$t=2\tau $ (i.e., the envelope $\exp
[-(\Delta -K/2)|t-2\tau |]$) for $\xi \ll (\Delta -\frac{1}{2}K)$.

We can similarly evaluate the contribution $R^{(2)*}_{m\tau }(t)$ of echoes at $t=m\tau $ for $m=3,4,\ldots$. For example, the result for the echo at $t=3\tau $ is $$R^{(2)*}_{3\tau }=\frac{2h^*_2h_3d_0d_1\Delta }{\Delta
-(K/4)}e^{-\xi (3\tau +t)}e^{-i\bar \omega (t-3\tau )}E(t-3\tau )
\ ,$$ $$E(t-3\tau )= \left\{ \begin{array}{ll} \exp [\Delta (t-3\tau )] \
, & {\rm for} \  t<3\tau \ , \\
\exp -[(\Delta -\frac{1}{2}K)(t-3\tau )] \ , & {\rm for} \
t>3\tau \ .
\end{array}
\right.$$ Thus, in the case $\xi =0$, the shape of the pulse envelope $E(t-3\tau )$ is asymmetric about $t=3\tau $, increasing at a more rapid exponential rate (namely, $\Delta )$ as $t$ increases toward $3\tau $, than the slower exponential rate of decrease (namely, $\Delta -(K/2)$) as $t$ increases away from $3\tau $. This is in contrast to the symmetrically shaped envelope $\exp [-(\Delta
-\frac{1}{2}K)|t-2\tau |]$ for the echo at $t=2\tau $.

In Appendix II we present an evaluation of $R^{(2)*}_{2\tau }(t)$ for the case of a Gaussian frequency distribution function, $$g(\omega )=g_G(\omega )\equiv [2\pi \Delta ^2]^{-1/2}\exp
[-(\omega -\bar \omega )^2/(2\Delta ^2)] \ .$$

F. The small coupling limit
---------------------------

We now consider a general frequency 