Field

[0001] The present disclosure relates to multiplexing and demultiplexing techniques. More particularly, embodiments of the present disclosure relate to multiplexing and demultiplexing techniques based on orbital angular momentum (OAM) modes.

Background

[0002] Twisted light, i.e. light associated with a twisted or helical wavefront, based on an unbounded set of orbital angular momentum (OAM) modes, can be exploited for mode division multiplexing (MDM), as a subset of space division multiplexing (SDM). OAM multiplexing uses physical properties of light to carry independent channels and therefore may be used to significantly increase transmission bandwidth or information capacity and may have a range of applications including for example in communications, imaging, sensing and encryption.

[0003] OAM multiplexing may use a spatial light modulator (SLM) for free-space twisted light manipulation. An SLM is generally of bulky size, relatively high in cost and has a relatively slow operation.

Summary of the disclosure

[0004] Methods and systems configured to assist with generating, controlling and detecting multiple OAM modes are described.

[0005] Aspects of the disclosure relate to an optical device for orbital angular momentum (OAM) multiplexing and/or demultiplexing, the optical device including: a metasurface for at least one of generating and receiving a plurality of OAM modes; and one or more single-mode waveguides; wherein one end of the one or more single-mode waveguides is coupled with the metasurface and the other end of the one or more single-mode waveguides is coupled with at least one of a light source and a light receiver; and the metasurface spatially matches one or more of the plurality of OAM modes to a corresponding one or more of the single-mode waveguides. [0006] In some embodiments, the metasurface and the one or more single-mode waveguides are integrated on a chip.

[0007] In some embodiments, the chip is formed from glass or an optical crystal. In some embodiments, the metasurface and the one or more single-mode waveguides are fabricated on a glass substrate. In some embodiments, the chip includes one or more guiding waveguides to provide one or more alignment markers for on-chip fabrication of at least one of the metasurface and the one or more single-mode waveguides.

[0008] In some embodiments, the one end of each of the one or more single-mode waveguides is located at a focal plane of the metasurface.

[0009] In some embodiments, the metasurface has a numerical aperture that substantially matches a numerical aperture of the one or more single-mode waveguides.

[0010] In some embodiments, the light source outputs light at a centre wavelength of at least 200nm.

[0011] In some embodiments, the metasurface includes a plurality of pillars. In some embodiments, at least one of height and in-phase rotation angle of each pillar of the plurality of pillars is varied to provide at least one of amplitude and phase responses to incident light.

[0012] Aspects of the disclosure relate to a method for orbital angular momentum (OAM) multiplexing and/or demultiplexing, the method including: by a metasurface: at least one of generating and receiving a plurality of OAM modes; and spatially matching one or more of the plurality of OAM modes to a first end of a corresponding one or more of single-mode waveguides; and at least one of: providing light from a light source for the generation of the plurality of OAM modes at a second end of the one or more single mode waveguides; and receiving at a light receiver optically coupled to the second end of the one or more single-mode waveguides light based on the received plurality of OAM modes.

[0013] In some embodiments, the spatial matching includes: controlling, by the metasurface, at least one of focal plane and numerical aperture of the metasurface. In some embodiments, the first end of each of the one or more single-mode waveguides is at the focal plane. In some embodiments, the numerical aperture of the metasurface substantially matches the numerical aperture of the one or more single-mode waveguides.

[0014] In some embodiments, the method further includes: outputting light, by the light source, at a centre wavelength of at least 200nm.

[0015] In some embodiments, the method further includes varying at least one of height and in-phase rotation angle of each pillar of the plurality of pillars to provide at least one of amplitude and phase responses to incident light.

[0016] Aspects of the disclosure relate to a device for orbital angular momentum (OAM) multiplexing and/or demultiplexing, the device including: a metasurface for at least one of generating and receiving a plurality of OAM modes; and one or more microwave or millimetre wave waveguides or cables; wherein one end of the one or more microwave or millimetre wave waveguides or cables is coupled with the metasurface and the other end of the one or more microwave or millimetre wave waveguides or cables is coupled with at least one of a microwave or millimetre source and a microwave or millimetre wave receiver; and the metasurface spatially matches one or more of the plurality of OAM modes to a corresponding one or more of the microwave or millimetre wave waveguides or cables.

[0017] In some embodiments, the one end of each of the one or more microwave or millimetre wave waveguides or cables is located at a focal plane of the metasurface.

[0018] In some embodiments, the device is configured to multiplex and/or demultiplex millimetre or centimetre wave signals.

[0019] Aspects of the disclosure relate to a method for orbital angular momentum (OAM) multiplexing and/or demultiplexing, the method including: by a metasurface, at least one of generating and receiving a plurality of OAM modes; and spatially matching one or more of the plurality of OAM modes to a first end of a corresponding one or more microwave or millimetre wave waveguides or cables; and at least one of: providing microwave or millimetre wave signals from a source for the generation of the plurality of OAM modes at a second end of the one or more microwave or millimetre wave waveguides or cables; and receiving at a receiver coupled to the second end of the one or more microwave or millimetre wave waveguides or cables millimetre or centimetre wave signals based on the received plurality of OAM modes.

[0020] In some embodiments, the spatial matching includes: controlling, by the metasurface, at least one of focal plane and numerical aperture of the metasurface. In some embodiments, the first end of each of the one or more microwave or millimetre wave waveguides or cables is at the focal plane.

[0021] In some embodiments, the method further includes: outputting, by the microwave or millimetre wave source, millimetre or centimetre wave signals to the one or more microwave or millimetre wave waveguides or cables.

[0022] Further aspects of the present disclosure and further embodiments of the aspects described in the preceding paragraphs will become apparent from the following description, given by way of example and with reference to the accompanying drawings.

Brief description of the drawings

[0023] Figure 1 illustrates an arrangement of an OAM generation and detection system including an OAM multiplexer/demultiplexer.

[0024] Figure 2A illustrates an exemplary embodiment of the OAM multiplexer/demultiplexer in Figure 1.

[0025] Figures 2B illustrate design principles and a pillar structure suitable for fabricating a metasurface with complex-amplitude (amplitude and phase) response of incident light for OAM multiplexing/demultiplexing purposes.

[0026] Figures 2C illustrate design principles and a pillar structure suitable for fabricating a metasurface with phase-only response of incident light for OAM multiplexing/demultiplexing purposes.

[0027] Figure 2D illustrates an exemplary metasurface used in the OAM multiplexer/demultiplexer in Figure 2A. [0028] Figure 3 illustrates a simulated normalised light density plot on an end surface of waveguides used in the OAM multiplexer/demultiplexer in Figure 2A.

[0029] Figure 4A illustrates a set of simulated light density plots and a Fourier lens image for 4 OAM channels as output from the metasurface used in the OAM multiplexer/demultiplexer of Figure 2A.

[0030] Figure 4B illustrates a single simulated light density plot and a Fourier lens image for a single OAM channel as output from the metasurface used in the OAM multiplexer/demultiplexer of Figure 2A.

[0031] Figure 4C illustrates an exemplary phase pattern of the metasurface.

[0032] Figure 5 illustrates results from a simulation of an arrangement of waveguides providing light to an OAM mode-sorting metasurface (OMM).

Detailed description of embodiments

[0033] The embodiments are described primarily with reference to light signals. In other embodiments the same techniques and design principles may be applied to microwave or millimetre wave signals. For example, OAM modes of millimetre or centimetre wave signals may be generated/multiplexed/modulated and/or detected/demultiplexed/demodulated. In microwave or millimetre wave signal embodiments, the light source will be replaced by a microwave or millimetre wave source, the metasurface configured for microwave or millimetre wave signals, the light receiver replaced by a microwave or millimetre wave receiver, and optical fibres/waveguides replaced by microwave or millimetre wave waveguides or cables. In other embodiments, the same techniques and design principles may be applied to terahertz (THz) signals. For example, OAM modes of THz signals may be generated/multiplexed/modulated and/or detected/demultiplexed/demodulated. In THz signal embodiments, the light source will be replaced by a THz generator, the metasurface configured for THz signals, the light receiver replaced by a THz detector, and optical fibres/waveguides replaced by THz waveguides.

[0034] Metasurfaces provide an alternative to using a spatial light modulator (SLM) for twisted light manipulation. Metasurfaces can locally impart changes to one or more physical properties (e.g. amplitude, phase, polarisation state, collimation or divergence) of propagating light. Metasurfaces enable multiple optical functions to be achieved within a single metasurface element and may be fabricated in a compact size.

Therefore, the use of metasurfaces facilitates creation of small form factor optical systems.

[0035] In addition, a photonic integrated circuit (PIC) that combines multiple optical components on a single chip enables relatively dense packing of the optical components. Further reductions in the footprint of an optical system may be achieved by using a metasurface in a PIC. However, metasurfaces generally require external light excitation, which can makes them difficult to integrate on-chip with other components, such as the light source(s). In addition, PICs have limited photonic functionalities, for example, on multimode light shaping (e.g. generation, transmission and detection of OAM modes), polarisation control (e.g. generation and detection of polarised light), dispersion control (e.g. compensation for chromatic aberration), collimation and divergence control of the light, and limited free-space light controllability. An on-chip interface that can flexibly control light conversion between free-space and guided modes would therefore be useful.

[0036] Figure 1 illustrates an arrangement of an OAM generation and detection system 100. The system 100 includes a light source 102, a processing unit 104, an OAM multiplexer/demultiplexer 106 and a light receiver 108. In some embodiments, light 109 from the light source 102 is a guided optical signal, for example directed to the OAM multiplexer/demultiplexer 106 via one or more optical fibres. The light source 102 may be a coherent light source or an incoherent light source. The light source 102 may include an optical splitter for splitting light into one or more output optical channels, directed into the respective one or more optical fibres.

[0037] The one or more optical fibres may be directly coupled with the light source 102 and the OAM multiplexer/demultiplexer 106. In alternative embodiments the path over which light 109 traverses includes free space. For example, the light source 102 may be directly coupled with or direct light over free space into the one or more optical fibres, which output the light 109 to free space for coupling with the OAM multiplexer/demultiplexer 106, for example, with assistance of one or more lenses such as collimating lenses. In other examples, the light from the light source 102 is directed to the OAM multiplexer/demultiplexer 106 via free-space optics (e.g. one or more lenses) without fibres.

[0038] The operation of the light source 102 (e.g. wavelength and/or optical power and/or modulation of the output light) may be controlled by a processing unit 104 via one or more electrical signals. The processing unit 104 may include one or more processing devices. For example, the processing unit 104 may include a modulator for imparting a modulation (e.g. amplitude modulation, phase modulation, frequency modulation, code modulation) to the light signal of each optical channel, which may provide a mechanism for information communication. The modulator may be a Mach Zehnder modulator (MZM) or a semiconductor optical amplifier (SOA). In another embodiment, the light source 102 may include control circuitry to control one or more characteristics of the light. For example, the light source 102 may include the modulator for imparting an amplitude, frequency, code or phase modulation to the light signal of each optical channel. In this embodiment, the modulator may be an external modulator or a modulator integrated on the laser source 102. Alternatively or additionally, the processing unit 104 may include one or more processing devices selected from the group of a central processing unit (CPU), a graphics processing unit (GPU), an application specific integrated circuit (ASIC), a field-programming gate array (FPGA) and a digital signal processor (DSP). The processing unit 104 may include transient memory and non-transient memory device(s). The non-transient memory device(s) may store instructions for controlling the processing device(s) of the processing unit, including for example instructions to control the light source 102 and instructions to process signals detected by the light receiver 108.

[0039] The OAM multiplexer/demultiplexer 106 includes a mode expander 106A. The mode expander 106A receives the light 109 from the light source 102 and outputs light 103. The mode expander 106A is a functional description of optical components configured for a) transitioning between light 109 from the light source 102 and light 103 including a plurality of spatially separate light beams each with a Gaussian mode over a common or overlapping area of the OAM generator and/or detector 106B and/or b) transitioning between light including independent channels 105 each with a Gaussian mode originating from a common or overlapping area of the OAM generator and/or detector 106B as spatially separate light beams. An example configuration of waveguides (with respect to a metasurface), which operate as a mode expander is described with reference to Figure 2A.

[0040] Returning to Figure 1 , the light 103 is received by an OAM generator and/or detector 106B. The OAM generator and/or detector 106B is configured to generate/multiplex/modulate one or more OAM modes (i.e. to operate as an OAM generator/multiplexer/modulator). When operating as an OAM generator, the OAM generator and/or detector 106B outputs OAM-superposed beams 101 with one or more OAM modes, for further processing (e.g. modulation to carry information) and/or transmission.

[0041] When receiving OAM superposed beams 101, the OAM generator and/or detector 106B operates to detect/demultiplex/demodulate the OAM-superposed beams 101 (i.e. to operate as an OAM detector/demultiplexer/demodulator) and demultiplexes the OAM-superposed beams 101 with one or more independent OAM modes, each OAM mode being independently converted to a Gaussian mode. The OAM generator and/or detector 106B then outputs the one or more independent channels 105 each with a Gaussian mode. Each channel of the one or more independent channels 105 is independently received by the mode expander 106A. The mode expander 106A outputs the one or more Gaussian mode channels 111 to a light receiver 108 for detection and post-processing. An example OAM generator and/or detector in the form of a metasurface is described with reference to Figure 2A.

[0042] The light receiver 108 may be one or more photodetectors. In one example, the light receiver 108 includes an array of photodiodes. In another example, the light receiver 108 includes an array of charge-coupled devices (CCDs).

[0043] In some embodiments the OAM multiplexer/demultiplexer 106 may operate as a transceiver that utilises common components (e.g. a common metasurface may be used in the OAM generator and/or detector 106B for both outgoing and incoming light). In other examples, the optical system 100 may be a dedicated transmitter or a dedicated receiver. In still other examples, the outgoing light path and the incoming light path may be in parallel. For example the OAM generator and/or detector 106B may include a plurality of metasurfaces, one or more dedicated to outgoing light and one or more dedicated to incoming light.

[0044] Figure 2A illustrates an embodiment of the OAM multiplexer/demultiplexer 106 of Figure 1. The OAM multiplexer/demultiplexer 106 is in the form of an on-chip OAM multiplexer/demultiplexer 206. In this example, the mode expander 106A functionality is achieved by the configuration of one or more single-mode waveguides (110-1, 110-2, 110-3, ... , 110-M, M³1). That is, the one or more single-mode waveguides 110-1, 110- 2, 110-3,...110-M each transmit a single Gaussian mode to a metasurface (see below). Light with one (M=1) or more (M>1) Gaussian modes is received by the metasurface. It will be appreciated that the single-mode nature of the waveguides may reduce crosstalk between the Gaussian modes. Each of the one or more single-mode waveguides may be laser-inscribed within a chip 200. The chip 200 may be formed from a material selected from a group including glass and optical crystal materials. In one example, the one or more single-mode waveguides may be written within the chip 200 by a laser. The OAM generator/detector 106B may be in the form of a metasurface 206B, which is integrated on a surface of the chip 200 and coupled with the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M. The on-chip OAM multiplexer/demultiplexer 206 may also include one or more guiding waveguides to provide one or more illustration spots, which may offer one or more alignment markers for on-chip fabrication of at least one of the metasurface 206B and the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M. In one example as illustrated in Fig. 2A, the on-chip OAM multiplexer/demultiplexer 206 includes four guiding waveguides 106C-1, 106C-2, 106C-3 and 106C-4, each positioned at a corner of the plane where the metasurface 206B is to be fabricated on the chip 200 and extended along the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M.

[0045] In this embodiment, when the metasurface 206B is operated as an OAM generator, the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M direct light beams 103-1, 103-2, 103-3, ..., 103M, each with a Gaussian mode to the metasurface 206B, which controls the on-chip parallel generation of the one or more OAM modes each corresponding to the respective input Gaussian mode. The metasurface 206B generates one OAM mode for each of the light beams (103-1, 103-2, 103-3, ..., 103M). The metasurface 206B then outputs OAM-superposed beams 101 with the plurality of OAM modes superposed.

[0046] When the metasurface 206B is operated as an OAM detector, the one or more OAM-superposed beams 101 are received by the metasurface 206B for detecting, demultiplexing or demodulating. The metasurface 206B demultiplexes the OAM- superposed beams 101 with one or more independent OAM modes, each OAM mode being independently converted to a Gaussian mode. The metasurface 206B then outputs one or more independent channels 105-1, 105-2, 105-3, ..., 105-M each with a Gaussian mode. Each of the one or more channels 105-1, 105-2, 105-3, ..., 105-M is received by and transmitted within a single-mode waveguide of the one or more single mode waveguides 110-1, 110-2, 110-3, ... and 110-M. In this embodiment, the metasurface 206B integrated on the chip 200 can convert OAM incidence 101 into a grid of points, each point representing a specific Gaussian mode being converted by the corresponding OAM mode at the Fourier plane of the metasurface 206B for on-chip OAM detection/demodulation/demultiplexing. One end of the set of one or more single mode waveguides 110-1, 110-2, 110-3, ... and 110-M is then inscribed to couple with the one or more light channels, respectively. In some embodiments the ends of the set of single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M may be located in a plane 301. The other ends of the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M may be connected to one or more fibre pigtails (not shown).

[0047] The one or more fibre pigtails may be coupled with the light source 102 (directly or indirectly via free-space optics) when operating as the OAM generator or to the light receiver 108 (directly or indirectly via free-space optics) when operating as the OAM detector.

[0048] In one example, the ends of the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M that are coupled with the metasurface 206B (i.e. at the plane 301) are configured in a 2D profile. In particular, the end of each of the single mode waveguides 110-1, 110-2, 110-3, ... and 110-M may be located substantially at a focal point for the corresponding output beam 105-1, 105-2, 105-3, ..., 105-M. The focal points for the output channels 105-1, 105-2, 105-3, ..., 105-M may be located in the plane 301. The OAM multiplexer/demultiplexer 106 is configured so that substantially the same area across the metasurface 206B is used to generate a plurality of the OAM channels, up to all of the OAM channels as shown in Figure 2A. In particular, the waveguides 110-1, 110-2, 110-3, ... and 110-M are angled so that their respective beams are directed towards the centre of the metasurface 206B. In the embodiment shown in Figure 2A, the other ends of the one or more single-mode waveguides are configured in a 1 D profile. It will be appreciated that the ends of the one or more single mode waveguides may be configured in other profiles, including other 2D profiles.

[0049] The operation of the metasurface 206B for multiplexing and/or demultiplexing OAM channels is described below.

[0050] It will be understood that an OAM beam can be converted to or back- converted from a beam with a Gaussian mode by applying a helical phase termed as exp(il _j( p) (for OAM multiplexing, i.e. from Gaussian mode to OAM) or an opposite helical phase termed as exp( - il _j cp) (for OAM demultiplexing, i.e. from OAM to Gaussian mode), where l denotes the topological charge of the OAM mode.

[0051] In this regard, a complex-amplitude electric field distribution of each individual OAM demultiplexing channel is expressed as: where Zps the modal number of the OAM channel and f is the azimuthal angle in the polar coordinate system, x and y represent the Cartesian transverse coordinates in the metasurface 206B plane, and k _x ^] (k _x ^J = control diffraction angle of each OAM channel or converted Gaussian mode beam by, for example, adjusting its focal position (x^, y^) in the Fourier plane of the metasurface 206B, where k represents wavenumber (k = 2p/l, l is centre wavelength of the light beam). The parameters x^ and yl _j represent the Cartesian transverse coordinates in the Fourier plane and f is focal length of the metasurface 206B representing the distance between the metasurface 206B to the focal point of each output beam 105-1, 105-2, 105-3, ... , 105- M. [0052] With the OAM demultiplexing channel as expressed in Equation (1), each incident OAM beam (exp(jZ ₇ <p)) can be converted to a Gaussian mode beam due to the application of the opposite helical phase exp( - iZ ₇ <p) with a particular propagation direction controlled by parameters k _x ^} and k _y ^J of the metasurface 206B. Accordingly, a complex-amplitude electric field distribution for demultiplexing multi-OAM beams can be constructed by adding multiple phases expressed in Equation (1) with different parameters Z ₇ , k _x ^] and k _y ’ together as follows, which allows directing the one or more OAM incident beams into different spatial locations in the Fourier plane: where n represents the total number of OAM demultiplexing modes. As shown in Equation (2), each complex-amplitude OAM demultiplexing electric field is multiplied by a Fourier-transform lens function termed where k represents the wavenumber and f is the focal length of the metasurface 206B representing the distance between the metasurface 206B to the focal point of each output beam 105-1 , 105-2, 105-3, ..., 105-M. The effective numerical aperture (NA) of the metasurface is given as:

NA = sin tan ^-1 r/f, (3) where r is the radius of the metasurface 206B. In this regard, when coupled with the one or more single-mode waveguides, the numerical aperture of the metasurface can be designed based on Equation (3) to substantially match different numerical apertures of different waveguides.

[0053] It will be appreciated that the demultiplexing metasurface can be designed either based on the complex-amplitude modulation (i.e. according to Equation (2)) or a phase-only modulation by taking argument of the complex-amplitude electric field in Equation (2), i.e.:

0( y) _M = arg (E(x,y)„). (4)

[0054] As a result, the demultiplexing metasurface as designed either based on Equation (2) or Equation (4) may demultiplex the incident OAM superposed beams 101 which include one or more OAM beams each having an OAM mode by converting each of the one or more OAM modes to a corresponding Gaussian mode and also allow spatially separating the output one or more independent channels 105-1, 105-2, 105-3, ..., 105-M each with a Gaussian mode (i.e. one or more independent Gaussian mode beams). In addition, the demultiplexing metasurface as designed either based on Equation (2) or Equation (4) allows the focal points for the one or more independent Gaussian mode beams to be flexibly arranged in a 2D Fourier plane, where one ends of the one or more single-mode waveguides 110-1, 110-2, 110-3, ... and110-M may be located to receive the one or more independent Gaussian mode beams.

[0055] Based on the reciprocal nature of the metasurface 206B, a complex-amplitude electric field distribution of each individual OAM multiplexing channel is expressed as: where the grating function e ^l(fe ^ ^x+feyy) in the metasurface 206B can be cancelled out by an incident Gaussian mode beam with a diffraction angle (-k _x ^J ,-k _y ^J ), which is offered by the single mode waveguide output placed at the position (x^, yh) in the Fourier plane.

[0056] Similarly, to achieve OAM multiplexing, a complex-amplitude electric field distribution for multi-OAM beams multiplexing can be constructed by adding multiple phases expressed in Equation (5) with different parameters l _j , k[ and k _y ^] together as follows: where the sign of focal length f is positive.

[0057] It will also be appreciated that the multiplexing metasurface can be designed either based on the complex-amplitude modulation (i.e. according to Equation (6)) or a phase-only modulation by taking the argument of the complex-amplitude electric field in Equation (6), i.e.:

0'( _. *, U)M = arg (£"(x,y) _M ). (7) [0058] In this regard, the metasurface 206B as a multiplexing metasurface is allowed to receive each of the light beams 103-1, 103-2, 103-3, ..., 103M (each with a Gaussian mode) directed by the corresponding single-mode waveguide at a particular spatial location and output the OAM-superposed beams 101.

[0059] The metasurface 206B is then designed with a structure having the complex- amplitude (amplitude and phase) response of the incident light according to Equations (2) and (6) or having the phase-only response of the incident light according to Equations (4) and (7).

[0060] In one example for the metasurface 206B designed to have a complex- amplitude (amplitude and phase) response to the incident light, the metasurface 206B may have a 3D profile. In one example, a 3D metasurface for the complete and independent manipulation of both amplitude and phase of the incident light can be fabricated using 3D laser printing technology based on a photosensitive polymer material. For example, a low refractive index (e.g. n=1.52 @ 700 nm wavelength) polymer-based rectangular pillar (e.g. nano-pillar with dimensions in nanometre scale) with a high aspect ratio can be used as a meta-atom.

[0061] As illustrated in Figure 2B (a), the 3D metasurface may include a plurality of pillars (212-1, 212-2, 212-3, ..., 212-n, collectively 212) fabricated on a glass substrate 214. The height (H), in-plane (i.e. the plane that is parallel to the glass substrate 214) angle Q of each pillar and the distribution profile of the plurality of pillars may be adjusted to provide the required amplitude change, phase change and beam steering of the incident light according to Equations (2) and (6).

[0062] In particular, each of the plurality of pillars may exhibit strong birefringence, laying the physical foundation of the geometric phase response based on the in-plane phase rotation (Q). Further, varying the highlight (H) of each pillar may provide amplitude modulation for the incident light. In addition, the periodic structures in the metasurface (i.e. the distribution of the pillars) may also be designed based on Equation (1) to direct the output light of the metasurface to different spatial locations in the Fourier plane. Figures 2B (b) and (c) illustrate a pillar structure 210 suitable for fabricating the metasurface 206B with complex-amplitude (amplitude and phase) response of the incident light for OAM multiplexing/demultiplexing purposes in top view and oblique view, respectively.

[0063] In another example for the metasurface 206B having phase-only response to the incident light, the metasurface 206B may provide control of the propagation phase (i.e. from 0 to 2TT) of meta-atoms (i.e. pixels on the metasurface) by varying their height (i.e. using the height degree of freedom) continuously or discretely as illustrated in Fig. 2C (a). Figures 2C (b) and (c) illustrate a pillar structure 310 suitable for fabricating the metasurface 206B with phase-only response of the incident light for OAM multiplexing/demultiplexing purposes in top view and oblique view, respectively. Similarly, the 3D metasurface for the complete and independent manipulation of phase of the incident light can be fabricated using 3D laser printing technology based on a photosensitive polymer material. For example, a low refractive index (e.g. n=1.52 @

700 nm wavelength) polymer-based rectangular pillar (e.g. nano-pillar with dimensions in nanometre scale) with a high aspect ratio can be used as a meta-atom. The metasurface 206B may include a plurality of pillars (collectively 312) with varying height fabricated on a glass substrate 314.

[0064] As mentioned above, 3D laser printing (or 3D direct laser writing) technology may be used to fabricate complex-amplitude or phase-only metasurfaces for OAM multiplexing/demultiplexing. The metasurface 206B may be fabricated on the chip 200 with the laser-inscribed one or more single-mode waveguides. The metasurface 206B may be formed from a material selected from a group including glass and photoresists (e.g. SU-8 photoresist, polymethyl methacrylate (PMMA) photoresist, IP-dip, IP-S or IP- L photoresist) using the two-photon polymerization process via a tightly focused femtosecond laser beam. During the fabrication process, a laser beam is tightly focused into a photosensitive polymer sample through a microscope objective lens, and the photopolymerization process occurs when the photon energy inside the 3D focal spot is above the polymerization threshold, forming the unit cell or meta-atom or pixel of the metasurface. To form the whole metasurface pattern, the polymer sample needs to be mounted onto a translation stage. Controlled 3D-scanning of the laser focus with respect to the photosensitive sample gives rise to a metasurface pattern fabricated inside the polymer matrix. To achieve the best spatial resolution in the metasurface fabrication, some fabrication parameters need to be optimised (e.g. the laser power, scanning speed, laser dwelling time in the polymer sample, hatching and splicing distances of required structures), analytically and/or by experimentation. Following the laser printing process, the metasurface 206B may be further chemically developed for removing untreated photoresist, for example, immersed in propylene glycol monomethyl ether acetate (PGMEA) for 20 minutes, Isopropanol (IPA) for 5 minutes and methoxy- nonafluorobutane for 2 minutes. The fabricated metasurface is then dried in air by evaporation.

[0065] It will be appreciated that, to significantly increase the fabrication throughput using the above 3D laser printing method, galvanic mirror scanning can be used, instead of using the scanning stage. Alternatively, single-photon polymerization process can be used for metasurface fabrication, with a cost of a relatively lower spatial resolution, but with a benefit of low-cost laser sources (e.g., continuous wave lasers).

[0066] Other methods for fabricating the metasurface may include electron beam lithography by scanning a focussed electron beam across a suitable photoresist (e.g., SU-8) that is spin-coated on a pre-deposited high-refractive-index dielectric thin film (e.g., Ti02, Si, GaN, GaP, SiC) on the glass chip (e.g. chip 200). After the electron- beam lithography process, the resist development is performed and a hard mask (e.g., Ni) is deposited using electron-beam evaporation. After the lift-off process, high index metasurfaces are created using reactive ion etching. The Ni mask on the top of high index metasurfaces is then removed using chemical etching.

[0067] Figure 2D illustrates an exemplary metasurface 206B for use in the on-chip OAM multiplexer/demultiplexer 206 in Figure 2A. The metasurface 206B has a plurality of pixels 202-1, 202-2, ..., and 202-N. For example, the metasurface 206B may have dimensions of 1mm by 1mm and may include 2000*2000 pixels (i.e. N=4,000,000) evenly distributed on the metasurface 206B, resulting in a metasurface resolution (or pitch distance) of 500nm (i.e. 1 mm/2000). The metasurface 206B provides parallel generation/multiplexing/modulation and detection/demultiplexing/demodulation of a large number of OAM modes (e.g. a potential maximum of about 100 OAM modes). The large number of OAM modes facilitates embodiments with ultrafast and high-capacity operation and transmission. In addition, there is negligible crosstalk between the OAM modes. [0068] Figure 3 illustrates a simulated normalised light density plot 300 obtained at the plane 301 of the single-mode waveguides 110-1, 110-2, 110-3, ... and 110-M (M=4) used in the on-chip OAM multiplexer/demultiplexer 206B of Figure 2A. In this simulation example, the light source 102 provides the light 109 with a centre wavelength at 1550nm. It will be appreciated that other spectral ranges can also be used with the on- chip OAM multiplexer/demultiplexer 206 of Figure 2A (e.g. from ultraviolet band (i.e. from about 200nm wavelength) to the millimetre or centimetre frequency bands). The metasurface 206B has a the size of 1mm by 1mm with 2000 by 2000 pixels evenly distributed on the metasurface 206B, resulting in the metasurface having a resolution (or pitch distance) of 500nm for signal wavelength at about 1550nm. It will be appreciated that the size of the metasurface will be scaled with respect to the signal wavelength. Each of four single-mode waveguides is configured to locate at a corner of a square having a side length of 200pm. Each output of the single mode waveguide has a close approximation of Gaussian intensity profile as shown in the inset.

[0069] Figure 4A illustrates a set of simulated light density plots for 4 OAM channels as output from the metasurface 206B used in the OAM multiplexer/demultiplexer 206 of Figure 2A being operated as the OAM detector. Figure 4A also illustrates an exemplary phase pattern 400A-3 of the metasurface 206B, which is reproduced in Fig. 4C. In particular, Figure 4A illustrates a simulated density plot 400A-1 at the XZ plane. Each OAM channel is controlled to have a Fourier plane (or focal plane) A and a numerical aperture of 0.18 (NA=0.18) at the Fourier plane to substantially match the divergence angle of the corresponding single-mode waveguide when each coupling end of the single-mode waveguide is placed at the Fourier plane A. Figure 4A also illustrates a simulated density plot 400A-2 at the Fourier Plane A (i.e. at the XY plan) showing that each OAM channel has a close approximation of Gaussian intensity profile (i.e. 402-1, 402-2, 402-3 and 402-4). In this example, the distance between the planes A and B (i.e. focal length or coupling length) is 4.14mm.

[0070] Similarly, Figure 4B illustrates a set of simulated light density plots and a Fourier lens image for a single OAM channel as output from the metasurface 206B used in the OAM multiplexer/demultiplexer 106’ of Figure 2A being operated as the OAM detector. In particular, Figure 4B illustrates a simulated density plot 400B-1 at the XZ plane. The OAM channel is controlled to have a Fourier plane (or focal plane) C and a numerical aperture of 0.18 (NA=0.18) at the Fourier plane to match the divergence angle of the corresponding single-mode waveguide when the coupling end of the single mode waveguide is placed at the Fourier plane C. It is noted that the depth of focus (DoF) is about 200pm providing some tolerance of the placement of the coupling ends of the one or more single-mode waveguides. Figure 4B also illustrates a simulated density plot 400B-2 at the Fourier Plane A (i.e. at the XY plan) showing that the OAM channel has a close approximation of Gaussian intensity profile. In addition, Figure 4B illustrates a Fourier lens image 400B-3 at a plane D (i.e. at the XY plane) which locates right after the metasurface 206B. In this example, the distance between the planes C and D (i.e. focal length or coupling length) is 4.14mm.

[0071] Figure 4C illustrates the exemplary phase pattern 400A-3 of the metasurface 206B used in the simulations with a phase change indication bar 401 indicating a phase level to be any number within a range of 0 to 2p (inclusive), where black patterns indicate no phase change (i.e. phase change = 0) of the incident light while white patterns indicate 360-degree phase change (i.e. phase change = 2TT) of the incident light. As mentioned above, the phase pattern for the metasurface 206 can be achieved by varying the height of each of the pixels on the metasurface. It can be seen from the comparison between 400A-2, 400B-2 and 400B-3 that the phase pattern 400A-3 for the metasurface 206B used in the simulations allows creating one or more diffraction-limited focal points with substantially the same intensity distribution as the case of a single Fourier lens.

[0072] Figure 5 illustrates results from a simulation of an arrangement, in this example a circular geometry arrangement, of waveguides providing light to an OAM mode-sorting metasurface (OMM), for 10 OAM modes and 20 OAM modes. The 10 OAM modes were equidistantly spaced around the circular geometry at a radius of 150pm. An additional 10 OAM modes equidistantly spaced at a radius of 180pm was included to form the 20 OAM modes. The spacing of or in other words the topological step index of the topological charges, assigned to each of the orbital angular momentum light channels was simulated between 1 and 5. As shown in Figure 5, a spacing of = 3 or 4 has reduced crosstalk between the channels relative to each other spacing. The improvement in reduced crosstalk is larger for 10 OAM modes than for 20 OAM modes. [0073] Free-space OAM communication systems suffer from turbulence-induced phase distortions to propagating beams, which can destroy the OAM orthogonality and introduce modal crosstalk among the OAM information channels. Accordingly, setting the spacing or topological step index having regard to crosstalk may at least partially alleviate this issue.

[0074] In some embodiments of OAM multiplexer/demultiplexer the topological step index is set between 2 and 5 for 15 OAM modes or less, or set at 3 or 4 for 15 OAM modes or less. In some embodiments the topological step index is set between 2 and 5 for 10 OAM modes or less, or set at 3 or 4 for 10 OAM modes or less. In some embodiments the topological step index is set between 3 and 5 for 15 OAM modes or more, or set at 3 or 4 for 15 OAM modes or more. In some embodiments topological step index is set between 3 and 5 for 20 OAM modes or more, or set at 3 or 4 for 20 OAM modes or more. The geometrical arrangement of the waveguides may be circular or non-circular.

[0075] It will be appreciated that the on-chip OAM multiplexer/demultiplexer as described above may result in a compact, broadband and efficient optical or microwave or millimetre frequency device that is capable of providing parallel generation/multiplexing/modulation and detection/demultiplexing/demodulation of multiple OAM channels, each being independently controlled within the optical or microwave or millimetre device with negligible crosstalk between the OAM modes. Such optical or microwave or millimetre device may facilitate ultrafast and reliable data transmission for a range of applications including optical or microwave or millimetre communications, imaging, sensing and encryption.

[0076] It will be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text or drawings. All of these different combinations constitute various alternative aspects of the invention.

[0077] For the purposes of interpreting this specification, terms used in the singular will also include the plural and vice versa. [0078] As used herein, the term “and/or”, e.g., “X and/or Y” will be understood to mean either “X and Y” or “X or Y” and shall be taken to provide explicit support for both meanings or for either meaning.

[0079] As used herein, the term “about” refers to a quantity, value, dimension, size, or amount that varies by as much as 10%, 5%, 1% or 0.1 % to a reference quantity, value, dimension, size, or amount.

[0080] Throughout the present disclosure, various aspects of the disclosure can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the disclosure. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as a range of wavelengths from 200nm to 1600nm should be considered to have specifically disclosed subranges such as from 200nm to 300nm, from 200nm to 400nm, from 200nm to 500nm, from 150nm to 400nm, from 1500nm to 1600nm, from 1540nm to 1560nm etc., as well as individual numbers within that range, for example, 200nm, 255nm, 1300.8nm, 1550.26nm, 1553.1nm, 1562nm, 1568.79nm, and 1600nm. This applies regardless of the breadth of the range.