As the basis of emerging technologies such as quantum computing, communication, and key distribution, optical quantum information processing relies on single photons as an essential carrier for information encoding and transmission. Because of its outstanding anti-disruption performance, a single photon can maintain coherence and low loss during long-distance propagation. Therefore, a single-photon source with superior properties has become a study focus of attention. Among the various types of single-photon sources, solid-state quantum emitters are particularly significant. Commonly used quantum emitters include dye molecules [1], quantum dots (QDs) [2], two-dimensional material defect states [3,4], and color center structures in crystals [5]. Among these, semiconductor QDs have excellent photonic properties, including brightness, purity, and indistinguishability, positioning them as one of the most promising candidates for single-photon sources. However, due to the mismatch between their material refractive index and the external environment, the brightness and radiation efficiency of QDs are generally low, posing a challenge for optical communication and quantum information processing applications. To address this, researchers have integrated micro- and nanostructures, e.g., mesa [6], matalenses [7,8], nanowires [9], photonic crystals [10], micropillars [11,12], and circular Bragg resonators [13,14], to enhance the forward radiation performance of QDs.

Building on this, the advancement of quantum communication toward higher capability and higher dimension makes the modal modulation of semiconductor QD single-photon sources an important role in design and manufacture. For example, numerous researchers are focusing on light beams with orbital angular momentum (OAM), featuring a doughnut-shaped intensity distribution and a helical phase distribution. The phase term can be expressed as exp(ilφ), where φ is the azimuth angle, and l represents the OAM of lℏ carried by a photon, also known as the topological charge. Differing from the two-dimensional spin angular momentum (SAM), the infinite-dimensional nature of OAM mode has drawn growing attention in high-dimensional quantum information processing [15–17]. Various methods have been developed to generate OAM beams, including outer-cavity and intra-cavity modulation [18,19]. But these methods often face challenges in integration or efficiency. Achieving arbitrary and efficient generation of different OAM beams, along with their emission in specific spatially separated directions, is crucial for increasing the dimensionality of information processing.

All dielectric metasurfaces offer flexible and effective manipulation of the amplitude, phase, SAM, OAM, and propagation characteristics of light at the nanoscale [17,20], taking the advantages of planarization and low loss. These properties make metasurfaces promising materials for integration in various applications, such as deflectors [21], holograms [22,23], and vortex beam generation [24,25]. In recent years, the integration of quantum light sources with metasurfaces has gained widespread interest [26,27], with researchers using multifunctional metasurfaces to tailor emissions from solid-state quantum emitters [28,29]. Significant research has also focused on modulating output modes from single-photon sources, achieving OAM mode decomposition and generating OAM beams with controllable intensity, direction, and polarization [30–36]. While the metasurface structures designed in these studies demonstrate promising results, semiconductor QDs still face challenges related to fabrication and integration, making it difficult to achieve high-efficiency and high-dimensional single-photon sources with metasurfaces [37,38].

In this work, we theoretically propose a metasurfaces designing scheme based on a composite phase approach, combining both propagation and geometric phases. This scheme enables the construction of multi-channel photon emission with different propagation directions and allows for the flexible modulating spin-decoupling beams with distinct OAM modes. To verify its versatility, we integrate self-assembled semiconductor QDs in InAs/GaAs film with the designed metasurfaces, simplifying the fabricating process and improving collecting efficiency. First, we design a single-photon source that emits the desired collimated OAM beam. Next, we design another device to generate dual-channel OAM beams, which decouple LCP and RCP beams at different zenith angles (30° and 10°) and different directional angles (180° and 0°), carrying different topological charges (l=2 and l=1) while achieving good collimation. Additionally, we analyze the relationship of polarization between the output beams and QD emission to confirm the consistency of the performance of the device with the theoretical design. Furthermore, we demonstrate the generation of eight-channel OAM beams, decoupled into LCP and RCP states at different zenith angles (10° and 30°) and directional angles (270°, 180°, 90°, and 0°), carrying different topological charges (l=0, l=1, l=2, and l=3). Compared to our previous work [37,38], this demonstration offers a more flexible design with a wider variety of light field modulation effects. It also allows for easier fabrication due to the one-time positioning process. Additionally, it achieves higher collection efficiency by optimizing the materials and structures. Our approach holds significant potential for advanced optical applications and the progression of quantum information processing.

The generation of two-channel OAM beams using a combination of semiconductor QD and metasurfaces is shown in Fig. 1(a). We have devised a flat plate structure comprising GaAs QDs film, silicon dioxide, and a gold film integrated with a metasurfaces device for controlling the single-photon state of QD emissions. This design offers two key advantages. First, it simplifies the fabricating process by eliminating the need for QD positioning, followed by etching directly on the GaAs film to create nanostructures around the QD. This approach also reduces any adverse effects on device performance caused by these processes. Second, it utilizes gold and silica layers to enhance upward radiation of QDs, enabling significant energy manipulation by the metasurfaces and directing the output upwards. The detailed relationships between extraction efficiency and silica thickness tSiO2, GaAs film thickness tGaAs, and distance from QD to the lower surface of the GaAs film dQD-GaAs are described in Appendix A. We ultimately choose a self-assembled semiconductor QDs film with a thickness of 160 nm, where the QDs were embedded 30 nm from the lower surface of the GaAs film. Below this, a 40-nm-thick silica layer and a 100-nm-thick gold reflector are applied sequentially. This optimization process is aimed at enhancing the upward radiation of QD to achieve the higher collection efficiencies of our designed devices. In order to generate a higher-purity OAM beam, we use silicon with a high refractive index as the meta-atoms to arrange a metalens structure with diameter of 50 μm and focal length of 10 μm, embedded in silica. This metalens structure, separated from the semiconductor QDs film by a 10-μm-thick silica layer, effectively captures both the directly emitted single photons and those reflected from the gold layer. It collects single-photon emissions within an angular range corresponding to a numerical aperture (NA) of 1.35 according to the formula NA=nsinθ, where n=1.45 is the refractive index of silica, and θ is the half-angle of the cone of light entering the metalens. The composite phase-based metasurfaces we used can independently tailor the phase profiles for any pair of orthogonal polarizations by combining geometric and propagation phases. This enables independent and arbitrary modulation of the phase for the two spin states, effectively overcoming the phase conjugation limitation in using geometric phase alone. In this way, they facilitate the implementation of versatile multiplexing metasurfaces, enabling functionalities in our design such as spin-decoupling OAM states modulation and spatial radiation control [39,40]. In theory, the unit structure of metasurfaces combined with composite phases should satisfy the following formula (details can be found in Refs. [39,40]): {ψL(x,y)=φu+2θr,ψR(x,y)=φu−2θr|φu−φv|=π,,(1)where θr is the rotation angle of the meta-atoms, φu and φv are propagation phase for u and v polarizations, respectively, and ψL(x,y) and ψR(x,y) are the corresponding target phases of LCP and RCP beams, respectively. Based on Eq. (1), the theoretical propagation phase (φu, φv) and geometric angle θr required for selecting the meta-atoms can be obtained from the designed ψL(x,y) and ψR(x,y). By linearly combining these two phases, independent control of both LCP and RCP beams is achieved.

In order to achieve complete 2π modulation, we designed six nanopillars (numbered 1–6) with an equivalent phase step of π/3. Specifically, each meta-atom is engineered to be subjected to |φu−φv|=π, and it exhibits slightly different amplitudes (tu≠tv) between two orthogonal polarizations, where tu and tv represent the transmittance values of the meta-atoms under u and v directional excitation, as shown in Fig. 1(b). The results of transmittance (tll, trl) corresponding to the co-polarized and cross-polarized components of the six meta-atoms, along with the polarization conversion efficiency [defined as PCE=trl/(trl+tll)] under LCP incidence, are shown in Fig. 1(c). These results indicate that trl is all above 0.9, tll is almost zero, and the polarization conversion efficiency is close to one. This indicates that the optical loss of the nanopillar is less than 0.1, and the polarization states of the incident and transmitted light are almost opposite. As shown in Fig. 1(c), the transmittances of the six element structures are 91.7%, 92.2%, 90.1%, 91.7%, 92.2%, and 90.1%, respectively, while the reflectivities of the six element structures are calculated to be 7.5%, 6.6%, 8.5%, 7.5%, 6.6%, and 8.5%, respectively, which occupy a majority of the loss.

To demonstrate the functionality of the device, we design three devices (Devices 1, 2, and 3) using a 3D finite-difference time-domain (3D FDTD) simulation (Ansys Lumerical). In the corresponding simulations, we model the quantum dot emission as a dipole light source with linear polarization in different directions, as specified for the particular devices. In the simulations, the wavelength of the QD emission is 910 nm, consistent with our previous experimental work [37]. We start with a hyperbolic phase profile (ψCollimator) of the metalens, with a designed focal length (f) and operating wavelength (λ), given by ψCollimator=2πnλ(f−x2+y2+f2).(2)

Here, x, y are the coordinates. The depth of focus (DOF) of the metalens can be calculated to be 998 nm according to the formula DOF=λ/(n−n2−NA2) [38,41]. As described in Appendix A, to enhance the extraction efficiency, the distance between the semiconductor QDs and the gold film is set to 70 nm, corresponding to tSiO2=40nm and dQD-GaAs=30nm in Fig. 5 (Appendix A). This distance is smaller than the DOF, while also ensuring that the emitted light is not absorbed by the gold layer. As shown in Fig. 5(b), when the silica thickness is less than 40 nm, the extraction efficiency drops sharply due to the metal affecting the local densities of states of the QD or introducing additional loss. As a result, the metalens can efficiently collect and simultaneously modulate both the direct radiation from the single photons and reflection from the gold layer, offering a simpler design compared to the bifocal metalens in Ref. [37].

Next, to deflect the collimated light emitted by the QD to the desired direction, a phase gradient is added to the hyperbolic phase, followed by addition of OAM mode modulated phases to the desired spin-state channels. The corresponding phase profile of metasurfaces is expressed as ψLCP/RCP=ψCollimator+∑k=1Nexp(i(ψdeflectk+ψOAMk)),(3)where deflection phase can be defined as ψdeflectk=2πxλsinθkcosϕk+2πyλsinθkcosϕk.(4)

Here, θ and ϕ represent the zenith angle and azimuth angle, respectively. ψOAMk=lkψ represents the phase of standard OAM mode with topological charge l, and ψ=arctan(y/x), and k denotes the number of OAM modes corresponding to different spin-state channels.

To verify the spin-decoupling function of the composite structure, we design a dual-channel metasurface in Device 2 to modulate and generate two OAM beams, each directed differently and corresponding to LCP and RCP beams. The two OAM beams are designed to radiate at different zenith angles of 30° and 10° and different azimuth angles of 180° and 0°, carrying topological charges of 2 and 1, respectively. First, we set the QD emission in this device to be polarized along the x direction. The far-field pattern, shown in Fig. 3(a), reveals two doughnut-shaped spots of different sizes located in distinct directions. It represents the spatially separated beams carrying different topological charges. As depicted in Fig. 3(f) for the case of 0° linear polarization state (H) of QD emission, the total collection efficiency is 33%, which maintains a high level. Figures 3(b) and 3(c) display the far-field electric field intensity distributions of the extracted LCP and RCP components separately. The doughnut patterns appear slightly oval, due to oblique emission or superposition of different modes. The calculated degrees of polarization, defined as the ratio of the target polarized intensity to the total intensity of one beam in the integral radius equal to the FWHM, are 99.2% and 99.7% for LCP and RCP beams, respectively. This indicates that the designed metasurfaces effectively decouple the single-photon emissions into different spin-state channels. The clear helical wavefronts in the phase distributions represent the dominant topological charges carried by two beams, as shown in Figs. 3(d) and 3(e). We calculated the far-field mode purities corresponding to target LCP and RCP components separately. As depicted in Fig. 3(h) for the case of 0° linear polarization state (H) of QD emission, the mode purities of the target beams exceed 67%, demonstrating that the single photons from the QD are effectively modulated by the designed metasurfaces. This modulation results in the conversion of photons into the desired modes with specific topological charges while spatially splitting into two spin-decoupling beams. Furthermore, this phenomenon shows that our design not only breaks the left-right spin conjugation, but also overcomes the limitation of a topological charge difference of 2 between LCP and RCP beams in previous work [31,32,36]. This is because the composite phase-based metasurfaces we employed can independently modulate the phase for any pair of orthogonal polarizations by combining geometric and propagation phases [39,40]. This further proves that our design successfully achieves spin-orbit angular momentum conversion, allowing quantum information to be precisely and arbitrarily loaded onto the left or right spin beams. As depicted for the case of 0° linear polarization state (H) of QD emission in Fig. 3(g), the calculated divergence angles reach a maximum of approximately 5.0° and 3.7° for the LCP and RCP beams, respectively.

Moreover, we analyze the effects of different polarization states of QD emission of Device 2 in Figs. 3(f)–3(h), with details provided in Appendix B. When the QD emits linearly polarized light, the far-field spot remains unchanged after passing through the metasurfaces, producing LCP or RCP vortex beams. Collection efficiency, divergence angle, and mode purity stay consistent across different incident states. When the QD emits LCP or RCP light, the output beam achieves a high degree of polarization for the corresponding RCP or LCP beam. In this case, when QD emission is in the LCP state for example, the output LCP component is too weak to be effectively modulated by the designed metasurfaces, resulting in a low mode purity and off-target divergence angle due to the presence of an undesired mode.

In order to pursue higher-dimensional information processing and expand information channel capacity, we design and demonstrate another Device 3 as a multi-channel spin-decoupling modal modulating application, utilizing spatial and phase multiplexing principles. The design generates eight-channel OAM beams, comprising four LCP vortex beams and four RCP vortex beams. To achieve this, the zenith angles are designed to locate at 30° and 10° for LCP and RCP vortex beams. The azimuth angles are set to be 270°, 180°, 90°, and 0°, corresponding to the topological charges of 0, 1, 2, and 3 for LCP beams, and 3, 2, 1, and 0 for RCP beams at the same azimuth angles. The initial QD emission is set to be polarized along the x direction. The far-field plot in Fig. 4(a) reveals that the single photons can be simultaneously split into eight vortex beams with well-defined OAM modes and collection efficiency of 30%. The simulated far-field patterns of the extracted LCP and RCP components, as shown in Figs. 4(b) and 4(c), display the electric field intensity distributions of the four LCP and four RCP beams, each carrying distinct topological charges. This highlights the excellent spin-decoupling and modal modulating performance of our design. The maximum divergence angles of the output beams, shown in Fig. 4(f), confirm the good collection and collimation quality of the OAM beams. The calculated degrees of polarization are over 94.4% for the LCP beams and 97.6% for the RCP beams, demonstrating the impressive spin-decoupling function. To further verify the topological charge carried by the generated OAM beams, we show the far-field phase plots in Figs. 4(d) and 4(e) and calculate their mode purities, which exceed 48%, as shown in Fig. 4(g). It is worth highlighting that this design can be extended to higher-order of OAM modes.

As a high-performance single-photon source, semiconductor QDs are challenging to modulate efficiently. However, metasurfaces integrated with semiconductor QDs have emerged as an effective approach for controlling the radiation properties of these sources. In this work, we have ingeniously designed metasurfaces integrated with semiconductor QDs to effectively modulate single-photon emission. We successfully decouple the left and right spins of the single-photon source, breaking the conventional conjugation relationship and generating OAM beams with distinct topological charges that deviate from the conventional difference mass of two. Additionally, we design dual-channel and multi-channel devices to demonstrate effective spin-decoupling and OAM beam modulation, emitting in specific spatially separated directions from a single-photon source. The structure can be fabricated using the method described in Ref. [37]. First, a silicon dioxide and a gold film are grown sequentially on a GaAs/AlGaAs/GaAs film containing QDs. The composite structure is then transferred onto a silica substrate, with the AlGaAs film and GaAs substrate selectively etched away. Next, a 10-μm-thick silica and a 550-nm-thick silicon are deposited onto the sample. Finally, the silicon film is patterned into the desired metasurface structure using electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. This process requires only one positioning step for the QDs, simplifying it compared to previous methods [37]. Additionally, our device exhibits higher collection efficiency than Ref. [37]. In addition, we also discussed fabrication tolerances analysis of QD positions and thicknesses of structure layers in Appendix C. Similarly, we also discussed effects of QD emissions from Device 1 with different focal lengths of a metelens in Appendix D and different working wavelengths of semiconductor QDs in Appendix E. According to the design principles of our devices, more complex light field outputs, such as the generation of Laguerre-Gaussian beams [45] and cylindrical vector beams [46] by metasurfaces, can be realized in future research, offering broader application prospects.

In summary, we have achieved simultaneous control over the direction, polarization, and OAM modes of the single-photon emission from semiconductor QDs with higher efficiency and simpler fabrication than previous methods. These results enable diverse and flexible light field manipulation of high-performance single-photons emission, better meeting the needs of quantum information processing. Our work also presents a convenient, integrated quantum approach for on-demand manipulation of various photon degrees of freedom with high quality. It opens up promising avenues for high-capacity optical communication, high-dimensional quantum correlation, and high-precision interferometers. Furthermore, in-depth research on the combination of metasurfaces and quantum optical systems will drive new developments and breakthroughs in application areas such as quantum sensing [47], quantum holographic encryption [48], and quantum biological imaging [49].

Acknowledgment. J.L. is supported by the Guangdong Provincial Quantum Science Strategic Initiative.