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

Abstract

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 In such cases, the paraxial approach is no longer valid, and a nonparaxial treatment is required.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].

Vectorial optical fields: recent advances and future prospects

“…To fully understand these interactions, rigorous analysis is necessary which can be found in Refs. [69,70] under paraxial or non-paraxial conditions. Besides the linear interactions, interactions of vectorial optical fields with nonlinear med-ium have also attracted increasing attention.…”

Three-Dimensional Optical Spin Angular Momentum Flux of a Vector Beam with Radially-Variant Polarization in Near Field

“…Figure 1 shows the initial SoP alignment in a Gaussian beam cross-section. By using the Fourier transform of the initial RVVB, the transverse components of the vector angular spectrum Ax (ρcosϕ, ρsinϕ) and Ay (ρcosϕ, ρsinϕ) can be given as [20][21][22]:…”

“…The quantitative knowledge of the near-field properties of an optical field is required in many applications ranging from nanophotonics to optical imaging [16][17][18][19]. Recently, the characteristics of the evanescent wave for a vector optical field with radial polarization and azimuthal polarization have been reported [20][21][22]. These works indicate that the longitudinal component of both the evanescent wave and the propagating wave can be manipulated by the initial SoP alignments.…”

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

“…(8) and (9.b)). In a similar way to that used for the propagating term, we can formally write the evanescent part of the field in the form [19,20] …”

“…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.…”