Polarization of photon echoes from SF6molecules

We measured the polarization of the photon echo which was stimulated in a gas of S${\mathrm{F}}_6$ molecules by either linear-linear, circular-linear, or linear-circular pulse sequences from the $P\left(14\right)\mathrm{}$, $P\left(16\right)\mathrm{}$, $P\left(18\right)\mathrm{}$, $P\left(20\right)\mathrm{}$, $P\left(22\right)\mathrm{}$, and $P\left(24\right)\mathrm{}$ C${\mathrm{O}}_2$ laser lines near 10.4 μm. For $P\left(16\right)\mathrm{}$ a linear-linear pulse sequence with angle $\beta$ between the linearly polarized pulses produced a linearly polarized echo at angle $\varphi$ with the second pulse, and $\varphi$ rotated in the same sense as $\beta$; a left-circular-linear sequence produced an echo with right elliptic polarization, and a linear-left-circular sequence produced an echo with left-circular polarization. For all other lines a linear-linear sequence produced an echo polarized along the second pulse, and results were similar to the measurement of Gordon et al. on $P\left(20\right)\mathrm{}$. For $P\left(14\right)\mathrm{}$, $P\left(18\right)\mathrm{}$, and $P\left(20\right)\mathrm{}$ a circular-linear sequence produced an echo linearly polarized along the second pulse. For $P\left(14\right)\mathrm{}$ through $P\left(20\right)\mathrm{}$ a linear-left-circular sequence produced a left-circular echo. A theory is developed for these pulse sequences for arbitrary values of angular momentum $J_a$, and a simplification found for large $J_a$. For laser radiation in direction $Y$ and the linear polarization of the second pulse along $Z$, the polarization vector for a linear-linear sequence is approximately $\mp \left(\frac{1}{2}\right)\hat{X}sin\beta +\hat{Z}cos\beta$, and for a left-circular-linear sequence $\pm \left(\frac{i}{2}\right)\hat{X}+\hat{Z}$, where the upper sign refers to $J_a=J_b\pm 1$ or the $P$ and $R$ branches and the lower sign to $J_a=J_b$ or $Q$ branch. For a linear-left-circular sequence the echo is left circular for $J_a=J_b$,