plane. The angular dimensions and intensity
distribution of the optical image of a point source bear
the same relation to the wavelength and the telescope objective
diameter that the beam width and pattern of a large
radio antenna bear to its diameter and operating
wavelength. However, because there is no radio counterpart
of photographic film, radio telescopes typically are
built to examine only one resolvable direction at a time
rather than to form an extended image.
A universal antenna theorem states that the effective
area an isotropic radiator is _,2/4_r, and that this is the
effective area of any antenna averaged over all directions
(ref. 1). An antenna whose area is greater than
3,214rr in some direction must have an effective area less
than ;_2/41r in other direciions, and is therefore directive.
For a uniformly illuminated aperture of an area A, the
power gain, go, on axis is the ratio of A to X_]47r, that is,
g=Z= ' 0
go Z°
)1
where J! fs the first order Bessel function. The gain and
intensity fall to one half their on-axis values when
0 = 01/2 = (0.5145 ...)(X/d) so the beamwidth between
half power points is
(2)
X
201/2 = (1.029...)
--
d
radians (3)
THE FREE SPACE TRANSMISSION LAW
Assume a power Pt is radiated isotropicaUy. At
a distance R this power will be uniformly distributed
over a sphere of area 41rR 2. The amount received by an
antenna of area A r is therefore Pr = Pt A/4nR2" If the
transmitting antenna is now made directive, with a
power gain gt in the desired direction, we will have
Pr
Pt
gtAr
47rR2
(4)
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