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Photon chi-variable

also: Photon $\chi$-variable

Consider CRE-filtered beam. Its second quantization axis and the (common) linear polarization axis are presented below for the case when looking against the beam propagation.

Image image002

We need to assign some variable of the two axes to describe the photon state. It is impossible to define rotationally invariant variable, uniquely describing above figure. (Because of the sign ambiguity of the scalar product: the unit vector of the polarization axis has two degrees of freedom.) This is typical spinor ambiguity.

The angle from the polarization axis toward the second quantization axis in CCW direction is defined as photon $\chi$-variable. Thus defined, the $\chi$-variable corresponds to the phase with natural domain $[0, \pi)$ from the classical Poynting vector solution.

For fixed $\Lambda$- and $\chi$-variables there are two kinds of photons. They have opposite second quantization axes and are experimentally distinguishable. One more bit-like variable is required to identify them.

 

May 24, 2006
Author: T Kirilov