Full-duplex cylindrical vector beam multiplexing communication using spin-dependent phase modulation metasurfaces

Qingji Zeng; Jing Wang; Huihua Huang; Haisheng Wu; Jianjun Ren; Lvye Nong; Zhiqiang Xie; Junmin Liu; Huapeng Ye; Dianyuan Fan; Shuqing Chen

doi:10.1364/OE.501577

1. Introduction

Cylindrical vector beams (CVBs) with spatially variant polarizations are considered promising for enlarging optical communication capacity via mode multiplexing [1–4]. The CVB mode is independent of conventional physical dimensions involving wavelength and polarization, which enables it to be combined with wavelength division multiplexing (WDM) and polarization division multiplexing (PDM) for further enhancement of communication capacity density [5–7]. Additionally, CVB is capable of long-haul transmission, as it is the eigenmode of few-mode fiber (FMF) [8,9]. By multiplexing digital signals with CVB modes, wavelengths, and polarizations, the communication capacity has improved to Tbit/s [10,11]. However, most of these works have only focused on simplex multiplexing transmission, and few efforts have been devoted to full-duplex communication, which is expected to benefit bidirectional information interconnection with higher transmission traffic [12–14]. The pivotal procedure here is to parallelly couple and separate CVB modes in full-duplex multiplexing channels. Traditional optical devices such as phase-type spatial light modulators [15], digital micro-mirror devices [16], and spiral phase plates [17] have intrinsic uniform polarization responses, which constrains their ability to manipulate inhomogeneous vector modes. Birefringent liquid crystal (LC) devices, which provide an approach for the modulation of vector field based on the optical Pancharatnam–Berry phase, have been explored to perform the spatial separation of CVB modes by leveraging geometrical transformation [18–20]. Although this method can effectively handle massive multiplexed CVB channels, the rigorous pre-condition involving sloped wavefront structure and phase engineering makes it difficult to achieve the inverse process, thus rendering it only available for simplex CVB demultiplexing. In addition, the narrow working bandwidth of LC restricts its compatibility with wavelength-dependent operations. Hence, the exploration of a feasible modulation technique for parallel coupling and separating CVB modes remains a challenge in implementing full-duplex CVB multiplexing communication.

Herein we propose a full-duplex CVB multiplexing communication paradigm by introducing spin-dependent phase modulation metasurfaces that can simultaneously couple and separate multiple CVB modes. Metasurface, which is composed of two-dimensional subwavelength meta-atom arrays, allows for point-by-point regulation of light’s amplitude, phase, and polarization [21–24]. This enables it to be ideal for manipulating CVBs with inhomogeneous vector wavefronts. To operate CVBs via spin-to-orbit interactions, we performed the conjugate helical phase modulations by employing a spin-dependent geometric phase metasurface and created a pair of polarization-multiplexed CVBs (radial and azimuthal CVB) [6,25]. While this method can handle two specific CVB modes, its ability to handle other modes is limited. We have previously demonstrated that binary Dammann vortex gratings (BDVGs), stemming from the superposition and optimization of fork grating phases, can effectively couple and separate multiple CVB modes [10]. This technique represents not only an effective approach for (de)multiplexing CVBs but also a potential route for full-duplex communication by synergistically utilizing its reciprocal process. However, this has not yet been reported.

Using the spin-dependent phase modulation concept, we fabricated a metal–dielectric–metal reflection-type metasurface to implement full-duplex CVB multiplexing and demultiplexing. By engineering the planar sizes and orientations of the meta-atoms, we constructed a spin-dependent phase modulation metasurface that can impose two independent BDVG phases for the two spin eigenstates of input lights. We demonstrated that Gaussian modes and multiplexed CVB modes can be parallelly interconverted in both directions via spin-dependent orbital interactions by the metasurface. The full-duplex CVB mode coupling and separating were performed via the reversibility of the light path. Consequently, we constructed a 16-channel (including 4 CVB modes and 4 wavelengths) full-duplex CVB multiplexing communication system with a 5 km FMF transmission. The 800 Gbit/s quadrature-phase shift-keying (QPSK) signals were bidirectionally transmitted, and 2 radial CVB modes and 2 azimuthal CVB modes were successfully multiplexed and demultiplexed with the bit-error-rates (BERs) approaching 1.87 × 10⁻⁵.

2. Principles and results

2.1. Off-axis control of radial and azimuthal CVBs via BDVG

Considering that the non-uniform linear polarization distributions of CVB are associated with its polarization order and initial polarization orientation, a Jones matrix that describes the space-variant polarization field of m-th order CVB can be expressed as follows [26]:

(1)$$ECVB = A \cdot \left[ \begin{array}{c} \cos (m\varphi + {\varphi_0})\\ \sin (m\varphi + {\varphi_0}) \end{array} \right] = \frac{A}{2}\exp [i(m\varphi + {\varphi _0})]|L \rangle + \frac{A}{2}\exp [ - i(m\varphi + {\varphi _0})]|R \rangle$$

where A is the simplified amplitude, m is the polarization order, φ is the azimuthal angle, and ${\varphi _0}$ represents the initial polarization orientation. In particular, the vector field E_CVB represents the radial CVB when ${\varphi _0}$= 0 and azimuthal CVB at ${\varphi _0}$= π/2 [27,28]. For convenience, the radial CVB and azimuthal CVB are abbreviated as rCVB and aCVB, respectively. The two spin eigenstates correspond to Jones vectors: | L 〉 = [1 −i]^t, | R 〉 = [1 i]^t, and t represents a matrix transpose operator. From Eq. (1), it can be noted that a CVB can be considered as the superposition of two orthogonal circularly polarized beams with conjugate spiral phases. This facilitates the handling of CVB by tailoring its two spin components with opposite spiral wavefronts.

Here, a spin-dependent BDVG device that is capable of realizing spin-dependent spiral wavefronts modulation is introduced. As depicted in Figs. 1(b1) and (b2), the transmission function of the BDVG corresponding to the left- and right-handed circularly polarized (LHCP/RHCP) components in the polar coordinates (r, φ) is as follows:

(2)$$\Psi_{\textrm{L/R}}(r,\varphi ) = \exp [i\Phi_{\textrm{L/R}}(r,\varphi )] = \sum\nolimits_{\kappa ={-} N/2}^{N/2} C \kappa \exp \left[ {i\kappa \left( {\frac{{2\pi r\cos \varphi }}{T} \pm l\varphi } \right)} \right]\left[ \begin{array}{c} 1\\ \mp i \end{array} \right]$$

where Φ(r, φ) is the phase function, N is the total number of diffraction orders, κ is the diffraction order from − N/2 to N/2, |C_κ|² = 1/N is the normalized power of κth diffraction order, T is the period of grating phase, and l is the interval of topological charges. According to Eq. (2), a circularly polarized Gaussian beam acting perpendicularly on the BDVG will diffract off-axis into N orders carrying a topological charge of κ×l at κth order, as depicted in Figs. 1(c1) and (c2) (here N = 2 and l = 1). For a linearly polarized Gaussian beam (containing both LHCP and RHCP components) illumination, the superposed transmission function can be deduced as follows:

(3)$$\Psi_{\textrm{LP}}(r,\varphi ) = \sum\nolimits_{\kappa ={-} N/2}^{N/2} C \kappa \exp \left( {i\kappa \frac{{2\pi r\cos \varphi }}{T}} \right)\left[ \begin{array}{c} \cos (\kappa l\varphi + \xi )\\ \sin (\kappa l\varphi + \xi ) \end{array} \right]$$

where ξ depends on the incident polarization orientation. Specifically, for an incident beam with a linear x-polarization state [1 0]^t, ξ = 0, rCVB _+ 1 and rCVB₋₁ (subscript indicates the polarization order of CVB) are generated off-axis [Fig. 1(d)]. For a linear y-polarization state [0 1]^t, ξ = π/2, aCVB _+ 1 and aCVB₋₁ are obtained off-axis. This explains that the spin-dependent BDVG device allows for the off-axis interconversion of Gaussian mode and CVB mode for multiple channels, and radial and azimuthal CVB modes can be independently shaped by adjusting the incident polarization.

Fig. 1. Schematic of the off-axis control of CVBs via BDVG. (a) Schematic diagram of the spin-dependent BDVG device. The phase patterns and spiral wavefront responses of LHCP (b1, c1) and RHCP (b2, c2) components, respectively. (d) The output light field of generated rCVB _+ 1 and rCVB₋₁, where the red short line is a schematic illustration of their polarizations.

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2.2. Spin-dependent phase modulation metasurface design and its optical properties

To achieve the BDVG-based off-axis control of CVBs, we introduced a spin-dependent phase modulation metasurface that has the ability to independently impose the phase function Φ_L/R(r, φ) for the two spin components of input lights. In this scenario, a Jones matrix J(r, φ) describing the metasurface should satisfy: J(r, φ)| L 〉 = exp[i·Φ_L(r, φ)]| R 〉 and J(r, φ)| R 〉 = exp[i·Φ_R(r, φ)]| L 〉. In other words, this implies that each spin component will be converted to the opposite handedness compared to its incidence and carry different phase profiles. The required Jones matrix can be derived as follows:

(4)$$J(r,\varphi ) = \left[ {\begin{array}{cc} {\exp [i\Phi_{\textrm{L}}(r,\varphi )]}&{\exp [i\Phi_{\textrm{R}}(r,\varphi )]}\\ { - i \cdot \exp [i\Phi_{\textrm{L}}(r,\varphi )]}&{i \cdot \exp [i\Phi_{\textrm{R}}(r,\varphi )]} \end{array}} \right]{\left[ {\begin{array}{cc} 1&1\\ i&{ - i} \end{array}} \right]^{ - 1}}$$

Considering that the above J(r, φ) can be transformed into a canonical form J(r, φ) = ΓΛΓ⁻¹ owing to the symmetric and unitary conditions (in which Γ is a rotation matrix and Λ is a diagonal matrix) [29,30], it can be further written as follows:

(5)$$J(r,\varphi ) = \left[ {\begin{array}{cc} {\cos \theta }&{ - \sin \theta }\\ {\sin \theta }&{\cos \theta } \end{array}} \right]\left[ {\begin{array}{cc} {\exp (i\phi_x)}&0\\ 0&{\exp (i\phi_y)} \end{array}} \right]{\left[ {\begin{array}{cc} {\cos \theta }&{ - \sin \theta }\\ {\sin \theta }&{\cos \theta } \end{array}} \right]^{ - 1}}$$

where θ is the orientation angle of the fast axis of the meta-atom, ϕ_x and ϕ_y are the phase shifts along the x- and y-direction symmetry axes of the meta-atom, respectively. Combining Eqs. (4) and (5), the phase shifts and orientation angle of the meta-atom at each unit (r, φ) can be calculated as follows:

(6)$$\phi_x(r,\varphi ) = [\Phi_{\textrm{L}}(r,\varphi ) + \Phi_{\textrm{R}}(r,\varphi )]/2$$

(7)$$\phi_y(r,\varphi ) = [\Phi_{\textrm{L}}(r,\varphi ) + \Phi_{\textrm{R}}(r,\varphi )]/2 - \pi$$

(8)$$\theta (r,\varphi ) = [\Phi_{\textrm{L}}(r,\varphi ) - \Phi_{\textrm{R}}(r,\varphi )]/4$$

Figure 2(a) presents the schematic of parallel coupling and separating of CVB modes based on a metal–dielectric–metal reflection-type metasurface. When linearly polarized Gaussian beams are incident on the metasurface from ±1th diffraction orders, two mutually orthogonal CVBs with different vector modes are created and coaxially coupled in the zeroth diffraction order, as indicated by the white arrows. With the reversibility of the light path, the oppositely transmitted CVBs will be spatially separated and back-converted into Gaussian beams in their corresponding diffraction directions, as indicated using the blue arrows. By synergistically utilizing the reciprocal process, the full-duplex CVB (de)multiplexing operation can be achieved. As illustrated in Fig. 2(b), each meta-unit is composed of a rectangular gold (Au) meta-atom with a uniform height of 50 nm, a 150 nm-thick silicon dioxide (SiO₂) spacer layer, and a 200 nm-thick Au reflective layer in turn. The silicon (Si) is set as the substrate at the bottom, and the lattice constant is set to 800 nm. To ensure a sufficient phase shift and a high modulation efficiency at a working wavelength of 1550 nm, the height of the Au meta-atom and the thickness of the SiO₂-Au bilayers were carefully optimized. Thereafter, by determining the three tunable dimensions of the Au meta-atom (including its length l, width w, and orientation angle θ), the specified BDVG phases can be independently imposed on LHCP and RHCP components of the incident beam.

Fig. 2. Design of the spin-dependent phase modulation metasurface. (a) Schematic illustration of parallel coupling and separating of CVBs using the BDVG-based metasurface. (b) Perspective view of the meta-unit whose lattice period is set to P_x = P_y = 800 nm. (c) Measured phase shifts (ϕ_x, ϕ_y) of the three selected Au meta-atoms {S1, S2, S3} against the desired designs at 1550 nm. (d) Simulated polarization conversion efficiencies of the three Au meta-atoms over the spectral range of 1400-1700nm.

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Remarkably, the BDVG phase Φ_L/R(r, φ) has only two values, 0 and π. By calculating Eqs. (6) and (7), it can be found that only three planar sizes of the Au meta-atoms corresponding to {S1, S2, S3} are required for the spin-dependent phase modulation metasurface design. The phase shifts (ϕ_x, ϕ_y) corresponding to these three meta-atom structures respectively satisfy: S1(0, -π), S2(π/2, -π/2), and S3(π, 0). To determine the geometrical parameters of the three desired Au meta-atoms, full-wave simulations were implemented with the finite difference time domain (FDTD) technique to numerically calculate the phase shifts (ϕ_x, ϕ_y) of the Au meta-atoms with different sizes, which is detailed in Supplement 1. The measured phase shifts (ϕ_x, ϕ_y) of the selected Au meta-atoms {S1, S2, S3} at the wavelength of 1550 nm are indicated in Fig. 2(c), and they meet the design requirements. Further, the polarization conversion efficiencies of the three meta-atoms were numerically simulated by the FDTD method across the infrared spectral range, as depicted in Fig. 2(d). Here, the polarization conversion efficiency is defined as the optical power ratio of the output RHCP component to the input LHCP planar wave. It shows that the polarization conversion efficiencies are higher than 90% within the wavelength range from 1400 nm to 1620 nm, ensuring a broadband response and efficient operation of the designed metasurface.

For experimental verification, the proposed metasurface underwent fabrication using standard electron beam lithography technology. The overall size of the fabricated metasurface measured 640 × 640 um², structured in an array format of 800 × 800. Following fabrication, a dedicated measurement setup was constructed to meticulously investigate the optical properties of the produced metasurface, and these details are comprehensively outlined in Supplement 1. A collimated fundamental mode Gaussian beam with a horizontal or vertical linear polarization state was focused by a lens and made incident from +1th diffraction order onto the metasurface, and then the off-axis generated CVB was split into two beams in mutually perpendicular directions using a beam splitter (BS). One beam was directly collected by a charge coupled device (CCD) camera after passing through a quarter wave plate (QWP) and a linear polarizer (LP) in turn, whereas the other beam was be transmitted through a 5 km FMF before being collected.

Figures 3(a1) and (a3) illustrate the intensities and polarization patterns of rCVB _+ 1 and aCVB _+ 1, which are generated by linearly x- and y-polarized incident beams, respectively. The polarization patterns of CVB are numerically calculated by Stokes polarimetry (see Supplement 1). Both suggest that the generated vector mode fields have good cylindrical symmetry and azimuthal-variant linearly polarized distributions. However, the rotational symmetries are slightly degraded after 5 km FMF transmission perturbation, as indicated in Figs. 3(b1) and (b3). In this direction, we measured the optical insertion losses of rCVB _+ 1 and aCVB _+ 1, including the collimators and transmission losses, to be less than 3.1 dB. Figures 3(a2) and (a4), (b2) and (b4) depict the measured intensity profiles of rCVB _+ 1 and aCVB _+ 1 using an LP with variable rotation angles before and after FMF transmission. From these figures, the two optical side lobes rotating with the transmission axis of the LP indicate that the polarization order of the CVBs is +1 (the number of side lobes is twice that of the polarization order, and the polarization order is positive (negative) when the side lobes rotate in the same (opposite) direction as the transmission axis of the LP). The horizontal and vertical distribution of side lobes with respect to the transmission axis of the LP indicates that the generated CVBs are rCVB and aCVB, respectively, which is consistent with design expectations.

Fig. 3. Optical characterization of the fabricated metasurface. Measured results of the intensities and polarization distributions of rCVB _+ 1 and aCVB _+ 1 before (a1, a3) and after (b1, b3) 5 km FMF transmission at a fixed wavelength of 1550 nm. The corresponding LP detection results of rCVB _+ 1 and aCVB _+ 1 before (a2, a4) and after (b2, b4) 5 km FMF transmission. The black double arrow indicates the transmission direction of LP. Measured multiplexing efficiencies (c) and demultiplexing efficiencies (d) at different working wavelengths. “x,+1” represents the linearly x-polarized Gaussian beam incident from +1th diffraction order.

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We also measured the multiplexing efficiency (η) of the metasurface using linearly x- and y-polarized Gaussian beams incident from +1th and −1th diffraction orders, respectively [Fig. 3(c)]. The multiplexing efficiency is defined as follows:

(9)$$\eta = \frac{1}{N} \times \frac{{Pout}}{{Pin}}$$

where P_out is the output optical power of the converted CVB at the zero-order multiplexing channel, P_in is the input optical power, and N = 2 indicates that there are only two diffraction orders theoretically. We also measured the demultiplexing efficiency (γ, via a similar method as that of η) by using rCVB _+ 1/−1 and aCVB _+ 1/−1 normally incident on the metasurface and collecting the optical power converted back into Gaussian beam, respectively [Fig. 3(d)]. It is evident that the multiplexing efficiencies reach 83% and the demultiplexing efficiencies reach 84% within a wide wavelength range from 1528 nm to 1606 nm, which reflects an efficient and broadband (de)multiplexing performance of the fabricated metasurface. More light field characterizations in the broad range of wavelengths are illustrated in Supplement 1.

2.3. Full-duplex CVB multiplexing communication

To further demonstrate the device’s potential application in full-duplex CVB multiplexing communication, two identical metasurfaces compatible as CVB multiplexer and demultiplexer were employed in a 5 km FMF bidirectional transmission system with simultaneous WDM, as illustrated in Fig. 4(a). At the transmitting end of the system, 50 Gbit/s QPSK signals, generated by the programme pulse generator (PPG), were loaded on four WDM channels (1548.52 nm, 1550.12 nm, 1551.72 nm, and 1553.33 nm) using an in-phase/quadrature (IQ) modulator. And thereafter, these signals were equally divided into four branches. Each brancher carrying 200 Gbit/s QPSK signals was used as a transmitter port (Tx) for the uplink and downlink after undergoing separate amplification by an erbium-doped fiber amplifier (EDFA) and relative delay by a single mode fiber (SMF) for signal decorrelation. Afterward, these signal beams were coupled from the fibers to free space by means of fiber collimators. For the uplink, two fundamental mode Gaussian beams (outputting from Tx1 and Tx2 and carrying different signals) with a linear x-polarization state modulated by an HWP and a polarization beam splitter (PBS) were incident on the metasurface from ±1 diffraction order, and were transformed into coaxially transmitted rCVB _± 1 thereafter. At the same time, the back co-propagated aCVB _± 1 were multiplexed for the downlink by the interplay of the contralateral metasurface and linearly y-polarized Gaussian beams (obtained by modulating the polarization state of the signal lights from Tx3 and Tx4). Mutually orthogonal rCVB _± 1 and aCVB _± 1 as full-duplex multiplexing mode sets were coupled into a 5 km FMF for coaxially bidirectional transmission, then parallelly demultiplexed into spatially separated fundamental mode Gaussian beams (possessing the same linear polarization states as their incidence) for corresponding receiver port (Rx) by the opposite metasurface. The measured optical insertion losses of the uplink and downlink were less than 4.2 dB and 3.9 dB, respectively. It is worth mentioning that the two bidirectionally transmitting Gaussian beams (one for pre-coupling and the other from post-decoupling) in each coaxial port link maintained linear polarization orthogonality due to the reversibility of the light path. This allows the Tx channel and Rx channel to be separated effectively by simply utilizing a PBS. Next, we used an additional iris to filter out stray beams with other topological charges, and then the recovered Gaussian beams were coupled into fibers. After demultiplexing the wavelengths, adjusting optical amplification and linear polarization, the Rx signal beam with the local beam was coherently demodulated through a coherent receiver. The digital signals were sampled by a sampling oscilloscope and processed offline by a computer for communication performance evaluation.

Fig. 4. Experimental prototype system of full-duplex CVB multiplexing communication with four WDM channels. Col: collimator; HWP: half wave plate; PBS: polarization beam splitter; Lens: lens of 200 mm focal length; MG: metasurface gripper; PC: polarization controller; IQ Mod.: IQ modulator; OC: optical coupler; EDFA: erbium-doped fiber amplifier; SMF: single mode fiber; LO: local oscillator; ICR: integrated coherent receiver; OSC: oscilloscope.

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For the proof of concept, we demonstrated a 16-channel (including rCVB _± 1, aCVB _± 1, and 4 wavelengths) full-duplex CVB multiplexing communication that carries 800 Gbit/s QPSK signals. Figure 5(a) presents several BER curves of the 16 channels versus received optical powers. “r + 1, 1548” represents the rCVB _+ 1 channel at the wavelength of 1548.52 nm, and the others are labeled in the same manner corresponding to the above-mentioned wavelengths. It shows that all BERs are below 1.87 × 10⁻⁵ when the received optical power reaches −16 dBm. Figure 5(b) depicts the measured constellations and error-vector magnitudes (EVMs) of rCVB _+ 1 and aCVB _+ 1 channels at the received optical power of −19 dBm. The constellations are similar and convergent, and all EVMs are below 25.6%. These results suggest that the metasurfaces are effective and reliable for constructing full-duplex CVB multiplexing communication.

Fig. 5. Experimental results for full-duplex CVB multiplexing communication. (a) Measured several BERs of CVB channels at four wavelengths. “FEC threshold” denotes the hard-decision forward error correction threshold of 3.8 × 10⁻³. (b) Constellations and EVMs of rCVB _+ 1 and aCVB _+ 1 at four different wavelengths, respectively.

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3. Discussion

The next-generation optical communication systems will commit to high link utilization and large transmission capacity [31,32]. Full-duplex CVB multiplexing communication, where signal-carrying CVBs are coaxially multiplexed on a shared full-duplex link for bidirectional simultaneous transmission, presents a promising solution owing to the orthogonality of CVB mode. In this study, we introduced a spin-dependent phase modulation metasurface and experimentally confirmed its good performance in full-duplex CVB-wavelength hybrid multiplexing communication. Compared to previous full-duplex schemes based on cascading BS and PBS [12,14], the BDVG-based metasurface provides a compact platform for parallel coupling and separating of massive CVB channels. This significantly reduces the system redundancy and offers a high possibility for the integration and miniaturization of full-duplex communication systems. Moreover, the uniform energy diffractions of the BDVG facilitate the multiplexing and demultiplexing efficiency of CVB modes, enabling a good channel equalization in full-duplex communication. In addition to enhancing the signal modulation rate, the communication capacity can also be expanded by flexibly designing the BDVG to increase full-duplex CVB channels, such as increasing the N value in Eq. (2) or utilizing a two-dimensional grating structure [33,34]. Alternatively, the wide working wavelength capacity of the metasurface (ranging from 1528 nm to 1606 nm) allows for incorporating more wavelength channels, further elevating the system’s potential to achieve a Tbit/s data speed. However, the inherent ohmic loss of metal-type metasurfaces will impede the further increase in the number of CVB channels. The dielectric metasurfaces with low absorption loss and high transmittance [35,36] are expected to resolve this problem and profit the further improvement of (de)multiplexing efficiency.

Inter-mode crosstalk is an important indicator for evaluating the performance of CVB multiplexed in full-duplex communication. The homo-modal CVB multiplexing may increase the inter-mode crosstalk and deteriorate the communication performance due to the Rayleigh back scattering and Fresnel reflection in optical fibers during bidirectional transmission with the same modes [37,38]. To overcome this, we used the rCVB and aCVB generated by linearly x- and y-polarized Gaussian beams acting on the proposed metasurface as a set of orthogonal hetero-modal values for the uplink and downlink in bidirectional transmission. This approach breaks the symmetry of the bidirectionally transmitted CVB modes and ensures the performance of full-duplex communication. The rCVB and aCVB with same polarization order can be considered as distinct mode states for their polarization orthogonality [39,40], which ensures that the multiplexed CVB modes within and between bidirectional links are mutually orthogonal and facilitates low inter-mode crosstalk during bidirectional transmission. In the full-duplex communication system that we have implemented, the inter-mode crosstalk is lower than −13.0 dB in simple uplink/downlink and lower than -39.2 dB between bidirectional links at the wavelength of 1550.12 nm, which is detailed in Supplement 1. Furthermore, the hetero-modal CVB set can be flexibly reconfigured by specifying the multiplexed CVB mode states between bidirectional links. For example, the nonreciprocal metasurfaces [41,42] might enable the asymmetric CVB multiplexing and demultiplexing process in bidirectional transmission, of which multiplexed CVBs are odd polarization orders for uplink and even polarization orders for downlink.

4. Conclusion

In summary, we have proposed and implemented a spin-dependent phase modulation metasurface to simultaneously multiplex and demultiplex multiple CVB modes, and demonstrated the application of this metasurface in full-duplex communication combined with WDM. By multiplexing signals with 16 channels (4 CVB modes and 4 wavelengths), we achieved the bidirectional transmission of 800 Gbit/s capacity over a 5 km FMF, and the BERs approached 1.87 × 10⁻⁵. Our results illustrate that the proposed metasurface enables an effective way for parallel coupling and separating of CVB modes and has a promising prospect in full-duplex CVB multiplexing communication.

Funding

National Natural Science Foundation of China (62271322, 62275162); Guangdong Basic and Applied Basic Research Foundation (2021A1515011762, 2022A1515011003, 2023A1515030152); Shenzhen Science and Technology Program (JCYJ20200109144001800, JCYJ20210324095610027, JCYJ20210324095611030, SZWD2021013); Natural Science Foundation of Top Talent of SZTU (GDRC202204).

Acknowledgments

The authors also acknowledge the technical assistance from Photonics Research Centre of Shenzhen University.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Full-duplex cylindrical vector beam multiplexing communication using spin-dependent phase modulation metasurfaces

Abstract

1. Introduction

2. Principles and results

2.1. Off-axis control of radial and azimuthal CVBs via BDVG

2.2. Spin-dependent phase modulation metasurface design and its optical properties

2.3. Full-duplex CVB multiplexing communication

3. Discussion

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (5)

Equations (9)

Optics Express