We present an analytical formalism elucidating how information is stored in chirped optical probes by describing the effects of sinusoidal temporal modulations on the electric field. We show that the modulations produce spectral sidebands which can be interpreted as temporal sidebands due to the time-wavelength mapping, an effect we call temporally encoded spectral shifting (TESS). A derivation is presented for the case of chirped-pulse spectral interferometry showing how to recover both the amplitude and the periodicity of the modulation from a Fourier transform of the interferogram. The TESS effect, which provides an intuitive picture for interpreting pump-probe experiments with chirped pulses, is illustrated for probing wakefields from a laser-plasma accelerator.

Each successive generation of x-ray machines has opened up new frontiers in science, such as the first radiographs and the determination of the structure of DNA. State-of-the-art x-ray sources can now produce coherent high brightness keV x-rays and promise a new revolution in imaging complex systems on nanometre and femtosecond scales. Despite the demand, only a few dedicated synchrotron facilities exist worldwide, partially due the size and cost of conventional (accelerator) technology. Here we demonstrate the use of a recently developed compact laser-plasma accelerator to produce a well-collimated, spatially-coherent, intrinsically ultrafast source of hard x-rays. This method reduces the size of the synchrotron source from the tens of metres to centimetre scale, accelerating and wiggling a high electron charge simultaneously. This leads to a narrow-energy spread electron beam and x-ray source that is >1000 times brighter than previously reported plasma wiggler and thus has the potential to facilitate a myriad of uses across the whole spectrum of light-source applications.