Q: What is the phase-noise on my laser beat-note going to look like when locked with the D2-135 Offset Phase Lock Servo (OPLS)?

A: There are a lot factors that affect the final lock performance of the D2-135. Like frequency noise, phase noise is measured in terms of a noise density — or noise within a frequency band: dBc/Hz.  The “Hz” tells us the width of the frequency band is 1 Hz. The “c” in dBc is for “carrier” as dBc is the ratio of the power of the phase noise relative to the carrier. The density of noise will depend on the frequency and generally falls in to three distinct regimes:

1. High Frequency: The D2-135 servo loop will have some bandwidth. That bandwidth will depend on numerous factors, but primarily your laser and how you are adjusting your laser frequency. We’ve measured bandwidths as high as 3 MHz with the D2-135, but for the example here, let’s say your bandwidth is 100 kHz. For frequencies above 100 kHz, the D2-135 does nothing. Your phase noise at these frequencies is whatever your phase noise is on your lasers to begin with.
2. Loop Filter:  This is where the D2-135′s servo loop is performing like a text-book servo system: the phase noise is reduced ~ 1/G where G is the loop gain. See Introduction to Servos Part 1 for more details. If our bandwidth is 100 kHz, and we have a single integrator at 100 kHz, then phase noise at 10kHz will be reduced by a factor of 10. Phase noise at 100 Hz will be reduced by 1,000. Please note that in most situations, the output of the D2-135 adjust as laser’s frequency, not phase, and when this is the case, the loop filter is not proportional to the poles set on the feedback of the D2-135.
3. Noise limit: At lower and lower frequencies, the servo reduces more and more phase noise until eventually it hits a phase-noise floor. At this point, the phase noise will remain constant when going to lower frequencies. The phase noise floor is typically set by either the D2-135′s phase noise floor, or the phase-noise on the frequency reference used.  To determine the phase-noise floor, one must calculate both and use the larger number.  The phase-noise floor of the D2-135 is given by the formula:
   

   D2-135 Phase-Noise Floor = -213 +  20Log(N) + 10 Log(F_REF)

   where N is the divider setting (8,16,32 or 64) and F_REF is Reference Frequency.  When possible, use a lower N and a higher F_REF as this will lower your noise floor. As an example, say you want to lock to an offset of 4 GHz. You set N=32 and use the internal VCO reference (high mode) and tune the VCO until the Reference Frequency is 125 MHz (125 MHz * 32 = 4 GHz). Your noise limit is -213 +20*Log(32)+10*Log(125e6) = -102 dBc/Hz.

   The noise floor from the VCO is the VCO’s own noise floor multiplied by N as the phase-noise on the reference gets multiplied up to the beat note frequency by the OPLS.

   VCO Phase-Noise Floor = VCO Phase-Noise +  20Log(N)

   In our example, the phase-noise from the VCO is 32 times, or 30dB, greater than the VCO’s phase-noise. Once both the VCO Phase-Noise Floor and the D2-135 Phase-Noise Floor has been calculated, use the larger value (or technically add them, but usually one term is much smaller than the other and can be ignored).