In the case of a laser with external mirror, only the higher intensity left emission peak on the fluorescence response (right arm on the \(v^2\) vs \(x\) curve) is set oscillating. The low intensity right emission peak decayed. Only one mode is in the output of the laser.
This suggests \(\theta\) is polarization.
with,
\(-\theta\equiv\theta\)
negative \(\theta\) is equivalent to positive \(\theta\).
As the particle performs circular motion, \(x_d\) rotates along the perimeter of the circle. When we hold \(x_d\) fixed,
the particle performs circular motion in a rotating circle whose diameter traces the slant surface of a cone. The particle is always on \(x_d\); the circular path rotates at an incline \(\theta\) to the direction of \(x_d\), \(PO\). \(PO\) is the direction of incident.
This way,
\(-\theta\equiv\theta\).
If particle has energy oscillating in the orthogonal dimension, \(t_c\) (eg. \(g^{+}\), \(T^{+}\)), the particle in circular motion creates an \(E\) field given by the right hand screw rule. This field rotates as the circle rotates, and always makes an angle of \(\small{90^o-\theta}\) with \(PO\). This rotating \(E\) field does not mean circular polarization. Polarization as detected by rotating a polarizer in front of a laser is \(\theta\).
This rotating \(E\) field is consistent with the rotating dipole model from which we have,
\(B=i\cfrac{\partial\,E}{\partial x}\)
from the post "Whacko and the Free Photons" dated 30 May 2014.
The \(E\) field is always rotating given non zero \(\theta\). When \(\theta=90^o\), \(E\) is parallel to \(PO\). From,
\(E_p=\hbar\left\{\sqrt{tan(\theta_v)}-1\right\}\cfrac{c}{x_c}\)
\(E_p\to\infty\)
In this case, the particle travels along \(PO\) with circular motion. At the center \(O\), the particle is in circular motion but with \(v_{shm}\approx 0\). The particle no longer oscillate. Emission at \(\small{E_p\to\infty}\) occurs only once.
We are assuming that all forces on the particle are finite as such,
\(F_{cir}=m\cfrac{v^2_{cir}}{x_c}\)
\(x_c\to 0\), \(v_{cir}\to 0\) as \(\theta\to90^o\), for \(F_{cir}\) finite.
