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Optics Letters

Interferometry and coherence of nonstationary light

Matias Koivurova, Lutful Ahad, Gianluca Geloni, Tero Setälä, Jari P. Turunen, Ari T. Friberg

Published Jan 15, 2019• 8 citations
Publisher

Abstract

We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.

DOI
10.1364/ol.44.000522

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We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.
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We examine the temporal coherence properties of trains of nonidentical short optical pulses in the framework of the second-order coherence theory of nonstationary light. Considering Michelson's interferometric measurement of temporal coherence, we demonstrate that time-resolved interferograms reveal the full two-time temporal coherence function of the partially coherent pulse train. We also show that the result given by the time-integrated Michelson interferogram equals the true degree of temporal coherence only when the pulse train is quasi-stationary, i.e., the coherence time is a small fraction of the pulse duration. True two-time and integrated coherence functions produced by specific models representing perturbed trains of mode-locked pulses and supercontinuum pulse trains produced in nonlinear fibers are illustrated.
This thesis contains research related to random light fields.In particular, novel constructions of electromagnetic coherence in beam fields are introduced, and certain fundamental notions concerning the spectrum of light are assessed in the context of nonstationary fields.The singular-value decomposition (SVD) of the cross-spectral density matrix (CSDM) is analysed and interpreted for electromagnetic beams.In addition, the Gram matrix of the CSDM is invoked and combined with the SVD formalism.The Gram matrix shares the essential properties of the polarization matrix, thus appearing as a particularly potential descriptor of electromagnetic coherence.The SVD and the Gram matrix yield results analogous to those traditionally met in polarization theory of beam fields, but in the context of two-point spatial coherence analysis.In particular, two-point analogies of the usual decompositions of the polarization matrix are introduced by applying the SVD.In addition, the Poincaré sphere representation of electromagnetic coherence is established, which is analogous to the traditional Poincaré sphere in polarization optics.Cross-spectral purity and spectral invariance of light are two fundamental concepts concerning stationary random light fields, which were recently generalized to nonstationary fields.In this thesis, a reduction formula for time-integrated coherence functions of cross-spectrally pure nonstationary scalar fields is established.This reduction formula is an equivalent condition for the physical definition of crossspectral purity in nonstationary fields, similarly to the reducibility met in the case of cross-spectrally pure stationary light.In addition, optical systems consisting of hybrid refractive-diffractive lens designs which transform partially coherent isodiffracting pulsed beams into cross-spectrally pure or spectrally invariant nonstationary fields are developed.Furthermore, polarimetric measurement of temporal coherence in electromagnetic beam fields is performed.It is shown that the electromagnetic temporal degree of coherence can be deduced from these measurements, thus without the need for visibility detection or optical elements in the arms of the device, in contrast to earlier studies.
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve intensity correlations between multiple detectors and may have the advantage over the traditional second-order interference effect exhibited in only one detector. We discuss various scenarios with unbalanced delays in different paths in fourth-order interference exhibited in coincidence between two detectors. We find, in some cases, interference effect persists even when the delays are much larger than the coherence time of the sources. We also extend the discussion to nonstationary pulsed fields, which need to consider the pulse shape and require a different treatment. These results will be useful in remote sensing applications.
From the nonclassicality of photon superbunching to the basic property of intensity, we characterize light with correlation and coherence functions. The correlation functions for nonstationary sources, such as short pulses, depend deterministically on the time dependent shape of the field and change the probability of the ensemble in time. We start from the fundamental principles of detection and show how nonstationary fields result in a coherence function that depends not only on the statistics of the field but also on the field shape. This means that observations of bunching and superbunching with ultrafast sources are not indicative of the quantum state of the field.