# Accurately measure relative intensity noise (RIN) using RF spectral analyzer?

I'm trying to measure the relative intensity noise (RIN) of a laser using an RF spectrum analyser. It's a fairly common method (outline: How to measure relative intensity noise in lasers) although I wondered if someone more experienced might be able to help clarify some of the nuances of noise measurement for me.

As I understand, RIN is defined as the mean square intensity-fluctuation spectral-density of an optical signal divided by the average optical power. To measure this, we often put the laser into a photodetector, use a bias-T to measure the DC voltage (which is proportional to photodetector current and hence gives a measure of average power) and connect the AC output of the bias-T into an RF spectrum analyszer.

To plot RIN as a function of frequency, the measured RF spectral intensity values are divided by spectrum analyzer resolution bandwidth (i.e. put into dBm / Hz units) and then divided by the average electrical power

$$P_{avg} = \frac{V_{DC}^2}{50 \Omega}$$

This apparently gives a value with units dBc/Hz or dB/Hz.

dB is a relative scale, so dB/Hz makes sense in that we're measuring AC power at a certain frequency in reference to the DC power. However, dBc/Hz is the power referenced to the carrier and I'm not sure what that is in this case. Additionally, some authors present system noise floor measurements in units of dBc/Hz. Is this wrong since in this case there's no carrier? Or is this a system noise floor with reference to the power from the laser being measured?

Finally, in some cases I find that the trace on the RF spectrum analyzer shows harmonics as a series of peaks (EDIT: my laser is pulsed, so the harmonics are at the repetition rate of the pulses, as expected). The levels between peaks is at the same level as the background level (i.e. when there is no signal input). Can we therefore infer that the RIN at these points (i.e. if we integrate from 10 Hz, say, up to the 1st harmonic) is equal to or less than the system RIN? Or would we need to amplify the signal just to ensure we can see it above the system noise level.

This seems a complex topic and perhaps I'm overthinking it, so any tips or pointers / good references would be greatly appreciated!

Thanks

However, dBc/Hz is the power referenced to the carrier and I'm not sure what that is in this case.

I suspect the carrier in this case is the average optical power, which they may be thinking of as a many-terahertz carrier.

some authors present system noise floor measurements in units of dBc/Hz. Is this wrong since in this case there's no carrier?

It's not clear to me why somebody would choose those units for a noise floor. It may be wrong, but I'd want to see the context where you read it to say for sure.

I find that the trace on the RF spectrum analyzer shows harmonics as a series of peaks. The levels between peaks is at the same level as the background level (i.e. when there is no signal input). Can we therefore infer that the RIN at these points (i.e. if we integrate from 10 Hz, say, up to the 1st harmonic) is equal to or less than the system RIN?

In the RIN measurements I've seen, there are no measurable harmonics, just a single peak related to the laser's intrinsic relaxation oscillation frequency. Are you testing with a modulation signal applied to the laser? Most RIN measurement's I've seen were done with the laser operated CW, and I'd think the results are easier to interpret for a CW optical signal.

In general spectrum analyzers have a noise floor, but I wouldn't call it "RIN", because it is not "relative intensity" --- it doesn't change in proportion to the optical power. The measurement system noise is a fixed "floor" and you can't measure power spectral density below that floor. So whenever the trace is down at the noise floor, you're not measuring anything about the device you are testing, just the capabilities of the analyzer.

General comment

The RIN measurement is fairly difficult to do. Unless the laser has very bad performance you need a very low-noise detector, very low-noise preamplifier, and a very sensitive spectrum analyzer (with a low noise floor). You will want to test the noise floor of your whole receiver system (detector, preamplifier, spectrum analyzer) before measuring your laser to be sure you know when you're measuring the laser behavior and when you're just seeing instrument noise.

Edit

Sorry I'm not familiar with RIN measurements on pulsed lasers. But the units of dBc/Hz make a lot more sense now --- they're just talking about the fundamental of the pulse signal as the carrier.

The measurements I'm familiar with, you're most interested in the peak frequency in the RIN spectrum. I don't think you could do this with a pulsed laser because you'd have to pulse at a higher frequency than the RIN peak, which would also be beyond the modulation capabilities of the laser. But maybe there are tricks I'm not aware of.

I will suggest that for a pulsed RIN measurement, you don't need the bias tee, though you might want a blocking capacitor for the sake of your SA input. The peak of the fundamental of the pulse signal gives you the laser signal power that you'd be measuring the noise relative to.

is it fair to say then that the laser has equal or better noise performance?

I'd say it this way: if the laser noise is too small to measure on your detector/SA system, then the measurement system is not adequate to measure the noise of that laser.

how would you recommend characterising the system noise floor?

Typically, you turn on the photodetector and pre-amp, but don't apply any laser signal. Then take a sweep on the spectrum analyzer, using the exact settings you'll use for your measurement. This gives the combined floor for the detector plus the SA.

You should be able to display this for comparison to your laser RIN measurements by just using the save-trace features of the SA, without any need for calculations.

• To further complement the comment on SA noise. A FFT based SA does'nt have very good noise performance, where as modulator based SA's have ideal noise performance (i.e. Noise in band equivalent to the a $50\Omega$ noise source. that is why they are so expensive. note: SA = Spectrum Analyzer. – placeholder May 17 '13 at 21:05
• Thanks for your informative reply. I have now amended my question to say that the laser is pulsed, so the harmonics on the RF spectrum are at multiples of the pulse repetition rate, as expected. Sorry, I forgot to state it wasn't CW. In literature, RIN measurements are used for pulsed lasers, but typically they present RIN spectra only up to the fundamental frequency (so integrated RIN can be calculated before any harmonic peaks are observed). – IanRoberts May 18 '13 at 15:36
• I appreciate that if the background is equal to the signal level, then we're just measuring the analyzer capabilities. But is it fair to say then that the laser has equal or better noise performance? I'll take another look for the noise floor in dBc/Hz reference. But otherwise, how would you recommend characterising the system noise floor? I could just record the background trace in units of dBm on the SA and then divide by the resolution bandwidth to get dBm/Hz. Would it be possible to plot this alongside a RIN spectral density measurement with units dB/Hz or 1/Hz say? – IanRoberts May 18 '13 at 15:37