4.4 APD gain optimization

The APD gain is a parameter required to evaluate performance. For example, Eq. (2) depends on the gain. All numerical results in this paper use an optimized gain. For each value of $\bar n_b$, the numerical capacity or other needed quantity was computed over a range of gains, and the largest one chosen. In the interest of time, the gain was restricted to multiples of five. In all cases considered, a gain difference of five (and typically much more than five) from the optimal value made little difference in the numerical results. Shown in Fig. 6 are the optimal gain values. Optimal APD gains are also reported in [18].

Figure 6: Optimal gain, as a function of $\bar n_b$, for $\bar n_s=100$, $T_s=31.25$ ns, $T_d = 432000$ ns, and the SLiK APD detector.