Limitations of Laser Communicators

Some writers use tight-beam laser communicators as a panacea for the problem of secure communications in their science fiction stories. I couldn't help but think that this might not necessarily be so, so I have looked into it a little.

From what I can find a collimated laser beam is the best for communications, as it diverges the least. However, without invoking some sort of technological magic outside of what is currently known of physics, a perfectly collimated beam cannot be created, due to diffraction. Thus all laser beams diverge, at least to some extent.

As a best case, that is one with the least divergence, a perfect laser beam will diverge by a factor of 1.414 (the square root of 2) over a distance given by the Rayleigh Length, which is given by:

rayleigh_length =

π * beam_radius²

laser_wavelength

For a 1 metre diameter laser emitter, this means that beam width as a function of laser wavelength at different distance from the emitter is as shown in the table below.

EM Radiation	Laser Wavelength	Width of Beam at Given Distance (metres)
EM Radiation	Laser Wavelength	100 km	1000 km	10000 km	100000 km	1 Mkm	10 Mkm	100 Mkm	1 Gkm
X-rays (Short)	0.01 nm	1	1	1	1	1	1	3	19
X-rays (Long)	10 nm	1	1	1	3	19	181	1802	18007
UV	100 nm	1	1	3	19	181	1802	18007	180064
Blue Light	400 nm	1	2	8	73	721	7204	72026	720254
Red Light	700 nm	1	2	14	127	1261	12605	126045	1260444
Near IR	0.001 mm	1	3	19	181	1802	18007	180064	1800634
Thermal IR	0.1 mm	19	181	1802	18007	180064	1800634	18006327	180063264
Microwaves	1 cm	1802	18007	180064	1800634	18006327	180063264	1800632633	18006326324

So a short-wavelength x-ray laser communication beam will still be pretty small at a billion kilometres, at perhaps 19 metres in diameter. However, the aiming of such a beam at a moving target from a moving source and keeping it there will be pretty horrendous. It would only take a rotation of the transmitter of 1.1 nanodegrees to shift a point target outside the beam; this is equivalent to tracking a moving target of the thickness of the thickest human hair at a distance of nearly 9470 kilometres. I imagine such accuracy would be do-able, but hard.

A UV laser, on the other hand, would be some 180 metres across before it gets to a million kilometres out, so it is quite likely that at least some of the beam will go past the target and so be detectable behind it. On the other hand it requires a rotation of the transmitter of some 10 microdegrees to shift a point target outside the beam; this is equivalent to tracking something of the thickness of the thickest human hair at a distance of some 995 metres.

The further away you go and the shorter the beam wavelength the more this tracking problem grows.

Making your laser beam have a smaller diameter only gets you so much as the divergence quadruples for each halving of the beam diameter, while doubling the beam wavelength only halves the divergence. Thus shorter wavelength, large diameter transmitters would be the best for a collimated beam, but transmitting wide laser beams through space obviously has problems of its own in terms of detectability.

I guess ideally what you want would be a large diameter laser emitter on your transmitting ship to allow a finely collimated beam to be transmitted to the sensor drone or whatever in the target area (though of course this has the problem that is is a large diameter beam and so is detectable because of this). The drone or whatever that is transmitting back, if it has to worry less about being detected (for example if it is transmitting away from the enemy), can get away with a smaller diameter, and so a more diverging beam.

Send any comments to me at tony {dot} website {at} clockworksky {dot} net.

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