High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrologySelf-referencing without a spectral shear. A displacement along the frequency axis is the mostcommon operation used in self-referenced spectral interferometry. However, a recent developmentis the use of a nonlinear pulse shortening operation — essentially a pinhole in time [205].This has the effect of flattening phase variations, producing a “reference” which is closer to thetransform limit than the test pulse. Interferometric measurement of the phase difference betweenthe test pulse and its shortened replica provides an estimate of the unknown pulse.2.3.6.3 Summary — self-referenced interferometrySpectral shearing is almost unique in enabling spectral interferometry to become self-referenced.Implementations have been demonstrated for wavelengths from the ultraviolet to the infrared,and for pulse durations down to the few-cycle regime. Its advantages are a one-dimensional encodingand a direct and easily invertible relation between the signal and the phase of the unknownpulse. However it requires careful calibration of the delay between the sheared pulse replica andsynthesis of a shearing operation of reasonable fidelity.2.3.7 TomographyTomographic methods operate by principles analogous to spatial imaging, based on the correspondencebetween the pair of transverse space and wavenumber co-ordinates (x,k x ) and timefrequencyco-ordinates (t ,ω).Paraxial diffraction over a distance L is a quadratic phase factorin transverse wavenumber exp[iL/(2k 0 ) kx 2 ], exactly the same mathematical form as secondorderdispersion exp[i φ 2 /2 ω 2 ]. An aberration-free lens of focal length f introduces a spatialphase exp[−ik 0 /(2f ) x 2 ], of the same form as the action of a quadratic temporal phase modulatorexp[i ψ/2 t 2 ]. By associating dispersion with diffraction and a lens with a quadratic temporalphase modulator, spatial imaging systems may be transformed to the time-frequency domain.However, achieving suitable quadratic phase modulation for subpicosecond pulses is difficult, andthe best temporal resolutions that have been achieved using tomographic methods are around200 fs. For this reason, tomographic methods do not at present represent a viable alternative tothe techniques discussed in this thesis and so will be discussed briefly.49