Tailoring light intensity along caustic trajectories.

A current challenge in a caustic beam design is to tailor the intensity distribution along the curved trajectory. To address this matter, we present a robust theoretical framework that relates the propagated complex wave field amplitude with the input spectral signal encoded onto a spatial light modulator which is suitable for fold-type monotonic trajectories as well as for cusp-type nonmonotonic trajectories. Specifically, we derive a general closed-form expression that relates the field amplitude along the beam trajectory with the spectral amplitude and the third derivative of the spectral phase for both monotonic and nonmonotonic curved trajectories. This proposal is suitable for direct experimental implementation in a Fourier transform scheme around the focal region, allowing straightforward beam intensity design by selecting the proper spectral amplitude and phase while preserving the beam trajectory. Experimental results from the famous cubic spectral phase support the theoretical predictions. This research lays the foundation for engineering the intensity of curved beams, which can be useful in applications where a specific modulation of the intensity is required over specific regions of the trajectory such as in optical trapping and laser micromachining.

Abruptly autofocusing beams from phase perturbations having forced symmetry.

A controllable manipulation of the energy distribution of caustic beams possessing rectangular symmetry is presented. The beams are designed from the spectral phase by adding a linear and/or quadratic perturbation having forced symmetry. This approach breaks the overall caustic structure into branches, allowing a fully controllable displacement of each branch. The caustic breaking leads to peculiar propagation configurations for rectangular beams. Among them, we highlight the abruptly autofocusing beam, which until now was exclusively associated to caustic beams with circular symmetry. Thereby, the abruptly autofocusing effect can be yielded for one-dimensional light sheets, contrary to what happens for circularly symmetric beams. The theoretical predictions are supported by experiments. Besides, the focus width of such rectangular beams can be reduced beyond the standard diffraction limit.

Caustic beams from unusual powers of the spectral phase.

Caustic optical beams arising from a spectral phase whose power lies in an unusual range of values less than two are presented. Unlike what happens for conventional phase powers greater than two, it is feasible to generate caustic structures having properties that do not follow the established sorting. For instance, an asymptotic cusp caustic beam having a cusp point at infinity is demonstrated. For the sake of completeness, the caustic beam properties are analyzed within the whole real range of the phase power. Accurate behavior rules between the symmetries of the beam spectral phase and its intensity distribution are found. These findings strengthen the fundamentals and engineering on caustic beams in diverse optical and physical branches.

Symmetric Airy beams.

In this Letter a new class of light beam arisen from the symmetrization of the spectral cubic phase of an Airy beam is presented. The symmetric Airy beam exhibits peculiar features. It propagates at initial stages with a single central lobe that autofocuses and then collapses immediately behind the autofocus. Then, the beam splits into two specular off-axis parabolic lobes like those corresponding to two Airy beams accelerating in opposite directions. Its features are analyzed and compared to other kinds of autofocusing beams; the superposition of two conventional Airy beams having opposite accelerations (in rectangular coordinates) and also to the recently demonstrated circular Airy beam (in cylindrical coordinates). The generation of a symmetric Airy beam is experimentally demonstrated as well. Besides, based on its main features, some possible applications are also discussed.

Negative propagation effect in nonparaxial Airy beams.

Negative propagation is an unusual effect concerning the local sign change in the Poynting vector components of an optical beam under free propagation. We report this effect for finite-energy Airy beams in a subwavelength nonparaxial regime. This effect is due to a coupling process between propagating and evanescent plane waves forming the beam in the spectral domain and it is demonstrated for a single TE or TM mode. This is contrary to what happens for vector Bessel beams and vector X-waves, for which a complex superposition of TE and TM modes is mandatory. We also show that evanescent waves cannot contribute to the energy flux density by themselves such that a pure evanescent Airy beam is not physically realizable. The break of the shape-preserving and diffraction-free properties of Airy beams in a nonparaxial regime is exclusively caused by the propagating waves. The negative propagation effect in subwavelength nonparaxial Airy beams opens new capabilities in optical traps and tweezers, optical detection of invisibility cloacks and selective on-chip manipulation of nanoparticles.

Effect of ABCD transformations on beam paraxiality.

The limits of the paraxial approximation for a laser beam under ABCD transformations is established through the relationship between a parameter concerning the beam paraxiality, the paraxial estimator, and the beam second-order moments. The applicability of such an estimator is extended to an optical system composed by optical elements as mirrors and lenses and sections of free space, what completes the analysis early performed for free-space propagation solely. As an example, the paraxiality of a system composed by free space and a spherical thin lens under the propagation of Hermite-Gauss and Laguerre-Gauss modes is established. The results show that the the paraxial approximation fails for a certain feasible range of values of main parameters. In this sense, the paraxial estimator is an useful tool to monitor the limits of the paraxial optics theory under ABCD transformations.

Polarization and phase-shift properties of high spatial frequency holographic gratings in a photopolymerizable glass.

Polarization properties of transmission volume holographic phase gratings recorded in a photopolymerizable glass modified with high refractive index species are reported. The gratings are recorded by the interference of two parallel s-polarized writing beams with orthogonal propagation directions. High optical quality, low scattering, and diffraction efficiency of 99.4% are achieved. Degrees of polarization of 0.987 and 0.999 are obtained for transmitted and diffracted light, respectively. Furthermore, phase analysis of the transmitted light reveals a phase discontinuity of pi at the Bragg angle.