to a hyperfine transition using fm modulation spectroscopy. The pump laser is scanned around the same set of transitions. The beams are mixed in a polarizing beamsplitter cube (PBS) and [*copropagate*]{} through a room-temperature vapor cell (5 cm long) with orthogonal linear polarizations. Halfwave retardation plates in the path of each beam allow precise control of their powers. The probe beam is separated using a second PBS, and its transmitted signal is detected with a photodiode. The PBS’s have extinction ratios of $1000:1$, ensuring good purity of the detected signal.

Spectrum in $^{87}$Rb, $F=2 \rightarrow F'=1,2,3$
-------------------------------------------------

As mentioned before, the main advantage of the co-propagating configuration is the absence of spurious crossover resonances. This difference is seen clearly in Fig. \[satabs\]. In (a), we show the usual saturated-absorption spectrum for the $F=2 \rightarrow
F'=1,2,3$ transitions in $^{87}$Rb. The spectrum is Doppler corrected, which is necessary because probe absorption through a vapor cell will show a broad Doppler profile when the probe addresses a velocity group different from that resonant with the pump. When the pump and probe are resonant with the same velocity class, we get transmission peaks. As expected, there are three hyperfine peaks and three crossovers. The 