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Conerefringent optics

also: CR optics

The conerefringent optics is akin to the birefringent optics by their common progenitor: the lateral shift of a light beam. If the lateral shift is bigger than the beam diameter, the outgoing beam splits. In this case, the birefringent element /BRE/ and the conerefringent element /CRE/ can be considered as Stern-Gerlach filters.

Compare the performance of BRE and CRE as filters:

1a) The BRE splits a scalar beam in two beams. The one BRE-filtered beam does not split more passing through second BRE with identical orientation. The BRE-filtered beam is (quantum mechanically) “pure” or polarized beam with zero-helicity, also with the terms of optics it is named linearly polarized.

1b) The CRE splits a scalar beam in continuum of beams with the form of ring, see internal conical refraction. One CRE-filtered beam does not split more passing through second CRE with identical orientation. That is why the CRE- filtered beam is also (quantum mechanically) “pure” or polarized beam.

2a) The CRE-filtered beam can not be further filtered by BRE filter. The photons from one CRE-filtered beam are in basis state of the BRE filter; with the terms of optics it is linearly polarized.

2b) The BRE-filtered beam is further filtered by CRE filter. The photons from one BRE-filtered beam are not in basis state of the CRE filter.

3a) When BRE-filtered beam passes through a second BRE, rotated by angle $\omega$ relative to the linear polarization axis, the passed-through beam splits in two beams. The transition amplitudes transform as $e^{iw}$. Therefore the basis states of the BRE filter are vector states.

3b) When CRE-filtered beam passes through a second CRE, rotated by angle $\omega$ relative to the second quantization axis, the passed-through beam splits in two beams. The transition amplitudes transform as $e^{iw/2}$, see frame rotation. Therefore the basis states of the CRE filter are spinor states.

From 1) and 2) follows that the photons from BRE-filtered beam and the photons from CRE-filtered beam are experimentally distinguishable even if they have the same all variables (spin, wavelength and 3-momentum) characterizing the photon as fundamental particle. From 3) follows that the photon transforms on an equal foot as bosonic or as fermionic particle.

The birefringent optics uses expediently the basis states of BRE.

Define the conerefringent optics as an expedient use of the basis states of CRE.

 

May 24, 2006
Author: T Kirilov