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Pure and Applied Optics Journal of the European Optical Society Part A

Time-varying coherency matrices and spectral coherency matrices

Tiberiu S. Tudor, Istvan Vinkler

Published Nov 1, 1998• 3 citations
Publisher

Abstract

The problem of spectral analyses, in terms of optical observables, of the time-varying spinorial fields encountered in optics is presented. Time-varying coherency matrices and spectral coherency matrices are introduced. The spectral analyses of the output of a KDP electro-optical modulator is presented as an example. The paper is conceived as a contribution to the development of the language of the optics of observables.

DOI
10.1088/0963-9659/7/6/021

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The problem of spectral analyses, in terms of optical observables, of the time-varying spinorial fields encountered in optics is presented. Time-varying coherency matrices and spectral coherency matrices are introduced. The spectral analyses of the output of a KDP electro-optical modulator is presented as an example. The paper is conceived as a contribution to the development of the language of the optics of observables.
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.
The problem of spectral filtering of quantized light fields is studied, based on the recently developed quantum-optical theory of the action of passive, lossless optical systems [L. Kn\"oll, W. Vogel, and D.-G. Welsch, Phys. Rev. A 36, 3803 (1987)]. Expressions for the operator of the electric field strength of the light and the normally and time-ordered field-correlation functions are derived for the case of a Fabry-P\'erot interferometer being present. Various kinds of field decomposition that are usually considered in classical optics are studied. The results are compared with the Fourier approach to spectral properties of light. It is shown that, dependent on the experimental scheme used, new quantum effects appear, which may prevent the observation of the Fourier structure of the light as predicted from classical optics. Quantitatively this is demonstrated for the example of spectral squeezing in resonance fluorescence, where significant discrepancies between the measured and the full Fourier spectrum are found.
The book embraces a wide spectrum of problems falling under the concepts of "Quantum optics" and "Laser experiments". These actively developing branches of physics are of great significance both for theoretical understanding of the quantum nature of optical phenomena and for practical applications. The book includes theoretical contributions devoted to such problems as providing a general approach to describe electromagnetic field states with correlation functions of different nature, nonclassical properties of some superpositions of field states in time-varying media, photon localization, mathematical apparatus that is necessary for field state reconstruction on the basis of restricted set of observables, and quantum electrodynamics processes in strong fields provided by pulsed laser beams. Experimental contributions are presented in chapters about some quantum optics processes in photonic crystals - media with spatially modulated dielectric properties - and chapters dealing with the formation of cloud of cold atoms in magneto optical trap. All chapters provide the necessary basic knowledge of the phenomena under discussion and well-explained mathematical calculations.
The possibilities of obtaining information on the time dependence of the amplitude and phase of an optical signal by the spectral modulation method are analysed. Three variants of the signal analysis are considered: a direct analysis of the signal whose parameters are changing in time; studies of the time-dependent optical characteristics of an object or a medium under study by probing them with radiation of the known structure; and measurements of the parameters of radiation propagated through the object and simultaneous determination and analysis of time-dependent structures of the signal and transfer function describing the effect of the transfer medium, the object, or an optical system on the propagated signal.