Multi-plane light conversion is a method of performing spatial basis transformations using cascaded phase plates separated by Fourier transforms or free-space propagation. In general, the number of phase plates required scales with the dimensionality (total number of modes) in the transformation. This is a practical limitation of the technique as it relates to scaling to large mode counts. Firstly, requiring many planes increases the complexity of the optical system itself making it difficult to implement, but also because even a very small loss per plane will grow exponentially as more and more planes are added, causing a theoretically lossless optical system, to be far from lossless in practice. Spatial basis transformations of particular interest are those which take a set of spatial modes which exist in the same or similar space, and transform them into an array of spatially separated spots. Analogous to the operation performed by a diffraction grating in the wavelength domain, or a polarizing beamsplitting in the polarization domain. Decomposing the Laguerre-Gaussian, Hermite-Gaussian or related bases to an array of spots are examples of this and are relevant to many areas of light propagation in free-space and optical fibre. In this paper we present our work on designing multi-plane light conversion devices capable or operating on large numbers of spatial modes in a scalable fashion.

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Laguerre-Gaussian mode sorter.

The terahertz range possesses significant untapped potential for applications including high-volume wireless communications, noninvasive medical imaging, sensing, and safe security screening However, due to the unique characteristics and constraints of terahertz waves, the vast majority of these applications are entirely dependent upon the availability of beam control techniques Thus, the development of advanced terahertz-range beam control techniques yields a range of useful and unparalleled applications This article provides an overview and tutorial on terahertz beam control The underlying principles of wavefront engineering include array antenna theory and diffraction optics, which are drawn from the neighboring microwave and optical regimes, respectively As both principles are applicable across the electromagnetic spectrum, they are reconciled in this overview This provides a useful foundation for investigations into beam control in the terahertz range, which lies between microwaves and infrared

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Tutorial: Terahertz beamforming, from concepts to realizations

We present the generation of arbitrary order Bessel beams at 0.3 THz through the implementation of suitably designed axicons based on 3D printing technology. The helical axicons, which possess thickness gradients in both radial and azimuthal directions, can convert the incident Gaussian beam into a high-order Bessel beam with spiral phase structure. The evolution of the generated Bessel beams are characterized experimentally with a three-dimensional field scanner. Moreover, the topological charges carried by the high-order Bessel beams are determined by the fork-like interferograms. This 3D-printing-based Bessel beam generation technique is useful not only for THz imaging systems with zero-order Bessel beams but also for future orbital-angular-momentum-based THz free-space communication with higher-order Bessel beams.

Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range.

Structured light, especially beams carrying orbital angular momentum (OAM), has gained much interest due to its unique amplitude and phase structures. In terms of communication systems, multiple orthogonal OAM beams can be potentially utilized for increasing link capacity in different scenarios. This review describes challenges, advances, and perspectives on different aspects of the OAM-based optical communications, including (a) OAM generation/detection and (de)multiplexing, (b) classical free-space optical communication links, (c) fiber-based communication links, (d) quantum communication links, (e) OAM-based communications in different frequency ranges, (f) OAM-based communications using integrated devices, and (g) novel structured beams for communications.

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Orbital angular momentum of light for communications

Multi-beam antennas are critical components in future terrestrial and non-terrestrial wireless communications networks. The multiple beams produced by these antennas will enable dynamic interconnection of various terrestrial, airborne and space-borne network nodes. As the operating frequency increases to the high millimeter wave (mmWave) and terahertz (THz) bands for beyond 5G (B5G) and sixth-generation (6G) systems, quasi-optical techniques are expected to become dominant in the design of high gain multi-beam antennas. This paper presents a timely overview of the mainstream quasi-optical techniques employed in current and future multi-beam antennas. Their operating principles and design techniques along with those of various quasi-optical beamformers are presented. These include both conventional and advanced lens and reflector based configurations to realize high gain multiple beams at low cost and in small form factors. New research challenges and industry trends in the field, such as planar lenses based on transformation optics and metasurface-based transmitarrays, are discussed to foster further innovations in the microwave and antenna research community.

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Quasi-Optical Multi-Beam Antenna Technologies for B5G and 6G mmWave and THz Networks: A Review

We first demonstrate the accelerating terahertz (THz) Airy beam with a 0.3-THz continuous wave. Two diffractive elements are designed and 3D-printed to form the generation system, which cannot only imprint the desired complex phase pattern but also perform the required Fourier transform (FT). We both numerically and experimentally demonstrate the propagation dynamics of the accelerating THz Airy beam and investigate its self-healing property during propagation in the free space. Our observations are in good agreement with the numerical simulations. Such an accelerating THz Airy beam could be able to develop novel THz imaging systems and robust THz communication links.

3D-printed diffractive elements induced accelerating terahertz Airy beam

Vortex beams have received considerable research interests both in optical and millimeter-wave domain since its potential to be utilized in the wireless communications and novel imaging systems. Many well-known optical beams have been demonstrated to carry orbital angular momentum (OAM), such as Laguerre-Gaussian beams and high-order Bessel beams. Recently, the radially symmetric Airy beams that exhibit an abruptly autofocusing feature are also demonstrated to be capable of carrying OAM in the optical domain. However, due to the lack of efficient devices to manipulate terahertz (THz) beams, it could be a challenge to demonstrate the radially symmetric Airy beams in the THz domain. Here we demonstrate the THz circular Airy vortex beams (CAVBs) with a 0.3-THz continuous wave through 3D printing technology. Assisted by the rapidly 3D-printed phase plates, individual OAM states with topological charge l ranging from l = 0 to l = 3 and a multiplexed OAM state are successfully imposed into the radially symmetric Airy beams. We both numerically and experimentally investigate the propagation dynamics of the generated THz CAVBs, and the simulations agree well with the observations.

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Terahertz circular Airy vortex beams.

We present an efficient method to discriminate orbital angular momentum (OAM) of the terahertz (THz) vortex beam using a diffractive mode transformer. The mode transformer performs a log-polar coordinate transformation of the input THz vortex beam, which consists of two 3D-printed diffractive elements. A following lens separates each transformed OAM mode to a different lateral position in its focal plane. This method enables a simultaneous measurement over multiple OAM modes of the THz vortex beam. We experimentally demonstrate the measurement of seven individual OAM modes and two multiplexed OAM modes, which is in good agreement with simulations.

Discrimination of orbital angular momentum modes of the terahertz vortex beam using a diffractive mode transformer

We design a plano-convex lens working in the terahertz (THz) frequency range and fabricate it using three-dimensional (3D) printing technology. A 3D field scanner is used to measure its focal properties, and the results agree well with the numerical simulations. The refractive index and absorption coefficient measurements via THz time-domain spectroscopy (THz-TDS) reveal that the lens material is highly transparent at THz frequencies. It is expected that this inexpensive and rapid 3D printing technology holds promise for making various THz optical elements.

Changming Liu

Papers

Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range.

3D-printed diffractive elements induced accelerating terahertz Airy beam

Terahertz circular Airy vortex beams.

Discrimination of orbital angular momentum modes of the terahertz vortex beam using a diffractive mode transformer

Rapid fabrication of terahertz lens via three-dimensional printing technology