Photon lifetime in an optical cavity
You've calculated the time for a photon to take one round trip around the cavity. But you haven't considered any of the loss mechanisms, so you haven't determined how many round trips it can make, on average before it is absorbed or emitted out of one of the facets.
You want to use the equation
$$\frac{1}{\tau_p}=v_g \alpha + \frac{v_g}{L}\log\frac{1}{\sqrt{R_1 R_2}}$$
where \$\tau_p\$ is the photon lifetime, \$v_g\$ is the propagation velocity in the cavity, \$\alpha\$ is the distributed loss, \$L\$ is the cavity length, and \$R_1\$ and \$R_2\$ are the mirror reflectivities.
Note that the term \$\frac{1}{L}\log\frac{1}{\sqrt{R_1 R_2}}\$ is often called the &quot;distributed mirror loss&quot;. That is, it's the loss you would need to add to the material and waveguide loss (\$\alpha\$) to give the same effect over one round trip, as the two discrete mirrors.