The orbital angular momentum of light is distinct from the angular momentum associated with the spin or polarisation state of the light. Thus linearly polarised modes can carry angular momentum. Laguerre-Gaussian laser modes have been identified as a class of modes that can possess such orbital angular momentum. Hermite-Gaussian modes may be converted to Laguerre-Gaussian modes, characterised by two integer indices l and p, by the use of a mode converter. The l index occurs in the azimuthal phase factor eil ϕ in the field distribution of Laguerre-Gaussian beams which possess an orbital angular momentum equivalent to lħ per photon 1.

Second Harmonic Generation and the Orbital Angular Momentum of Light

Optical vortex beams can be used as carriers of information in optical communication and quantum optics applications. Owing to their spatial orthogonality, these beams can be multiplexed and demultiplexed, but up until now this was primarily achieved by bulky and large devices. In this work, a new approach is used to fabricate miniature vortex mode sorters based on three-dimensional laser printing, thereby enabling direct integration into optical systems. Mode sorters that are composed of two separate elements as well as a single integrated device are presented. These devices can handle both pure and mixed vortex beams with topological charge |l|≤3 and |l|≤2 for the dual-element device and integrated system, respectively. Mode-sorter spectral bandwidth and surface-quality effects are also discussed.

Miniature wide-spectrum mode sorter for vortex beams produced by 3D laser printing

We demonstrate experimentally spatial-mode conversions of light beams generated in a quadratic nonlinear process by micron-scale structures placed on the facets of nonlinear crystals. These structures were printed on the crystal facets using a three-dimensional (3D) direct laser writing system. The functional structures were designed to modify the phase of the beam at specific wavelengths, thereby enabling conversion of a fundamental Gaussian laser beam into different high-order Hermite-Gaussian modes, Laguerre-Gaussian modes, and zeroth-order Bessel beams of the second harmonic. This facet functionalization opens exciting new opportunities for robust and compact beam shaping in a nonlinear interaction without compromising the conversion efficiency.

Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals.

We report complete spatial shaping (both phase and amplitude) of the second‐harmonic beam generated in a nonlinear photonic crystal. Using a collinear second‐order process in a nonlinear computer generated hologram imprinted on the crystal, the desired beam is generated on‐axis and in the near field. This enables compact and efficient one‐dimensional beam shaping in comparison to previously demonstrated off‐axis Fourier holograms. We experimentally demonstrate the second‐harmonic generation of high‐order Hermite–Gauss, top hats and arbitrary skyline‐shaped beams.

On-axis shaping of second-harmonic beams

Experiments on autofocusing ring-Airy beams reveal that the harmonics preserve the phase distribution of the fundamental beam. This ``phase memory'' inherits the harmonics of the abrupt autofocusing behavior of the Airy beam.

Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams.

We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump’s radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new “virtual beam” having multiple values of OAM that are determined by the nonlinear process.

/pdf/azimuthal-and-radial-shaping-of-vortex-beams-generated-in-3dl8z35tuz.pdf

Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.

Functional facets for nonlinear crystals

The most efficient nonlinear interaction in quasi phase-matched crystals occurs in periodic crystals when the interacting beams are Gaussian beams. The generated beams can be then routed, filtered or shaped by various elements - mirrors, lenses, pinholes, gratings, spatial light modulators, etc. In order to save space and cost, it is desired to combine the nonlinear process and the above mentioned functions into a single element. One option is to spatially modulate the periodic structure used for phase-matching, for example Ref. [1,2]. However, this technique may reduce the conversion efficiency and requires complex two-dimensional poling capability. We suggest a new approach in which the nonlinear crystal itself is perfectly periodic and the modulation is imposed by patterning a nano-layer of gold sputtered at the exit facet of the crystal. This patterning is achieved with focused ion beam (FIB) milling. The gold layer serves as an amplitude mask that can be patterned to serve as a computer generated hologram (CGH) [3] for beam shaping or as a spatial pinhole for beam quality improvement. In the nonlinear process of second harmonic generation (SHG), both frequencies are passing through the same holographic mask but since the central angle of the diffraction order is proportional to the wavelength, the beams are spatially separated.

Functionalizing nonlinear crystals

We present experimental observation of self-accelerating parabolic beams in quadratic nonlinear media. We show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another in the two transverse coordinates. In addition, the two coupled harmonics have the same acceleration within and after the nonlinear medium. We also study the evolution of second harmonic accelerating beams inside the quadratic media and their correlation with theoretical beams.

https://www.eng.tau.ac.il/~ady/Dolev%20Parabollic%20beams%20APL%20101%20101109%20(2012).pdf

Self-accelerating parabolic beams in quadratic nonlinear media

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Papers

Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.

Functional facets for nonlinear crystals

Functionalizing nonlinear crystals

Self-accelerating parabolic beams in quadratic nonlinear media