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In the course of circuits and electronics, I remember there is an experiment to show the polarization of the wave as lissajous figures. I am wondering for polarized laser, is there any way to visualize the polarization in the similar way? I try to use a light splitter to split the (circular) polarized light into two perpendicular beams and used photo detector to receive the beam and send them into oscilloscope in X and Y channel. But the scope doesn't really show the 'lissajous' figure. So I am wondering if this is the right way to visualize the polarized light? Thanks

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(Interesting) Lissajous figures require two different frequencies; you're not going to see them this way. Polarization of monochromatic light is an oval in general. –  Mark Eichenlaub Nov 22 '12 at 2:31
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Circularly polarized light should create a circle on the oscilloscope, which is a type of Lissajous curve. Any polarization of light produces a Lissajous curve with the restriction that the two frequencies of the x and y parameters are the same. So the only possibilities are a circular, elliptical, and linear polarization.

If your oscilloscope doesn't show a circle for circularly polarized light, something has gone wrong in the experiment.

Edit: this does assume your laser is a simple harmonic wave, so that the electric field varies sinusoidally and we therefore have in-phase x and y components. Also, see polarization.

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-1. That would be true, except that the Lissajous curve is being traced at the optical frequency, and no electronic detector or circuit is going to have the frequency response necessary to follow that. –  user2963 Nov 22 '12 at 1:46
    
If that is the case, then that explains why user1285419 isn't seeing the result on his/her oscilloscope. So to answer the question, then: the reason you aren't seeing a lissajous figure is that the laser operates at a frequency to which the circuit responds poorly. However, YES, it is the correct way to visualize polarization with the restriction I mentioned above. –  PatEugene Nov 22 '12 at 1:55
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It's not just that the circuit responds poorly, it's that with our current and foreseeable future electronic technology it's flat out impossible to visualize a frequency this fast. To make it more explicit, some common frequencies: AM radio ~= 1 MHz, FM radio ~= 100 MHz, WiFi = 2000 MHz, fastest transistor ever made ~= 100,000 MHz, green light ~= 600,000,000 MHz. –  user2963 Nov 22 '12 at 2:04
    
Thanks guys. So based on all those explanation and my understanding, I think the way to visualize the polarization is technically correct, but the photo detector can only detect the 'average' signal (some high frequency components will be averaged out), so it is not feasible to render the lissajous figure, is that correct? So is that any idea to actually visualize the polarization of laser beam? Thanks. –  user1285419 Nov 22 '12 at 2:32
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That is correct. It is still a useful way to visualize it, but it is only experimentally measurable at radio frequencies. –  Emilio Pisanty Nov 22 '12 at 17:15
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