An Ultra-Degree-of-Freedom Structured Vector Beam

Typically, light emitted from standard lasers has a controllable degree of freedom (DoF) which may be polari­zation or beam shape. By suitably mani­pulating a laser with the introduction of specialized optical components, an output with 2 DoFs, such as vector vortex beams with controllable polari­zation and orbital angular momentum (OAM). The term vector describes a structured change in the polari­zation across the beam and vortex describes the twisting of the phase in the beam (OAM), much like a twisting tornado. Transcending 2 DoFs from a laser was not possible. By exploiting ray-wave duality in a frequency-dege­nerate laser, a vector beam with 5 DoFs can now be selected.

Illustration of an ultra-degree-of-freedom structured vector beam. (Source: Y. Shen)

The concept of ray-wave duality inside lasers may be described as a mode wave pattern that is associated with a periodic ray trajec­tory. A standard laser has a mode pattern that oscillates between the centre of two mirrors on a straight path that is perpen­dicular to the mirrors. However, in the case of a periodic trajectory, the mode pattern also oscil­lates between two mirrors but follows a non-perpen­dicular path, similar to a zig-zag pattern. Prior studies have only reported on a single trajectory with a certain transverse size, however, this work demonstrated the selection of two trajec­tories with different transverse sizes and oscillating phases, associated with astigmatic trans­formation.

This exotic output constitutes 4 DoFs, namely, periodic number (number of rays), transverse index (number of output rays), oscillating phase, and astig­matic degree. This results in a vector structured output and in turn, the 5th degree of freedom. With this, the output is transformed into a twisted trajectory by converting the transverse index into one that possesses OAM with an external astig­matic mode convertor. Importantly, this ray-wave structured output is said to be non-separable, akin to the quantum mechanics description of entangled states, in the orientation angle between the transverse indices.

“We believe it holds great novelty, because the creation of such ultra-DoF vectorial light is highly beneficial in describing and further exploring funda­mental physical phenomena such as optical spin Hall effects, for extending new applications in optical tweezers and communi­cations and to manipulate new quantum-like classical states,” says Yijie Shen of the University of Southampton.

The experimental demons­tration comes from an otherwise empty laser cavity, the absence of specialized optical components. This poses an additional benefit in that the laser consists of a simple archi­tecture, however, outputs a vector beam with 5 DoFs, certainly beyond an incre­mental advance. “The number of rays in the twisted output may be easily be manipulated by careful control of the laser parameters such as the distance between the mirrors and the pump position, which provides a simple, compact, and elegant at-the-source solution,” says Darryl Naidoo of the CSIR.

The laser concept is likely to attract interest from both the academic and industrial communities. This output holds promise to conveniently extend appli­cations in the vector beam space and having such beams on demand from a laser will certainly open up new appli­cation areas. (Source: CAS)

Reference: Z. Wang et al.: Astigmatic hybrid SU(2) vector vortex beams: towards versatile structures in longitudinally variant polarized optics, Opt. Exp. 29, 315 (2021); DOI: 10.1364/OE.414674

Link: Optoelectronics Research Centre, University of Southampton, Southampton, UK

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