of the excited atoms by the MOT beams. This is because we go well above the saturation intensity of the atoms, even at the detuned frequencies of the MOT beams, for the case in Fig. \[motpowgrid\]. In this case, the spontaneous emission that the blue detuned peak represents competes poorly against stimulated emission into the MOT beams, compared with the red detuned peak. This provides experimental evidence of crucial differences between the blue and red detuned emission peaks observed.

![Mode purity measurements. (a) Polarisation diagnosis of the light coming out of the cavity. Blue empty squares denote the height of the blue detuned peak, and red dots denote the height of the red detuned peak. Red dashed and blue dashed are peak values when we do not have a polariser in the cavity output path multiplied by transmission coefficient of the polariser. The smooth curves are obtained by fitting cosine function multiplied by a linear function, $\left(a+b\cos{[\frac{\pi}{180}x]}\right)\left(1-c x\right)$. The linear function is used to correct for the systematic effect of atom number decrease during long measurements. (b) Cavity output profile for different polariser angles. Here, $N_c = (26 \pm 1) \times 10^3$ for the above graphs. (c) Modes of the 