Energy Cost Per Photon
The most comment argument presented by the Microwave SETI community to justify their opposition to Optical SETI is the grossly misleading statement that optical photons are a lot more energy expensive than microwave photons. While is is not clear that a comparison between the energy costs of microwave and optical photons is the best criteria for establishing the efficacy of the an interstellar communications system used by a very advanced technical civilization, we will assume that this is the case for the purposes of this analysis.
The proof that optical photons are not more expensive than microwave photons now follows, with the assumption that the "wall plug efficiency" is the same for both microwaves and lasers, and that diffraction-limited performance is available from both types of uplink. For signal comparison purposes, the numbers have been normalized to an uplink power of 1 kW. If the optical uplink is constrained to be of very small aperture so that the gain is severely limited, as suggested on page 50 of the Cyclops Report, then indeed, the energy cost to land an optical photon on a target is far higher than for a microwave photon:
Note that the number of photons collected per second by a receiver aperture is given by the received power divided by the product of Planck's constant (6.63 x 10^-34 J.s) and the microwave or optical frequency. This comparison does not allow for the large difference in effective noise temperatures between receivers.
The comparison is done only on the basis of the energy required to get each type of photon to its target. Thus, it is assumed here that the effective quantum efficiency of the receiver is unity, that is why the word "collected" is used, rather than the word "detected". For each frequency regime, the link is assumed to be symmetrical, i.e., the receiver aperture size is identical to that of its corresponding transmitter (uplink). The theory for this analysis may be found in:
Microwave transmitter (uplink) based on the 300 m Arecibo dish:
Gain for a signal at 1.5 GHz = 73.5 dB
EIRP for a 1 kW continuous wave signal at 1.5 GHz = 103. 5 dBW
Signal intensity received at a range of 10 light years = -247 dBW per m^2
Signal captured by a 300 m receiving dish = -198.5 dBW
Equivalent number of "warm and fuzzy" microwave photons collected per second = 14,180
Visible laser transmitter (uplink) based on the phased array equivalent of a 10 m diffraction-limited visible telescope:
Gain for a signal at 656 nm = 153.6 dB
EIRP for a 1 kW continuous wave signal at 656 nm = 183.6 dBW
Signal intensity received at a range of 10 light years = -166.9 dBW per m^2
Signal captured by a "modest" 10 m telescope = -148.0 dBW
Equivalent number of "hot" optical photons collected per second = 5,280
Average number of microwave photons collected per second per watt of transmitter power = 14.2
Average number of optical photons collected per second per watt of transmitter power = 5.3
If the signals are pulsed with a very short duty cycle, instead of being a continuous wave, then the photons arrive in short bursts which can better override the effects of receiver noise and the noise from background radiation. However, because of interstellar dispersion and scintillation effects, there are severe limits to the minimum pulse width at microwave frequencies. This implies that pulsed lasers used for interstellar communications would be far more detectable than their microwave counterparts. A laser transmitter with a mean power of 1 GW would result in 5.3 billion photons per pulse being collected at the target! This is quite a signal which wouldn't require a sensitive photon-counter for its detection - just a very fast direct detection receiver or desensitized photon-counter. Note that in analysis presented elsewhere (9402-001 & 9512-001), a figure of 68 million photons per pulse is given for a 10-meter receiving telescope at a wavelength of 550 nm, but that assumes a very conservative overall detection efficiency of only 1%, as against the 100% efficiency assumed above. The reader can perhaps now better appreciate why it is sensible to suggest that 25.4-cm aperture telescopes could detect such attention-getting pulsed laser beacon signals.
On a watt for watt basis, the energy cost per photon landed at targeted star system is of the same order at microwave and optical wavelengths. The scenario model used above indicates a microwave advantage of about three to one, though this is very dependent on the assumed aperture sizes. The advantage would pass to the visible system if the assumed optical aperture size was a little larger. As always, the performance characteristics of free-space interstellar communication links are thus very dependent on the assumptions made.
THUS, THE STATEMENT PUT OUT BY THE MICROWAVE SETI COMMUNITY THAT "OPTICAL PHOTONS ARE FAR MORE ENERGY EXPENSIVE THAN THE MICROWAVE VARIETY" IS NOT TRUE!