What is the theoretical maximum data transmission rate of an optical laser at 400nm and at 800nm, with optimal pulse width? I want to know what the highest possible data transfer is for visible light with regards to the frequency, disregarding noise.
Using the shannon-hartley formula wasn't of much use, as it operates with bandwidth. With a bandwidth of 1 Hz it doesn't get very impressive.
Basically, a nyquist rate for lasers I guess...
 A: Bandwidth is the most important thing here. In order to send information you need distinguishable pulses, which can be interpreted as 0 oder 1 for no pulse or pulse respectively. The optical bandwidth and pulse duration are related by the time bandwidth product
$$
0.44 < \Delta t \Delta f \approx \frac{c}{\lambda^2} \Delta t \Delta \lambda
$$ 
Note the inequality sign, this is only an lower bound for $\Delta t$. Even with a very large bandwidth you are not able to generate short pulses if you are not able to enforce a stable phase in fourier space (e.g. thermal radiator).
In order to distinguish two pulses reliably they must be seperated at least in the order of the pulse duration. This means that the repetition rate $f_\text{rep}$ is given by
$$
f_\text{rep}\approx \frac{1}{\Delta t} < \frac{\Delta f }{0.44}
$$
So the maximal achievable bandwidth in terms of bits per second is directly related to the optical bandwidth of the light source. The shortest possible pulse duration for a given wavelength must be at least few times the optical period, which is 2.7 and 1.3 femtoseconds for 800 and 400 nm respectively. This means the maxium transmission rate is roughly 100 TBit/s for 800 nm and and 200 Tbit/s for 400 nm. This is roughly equal to the total internet traffic.
Caveat: You need electronics operating at $\sim 100$ Thz to switch the light source and detect the signal.
