I have read that monochromatic light is always polarized as they say that there is always a constant phase difference between the x and y components of the electric field. And that the unpolarized light happens only with a band of frequencies.
1. Isn't it possible for the light to be have single frequency but have its electric field vector in random directions at different instants of time?
2. Can we have polarized light with multiple frequencies?
If we stress on dogmatism then we should also admit that strictly monochromatic light is not possible at all:
classically, because it would require a wave of infinite length and hence infinite energy content.
quantum-mechanically, because it would require the production of a Glauber state, which is a superposition of states with all possible numbers of photons...
If the question is more practical, and the quality of a good laser is sufficient for using the term "monochromatic" then I'd be interested to know what kind of state we obtain after hitting a good depolarizer (such devices exist afaik) with the laser beam.
Randomly polarized light implies that it is not strictly monochromatic. This is straightforward to show if we decompose the electric field into orthogonal polarizations:
E=A cos(2 pi f t + phi) a_x + B cos (2 pi f t + psi) a_y
where a_x, a_y are unit vectors in x and y directions. The amplitudes A and B as well as the phases psi and phi are random variables. Taking the fourier transform of the field will yield a spectral density with a finite linewidth. This means that the light is not strictly monochromatic. Random polarization requires some form of noise process that spreads the spectrum of the signal.
The answer to your second question is yes. Imagine several "carriers" with different frequencies with electric field vectors aligned along one axis.
Dear Sumanth,
I agree with George. I wish specify that in your question 1), the amplitude of the electric vector can also be constant; that is, it can change the direction (spatial lying position) only. In this case, A and B are not independent. However, even in this case, the light is not strictly monochromatic. To convince yourself, you can think the time as a continuous variable and not in a step by step way where the time seems disappearing.
Best Regards
The point being that, for the light to be unpolarized, the two components must be uncorrelated, which is only possible if A and B are random functions of time. You can get approximately monochromatic unpolarized light though.
If we stress on dogmatism then we should also admit that strictly monochromatic light is not possible at all:
classically, because it would require a wave of infinite length and hence infinite energy content.
quantum-mechanically, because it would require the production of a Glauber state, which is a superposition of states with all possible numbers of photons...
If the question is more practical, and the quality of a good laser is sufficient for using the term "monochromatic" then I'd be interested to know what kind of state we obtain after hitting a good depolarizer (such devices exist afaik) with the laser beam.
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