FOCS Physics 101

OpticAmpere's fiber optic current sensors (FOCS) exploit Faraday rotation of plane polarized optical fields to measure magnetic field intensity, but the quantum-level magneto-optical interactions which create Faraday rotation are described with the Zeeman effect, where a counter-clockwise plane rotation, or precession, of the naturally oscillating electrons within the optical field (E) is induced by an external magnetic field (H), with the rotation rate determined by the Larmor frequency, which is directly proportional to the magnetic field (H).  A perfectly longitudinal observation path of the polarized optical field (E) in the FOCS module, with respect to the electric conductor's magnetic field vector orientation, excites right and left circularly polarized modes within the optical field (E), at frequency bands determined by the difference of the Larmor precession frequency corresponding to the magnetic field (H), and the natural frequency of the oscillating electrons which comprise the optical field (E), which induces circular birefringence in the optical fiber, resulting in Faraday rotation, or modal coupling between the birefringent transmission axes, for the ideal scenario of a FOCS module which is installed at an angle exactly normal to the conductor path. 

In practice, FOCS modules may be required to be installed at offset angles relative to the conductor, for a variety of mechanical or clearance reasons, or perhaps guaranteeing a six-sigma level of perpendicularity when installing is simply not possible.  OpticAmpere's FOCS modules operate using any offset angle of the passive fiber optic current sensor loop with respect to the conductor, as post-installation calibration factors the effect of observation angle between the optical field path of the FOCS module, and the magnetic field vector of the electric conductor, into the scaled fiber optic sensor output.  This mechanical installation flexibility introduces a transverse Zeeman effect in operation, which does not produce Faraday rotation, where linearly polarized modes are excited at both the Larmor-deviation and natural frequencies of the orbiting charges within the FOCS' polarized optical field, resulting in an elliptical state of polarization of the FOCS light source atomic emission spectra, at the positive and negative Larmor frequency deviations from the natural frequency, with the ellipticity being the result of the superposition of the longitudinal and transverse Zeeman effect components, as the vector superposition of right and left circularly polarized modes, as excited by the longitudinal Zeeman effect, which induces circular birefringence in the FOCS, resulting in measurable Faraday rotation, with the linear vertical polarized modes excited at the Larmor-deviation frequencies of the polarized optical field by the transverse Zeeman effect, results in an overall elliptical polarization state of the spectral lines emitted by the FOCS' optical field, at the positive and negative Larmor-deviation frequencies, with a linear horizontal polarized spectral line emitted at the natural frequency.

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