Power requirement for transmitting communications further than 1 ly? The StarShot project from Breakthrough Initiatives aims to send a paper light spacecraft to alpha centauri using pressure from a laser located on earth at 20,000kms. 

What are the options for a transmitter that can be received from 1-4 lyrs away, if the transmitter weighs the same as a few jellybeans (&lt;10 grams)? What wavelength and power range can they work with for that distance using that weight of equipment?
It's possible to transmit an intelligible signal to a target roughly 4.3 light-years away using 0.1 milliwatts. The trick for that particular level of power is that both the sender and receiver have to be carefully positioned several hundred AU from a star, with those stars lined up between them, in order to take advantage of a gravitational lensing effect. If only one of the two radios can be positioned at a star's gravitational focus, then the necessary power rises, but can be under 40 watts, according to one of the diagrams reprinted at https://www.centauri-dreams.org/?p=10123 .