= Unbounded pulse energy at fixed peak and FWHM
\b[Unbounded pulse energy at fixed peak and FWHM] means there is no universal finite energy upper bound from those two quantities alone. Each pulse can still have finite duration and finite energy. The <nonuniqueness of pulse energy at fixed peak power and FWHM> article constructs a rectangular core of width $\tau$ and a below-half-maximum pedestal of height $\alpha P_{\rm pk}$ extending to total duration $D$.
For any desired energy above the core energy, choose
$$
D=\tau+\frac{U/P_{\rm pk}-\tau}{\alpha},\qquad 0<\alpha<1/2.
$$
This is finite for every finite desired $U$ while keeping the peak and power FWHM unchanged. For an original numerical case, take $P_{\rm pk}=3\,\mathrm W$, $\tau=4\,\mathrm{ns}$ and $\alpha=0.20$. An energy of $1\,\mathrm{\mu J}$ requires $D\approx1.651\,\mathrm{\mu s}$ in this ideal profile. The core contributes only $12\,\mathrm{nJ}$.
Additional information changes the problem. If the signal support is bounded by $D_{\max}=20\,\mathrm{ns}$ and power outside the FWHM interval is at most $0.20P_{\rm pk}$, then
$$
U\leq P_{\rm pk}\tau+0.20P_{\rm pk}(D_{\max}-\tau)=21.6\,\mathrm{nJ}.
$$
These <pulse-energy bounds from tail duration and pedestal height> require independently justified tail constraints. A FWHM definition alone fixes a threshold width, not the below-threshold integral.<Plane wave and beam source - Simulation object in Ansys Optics documentation>[PULSELENGTH definition]{ref} The construction concerns isolated ideal pulse profiles, not a claim that an actual laser or finite-period pulse train can have arbitrary tails.
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