High-resolution Interferometric Diagnostics for Ultrashort Pulses

2. BACKGROUNDspectrally selective response H(ω) =δ(ω − ω 0 ); this represents an ideal spectrometer. Ultrashortpulse characterisation therefore requires at least one nonlinear or time-nonstationary element.Because a spectrometer can be produced using linear time-stationary elements, knowledgeof the spectrum is generally taken as a given when discussing ultrashort pulse characterisationmethods, and the problem is reduced to finding the unknown spectral phase φ(ω). Similarly, mostcharacterisation methods can be viewed as a means of encoding the profile of the unknown pulseinto the spectrum.A variety of physical processes are used as nonlinear or time-nonstationary elements. Themost common is a nonlinear optical response, almost universally of second or third order. Sincenonlinear optics arises from the anharmonic motion of bound electrons, it benefits from an effectivelyinstantaneous response, at least for pulse durations above one femtosecond. The disadvantageis a lack of sensitivity. Electro-optic modulators provide a stronger signal, but struggle withtimescales below 200 fs. For extended ultraviolet (XUV) and soft x-ray pulses, which are capable ofphotoionising atoms, electron momentum streaking can be performed with an ancillary infraredpulse, and will be described in chapter 6. Regardless of the particular method, the process is oftenrepresented as a temporal gate at time τE (t )=E (t )G (t − τ). (2.20)It must be emphasised that this is in many cases a mathematical idealisation. For example thelimited phase-matching bandwidth of nonlinear optical processes means that the signal involvesa convolution, or smoothing operation. Furthermore, in many cases the gate is derived from thepulse itself, and in some cases is even equal to it, so that the assignment of the roles of pulse andgate are arbitrary. Nonetheless, the “gated-pulse” picture is useful for describing many characterisationtechniques.This concludes the generic discussion of ultrafast metrology. The rest of this section coversspecific concepts and implementations. The discussion is organised in rough order of complexity,starting with the incomplete or nonself-referenced methods and moving through to complete,24