The Structure of Partially Coherent Fields

Gbur, Greg; Visser, Taco D.

doi:10.1016/b978-0-444-53705-8.00005-9

Cited by 112 publications

(68 citation statements)

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“…In those cases, the phase of the wave field is a random quantity. Therefore, when a partially coherent field is focused (as described in [13][14][15][16][17][18][19][20]), the Gouy phase is undefined; i.e., it has no physical meaning. In the space-frequency domain, a partially coherent optical field is characterized by two-point correlation functions, such as the cross-spectral density or its normalized version, the spectral degree of coherence [21].…”

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Generalized Gouy phase for focused partially coherent light and its implications for interferometry

2012

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The Gouy phase, sometimes called the phase anomaly, is the remarkable effect that in the region of focus a converging wave field undergoes a rapid phase change by an amount of π, compared to the phase of a plane wave of the same frequency. This phenomenon plays a crucial role in any application where fields are focused, such as optical coherence tomography, mode selection in laser resonators, and interference microscopy. However, when the field is spatially partially coherent, as is often the case, its phase is a random quantity. When such a field is focused, the Gouy phase is therefore undefined. The correlation properties of partially coherent fields are described by their so-called spectral degree of coherence. We demonstrate that this coherence function does exhibit a generalized Gouy phase. Its precise behavior in the focal region depends on the transverse coherence length. We show that this effect influences the fringe spacing in interference experiments in a nontrivial manner. © 2012 Optical Society of America OCIS codes: 030. 1640, 050.1960, 180.3170, 120.3940. In 1890 Gouy found that the phase of a monochromatic, diffracted converging wave, compared to that of a plane wave of the same frequency, undergoes a rapid change of 180°near the geometric focus [1][2][3][4] Under many practical circumstances, light is not monochromatic, but rather partially coherent. Examples are light that is produced by a multimode laser or light that has traveled through the atmosphere or biological tissue. In those cases, the phase of the wave field is a random quantity. Therefore, when a partially coherent field is focused (as described in [13][14][15][16][17][18][19][20]), the Gouy phase is undefined; i.e., it has no physical meaning. In the space-frequency domain, a partially coherent optical field is characterized by two-point correlation functions, such as the cross-spectral density or its normalized version, the spectral degree of coherence [21]. These complex-valued functions have a phase that is typically welldefined. As we will demonstrate for a broad class of partially coherent fields, the phase of both correlation functions shows a generalized phase anomaly, which reduces to the classical Gouy phase in the coherent limit. Furthermore, this generalized Gouy phase affects the interference of highly focused fields, in microscopy for example, altering the fringe spacing compared to that of a coherent field.Consider first a converging, monochromatic field of frequency ω that is exiting a circular aperture with radius a in a plane screen (see Fig. 1). The origin O of the coordinate system coincides with the geometrical focus. The amplitude of the field is U 0 r 0 ; ω, r 0 being the position vector of a point Q in the aperture. The field at a point Pr in the focal region is, according to the Huygens-Fresnel principle [4, Chap. 8.2], given by the following expression:where the integration extends over the spherical wave front S that fills the aperture, s jr − r 0 j denotes the distance QP, and k 2π∕λ is the wavenumber a...

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Generalized Gouy phase for focused partially coherent light and its implications for interferometry

2012

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“…In such fields the phase is a random quantity and therefore they do not contain "traditional" phase singularities. However, the statistical properties of these fields are described by two-point correlation functions, which do have a definite phase [16][17][18]. A few years ago it was pointed out that these functions can also exhibit singular behavior [19].…”

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confidence: 99%

Topological reactions of correlation functions in partially coherent electromagnetic beams

2013

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It was recently shown that so-called coherence vortices, singularities of the two-point correlation function, generally occur in partially coherent electromagnetic beams. We study the three-dimensional structure of these singularities and show that in successive cross sections of a beam a rich variety of topological reactions takes place. These reactions involve, apart from vortices, the creation or annihilation of dipoles, saddles, maxima and minima of the phase of the correlation function. Since these reactions happen generically, i.e., under quite general conditions, these observations have implications for interference experiments with partially coherent, electromagnetic beams.

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“…On the other hand, since their introduction, optical vortices are a subject of great interest [16]- [19] both from theoretical point of view as well as due its potential applications as particle manipulation. In this work a physically realizable planar light source with optical vortex and degree of coherence depending on the radius and on the phase difference is proposed.…”

Section: Introductionmentioning

confidence: 99%