Tailoring accelerating beams in phase space

Abstract

This is the final published version of the article (version of record). It first appeared online via APS Physics at https://doi.org/10.1103/PhysRevA.95.023825 . Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW A 95, 023825 (2017) Tailoring accelerating beams in phase space An appropriate wave-front design will enable light fields that propagate along arbitrary trajectories, thus forming accelerating beams in free space. Previous strategies for designing such accelerating beams rely mainly on caustic methods, which start from diffraction integrals and deal only with two-dimensional fields. Here we introduce an alternate perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find that such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space, respectively. Moreover, this approach applies to the construction of both two-and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open a new route for construction of highly tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.

Construction, characteristics, and constraints of accelerating beams based on caustic design

“…As the radius of the circular caustic increases, it is noted that the intensity of the main lobe is no longer smooth along the whole nonconvex trajectory, and the breakup position almost matches the point with a phase difference ϕ π Δ = as denoted by the end points of the depicted caustic, which confirms the above constraint for an available smooth nonconvex trajectory of accelerating beams designed by superposition caustic methods. Apart from the 2D cases discussed in this work, accelerating beams in 3D space are also available by associating the propagating trajectories with 3D caustics, which have been demonstrated recently [24,29]. In the 3D case, the problem of interference or intersection between light rays tangential to a caustic discussed above can be easily avoided and thus a smooth main lobe can be obtained without breaking up into pieces, while there also exists another inherent constraint as discussed in [24].…”

“…Apart from the 2D cases discussed in this work, accelerating beams in 3D space are also available by associating the propagating trajectories with 3D caustics, which have been demonstrated recently [24,29]. In the 3D case, the problem of interference or intersection between light rays tangential to a caustic discussed above can be easily avoided and thus a smooth main lobe can be obtained without breaking up into pieces, while there also exists another inherent constraint as discussed in [24].…”

“…Although enhanced intensity around a caustic has been recognized for some time [34] and recently employed for the construction of accelerating beams [20][21][22][23][24][25][26][27][28][29][30][31], to the best of our knowledge, the discussion on the phase distribution along the caustic is missing in the literature, which is actually an important and elegant characteristic as pointed out in this work. The phase of the light field on the caustic can be calculated based on the aforementioned analysis (Appendix A), which is found to be…”

“…This method was first demonstrated with real-space design in the paraxial regime and achieved on-demand convex propagating trajectories for twodimensional (2D) light fields [22]. Later it has been widely extended, from real-space design to Fourier-space design [23] and even phase-space design [24], from paraxial regime to nonparaxial regime [25], from convex trajectories to nonconvex trajectories [26,27], from 2D light fields to 3D light fields [28,29], and from the phase-only modulation to the combined phase and amplitude modulation [30,31]. Such scheme does greatly extend the available propagating trajectories, and therefore there is often a claim in some papers that arbitrary propagating trajectories are obtainable, which is actually not the case.…”

Highly adjustable helical beam: design and propagation characteristics (Invited Paper)

“…which actually can be explained as a mean approximation in the perspective of the Wigner distribution [13,30] . Furthermore, by employing the chain rule between the polar coordinates and the rectangular coordinates, the derivatives of phase function in the polar coordinate system are…”