Partially coherent Airy beams: A cross-spectral-density approach

Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they also manifest in the case of partially coherent Airy-type beams. Here, these properties are further investigated by introducing and analyzing a class of partially coherent Airy beams under both infinite and finite energy conditions. The key element within the present approach is the so-called cross-spectral density, which enables a direct connection with the quantum density matrix, making the analysis exportable to the quantum realm to study the dynamics of Airy wave packets acted by both incoherence and decoherence. As it is shown, in the case of infinite energy beams both properties are preserved even under the circumstance of total incoherence provided the underlying structure of the beam remains equal to that of an Airy beam. In the case of finite energy beams, a situation closer to a realistic scenario as experimental beams cannot have an infinite extension, it is shown that a propagation range along which both properties are preserved can be warranted. This is controlled by a critical distance, which depends on the spread range determined by the parameters ruling the extension of random field spatial fluctuations. Such a distance is determined by defining a position-dependent parameter that quantifies the degree of overlapping between the propagated beam and the input one displaced by an amount equivalent to the propagation distance

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

The contribution of the propagating and the evanescent waves associated with freely propagating non-paraxial 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 donut-like beams with transverse azimuthal polarization at some plane

Synthesis of light needles with tunable length and nearly constant irradiance

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques. In this way, a polarized input beam is shaped and subsequently focused using a high numerical aperture (NA) objective lens. As a result, needles with variable length and nearly constant irradiance are produced using conventional optics components. This procedure is experimentally demonstrated obtaining a 53 lambda-long and 0.8 lambda-wide needle

Design of highly focused fields that remain unpolarized on axis

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. Some numerical results that corroborate theoretical predictions are provided

On the physical realizability of highly focused electromagnetic field distributions

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases

On the behavior of vector light needles using modulation functions with topological charge

In the present communication, we describe how to produce long light distributions in the focal area of a high numerical aperture optical system using a custom modulation function with spiral charge. This analysis expands our previous developments in the field. We analyze the effect of this new element on the behavior of light along the optical axis

Efficient calculation of highly focused electromagnetic Schell-model beams

The calculation of the propagation of partially coherent and partially polarized optical beams involves using 4D Fourier Transforms. This poses a major drawback, taking into account memory and computational capabilities of nowadays computers. In this paper we propose an efficient calculation procedure for retrieving the irradiance of electromagnetic Schell-model highly focused beams. We take advantage of the separability of such beams to compute the cross-spectral density matrix by using only 2D Fourier Transforms. In particular, the number of operations depends only on the number of pixels of the input beam, independently on the coherence properties. To provide more insight, we analyze the behavior of a beam without a known analytical solution. Finally, the numerical complexity and computation time is analyzed and compared with some other algorithms

Beam quality changes in Hermite-Gauss mode fields propagating through Gaussian apertures

The beam quality behavior of Hermite-Gauss laser modes propagating through Gaussian apertures is analyzed

Linear Gaussian intensity distributions synthesized by reflection on elliptic cylinders: a proposal

A Procedure for obtaining linear (one-dimensional) Gaussian intensity distributions over certain plane regions is proposed. The method is based on the reflection of plane beams on elliptic cylinders