I spent a while working with MgF2-windowed xenon flash / discharge lamps. Primarily, I characterized their spectra with two normal-incidence spectrometers against a calibrated Deuterium lamp. In this particular case, it included a Czerny-Turner-type design.

As side investigation, I rotated one of the xenon flash lamps by 360° in about 45° steps and took time-resolved spectra in the range of 200 to 500 nm for each rotation step. Time-resolved means, that I took measurements / spectral scans at an interval of 0.1 µs with an exposure time of 0.168 µs. Because the exposure time is longer that the interval, I took only one spectral scan per one flash, for each flash delayed by another 0.1 µs. I assume this is ok because the intensity of the light emitted by the discharge over its entire spectrum is stable with $$ \sigma = 0.0294 $$ So for each rotation step and each interval, I integrate over an entire calibrated spectrum. If I plot the result, it looks somewhat like this: some plot

(The actual flash is "visible" for about 1.5 µs, while there is an "afterglow" mostly in longer wavelengths with less than 5% of the maximum intensity for about another 40 µs.)

My understanding is, that normal-incidence spectrometers behave like polarization filters. So I would expect perfect ellipses - point symmetric - if the the light is (partially) polarized. What I see looks different, unsymmetrical.

If have also done another type of plot. The first one shows how it theoretically should look like: some plot

And this is what I get: another figure

I assume, that I see ellipses. The semi-major-axis / maximal radius is indicated red (1), the semi-minor-axis / minimum radius is indicated blue (-1).

My questions ... is there any physical context, that could explain the unsymmetrical behaviour (other than uncertainties in measurements?). If there is not, would it be appropriate to fit ellipses into the data?

EDIT (1): another one Based on the reply by @akhmeteli, I looked into different wavelengths. Top left: 230 nm; top right: 260 nm; bottom left: 362 nm; bottom right: 461 nm. The first three represent spectral lines, the fourth one is a random choice without any specific feature. My data has a resolution of 0.2nm. Here, I integrated from lambda-0.2 to lamda+0.2 nm, kind of as narrow as possible. My impression is, that the observed effect does not (very much) depend on the wavelength.

  • $\begingroup$ I had cause to use a (plain boring Argon-nitrogen) flash lamp once, and have since then had a soft spot for them (actually I have a soft spot for lots of antiquted kit that still find the occasional specialized use). Mind if I ask what your application is? $\endgroup$ Dec 17, 2012 at 14:04
  • $\begingroup$ Plain boring ... yep, that's a nice description of my lamps. They were used for photo-ionizing dust / particles, basically. $\endgroup$
    – s-m-e
    Dec 18, 2012 at 10:40
  • $\begingroup$ I assume the flash lamp is in some kind of transparent enclosure having its own refraction pattern of some unhelpful shape. I wonder if that's contributing to what you see. $\endgroup$ Dec 18, 2012 at 14:25

2 Answers 2


It is not obvious that the radiation is polarized in the same way at each wavelength. Grazing-incidence reflection depends on the wavelength. So even if we assume that you would get an ellipse for each wavelength (and even that is not quite clear for me: for example, if linearly polarized light goes through a polarizer, one would expect something looking like a figure-8, but I may be mistaken), it is not obvious that you'll get an ellipse after integration. To check this, you may wish to do the same measurement integrating over a small part of the spectrum.

EDIT (12/20/2012): @ernestopheles convinced me that integration over wavelength cannot explain the results. However, it is still possible that integration over time can explain the results, as the intensity varies dramatically over the integration time, and it is not obvious that polarization does not vary with time. To check this, one can decrease the integration time.

  • $\begingroup$ Thanks for the answer. I edited my initial question and added another plot - looking into different wavelengths. It looks rather similar that before ... (?) $\endgroup$
    – s-m-e
    Dec 17, 2012 at 10:12
  • $\begingroup$ @ernestopheles: I agree. Could you tell me more about the spectroscope - e.g., is specular spectroscopy used or something else? Did you check if Fresnel coefficients can explain your data? $\endgroup$
    – akhmeteli
    Dec 17, 2012 at 12:11
  • $\begingroup$ I used a stand-alone device ... lot-oriel.com/files/downloads/andor/en/… $\endgroup$
    – s-m-e
    Dec 18, 2012 at 11:17
  • $\begingroup$ @ernestopheles: It looks like this is not a grazing-incidence spectrometer: andor.com/pdfs/specifications/… . Am I missing something simple? $\endgroup$
    – akhmeteli
    Dec 19, 2012 at 1:28
  • $\begingroup$ I think you do not. My mistake, it includes a Czerny-Turner monochromator at normal incidence. Though, the question basically remains. (There are in fact grazing incidence Czerny-Turner devices, but that's not the case here.) $\endgroup$
    – s-m-e
    Dec 19, 2012 at 7:24

This looks like thermally induced stress birefringence of the windows to me. The time dependence is the key signal here. It's hard to see what happens in the first μs, but for the next ~20 μs you see the expected polarization behavior, then things go crazy, showing a doubling of the pattern at about 32 μs and then some randomness.

It appears the lamp window is heating up, expanding, then experiencing some stress because of the way it is mounted. The stress changes the birefringence differently at different positions of the window (See, for example, https://en.wikipedia.org/wiki/Photoelasticity), and what you measure is some average polarization over the whole surface of the window. As the window cools following the pulse, the stress redistributes, changing the polarization.

MgF2 is birefringent to begin with (https://en.wikipedia.org/wiki/Magnesium_fluoride#Optics), although the window is probably cut across the c-axis of the crystal to minimize this. From my own experience, c-axis-cut sapphire windows will show stress birefringence, too.

This is a difficult effect to avoid even at constant temperatures, and sometimes heroic efforts are needed to mount windows without stress for polarization sensitive applications. See, for example, http://dx.doi.org/10.1063/1.3606437 (Sorry for the paywall, but the main idea is in the abstract.)


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