High-resolution Interferometric Diagnostics for Ultrashort Pulses

3 Phase reconstruction algorithm for multiple spectralshearing interferometryThis chapter presents a method for reconstructing the spectral phase of an optical pulse usingseveral spectral shearing interferometry (SSI) measurements taken using different shears. Thisimproves the precision above that which can be achieved using a single shear. The improvementincreases with the degree of modulation of the spectral intensity. In the extreme case of a spectrumwith one or more islands of zero spectral intensity, or spectral nulls, the use of multiple shearscan enable determination of the relative spectral phase across the null, a property to which a singleshear reconstruction would be completely insensitive. A limitation of the method is that thenull must be smaller than the largest nonzero spectral region. It is, however, a significant improvementover the single shear case which would require the null to be smaller than the spectralshear, a somewhat contradictory requirement since the spectral shear defines the resolution ofthe measurement. As such, the use of multiple shears offers partial resolution of the relative phaseambiguity of SSI.The ambiguity in the relative phase of separate spectral components in SSI is well known, andthe possibility of using multiple shears to recover it has been previously suggested [81, 186, 266]but not implemented.This chapter develops the multiple shear spectral interferometry algorithm, which accepts asits input the extracted interferometric phase differences. This leads into chapter 4, which presentsan arrangement for acquiring such data sequentially and provides a first proof-of-principle experimentaldemonstration of multiple SSI. Chapter 4 also presents an arrangement for acquiringmultiple shears simultaneously on a two-dimensional detector, and demonstrates the resolutionof the relative phase ambiguity. The work in this chapter formed part of the publications “Highprecision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry”[267] and “Resolution of the relative phase ambiguity in spectral shearing interferometryof ultrashort pulses” [267].This chapter is organized as follows: section 3.1 presents some qualitative reasons for devel-63