High-resolution Interferometric Diagnostics for Ultrashort Pulses

2. BACKGROUNDcomplete. Methods which only return limited information on the pulse, or equivalently possessa massive and usually infinite number of ambiguities represent partial characterisations. Thereis some slackness in this distinction — a partial method combined with some assumptions is oftensufficient to define the pulse with a precision that qualifies as complete. For example, thespectrum is a partial characterisation, but if the pulse is known to be transform-limited then thecharacterisation can be said to be complete.The topic of ambiguities is often nebulous and occasionally controversial. An almost universalambiguity of self-referenced methods is that of the absolute phase — this can only be determinedusing ultrabroadband pulses such that different orders from a nonlinear interaction overlap inthe frequency domain. One example is f -2f interferometry used in CEO phase stabilisation [80].Another common ambiguity is the arrival time of the pulse. Exact ambiguities, such as those ofthe absolute phase and arrival time, can be proven exactly given the mathematical form of theacquired signal. The standard diagnosis of such an ambiguity is the substitution of two differentpulses into the mathematical expression for the signal; if the results are identical, then an ambiguityis present.Other approximate ambiguities are harder to classify because they may depend on experimentalissues: the signal-to-noise ratio (SNR), discretisation of the data and the algorithm whichis being used. Examples of this class are the relative phase ambiguities [81] between componentsof the pulse which are separate in the time and/or frequency domains. For small separations, therelative phase is usually returned correctly, but as the separation increases the estimated valuebecomes increasingly susceptible to detector noise. A more general issue is the precision withwhich the spectral phase is retrieved in the low-intensity tails of the spectrum. The notion of anambiguity then folds into more general questions of accuracy and precision. For a given measurementprotocol, accuracy quantifies the similarity between the retrieved pulse and the physicalpulse, whilst precision quantifies the spread of pulses retrieved from repeated measurements ofthe same physical pulse. Things which commonly affect accuracy and precision include detectornoise, vibrations and instability of the device, incorrect calibrations, violation of the assumptionsrequired of a pulse for a procedure to be valid, misalignment and general user error.22