Cryptography Reference
In-Depth Information
In a standard collimating telescope the small-diameter beam is defocused by
a negative lens and expands to fill the output lens, which collimates to near
the diffraction limit. We can ensure that 98% of our Gaussian beam passes
through this lens of diameter
D
when 2
W
0
=
0
.
7
D
. This sets the minimum
divergence of our collimated beam to
1
.
D
8
2
θ
=
(9.4)
For instance the typical full divergence for a 125 mm lens illuminated by
650 nm light is thus
∼
10 µ
R
. At the receiver (range
R
)
we intercept a large
Gaussian beam diameter 2
W
=
2
θ
R
; with small-diameter telescope
D
T
we
will collect a fraction
exp
2
D
T
(
D
T
2
W
2
L
g
=
1
−
≈
(9.5)
2
W
)
2
Another source of beam broadening is the atmospheric turbulence. This
causes beam wander and also scintillation. We estimate from our results at
high altitude [10] that scintillation will cause effective beam wander of order
10-40 µ
R
, depending on atmospheric conditions. Looking upwards from a
high altitude ground station, this could be as low as 3-5 µ
R
. Losses due to scat-
tering from aerosols in the atmosphere are low at altitudes greater than 2000 m,
being approximately 0.04-0.06 dB/km in clear weather. Obviously haze and
cloud can increase these values significantly. Experiments at sea level will tend
to have higher aerosol attenuation. Further simulation of atmospheric trans-
mission using programs such as Modtran would improve these estimates.
We summarize the typical losses to be expected in various experimental
scenarios in Table 9.2. For the comparison of systems we assume that satellite
transmitter optics should be small and limit ourselves to 125 mm apertures
where possible. This then gives a 10 µ
R
diffraction spread (assuming light of
around 650 nm wavelength), and we assume that pointing can be achieved
to much better than this accuracy. In particular cases (GEO-to- ground and
teleportation experiments) we allow for larger 300 mm apertures. This gives
a smaller diffraction spread
4 µ
R
(we assume some improvement from ex-
isting classical experiments [14]), which is balanced against greater problems
from pointing errors. The receiver optics need not be pointed to the diffrac-
tion limit as detectors can have a relatively wide field of view (up to 50 µ
R
∼
.
However, space telescopes are still limited in dimension by weight. We limit
our table to space receiver telescopes of aperture 300 mm in diameter. On the
ground, tracking optical telescopes are available up to1mindiameter, while
fixed telescopes up to2mindiameter might be used for ground-to-GEO
systems.
Also included in the table is a next-generation high-altitude experiment
where we might aim for 150 km key exchange using a faint pulse system as
shown in Figure 9.3, Figure 9.4, and Figure 9.5. We also have options for an
up-looking key exchange to LEO satellite Alice and a down-looking system
with a ground Alice. For the entangled-state system we include losses from
both arms and limit the satellite range to 700 km to limit loss. What is clear is
)
