More on the question: Can monochromatic light be unpolarized? (original) (raw)

Posted on 2025-07-30 as part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2025_07_30.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG

Abstract: The question whether monochromatic light can be unpolarized is addressed with an interesting gedanken experiment. Different definitions of monochromacity can be used, but which one makes most sense?

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On 2019-08-26, I published the Spotlight article “Can Monochromatic Light be Unpolarized?”, and I encountered that topic again when finally writing an Encyclopedia article on unpolarized light. Here are some interesting new thoughts: a gedanken experiment illuminating the matter.

A Gedanken Experiment

Imagine that we start with strictly monochromatic light which is linearly polarized, and then make it unpolarized by applying time-dependent polarization changes — for example, using some combination of electro-optic modulators driven with pseudo-random voltages. That might in practice well include some phase modulation, but imagine that we could make a device which only modulates the direction of linear polarization without affecting phase or amplitude. That way, we could in principle achieve complete depolarization if the modulation is fast enough for the anticipated measurement time.

The question is now: Can that light output still be considered monochromatic?

I first asked ChatGPT 4o. It said: “Yes, the light will still be monochromatic, provided that the device only modulates the polarization direction and does not alter the frequency (or wavelength) of the light.” It provided further justification, e.g. emphasizing that monochromaticity relates purely to the temporal oscillation of the electric field vector, not its direction.

Basically, the answer must depend on how exactly we define monochromaticity:

• You could define it such that you explicitly do not care about the polarization direction and only consider the still sinusoidal oscillation of the electric field. Then you consider that light monochromatic.
• Alternatively, you may look at the electric field components ($E_x$) and ($E_y$) (for propagation in ($z$) direction). These will no more exhibit sinusoidal oscillations; they are affected by the polarization modulation. As a result, these components are no longer monochromatic! You may consequently state that the whole light field is not monochromatic.

Deciding for the More Appropriate Definition of Monochromacy

Now, what definition of monochromacy makes more sense? I propose it is the one which is physically more meaningful. I thus consider what happens to an atom exposed to that light, assuming it has a narrow electronic resonance at the considered light frequency. It can serve as a kind of oscillator for testing that light field. Will absorption of light be affected by the modulation?

To answer that question, purely classical (non-quantum) considerations suffice. An oscillator may react to both electric field components ($E_x$) and ($E_y$), and it will certainly be affected by their modulation. The building up of oscillation amplitude with time can be seriously hindered. Also, if there is some finite offset between resonance frequency and light frequency, we will not expect the same behavior as for unmodulated light: The difference between the cases with and without frequency offset can be substantially reduced. This suggests a finite bandwidth of the obtained light.

So the physical argument clearly favors the second definition and the result that the light is not monochromatic.

Another consideration is what is mathematically more natural. I think that leads to the same result: It is not natural to take a field with fluctuating ($E_x$) and ($E_y$) components, then first take the modulus of that, but also somehow define the suitable sign, in order to only then apply harmonic analysis. The clearly more straightforward way is to perform the harmonic analysis directly on ($E_x$) and ($E_y$).

Conclusions

We can draw some conclusions:

• First of all, it is stimulating to carefully and actively think about such things. That way, we get to a clearer understanding. Just reading textbooks will not result in the same buildup of expertise!
• Second, we realize that a lack of polarization is not a trivial thing, nor is it the transformation of polarized light into unpolarized light. Some kind of randomness plays a crucial role, and that also affects the optical spectrum.
• Third, don't just believe AI! Language models are not reliable expert systems, and maybe never will be. By their nature, they produce text which looks like being likely said in a certain situation. Real understanding is something else! (See also my previous Spotlight article “Have AI bots like ChatGPT Got Better on Photonics Questions?”.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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