cavity as seen on a CCD camera at various detunings of the cavity. Lower case Roman numerals (i)-(viii) are for TEM$_{01}$ mode and (ix)-(xiv) are for TEM$_{10}$ mode. (xv) shows an instance of TEM$_{00}$ mode. Here, for TEM$_{00}$ mode $N_c = (33 \pm 1) \times 10^3$, it will be lower for higher order modes. The power of MOT cooling laser is 36 mW/cm$^2$ for all the cases.[]{data-label="pol"}](modes_plus_polarization.pdf){width="15cm"}

Signatures of lasing
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The threshold behaviour seen only in the red detuned peak in Fig. \[atnogrid\](c) is suggestive of lasing in this driven atomic system coupled to the cavity mode. Since during lasing one mode experiences large gain compared to others as stimulated emission ensures that the dominant mode wins, so to check for lasing by the atom-cavity system, we check for purity of the state of light that comes out of the cavity. The first check is for the polarisation state of the cavity emitted light using a polariser (Thorlabs LPNIRE100-B) with variable polarisation angle in between the cavity mirror and the PMT. Fig. \[pol\](a) shows the change in peak height of both red and blue detuned peaks as the polarization angle is changed. The polarisation of the red detuned peak 