Designing a Cir-Pol Sensitive to Left-Handed Light.

A concept which the reader may already be familiar with, is a Circular Polarizer, which first linearly polarizes light, and then renders the result circularly-polarized. But somebody might be interested, in creating a filter which is only sensitive to light circularly-polarized in one direction. Well, it turns out that this is as straightforward to achieve, as the first example, if we can assume that we have a birefringent layer, light with one known wavelength, and that we can adjust the thickness of the birefringent layer as needed.

cir-pol-inv_1-svg

 

cir-pol-inv_4

 

If we assume that light can first be linearly polarized, and then passed through the birefringent layer, whose extraordinary and ordinary axes are both at a 45⁰ angle to that of the original plane-polarization, then due to the higher refractive index of the extraordinary axis, its wave-function – i.e., dipole-moment – will become delayed with respect to that of the ordinary axis, until the former is phase-delayed by 90⁰, which is also 1/4 the wavelength of the light, with respect to the latter. In the example shown above, left-handed, circularly-polarized light has been achieved.

But the question could next be asked, what would happen if, we passed this helical beam of light, whose dipole-moments propagate as a left-handed helix, through another birefringent layer, that exactly matches the previous one. And the result which we’d obtain, is that the phase-position of the wave-function along the extraordinary axis, which has already been phase-delayed 90⁰, will be phase-delayed again, by another 90⁰, so that now its phase-position will be at 180⁰ to that, along the ordinary axis. And so where the diagram above showed full amplitude, it will consistently show zero amplitude, and full amplitude will take place perpendicularly, to where it had been before.

Thus, by controlling in which direction the extraordinary layer is followed by the transmitting direction of the linear polarizer that comes next, we can control whether the combination will be sensitive to left-handed or right-handed light.

I suppose that the mental exercise can be taken one step further, and we can ask what would happen, if directly after circularly-polarized light was achieved, said beam was bounced off a metallic mirror, with the directions of propagation before and after, ‘normal’ to the surface of that mirror.

And then what we’d get, is that dipole-moments that advanced counter-clockwise as observed, when propagating away from the viewer, will still be advancing counter-clockwise, and propagating towards the viewer. Only, this will now correspond to right-handed light and not left-handed. And the reason for that would be that the same, consistent dipole-moments, would be seen as advancing clockwise now, as would be observed ‘from behind the mirror, looking back’ (in the new direction of propagation). And so, the same geometries in the filter, will result in absorption.

Dirk

 

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