Quantum indeterminacy relationship for optical video pulses

A theoretical investigation is made of the conditions under which an optical video pulse of femtosecond duration can be represented using classical optics. It is shown that the minimum value of the indeterminacy (uncertainty) parameter $E\tau_0\hbar^{-1}$ ($E$ is the energy and $\tau_0$ is the duration of a pulse) depends on the dimensionless quantity $\omega_{\max}\tau_0$ ($\omega_{\max}$ is the upper frequency limit which determines the precision of reconstruction of the shape of an optical video pulse) and on the average number of photons in a mode $\langle N_{\min}\rangle$. The latter parameter is related to indeterminacy of the mode phase and is a consequence of the quantum nature of light.