# Determing aperture size for space-based-solar-power laser transmitter

I have hit a bit of a roadblock in my simulation. In the equation I require the aperture size for the laser source.

$$I_a ≈ \frac{\lambda d}{A}$$

• $I_a$ = aperture atop the atmosphere ($m$)
• $\lambda$ = wavelength of laser (in this case 1023nm)
• $A$ = aperture of the laser transmitter (...? $m$)
• $d$ = distance from SPS to atmosphere (39,000km)

But all the articles I have read from NASA, JAXA, ESA, sciencedirect concepts, no one specifically talks about the details of laser transmission if used for SBSP.

I just need some reasonable value for the aperture size. So we are talking about GW scale laser transmission from a single main source, if anyone has knowledge of optics/photonics/lasers, could you recommend me a sensible size along with a citation.

Thanks

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It would be in metres. Aperture is a diameter, and I meant "aperture atop atmosphere" not "irradiance atop atmosphere", edited that now. – Astral Aug 4 '13 at 15:47
I'd be glad to help but I'm confused and have a few questions first. Is this solar-powered laser transmitter? Are you asking about the aperture of the solar collector? Or the aperture of the laser transmitter? Or both? What is meant by "aperture atop the atmosphere"? Why are there two aperture sizes in your equation? And also, the units in your equation do not add up -- you have units of length-squared on the left hand side and you are unitless on the right hand side (if I understand you correctly). – Joe Aug 5 '13 at 15:31
Hello. I solved it. But firstly someone edited my equation, I don't if it was you or not. It is in m not m^2... I found a paper finally, talking of a 20km stratospheric aerostat PV collector. So I simply reversed the equation, to obtain a 50m diameter SPS laser transmitter dish... So to clear things up. My 40,000km SPS laser transmitter dish has a diameter of 50m, transmitting 5GW. It is received at the atmosphere altitude of 1000km at 9.51 MW/m^2 with a 25.8m diameter... My other more complex functions then take over and deal with atmospheric laser transmission, attenuation coefficients, etc. – Astral Aug 5 '13 at 16:17
glad you solved your problem. Out of curiosity, when you are specifying your apertures with units of length, is that supposed to be the radius or diamater? It is quite unconvential to use A to represent a radius or diamater of an aperture rather than an area. – Joe Aug 6 '13 at 16:36
It is diameter. 'A' stood for aperture. Though 'd' could of been used instead, and then R for the distance. – Astral Aug 7 '13 at 15:08