Given that the CO₂ laser power supply seems just as happy with an analog input as a digital PWM signal, one might wonder about the bandwidth of each mode. Rather than feeding the supply with a function generator, raster-scanning a grayscale target should suffice.
For example, this would generate five square waves:
The bars are 10 pixels wide, so scaling the image at 254 dpi makes them 1 mm wide:
As before, the first and last bars are 100% (white), with 0% (black) bars just inboard. The other bars are 10% and 90% to stay a little bit away from the 0 V and 5 V limits. I set Lightburn to invert the colors so that 100% = full power and 0% = beam off.
Engraving the pattern at 100 mm/s makes each bar 10 ms wide and the risetimes and falltimes are easy to see:
[Edit: Clicked the wrong picture.]
Although it’s a bit handwavy, a 1.5-ish ms risetime suggests a single pole (ordinary RC) time constant τ = 700 µs = 1.5 ms/2.2, so the controller’s output filter cutoff would be around 200 Hz = 1/(2π τ).
The laser tube current looks a little slower than that, so there’s a definite tradeoff among engraving speed, edge crispness, and power level.
More study is definitely needed …