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MULTIPLY Fellow Yijie Shen created ultra-degree-of-freedom structured laser beams

Artists impression of ultra-degree-of-freedom vector ray-wave structured light laser

Recently, MULTIPLY Fellow Yijie Shen leads an international research team demonstrated a laser that is able to produce a new type of structured beam. Such a beam, having five degrees of freedom (DoFs), breaks the paradigm of the conventional vector vortex beam limited by two DoFs. These so-called vector ray-wave structured light beams opens the way to manipulate new quantum phenomena leading toward large-capacity quantum communications.

Typically, light emitted from standard lasers has one degree of freedom which may be polarisation or beam shape. By suitably manipulating a laser with the introduction of specialised optical components, an output with 2 DoFs, such as polarisation and orbital angular momentum (OAM) may be selected. Here, such beams are referred to as vector vortex beams where the term ‘vector’ describes a structured change in the polarisation 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 has not been possible, until now. By exploiting ray-wave duality in a sophisticatedly designed laser, a vector beam with 5 DoFs can now be selected.

The concept of ray-wave duality inside lasers may be described as a mode pattern that is associated with a periodic 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. Here, the starting position of the trajectory (the oscillation phase) is located at some position away from the centre of the mirrors and the period of the trajectory is the number of rays between the mirrors. 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. This exotic output constitutes 3 DoFs, namely, periodic number (number of rays), transverse index (number of output spots) and oscillating phase.

Our novelty was to realise two trajectories simultaneously oscillating in a standard laser cavity, by using birefringent laser crystal and off-axis pumping,” says Dr. Shen. The introduction of the birefringent crystal means that the two trajectories impinge the crystal at different angles and thus undergo different polarisation modulations, an effect provided by nature. This results in a vector structured output and in turn, the 4th 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. Optica’s July issue 2020 published this work and select it on the journal cover (

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 Dr. Shen. Moreover, the experimental demonstration comes from an otherwise “empty” laser cavity, the absence of specialised optical components. This poses an additional benefit in that the laser consists of a simple architecture, however, outputs a vector beam with 4 DoFs, certainly beyond an incremental advance.

Note that, recently this 4-DoF laser scheme was associated with astigmatic transformation, this ultra-DoF laser beam recently has a new extended formation including 5 controllable DoFs ( Moreover, when further associated with external spatial light modulation, the upgraded laser beam can create high-dimensional quantum-like classical light to emulate eight dimensional entangled states, a new world record ( 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.

Publication Information:

  1. Shen*, X. Yang, D. Naidoo, X. Fu, and A. Forbes, Structured ray-wave vector vortex beam in multiple degrees of freedom from a laserOptica7(7), 820–831 (2020).
  2. Wang, Y. Shen*, D. Naidoo, X. Fu, and A. Forbes, “Astigmatic hybrid SU(2) vector vortex beams: towards versatile structures in longitudinally variant polarized optics,” Opt. Express 29(1), 315-329 (2021).
  3. Shen*, I. Nape, X. Yang, X. Fu, M. Gong, D. Naidoo, and A. Forbes, “Creation and control of high-dimensional multi-partite classically entangled light,” Nature | Light: Sci. & Appl. 10, 50 (2021).