# Unexpected wavelength jumps in a laser observed: a fundamental noise source in VCSELs?

I observed an unexpected signal while developing an interferometric sensor using a VCSEL laser. In order to debug this noise I designed the following device that converts minute changes in the laser's wavelength to large changes in optical intensity:

The 850 nm laser is biased above threshold using a low noise circuit (battery + resistor) and coupled to a fiber-based Mach-Zehnder interferometer that performs wavelength-to-intensity conversion, observable with a photodiode.

The voltage signal out of the photodiode looks like this: Depending on the wavelength of the laser, the average voltage can be anywhere between total constructive interference (0.57 V) and total destructive interference (0.02V). [This range is marked with horizontal bars in the plot above].

The interesting observation appears when we zoom-in the signal:

We can observe discrete jumps in the photodiode's voltage, corresponding to discrete jumps in the lasing wavelength. Knowing the distance difference in the two arms of the interferometer $$\Delta L =$$ 34 mm and the voltage range in the output $$V_{pp} =$$ 0.55 V it is possible to convert voltage noise to wavelength (or wavenumber $$k=2\pi / \lambda$$) as

$$\delta k = \frac{2}{V_{pp} \Delta L} \delta V \simeq 107 \frac{\mathrm{m^{-1}}}{\mathrm{V}} \delta V.$$

We can then infer that the central jumps represent a wavelength jump below 0.12 pm or 51 MHz

Now the question is: What can be causing such minute but discrete wavelength jumps in a laser with supposedly no mode jumps? Is it a fundamental, quantum effect?

Please note that my knowledge in solid state physics is quite limited, so maybe I am missing something out here. Any pointers on the possible source of such jumps or which experiments I can perform to narrow down their origin would be heavily appreciated!

Some observations (to the best of my knowledge):

• The jumps are NOT caused by quantization of the ADC or photodiode.
• VCSEL lasers are not supposed to have longitudinal mode jumps.
• We observe a similar signal using a different VCSEL laser from different manufacturer.
• We don't observe such a signal when using a DFB laser.
• When the interferometer works at either total constructive or total destructive interference, the jumps in the signal are no longer visible, pointing out that the jumps are predominantly in wavelength and not in intensity.
• We nevertheless observe a similar (but much, much smaller) signal if we measure the output power of the laser directly with a photodiode.
• The power spectral density of the observed noise is ~1/f and with no peaks.

UPDATE:

• The VCSEL is fiber coupled by factory into a single-mode fiber. Thus we are only observing the TEM00 transverse mode. Given that the intensity fluctuations are below -140 dB, I am assuming that no power is going to higher order modes.

• The hops depicted above happen at multiple biasing points and far away from the maximum driving current. Furthermore, there are more than two wavelengths where the VCSEL locks. That would speak against polarization hops (?)

• Using an isolator between the fiber-coupled VCSEL and the laser did not solve the problem

• Do you have a datasheet for your vcsel? Are you taking any precautions to avoid back-reflections returning light into the vcsel? Apr 27 '19 at 14:20
• Is the VCSEL temperature stabilized? Apr 27 '19 at 14:39
• Thanks for the comments - @JonCuster The VCSEL is not temperature stabilized and I indeed observe a slow drift in the wavelength. But given the abrupt nature of the jumps (in the microsecond range), I suspect there should be something else. Apr 27 '19 at 18:22
• - @ThePhoton One of the VCSELs that I tried is from RayCan: raycan.com/image/pdf/RC12xxx1-T.pdf Apr 27 '19 at 18:22
• @svilches, it's entirely possible that a VCSEL like that operates normally with multiple output modes. You might be seeing transitions from one set of operating modes to another, or you might be seeing polarization hops in one of the operating modes at a time. Nothing in its usual application requires suppressing the tiny mode hops you saw, so the vendor won't specfiy anything that promises eliminating mode hops. There may even be enough back-reflection from the provided window to cause mode hops that are problematic for your application. Apr 27 '19 at 18:29

VCSEL lasers are not supposed to have longitudinal mode jumps.

VCSEL generally don't have longitudinal mode hops.

But many VCSELs have transverse mode hops.

And they can very easily have polarization mode hops, given the typical symmetric aperture design.

These mode hopes will be more likely if there is back-reflected light returning into the VCSEL output aperture. The typical VCSELs I see in my work (optical communications) have their wavelength and power stability specified only when emitting into a return loss of -40 dB or lower for this reason. However your VCSEL could be very different from the ones I'm familiar with.

Lack of temperature control could also contribute to mode hops.

• I am suspecting of these transverse mode hops. Do you have an intuition about the spectral spacing of such jumps? This paper [doi 10.1109/3.985571] shows a spectral spacing of ~100 GHz between transverse modes, while I am observing ~50 MHz hops (3 orders of magnitude difference...) Apr 27 '19 at 18:28
• @svilches, do you have an optical spectrum analyzer or spectrometer available? That would be the easiest way to tell. One possibility is that polarization hops cause much smaller frequency deviation than transverse mode hops. The other is that you have 4-10 modes operating (typical for the kind of laser you linked to in another comment), so when one of them hops it doesn't cause as big a change in your MZ interferometer output as it would if you had a single mode laser where all the output power hopped at the same time. Apr 27 '19 at 18:32
• To test whether you're getting polarization hops, put a polarizing filter in before your inteferometer (or better yet, use a spectrum analyzer/spectrometer). Apr 27 '19 at 18:34
• "single mode" should mean a single transverse mode. I didn't catch that in the datasheet earlier. But, for example, if you're giving it more back-reflection than it's designed for, or driving it with more current than it's designed for, it might go multi-mode. Also, given the small effects you're seeing, it's possible that hops in the side-modes could be part of the effect. Apr 27 '19 at 18:39
• Also, given the fairly sparse details in the datasheet (Output power is 1 mW, but they don't even say how much forward current is needed to get that power) this vendor may not be entirely conservative about their specs. Apr 27 '19 at 18:41

After some debugging I have come to the conclusion that those jumps are longitudinal mode jumps created by the interaction of the VCSEL with a parasitic external cavity, created by the end connector of the optical fiber pigtailed to the VCSEL. This fits to the expected fiber cavity length of the 51 MHz jumps: $$z_{cavity}=\frac{c}{2 \nu n}=1.96\textrm{ m}$$