Glossary entry

Photon lifetime (τ_p)

The mean residence time of a photon in an optical cavity before being lost to absorption, scattering, or output coupling. Sets resonator response time, linewidth, and modulation bandwidth.

For a cavity with total photon loss rate $\kappa$ :

\tau_p \;=\; \frac{1}{\kappa}.

Equivalently, the photon density inside the cavity decays as $\exp(-t/\tau_p)$ in the absence of stimulated emission or external pumping.

Relation to quality factor:

\tau_p \;=\; \frac{Q}{\omega_0} \;=\; \frac{Q \, \lambda_0}{2\pi c}.

At $\lambda_0 = 1550$ nm, the conversion is $\tau_p \, [\text{ps}] = Q / 1.215 \times 10^6$ . Numerical examples:

$Q$	$\tau_p$ at 1550 nm
$10^4$	8.2 ps
$10^5$	82 ps
$10^6$	820 ps
$10^7$	8.2 ns
$10^8$	82 ns

For a Fabry–Pérot cavity of length $L$ with internal loss coefficient $\alpha_i$ and mirror reflectivities $R_1$ , $R_2$ :

\tau_p \;=\; \frac{n_g L}{c \left[ \alpha_i L + \frac{1}{2}\ln\!\frac{1}{R_1 R_2} \right]}.

The bracketed term in the denominator is the total round-trip loss in nepers.

Photon lifetime controls several important timescales:

Spectral linewidth of resonator transmission: $\Delta\nu_{1/2} = 1/(2\pi \tau_p)$
Relaxation oscillation frequency of a laser diode: $\omega_R = \sqrt{1/(\tau_p \, \tau_n)}$ , where $\tau_n$ is carrier lifetime
Direct modulation bandwidth limit: typically $f_{3\text{dB}} \approx 1.55 \, f_R$
Photon round-trip time vs $\tau_p$ ratio sets the cavity feedback dynamics

For semiconductor lasers, $\tau_p$ is typically picoseconds (Fabry–Pérot edge emitters) to nanoseconds (high- $Q$ VCSEL designs and DBR lasers). For passive resonators, $\tau_p$ ranges from sub-picosecond (lossy waveguide rings) to milliseconds (whispering-gallery-mode crystalline resonators with $Q > 10^{10}$ ).