Closely-Spaced Modes in Birefringent Single-Mode Fibers?

[Twigg]

So I was messing around looking at the output (423nm) of a misaligned polarization-maintaining (PM) fiber with a CCD camera, and more than once I noticed the beam profile significantly change (if you're not familiar with what PM fibers are, see last paragraph for explanation). I have video if anyone's interested. Mode-hop occurs at 0:02. Maybe I'm reading too much into the change, but it seems to hop from gaussian profile to "gumdrop" profile. Note: when I said above that the PM fiber was "misaligned", I meant the input polarization was not parallel to either axis. Also, I should add I've seen it happen like this more than once. When I repeated the experiment with a regular (non-PM) single-mode fiber, I didn't see this effect.

When trying to explain this, my first thought was "voodoo magic". But after a little more thinking I came up with a somewhat (only somewhat) less far-fetched possibility. Could there be additional modes nearby in the PM fiber whose symmetry is broken by its large birefringence? I know this is an annoying question with no practical importance, but still I'm curious.

About PM fibers:
PM fibers are single-mode optical fibers with a large birefringence. The idea is that a non-PM fiber is slightly birefringent. Since the birefringence is small, there's no easy way to tell if the polarization of your input light is parallel to the fast (or slow) axis of the non-PM fiber. Because you're off-axis, the fiber acts like a super high-order waveplate and adds a phase shift to the polarization that depends on the length of the fiber. In real life, the fiber heats up and cools down with fluctuations in ambient temperature and laser power, so the length changes. This means you do not get a very consistent polarization out of the non-PM fiber. The PM fiber fixes that by having a huge birefringence, so it is easy to tell if you're on the fast (or slow) axis or not (disclaimer: it's still not easy to actually do). So, in short, it is a highly birefringent single-mode fiber.

 

[Andy Resnick]

It's tough to tell from the video- when I watch it, the spot intensity is essentially binary (on/off) and broadly changes shape- did you threshold the image?

 

[Twigg]

Not sure what you mean by "threshold the image". The change in the image isn't resolution-limited, if that's what you mean. The beam actually changed by that much.

I did some more looking into what was going on when this happened. The laser I was coupling into this fiber was not as well frequency-locked as I had thought. It's very possible that the abrupt change could be a mode hop of the laser cavity. Unfortunately, I didn't have the foresight to log the laser frequency. On first principles, a mode hop doesn't explain the change in profile, but I should add that the CCD I used to get that video had some hefty neutral density filters on it. It could just be that the ND filters distort the profile in a power-dependent way. Unfortunately, I don't think I recorded enough data to get to the bottom of this :(

On another note, I am currently using a different PM fiber at the same wavelength, with the laser locked to within 1MHz frequency drift. I see anomalous drifts in beam alignment (~40um) and power coming out of the fiber, but no abrupt stuff like above. If I see anything like it, I'll be sure to update this thread.

 

[Andy Resnick]

Not sure what you mean by "threshold the image". The change in the image isn't resolution-limited, if that's what you mean. The beam actually changed by that much.

"thresholding" means to replace all grey values less than the threshold value with (usually) zero and all grey values above the value to (usually) 255. Thresholding can be more complex, but the posted video appears to show binary values of the intensity (low and high) rather than a greyscale.

 

[Twigg]

"thresholding" means to replace all grey values less than the threshold value with (usually) zero and all grey values above the value to (usually) 255. Thresholding can be more complex, but the posted video appears to show binary values of the intensity (low and high) rather than a greyscale.

Thanks for the explanation. It's actually not thresholded. I think I just saturated the camera. Not sure why the beam profile is so flat-top-like, but I can say for a fact that I did not intentionally threshold it. If you look really close to the edges you can see a little bit of intermediate.

Since I didn't really collect enough experimental info to figure out what's going on in the video, I'd like to ask a more answerable, more theoretical follow-up question. Does birefringence create additional modes in a fiber (or waveguide, if there's more literature on that)? And theoretically, what should the mode-spacing (if there is mode splitting) be like due to a birefringence on the order of 10^-4 in a fiber with a mode-field diamater on the order of 1 micron? (If anyone is wondering, the exact fiber I am using is Thorlabs' PM-S405-HP.)

 

[Andy Resnick]

Since I didn't really collect enough experimental info to figure out what's going on in the video, I'd like to ask a more answerable, more theoretical follow-up question. Does birefringence create additional modes in a fiber (or waveguide, if there's more literature on that)? And theoretically, what should the mode-spacing (if there is mode splitting) be like due to a birefringence on the order of 10^-4 in a fiber with a mode-field diamater on the order of 1 micron? (If anyone is wondering, the exact fiber I am using is Thorlabs' PM-S405-HP.)

I pulled up the spec, and there is an item of interest: Beat length = 1.8mm @ 405 nm

This an important metric: this is a 'high birefringence' fiber, and the birefringence will strongly drift with temperature. Depending on how linear and well matched the polarization state of your input is to the eigenmodes of the fiber, you could see appreciable drift, which could cause the effect you see.

Phil Hobbs' excellent book "Building electro-optical systems" has a section on using PM fiber with details on how to 'correctly' launch light into the fiber. Briefly, use a half-wave plate to rotate the input polarization, adjusting the orientation of the plate until the output intensity 'jiggles' the least when you 'jiggle' the fiber (his words!- it really is an excellent book.)

Hope this helps...