[Expectant_Philosopher (OP)]

Can we use lasers to heat a specific focal area of the atmosphere to create artificial atmospheric ducting or lensing, to improve the transmission of radio communications?  This is basically attempting to harness what we see in nature as mirages.  It has been shown that a radio signal entering a natural atmospheric duct can travel much further, even over the horizon, with less attenuation of the signal.  What if instead of having a series of microwave towers set in line of sight corridors to transmit, we had one tower and a satellite based laser system that would create optimal ducting to direct the signal to the distant end, even over the horizon?  This would not be a form of satellite relay, it would avoid  costly signal delays found in satellite communications keeping the signal within the atmosphere close to the surface of the planet.

[RD]

What about reflection ... https://en.wikipedia.org/wiki/Skywave

[evan_au]

Radio reflection from the ionosphere is caused by the upper atmosphere being ionised by ultraviolet and X-Ray radiation from the Sun during the day (plus some cosmic ray activity which continues during the night).

A satellite would need to produce a similar flux to ionise the atmosphere. The Sun produces most power at visible and infra-red wavelengths, but this still represents a considerable amount of power to inject into the atmosphere from a satellite. Any human-injected power would be overwhelmed by a solar flare.

As someone who often listened to international shortwave radio broadcasts as a child, I can assure you that optical fibers provide a much faster and more reliable transmission medium than bouncing signals off the ionosphere (sometimes with an ocean bounce in-between).
See: http://en.wikipedia.org/wiki/Ionosphere#Geophysics

[Expectant_Philosopher (OP)]

I really want to get to a change in the refractive index of the atmosphere.  If we used a perpendicular polarization of the laser to the refractive index of a spot in the atmosphere, and used two lasers to intersect at a point, we could cause both heating and power absorption to increase the refractive index, but if we used a parallel polarization of the laser pump we would get heating and a decrease in the refractive index.  Using these as controlling mechanisms, we could finely shift the refractive index to give us at one time a reflective lens and at another time a atmospheric duct.  Experimentation with such a system might fine tune the effect to redirect the communications to multiple terminal points. 

[Bored chemist]

You do realise that laser beams tend to go through air without heating it, don't you?

[Expectant_Philosopher (OP)]

High energy laser beams used in the Star Wars defense program experienced unwanted thermal blooming as a result of the nonlinear interaction of laser radiation with the air, which is heated by the absorption of a fraction of the radiation. Instead of trying to minimize the thermal blooming we want to go the other way and maximize thermal blooming.  Another phenomena to consider when altering the refractive index is the Optical Kerr Effect, which relates electric fields and lasers.   Having multiple lasers allow more control of the phenomena.

[CliffordK]

In the 1960's the USA put 480,000,000 copper needles in space to improve radio communications at 8 GHz.

They apparently were put at an altitude between 3,500 and 3,800 kilometers.  They had planned on a rapid orbital decay, which would have happened if they had placed them at 100 miles or so.