estimate (\[rad\]) for the tail’s amplitude yields $N_{\mathrm{rad}}\sim 10^{-7}$, therefore the leaky modes have definite values of the norm, as indicated in the caption to Fig. \[symmetric and asymmetric modes\](b).

For the sake of direct comparison between leaky and trapped modes, in Fig. \[symmetric and asymmetric modes\](c) we display stationary states with the same propagation constant as in Fig. \[symmetric and asymmetric modes\](b), but in the case when they are confined by impenetrable (infinitely tall) outer potential barriers in Eq. (\[potential\]). It is seen that, similar to the situation shown in Fig. \[symmetric and asymmetric modes\](b), the smaller and larger values of $N$ correspond to the broken asymmetric and unbroken symmetric modes, respectively. However, in the infinitely deep potential box the profiles of the wave functions are, naturally, narrower and taller.

The symmetric modes displayed in Fig. \[symmetric and asymmetric modes\] feature split peaks, due to the fact that the inner potential barrier in Eq. (\[potential\]) is relatively high. On the other hand, the same potential structure with an essentially smaller barrier’s height $A$ supports single-peak symmetric modes, see Fig. \[unstable evolution\] below.

SSB of radiation tails in leaky modes
-------------------------------------

As mentioned above, the SSB of trapped modes is 