Fully vectorial highly nonparaxial beam close to the waist

Abstract

I use the angular spectrum representation to compute exactly the Gaussian beam close to the waist (w(0)) in the case of a highly nonparaxial field (w(0)<lambda). The computation is done in the vectorial case for a polarized Gaussian beam. In the area of the waist, the contribution of the propagating and evanescent waves is discussed. Moreover, the Gaussian wave is developed in terms of a series, which permits one to get analytical expressions for both propagating and evanescent waves when the observation is close to the waist.

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

“…In particular, the propagating electric-field solution has been written as the sum of two terms [16]: one of them is transverse to the propagation direction; another one exhibits a non-zero longitudinal component and its associated magnetic field is also transverse. Such analytical description differs from alternative proposals appeared in the literature, also based on the plane-wave spectrum (see [5] and references therein).…”

“…In such cases, the paraxial approach is no longer valid, and a nonparaxial treatment is required.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

“…Among them, several types of representations based on the plane-wave angular spectrum have been reported in the last years [5,14,15]. Such kind of decomposition has revealed to be useful because it allows separate the contribution of the propagating and evanescent waves.…”

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

“…Applications of such fields range from particle trapping or high resolution microscopy to material processing, among others. In particular, when the beam is focused in a spot smaller than the wavelength, the paraxial approach cannot be used and a nonparaxial treatment is required [1][2][3][4][5][6][7][8][9].…”

“…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.…”