# Anisotropic Behavior of Glass in the Faraday Effect Experiment

I'm currently working on an experiment that uses the Faraday effect to determine the Verdet constant of SF-57 glass.

Basically, similar to the photo above, I have a LED that generates a 405nm light. This goes into a polarizer, then goes through the SF-57 glass. The SF-57 glass is wrapped with some coils connected to a signal generator such that a magnetic field is generated. This will change polarization of the light while travelling through the glass due to the Faraday effect. Finally, the light is sent through another polarizer (at a different angle), and a photodiode at the end detects the intensity of the remaining light which will tell us how much the angle changed by, thus determining the Verdet constant.

All works well, and the known Verdet constant is found with reasonable accuracy, but there's just one problem:

When I switch the polarity of the AC current going into the coil (basically when I swap the two wires feeding the AC current into the coil), the measured Verdet constant changes by roughly 1.5 times. This is really confusing, since the coils and the glass should both be very isotropic (at least not enough to change things to this degree), and I'm using an AC current so swapping shouldn't change anything.

I've tested with different SF-57 glass+coils, but they all have the exact same problem; swapping the polarity of the current changes the measured value by 1.5 times. Essentially, all the coils give two sets of consistent measured values - one for each polarity.

I've thought about this for quite a while, but have no idea why this should be so. (Trying it with a different circuit board / photodiode / entire new setup also had the same results).

Does anyone have any idea on why this anisotropic behavior is happening? Thank you!

There is insufficient information to identify the problem with your measurement, but here are a few debugging suggestions:

• Have you made a DC measurement of the Verdet constant, and does that value change when you swap the current leads?

• Does your measured Verdet constant change as a function of peak AC current?

The AC measurement is normally done using a lock-in amplifier, which is usually confusing for first-time users.

• What AC frequency is being used? It is bad idea to use the local AC mains frequency (60 or 50 Hz, depending on where you live), since any wires or circuit will have 60 or 50 Hz noise that may throw off your measurements. For low frequency lock-in measurements, I typically use a frequency that is a prime number about half-way between the local mains frequency (60 or 50 Hz) and its first harmonic (120 or 100 Hz).
• When you swap the current leads, unless you have a lucky coincidence, the phase of input signal will change relative to the lock-in reference signal. A research-grade lock-in will have the option to automatically adjust the phase, but a pedagogical lock-in may not. Does your lock-in automatically adjust for this phase change, and if not, do you adjust the phase to correct for this shift and maximize the lock-in DC output for each of the two lead arrangements?

The statement in the question that "All works well, and the known Verdet constant is found with reasonable accuracy, " does not seem consistent with a 50% change in the constant when the leads are switched. Whether the expected value lies between or outside the two measured values could be an important debugging hint.

If you change the source voltage, it is the magnetic field strength that changes, not the Vernet constant. Keep that in mind