Local polarization of tightly focused unpolarized light

Lindfors, Klas; Priimägi, Arri; Setälä, Tero; Shevchenko, Andriy; Friberg, Ari T.; Kaivola, Matti

doi:10.1038/nphoton.2007.30

Cited by 82 publications

(57 citation statements)

References 17 publications

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“…Optical fields can thereby be classified into one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) light, depending on the minimum number of orthogonal coordinate axes required to represent them. The dimensional nature of light plays an essential role in addressing polarization characteristics of complex-structured light fields, e.g., electromagnetic near and surface fields [3][4][5] as well as tightly focused optical beams [6][7][8][9], which are frequently exploited in near-field probing [10], singlemolecule detection [11], particle trapping [12], among other polarization-sensitive applications. Yet, no systematic theory has so far been developed which provides rigorous means to categorize and to characterize the dimensionality of light.…”

Section: Introductionmentioning

confidence: 99%

Dimensionality of random light fields

Norrman

Friberg

Gil

et al. 2017

J. Eur. Opt. Soc.-Rapid Publ.

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Background:The spectral polarization state and dimensionality of random light are important concepts in modern optical physics and photonics. Methods: By use of space-frequency domain coherence theory, we establish a rigorous classification for the electricfield vector to oscillate in one, two, or three spatial dimensions. Results: We also introduce a new measure, the polarimetric dimension, to quantify the dimensional character of light. The formalism is utilized to show that polarized three-dimensional light does not exist, while an evanescent wave generated in total internal reflection generally is a genuine three-dimensional light field. Conclusions:The framework we construct advances the polarization theory of random light and it could be beneficial for near-field optics and polarization-sensitive applications involving complex-structured light fields.

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Section: Introductionmentioning

confidence: 99%

Dimensionality of random light fields

Norrman

Friberg

Gil

et al. 2017

J. Eur. Opt. Soc.-Rapid Publ.

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“…We have presented results at the focal plane (u = 0) of an air aplanatic lens with NA = 0.9. Results were evaluated for homogeneously polarized [30] and completely unpolarized [31] cases of nonvortex beam compared, and good agreement is found between both.…”

Section: Resultsmentioning

confidence: 96%

“…A fair amount of literature is available on the coherence matrix to deal with such situation. Modification has also been made in the coherence matrix to take consideration of the vectorial nature and 2 International Journal of Optics 3D characteristics of the tightly focused beam [29][30][31]. Detailed study on the tight focusing of uniformly partially polarized radiation has been carried out in the past [30].…”

Section: Introductionmentioning

confidence: 99%

Tight Focusing of Partially Coherent Vortex Beams

Singh

2012

International Journal of Optics

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“…Obtaining these specific features involves the suitable design of the input field [1][2][3][4][5][6]. Research on the polarization properties of highly focused fields has been mainly devoted on fully polarized light, whereas partially polarized waves have received less attention [7][8][9]. Moreover, the use of partially coherent fields has been recently proposed as a suitable light source for optical trapping systems [10]; this kind of fields are also useful in tomography [11], plasmonics spectroscopy [12], or invisibility cloaking [13].…”

mentioning

confidence: 99%

“…In order to illustrate the behavior of this kind of beams, the 3D-degree of polarization P 3D and the profile of the transversal (I t W 11 W 22 ), longitudinal (I z W 33 ), and total (I T I t I r ) irradiances are calculated as a function of r. Although several measures for the 3D-degree of polarization have been proposed (see, for instance, [20] and references therein), in what follows the P 3D is calculated according to Eq. (32) [3,8] …”

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confidence: 99%

Design of highly focused fields that remain unpolarized on axis

2014

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Research on the properties of highly focused fields mainly involved fully polarized light, whereas partially polarized waves received less attention. The aim of this Letter is to provide an appropriate framework, for designing some features of the focused field, when dealing with incoming partially polarized beams. In particular, in this Letter, we describe how to get an unpolarized field on the axis of a high numerical aperture objective lens. The study of field distribution, in the focal region of a high numerical aperture (NA) focusing system, is attracting increasing attention because of their possible applications in many fields, e.g., electron acceleration, nonlinear optics, or particle trapping and manipulation. In general, these techniques require three-dimensional (3D) focused electromagnetic fields, with special characteristics: shape, polarization coherence, and so on. Obtaining these specific features involves the suitable design of the input field [1][2][3][4][5][6]. Research on the polarization properties of highly focused fields has been mainly devoted on fully polarized light, whereas partially polarized waves have received less attention [7][8][9]. Moreover, the use of partially coherent fields has been recently proposed as a suitable light source for optical trapping systems [10]; this kind of fields are also useful in tomography [11], plasmonics spectroscopy [12], or invisibility cloaking [13]. Accordingly, the aim of this Letter is to provide an appropriate framework for designing some features of the focused field, when dealing with incoming partially polarized beams. First, we relate the circular components of the transverse incident field with the circular and longitudinal content of the focused field; then, this formalism is extended to quasi-monochromatic statistically stationary incident beams. Finally, we focus on getting an unpolarized field on the axis of an imaging system with a high NA. Moreover, the polarization over the focal plane is also analyzed.The electric field distribution, at any point in the focal region of a high NA focusing system, is given by the well- where A is a constant, related to the focal length and the wavelength; k is the wave number, r and ϕ denote in this Letter the polar coordinates at the focal plane; and angles θ and θ 0 are represented in Fig. 1. Pθ denotes the so-called apodization function. obtained from energy conservation and geometric considerations; and E 0 is the so-called vector angular spectrum; this angular spectrum is usually written aswhere f 1 and f 2 are, respectively, the azimuthal and radial components of incident field (which we assume transversal). The unitary vectors e 1 and e 2 are given by e 1 ϕ − sin ϕ; cos ϕ; 0;e 2 θ; ϕ cos θ cos ϕ; cos θ sin ϕ; sin θ:Frequently, it is useful to write the angular spectrum using a convenient change of basis [15][16][17]. Instead of using the conventional radial and azimuthal description, it is advisable to describe the angular spectrum in terms of the circular content of the beam (see below). Accor...

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Local polarization of tightly focused unpolarized light

Cited by 82 publications

References 17 publications

Dimensionality of random light fields

Dimensionality of random light fields

Tight Focusing of Partially Coherent Vortex Beams

Design of highly focused fields that remain unpolarized on axis

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