This paper sets forth the mathematical formulation of nonstationary optics, with an emphasis on pulsed beams.

Basic properties of pulses, such as pulse length and shape, propagation, and spatiotemporal coupling are discussed in detail.

Some experimental aspects are highlighted, such as spectral scale transformations, which allow ideal focusing.

Common pulse measurement schemes are discussed in relation to partial coherence.

Isodiffracting pulsed beams are generated in common spherical mirror laser cavities.

We developed a closed form analytical framework to discuss their properties.

In particular, they exhibit coupling between space and time, such that partial spatial coherence leads to reduced temporal coherence.

We discuss general methods for producing desired spectral scale transformations applicable to nonstationary fields.

As a particular case, we transform isodiffracting pulsed beams into spatiotemporally separable fields and spectrally invariant fields.

This allows one to either modulate the spatial or temporal properties individually, or produce fields with the same spectrum in all observation directions.

We also discuss hybrid refractive-diffractive imaging systems which are able to produce these transformations accurately in real experimental settings.

We establish what type of coherence information one can attain from time-integrating measurements.

The usual field autocorrelation is compared to an alternative implementation, as well as a field cross-correlation.

We employ numerical pulse ensembles of exotic light sources with nontrivial coherence properties: supercontinuum light and free-electron lasers.

We perform experimental studies on the beaming properties of a plasmonic lattice laser.

Such light sources do not employ regular laser cavities, but instead a lattice of plasmonic nanoparticles, overlaid with laser dye.

This is the first detailed analysis of beam quality in such systems and reveals the underlying physics of the observed polarization asymmetry.