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The Gaussian pulse field-envelope width is the full width at half maximum of the magnitude of a Gaussian electric-field envelope. It differs from the FWHM of radiant power. For a fixed spatial mode with $P(t)=K|A(t){|}^2$ and constant $K>0$,The Gaussian pulse energy and peak power article derives this relation. Power-FWHM is also the convention explicitly used for PULSELENGTH in the primary source documentation.^[ref]

For an original example, a power width of $12\mathrm{ns}$ corresponds to field-envelope width $16.97\mathrm{ns}$. At the field-envelope half-maximum points, the power is one quarter of its peak, since $(1/2{)}^2=1/4$. At the power half-maximum points, the field magnitude is instead $1/\sqrt{2}$ of its peak. A threshold applied to one measured quantity therefore does not define the other quantity's FWHM.

The envelope magnitude is distinct from the rapidly oscillating signed electric field. A direct photodetector generally supplies a power-related electrical trace, further modified by its impulse response; it is not a direct recording of the optical carrier's field envelope. Inserting an amplitude width into a power-width peak power formula consequently uses the wrong convention. State the observable and the response model with the reported pulse duration.

Nonuniqueness of pulse energy at fixed peak power and FWHM means that those two measurements do not determine the integral of an otherwise unspecified power profile. The pulse energy shape factor gives a rectangular/exponential counterexample. A stronger original construction shows there is no finite universal upper bound without restrictions on lower-level tails.

Fix $P_{\mathrm{pk}}>0$, power FWHM $\tau >0$, and $0<\alpha <1/2$. Choose any $D\ge \tau$. Let the power equal $P_{\mathrm{pk}}$ for $|t|\le \tau /2$, equal $\alpha P_{\mathrm{pk}}$ for $\tau /2<|t|\le D/2$, and zero afterward. The optical pulse pedestal is part of the stipulated signal, not an unrelated background. Its level stays below half maximum, so the peak and FWHM remain unchanged, butWith $\alpha =0.10$ and $D=101\tau$, the energy is $11P_{\mathrm{pk}}\tau$, compared with $P_{\mathrm{pk}}\tau$ for the pedestal-free rectangle. Increasing finite $D$ gives unbounded pulse energy at fixed peak and FWHM across this family of finite-duration ideal profiles.

This is an identifiability result, not a claim that a particular laser has arbitrarily long tails. The primary source definition of power-FWHM fixes a threshold width, not the integrated energy below that threshold.^[ref] A measured full profile, a justified shape family or additional tail-duration bounds supply information that peak and FWHM omit.

Pulse duration quantifies a pulse's temporal extent using a stated observable and width convention. A common optical convention is the full width at half maximum of the background-subtracted radiant power profile. The Ansys source documentation explicitly defines its PULSELENGTH parameter as the power-profile FWHM, rather than the width of the electric-field amplitude.^[ref]

For an original example, choose a triangular power pulseIts nonzero support extends from $-T$ to $T$, giving total support width $16\mathrm{ns}$. Its half-maximum crossings occur at $t=\pm T/2$, giving a power FWHM of only $8\mathrm{ns}$. Neither number is wrong when its convention is specified. The pulse energy shape factor additionally relates a chosen width to integrated energy and peak power.

A fast photodetector and oscilloscope record an electrical response to an optical pulse. For a linear response model, the recorded trace is a convolution with the instrument's impulse response; a slow response can broaden the measured feature. The readout width need not equal the optical width. State the observable, background treatment and instrument response when reporting a duration. Pulse energy baseline correction affects where the half-maximum threshold lies, while Gaussian pulse energy and peak power treats the conversion for a specific power-profile family.

The pulse energy shape factor is the dimensionless ratiowhere $U$ is laser pulse energy, $P_{\mathrm{pk}}$ is background-subtracted peak power and $\tau$ is a stated pulse duration. It belongs to the chosen profile and width convention. Here $\tau$ denotes the power full width at half maximum, the convention explicitly used by the primary source documentation.^[ref]

An original counterexample compares a rectangular pulse with a bilateral exponential pulse. Give both the same $P_{\mathrm{pk}}$ and power FWHM $\tau$. The rectangle is nonzero over a width $\tau$, so $U_{\mathrm{rect}}=P_{\mathrm{pk}}\tau$ and ${\kappa }_{\mathrm{rect}}=1$. Forthe half-maximum points are again $\pm \tau /2$, but integration of the two tails gives $U_{\exp }=P_{\mathrm{pk}}\tau /\ln 2$ and ${\kappa }_{\exp }=1/\ln 2\approx 1.4427$.

With $P_{\mathrm{pk}}=2\mathrm{W}$ and $\tau =5\mathrm{ns}$, the energies are $10$ and $14.43\mathrm{nJ}$. The same measured peak and FWHM therefore leave a 44.3 percent difference in this example. This nonuniqueness of pulse energy at fixed peak power and FWHM is a profile ambiguity, not an instrument-unit conversion.

The Gaussian pulse energy and peak power article gives the Gaussian-family relation. Reconstructing an arbitrary pulse's energy requires the full calibrated profile or an additional justified shape model; a width and peak alone cannot supply it.

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 $\alpha P_{\mathrm{pk}}$ extending to total duration $D$.

For any desired energy above the core energy, chooseThis is finite for every finite desired $U$ while keeping the peak and power FWHM unchanged. For an original numerical case, take $P_{\mathrm{pk}}=3\mathrm{W}$, $\tau =4\mathrm{ns}$ and $\alpha =0.20$. An energy of $1\mu \mathrm{J}$ requires $D\approx 1.651\mu \mathrm{s}$ 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 $0.20P_{\mathrm{pk}}$, thenThese 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.^[ref] The construction concerns isolated ideal pulse profiles, not a claim that an actual laser or finite-period pulse train can have arbitrary tails.