Yesterday I used the CTN network analyzer to look at the RF spectrum of a 1.0 mW beam from the ATF Lightwave with a New Focus 1811. This beam is picked off from the main ATF laser beam pretty much immediately after the laser head; there are some waveplates, PBSs, and lenses, but no EOMs or modecleaners. The laser was free-running, with nothing plugged into the temperature or frequency BNCs.

In addition to the spectrum of the beam intensity, I took a spectrum with the beam blocked to get a measurement of the dark current. In the plots below, I've referenced everything to the current through the diode. This means taking the W/Hz spectrum from the network analyzer, multiplying by 50 Ω and taking the square root to get the V/rtHz across the analyzer's internal 50 Ω resistor, then multiplying by 2 to get the V/rtHz put out by the 1811 (since its output impedance is 50 Ω), then dividing by the 4×10⁴ V/A figure given in the 1811 manual to get the A/rtHz across the diode. To get the 'expected photocurrent shot noise' given below, I watched the DC output of the 1811, which was at 680 mV with the 1.0 mW beam and 10 mV dark. So I divided 670 mV by the 1 V/mA figure given in the manual to get the DC photocurrent. The shot noise of this photocurrent is then sqrt(2eI). I haven't measured any of these 1811 conversion factors, so I don't have complete confidence in this shot noise value. However, the value for the DC current agrees roughly with what you get if you take the power measured with the ThorLabs meter (1.0 mW) and multiply by the quantum efficiency (0.7).

You can see in the first plot that the dark current is subdominant to the photocurrent all the way out to 100 MHz, and subdominant to the expected shot noise out to maybe 40 MHz or so. In the second plot I've taken the quadrature subtraction of the blue trace from the red trace to get an estimate of the photocurrent noise alone. The spectrum looks approximately white from 10 MHz out to 50 MHz and (if you at all believe the shot noise value) is about 1.7 times the shot noise. If this truly is the level of the excess noise, then to get excess intensity noise whose PSD is equal to 1% of the shot noise PSD at 20 MHz, we'll need a cavity pole at 5.6 MHz. If the calibration is spectacularly off and the total noise is 20 times the shot noise, we'd need at cavity pole at 1.4 MHz to get the excess intensity noise PSD to be 1% of the shot noise PSD at 20 MHz. The way I've arrived at this is as follows: if S(f) denotes the value of the linear spectral density at f relative to shot noise (f = 20 MHz and S(20 MHz) = 1.7 in this case), then

and so the suppression of the excess noise after transmission through a modecleaner is

and from this f_HWHM can be chosen to give the desired amount of suppression. Edit: actually, the right way to do this is to write the excess noise PSD as a relative intensity noise (which scales as P²), and to then compute the desired amount of suppression for the maximum amount of power we're going to send through the PMC (2 W or so). Computing the suppression relative to shot noise for a 1 mW beam is not sufficient, because the suppression requirement gets more stringent as the power increases. The RIN here at 20 MHz is 3×10^-8 /rtHz, and so for 2 W beam we require a cavity pole of 420 kHz to get a factor of 100 suppression below shot noise.

I think to do this measurement properly I'll need to get a better handle on the relative calibration of the DC and RF transimpedance gains of the 1811. It might also be nice to take a measurement both before and after an existing PMC, just to see the expected filtering effect.