Radiation Functionals for Non-stationary Optical Radiation and Their Determination

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Abstract
Investigation of non-stationary optical radiation, by means of a spectrometer or interferometer, results in a signal that is related to a functional of the electric field strength, the so-called radiation functional. The output spectrum of a spectrochronograph (which consists of a grating spectrometer combined with square-law detectors, e.g. a streak camera), depends on a radiation functional of second order in field strength. In the present paper a new general class of second-order radiation functionals is introduced that includes as special cases the time-dependent spectrum and the Wigner distribution function (recently used in treating this problem). Utilizing the aspect of time-ordering in spectral measurement, the suitability of various radiation functionals for the representation of the relationship between the input properties of the radiation and the measured output spectrum is studied. A radiation functional of first order in field strength is also introduced. Making use of a ‘generalized spectrochronograph’, more information (the magnitude as well as the phase of the complex amplitude) about the input signal can be obtained than is possible using an ordinary spectrochronograph.

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