The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation

Варга, П.; Török, Péter

doi:10.1016/s0030-4018(98)00092-3

Cited by 77 publications

(36 citation statements)

References 23 publications

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“…Among the different formulations for vectorial nonparaxial electromagnetic fields available in the literature [10][11][12][13][14], the description of such beams using the plane-wave angular spectrum framework has been proved particularly suitable [5,[15][16][17], since this approach enables us to separate the propagating and evanescent contributions of the electromagnetic field [1,5,[18][19][20]. Moreover, the propagating and evanescent waves can be described as the sum of two terms: a first one, transverse to the direction of propagation z, and a second one that is a non-zero longitudinal component along the z axis.…”

Section: Introductionmentioning

confidence: 99%

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

et al. 2013

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The contribution of the propagating and the evanescent waves associated with freely propagating nonparaxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysis is carried out within the framework of the plane-wave angular spectrum approach. These results are used to illustrate the behavior of a kind of doughnut-like beams with transverse azimuthal polarization at some plane.

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Section: Introductionmentioning

confidence: 99%

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

et al. 2013

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“…They are present, for instance, in high resolution optical microscopy, high density optical storage, or optical trapping, among other applications [15]. As is well known, non-paraxial beams have to be studied within the framework of the electromagnetic theory of diffraction [16,17]. Despite of the fact that it is not advisable to introduce this issue in undergraduate courses, the analysis of the longitudinal component in paraxial beams is affordable to these students.…”

Section: Introductionmentioning

confidence: 99%

On the longitudinal component of paraxial fields

et al. 2012

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Abstract. The analysis of paraxial Gaussian beams is a topic commonly present in undergraduate courses in Laser Physics, Advanced Optics, and Photonics. These beams provide a simple model of the field generated in resonant cavities of lasers, thus becoming a basic element for understanding the laser theory. Usually, uniformly polarized beams are considered in the analytical calculations, with the electric field vibrating at normal planes to the propagation direction. However, such paraxial fields do not verify the Maxwell equations. In this paper we discuss how to overcome this apparent contradiction and we evaluate the longitudinal component that any paraxial Gaussian beam should exhibit. Despite the fact that the assumption of a purely transverse paraxial field is useful and accurate, the inclusion of the above issue in the program helps students to clarify the importance of the electromagnetic nature of light, thus providing a more complete understanding of the paraxial approach.

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“…So far, different vectorial formulations of nonparaxial electromagnetic fields have been investigated in the literature (see, for example, [10][11][12][13]). Among them, several types of representations based on the plane-wave angular spectrum have been reported in the last years [5,14,15].…”

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confidence: 99%

Transverse and longitudinal components of the propagating and evanescent waves associated to radially polarized nonparaxial fields

et al. 2011

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A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freelypropagating radially-polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and compare the behaviour at two transverse planes. IntroductionAs is well known, the longitudinal component (along the propagation direction z) of a light beam is negligible in the paraxial approximation. Consequently, the electric field vector is assumed to be transverse to the z-axis, and represented by means of two components. This provides a considerable simplification in the calculations. However, in a number of applications (for instance, particle trapping, high-density recording and high-resolution microscopy, to mention only some of them), the light beam is strongly focused and raises spot sizes smaller than the wavelength. In such cases, the paraxial approach is no longer valid, and a nonparaxial treatment is required. This is a topic of active research, which has been extensively studied in the last years [1][2][3][4][5][6][7][8][9].

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The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation

Cited by 77 publications

References 23 publications

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

On the longitudinal component of paraxial fields

Transverse and longitudinal components of the propagating and evanescent waves associated to radially polarized nonparaxial fields

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