Also, to optimise data rate at a given power budget, you want to choose freq such that `d rate/d freq` is zero, which (assuming I didn't screw up the math) goes

Also, to optimise data rate at a given power budget, you want to choose freq such that `d rate/d freq` is zero, which (assuming I didn't screw up the math) goes like: 0 = d/df rate = d/df (log(power/0.5 hbar freq^2) * freq) = d/df log(power/0.5 hbar freq^2) * freq + log(power/0.5 hbar freq^2) * d/df freq = 1/(ln2 power/0.5 hbar freq^2) * d/dx (power/0.5 hbar freq^2) * freq + log(power/0.5 hbar freq^2) = 0.5 hbar freq^2 / ln2 power * power / 0.5 hbar * -2 freq^-3 * freq + log(power/0.5 hbar freq^2) = 0.5 hbar freq^2 / ln2 / 0.5 hbar * -2 freq^-3 * freq + log(power/0.5 hbar freq^2) = freq^2 / ln2 * -2 freq^-2 + log(power/0.5 hbar freq^2) = log(power/0.5 hbar freq^2) - 2/ln2 so log(power / 0.5 hbar freq^2) = 2/ln2 power / 0.5 hbar freq^2 = 2^(2/ln2) freq^2 0.5 hbar / power = 2^(-2/ln2) freq^2 = 2^(1-2/ln2) power / hbar freq = 2^(1/2-1/ln2) sqrt(power / hbar) So (again assuming I got that math right), the optimal single photon frequency to use (in the quantum noise floor regime) scales with the square root of your power budget. However, at one milliwatt it's 1600THz or 187nm, and only increases from there, so for practical purposes you probably just want to use the bluest light your fiber can carry, and worry more about classical noise.