Interstellar communication. XI. Short pulse duration limits of optical SETI

Previous and ongoing searches for extraterrestrial optical and infrared nanosecond laser pulses and narrow line-width continuous emissions have so far returned null results. At the commonly used observation cadence of $\sim 10^{-9}\,$s, sky-integrated starlight is a relevant noise source for large field-of-view surveys. This can be reduced with narrow bandwidth filters, multipixel detectors, or a shorter observation cadence. We examine the limits of short pulses set by the uncertainty principle, interstellar scattering, atmospheric scintillation, refraction, dispersion and receiver technology. We find that optimal laser pulses are time-bandwidth limited Gaussians with a duration of $\Delta t \approx\,10^{-12}\,$s at a wavelength $\lambda_{0}\approx1\,\mu$m, and a spectral width of $\Delta \lambda \approx 1.5\,$nm. Shorter pulses are too strongly affected through Earth's atmosphere. Given certain technological advances, survey speed can be increased by three orders of magnitude when moving from ns to ps pulses. Faster (and/or parallel) signal processing would allow for an all-sky-at-once survey of lasers targeted at Earth.