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Abstract
Free-space orbital angular momentum (OAM) communication is considered as one of the potential alternative on-chip optical interconnect solutions. The number of OAM modes determines the capacity of high-speed communication. However, existing integrated vortex beam emitters have a constraint relationship between the number of OAM modes and the emitter size, rendering it difficult to emit more OAM modes with a small-sized emitter. In view of the above, this study proposes an on-chip ultracompact multimode vortex beam emitter based on vertical modes, which permits more OAM modes without requiring an increase in the size of the emitter. Vertical modes in large-aspect-ratio waveguides are pointed out to enable multimode microrings with small radii because high-order vertical modes can maintain almost the same horizontal wave vector as that of the fundamental mode. Four-mode and five-mode vortex beam emitters with the same radius of 1.5 µm are designed and the effectiveness of these emitters is verified through simulation. Furthermore, a high-efficiency and low-crosstalk approach for high-order vertical mode coupling by varying the waveguide height is presented. This research not only promotes further integration of on-chip optical interconnection, but also provides a new strategy for optical waveguide mode selection in photonic integrated circuits design.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photonic integrated circuits (PICs) are important roles in various fields [1–5] such as biological sensors, metrology, and quantum information processing, which has attracted widespread research interest. The on-chip optical interconnection is one of the limitations that prevents the improvement for the further integration of PICs [6,7]. Compared with traditional on-chip optical interconnection employing two-dimensional solutions such as optical fibers or optical waveguides for data transmission [8], free-space orbital angular momentum (OAM) communication, as one of the potential alternative three-dimensional on-chip optical interconnect solutions, is considered a better choice to realize further integration [6,9,10].
Vortex beams, also known as OAM modes, comprise an azimuthal phase term $e^{il\theta }$ [11], where $\theta$ is the azimuthal angle and l is the topological charge, and permit free-space optical communication [12–17]. For stable eigen-OAM modes, the topological charge l of vortex beam is generally unbounded integer and vortex beams with different topological charges are orthogonal to each other, enabling mode division multiplexing (MDM) and providing a new method for high-capacity optical communication. Thus, free-space OAM communication is promising for on-chip applications. Several studies have demonstrated the superiority of on-chip OAM communication, which owns higher transmission bandwidth and lower power consumption with a smaller size [6,18–22]. Traditional vortex beam generation relies on large optical devices such as spiral phase plates (SPPs) [23] and spatial light modulators (SLMs) [24], which isn’t applicable to on-chip. Hence, integrated vortex beam emitters are the key for realizing on-chip OAM communication. The predominant integrated vortex beam emitters with superior performance [20–22,25–50] are mainly devices based on waveguides, plasmonic nanoslits, microrings, and metagratings [25]. Devices based on waveguides [50] can efficiently excite OAM modes inside the waveguide, but are not applicable for free-space OAM communication. Devices based on plasmonic nanoslits and metagratings [22,41,42,44] can generate vortex beam in free space and have superior performance in integration, but it is challenging to increase the number of OAM modes through the current design. Devices based on microrings [20,21,30–35,49] not only have the advantage of compact size, enabling on-chip applications, but also are promising to generate more OAM modes, which has great potential for OAM communication. In 2012, Zhang proposed an on-chip single-mode OAM communication scheme using a microring emitter with a radius of 16 µm, which effectively improved the transmission bandwidth [20]. Meanwhile, a silicon integrated vortex beam emitter that achieved two-mode OAM emission using a microring emitter with a radius of 3.9 µm was studied to reduce the emitter size [30]. In order to realize more OAM emission modes, a multimode OAM communication scheme was proposed in 2018, which achieved four-mode or six-mode OAM emission using a microring emitter with a radius of 9.95 or 19.144 µm [21]. However, either the fundamental mode or a high-order horizontal waveguide mode used in the above researches, introduced a positive correlation constraint between the number of OAM modes and emitter size due to the high bending loss in sharp bend. To fully exploit the potential of on-chip OAM communication, it is crucial to achieve coaxial multimode OAM emission under ultracompact conditions.
In this study, we propose an on-chip ultracompact multimode vortex beam emitter based on vertical modes, as shown in Fig. 1. Large-aspect-ratio waveguides supporting vertical modes are used in the entire structure. As the vertical mode enables small-radii multimode microrings, vortex beam emitters that can realize the emission of four and five OAM modes with the same microring radius of 1.5 µm are designed. Comparison of the vertical and horizontal modes shows that the horizontal wave vectors of the high-order vertical modes remain almost constant, guaranteeing the propagation of the waveguide modes in super-sharp bends. Furthermore, for high-order vertical mode coupling, we propose a phase matching approach by varying the waveguide height to achieve high-coupling efficiency and purity. It is worth noting that our design has the advantage of multimode emission at an ultracompact size and the potential to introduce more OAM modes without increasing the emitter size, overcoming the constraint relationship between the number of OAM modes and the emitter size. This proposed emitter is expected to be utilized for on-chip OAM communication, enhancing the integration and transmission bandwidth.
Fig. 1. Conceptual illustration of the on-chip ultracompact multimode vortex beam emitter based on vertical modes. Using a large-aspect-ratio waveguide that supports vertical modes, multimode emission can be achieved in an ultracompact (R=1.5 µm) microring-based vortex beam emitter. The four-mode OAM emission case is depicted here. The $TM_{0}$ and $TM_{1}$ modes are input in the forward and reverse directions, and vortex beams with topological charges of +1, -2, -1, and +2 are generated. Significantly, the proposed design does not require an increase in the emitter size for introducing more waveguide modes to enable more OAM emission modes.
Next, we will discuss the vertical modes and the multimode vortex beam emitters that we designed. The modes supported by different sizes of waveguide cross-sections are analyzed, and the bending loss between the vertical and horizontal modes is compared, which shows the advantages of the vertical modes. Furthermore, a high-order vertical mode coupling approach is presented (see Section 2.1). The ultracompact four-mode and five-mode vortex beam emitters are designed, and simulation results show the effectiveness of the design (see Section 2.2).
2. Results and discussion
2.1 Vertical-mode analysis and high-order-mode coupling approach
Multimode waveguides, which can limit propagation of light through total reflection, support a group of orthogonal waveguide modes and enable MDM. Generally, the effective index of the different waveguide modes is considered. However, the mode profile can provide additional characteristics, which has potential research value. Figure 2(a) shows an Si waveguide built on an $SiO_2$ substrate, where the aspect ratio (height/width) determines the mode profile of the optical waveguide. Based on Maxwell’s equations, the mode profile in the waveguide can be expressed as follows [51]:
where $U(x,y)$ is the main component of the waveguide mode, $u$ is the amplitude coefficient, $k_{x}$ and $k_{y}$ are the horizontal and vertical wave vectors, respectively, and $\varphi _{x}$ and $\varphi _{y}$ are the phase factors. For an operating wavelength of approximately 1.55 µm, when the aspect ratio is small, high-order horizontal modes tend to exist, as shown in Fig. 2(b). In contrast, when the aspect ratio is large, high-order vertical modes tend to exist. When the width of the waveguide is less than or equal to 0.2 µm, only the vertical TM modes exist in the multimode waveguide [52], facilitating the control of the polarization state and avoiding the influence from the TE modes, as shown in Fig. 2(c). Compared to the horizontal modes, the vertical modes have lower bending loss [53]. We calculated the respective bending loss in the horizontal and vertical modes in two multimode waveguide cross-sections using Lumerical Mode Solutions. The results depicted in Fig. 2(d) indicate that for the same-order modes, the bending loss in the horizontal modes (dashed line) is several orders of magnitude higher than that in the vertical modes (solid line). As a result, vertical modes can propagate in super-sharp bends and therefore, enable multimode microrings with small radii. This is because in a small-radius microring, the super-sharp bend renders the total reflection condition on the sidewalls stringent. However, a high-order horizontal mode introduces more peaks in the horizontal direction resulting in a larger horizontal wave vector ($k_{x}$) compared to the fundamental mode, implying a smaller incidence angle on the sidewalls. Thus, the light of the high-order horizontal modes in a super-sharp bend cannot satisfy the total reflection condition and the waveguide mode decays rapidly, as shown in Fig. 2(e). For high-order vertical modes, there is only one peak in the horizontal direction, indicating that the variation in $k_{x}$ is very less. Therefore, the total reflection condition can always be satisfied in a small-radius microring, and the decay of the vertical modes is less, as shown in Fig. 2(f).Fig. 2. Analysis of the horizontal and vertical modes. (a) Cross-section of an Si waveguide built on an $SiO_2$ substrate. (b) TE modes in a waveguide with a small aspect ratio (height = 0.2 µm, width = 1.2 µm). (c) TM modes in a waveguide with a large aspect ratio (height = 1.2 µm, width = 0.2 µm). (d) Simulated bending loss in the horizontal and vertical modes. (e) Comparison between the fundamental and high-order horizontal modes propagating in a small-radius microring. (f) Comparison between the fundamental and high-order vertical modes propagating in a small-radius microring.
Although the vertical modes have better bending propagation capability and have the potential to enable small-radii multimode microrings, most of the existing work on multimode waveguides use horizontal modes because of the simpler mode coupling approach and easier fabrication of the structure. Here, for the case where the waveguide width is less than or equal to 0.2 µm (only the TM modes are allowed), we propose a high-order vertical mode coupling approach, which can excite a particular mode by varying the waveguide height for phase matching. Figure 3(a) depicts the coupling structure for the $TM_{1}$ mode. The height of the input part is 0.399 µm in the coupling structure, which is a single-mode waveguide supporting the $TM_{0}$ mode alone. The height of the output part is 0.820 µm, which supports the $TM_{0}$ and $TM_{1}$ modes, and can couple with the fundamental mode ($TM_{0}$) in the input and efficiently excite the pure $TM_{1}$ mode. The design of the coupling structure can be divided into two steps: (1) determination of the height of the two parts of the structure through effective index matching, and (2) optimization of the waveguide gap (distance between the two waveguides) and coupling length (length of the straight input waveguide parallel to the output waveguide) to achieve high-efficiency and low-crosstalk mode coupling. For the first step, effective index matching is generally applied for the excitation of particular high-order waveguide modes [54]. Excitation of the high-order horizontal modes can be achieved by varying the width of waveguide. However, for high-order vertical modes, effective index matching by varying the width cannot realize the expected excitation. So, we propose effective index matching by varying the height, as shown in Fig. 3(b). For the second step, we use Lumerical FDTD Solutions to perform a parameter sweep of the waveguide gap and coupling length, and calculate the coupling efficiency of $TM_{0}$ and $TM_{1}$. The results are shown in Figs. 3(c) and (d), respectively. At the marked points in the figure (gap = 0.19 µm, coupling length = 4 µm), the $TM_{1}$ mode coupling efficiency is more than 90$\%$ and the crosstalk (from the $TM_{0}$ mode) is only -23 dB, achieving ideal $TM_{1}$ mode excitation. In addition, we perform wideband simulation of the coupling structure from 1.51 µm to 1.57 µm, and find that the structure has high-coupling efficiency and low-crosstalk in the wideband, as shown in Fig. 3(e). The above results demonstrate the effectiveness of our proposed coupling structure. Besides, the method of varying the height for effective index matching is effective for other higher-order vertical TM mode coupling as well.
Fig. 3. High-order vertical mode coupling approach by varying the height for phase matching. (a) Conceptual illustration of the $TM_{1}$ mode coupling structure. The fundamental mode is excited at the input port, and through the coupling structure, the expected high-order vertical TM mode can be obtained at the output port. Inset is the electric field profile of the input mode, output mode, and coupling region. (b) Effective index of the $TM_{0}$ and $TM_{1}$ mode. The fundamental mode ($TM_{0}$) in the input part has the same effective index as the $TM_{1}$ mode in the output part, satisfying the phase matching condition. (c)- (d) Simulated $TM_{0}$ and $TM_{1}$ coupling efficiency at the output when the wavelength is 1.53669 µm. (e) Simulated wideband coupling efficiency and crosstalk of the mode coupling.
2.2 Design and simulation of ultracompact multimode vortex beam emitters
Vortex beam emitters based on microrings, proposed in a previous work [30], have been proven effective for realizing on-chip vortex beam emission. The angular grating embedded within the microring can scatter the waveguide modes into free space, coupling the whispering gallery modes (WGMs) in the microring into the free-space OAM modes. The topological charge l satisfies the following equation [30]:
where $p$ is the number of optical periods of the WGM involved and $q$ is the number of grating elements around the microring. According to our above analysis, the vertical mode permits a small-radius multimode microring. Based on this advantage, we propose an on-chip ultracompact multimode vortex beam emitter. In the process of device design, we have elaborately designed p and q of the structure. The p of WGMs excited by different waveguide modes is related to the microring radius and operating wavelength. Here, we focused on adjusting the operating wavelength corresponding to p by designing the waveguide height and the length of grating elements to achieve the alignment of the resonant wavelengths of different waveguide modes in the multimode microring (see Supplement 1, S5). In addition, considering that it is difficult to generate high-purity high-order OAM mode with a finite number of grating elements [55], we choose a suitable q to ensure that the overall orders of OAM modes are kept at a low level.When the width of the Si waveguide is 0.2 µm and its height is 0.82 µm, only two waveguide modes, $TM_{0}$ and $TM_{1}$, are supported. For these two modes, as the number of optical periods of the WGMs in the microring differ at the same wavelength, different OAM modes can be coupled. Considering the forward and reverse directional inputs that excite clockwise and counterclockwise WGMs, respectively, up to four-mode OAM emission can be realized theoretically. To verify the effectiveness of our design, we performed simulations using Lumerical FDTD Solutions. The forward input case alone was considered because only the direction differs between the forward and reverse inputs. Figure 4(a) shows the simulated structure of the four-mode vortex beam emitter, which comprises three parts: the $TM_{0}$ input, $TM_{1}$ input, and vortex beam emitter. The $TM_{0}$ port is a single-mode waveguide with a width of 0.1 µm, and the $TM_{0}$ mode is transitioned into a 0.2-µm wide multimode waveguide by a 6-µm long tapered section, which is sufficiently long to avoid high-order mode coupling. The $TM_{1}$ port refers to the $TM_{1}$ coupling structure, which can effectively excite the $TM_{1}$ mode in the multimode waveguide. The radius of the vortex beam emitter is 1.5 µm, which approximates the minimum size of the multimode microring. Considering that high efficiency is attractive to most practical devices [34,56–58], grating elements are placed on top of the microring, thus increasing the emission efficiency of the vortex beam compared to the case where gratings are placed on the sidewall in the previous work [30]. Through simulation, we obtained the emission efficiency of the structure, as shown in Fig. 4(b). The $TM_{0}$ and $TM_{1}$ modes are coupled to vortex beams with topological charges of the +1 and -2, respectively, and both have more than 20$\%$ emission efficiency at a wavelength of 1.53669 µm. Figures 4(c)–(h) depict the electric-field amplitude profile, phase profile, and Poynting vectors of the two vortex beams, as we expect. As the grating elements are placed on top of the microring, they will interact mainly with the electric field components distributed in the horizontal direction on top of the microring. For the vertical TM modes, the $E_{z}$ components have a focused distribution on top of the microring with high intensity, while the $E_{x}$ components mainly distribute at the four vertices of the waveguide cross-section with lower intensity. Therefore, the grating elements mainly interact with the $E_{z}$ components, and the vortex beam generated by the emitter is mainly azimuthally polarized vector vortices [33]. Figure 4(i) shows that the purity of the two vortex beams is more than 90$\%$, proving that our design can effectively emit multimode vortex beams.
Fig. 4. Structure and simulation data of a four-mode vortex beam emitter. (a) Structure of the four-mode vortex beam emitter. (b) Simulated emission efficiency of the two vortex beams. (c) – (e) Amplitude profile, phase profile, and Poynting vectors of the OAM ($l=+1$) generated by the $TM_{0}$ mode. (f)– (h) Amplitude profile, phase profile, and Poynting vectors of the OAM ($l=-2$) generated by the $TM_{1}$ mode. (i) Simulated emission purity of the two vortex beams.
The above design uses two waveguide modes to achieve four-mode OAM emission. According to the previous analysis of the vertical modes, our design can introduce more high-order vertical modes without increasing the emitter size to realize more OAM emission modes. We designed a five-mode vortex beam emitter maintaining the emitter radius at 1.5 µm to demonstrate the advantages of the vertical modes. We selected a waveguide with a width of 0.2 µm and height of 0.968 µm that supports only three modes, $TM_{0}$, $TM_{1}$, and $TM_{2}$, and designed a vortex beam emitter to couple the three waveguide modes $TM_{0\setminus 1\setminus 2}$ into vortex beams with topological charges of +2\0\-4. In this case, there are at most five OAM modes ($l = 0, \pm 2, \pm 4$). We considered only the forward input as in the previous case. The simulated OAM emission efficiency of the five-mode emitter is depicted in Fig. 5(a), where mode splitting appears in the emission spectrum of the $TM_{1}$ mode, caused by the Bragg back-reflection of the gratings when the topological charge is zero. Similar phenomena were observed in the previous work [30]. The OAM emission purity is shown in Fig. 5(b). The purity of the two modes generated by $TM_{0}$ and $TM_{1}$ is ideal. One of the reasons for the significant decrease in the OAM purity generated by $TM_{2}$ is the limited number of grating elements due to the small-radius microring, which has an impact on the purity of the higher-order OAM modes [55]. Although the emission purity can be improved by optimizing the structural parameters, in this five-mode vortex beam emitter design, we selected the parameters for aligning the resonant wavelengths of the three waveguide modes in the microring. The far-field intensity and phase of the vortex beam generated by the three waveguide modes are presented in Figs. 5(c)–(h). The simulation results establish the effectiveness of the five-mode vortex beam emitter.
Fig. 5. Simulation results of the five-mode vortex beam emitter. (a) Simulated emission efficiency of the three vortex beams. (b) Simulated emission purity of the three vortex beams. (c)– (d) Far-field intensity and phase of the OAM ($l=+2$) generated by the $TM_{0}$ mode. (e)– (f) Far-field intensity and phase of the OAM ($l=0$) generated by the $TM_{1}$ mode. (g)– (h) Far-field intensity and phase of the OAM ($l=-4$) generated by the $TM_{2}$ mode.
The above simulation results show that our design achieves multimode emission at an ultracompact size, overcoming the constraint relationship between the emitter size and the number of OAM modes by using vertical modes. Table 1 compares the results of several previous studies on microring-based emitters with those of our study. It can be observed that, the size of the multimode vortex beam emitter can be reduced by an order of magnitude or more while emission efficiency is up to an approximate level of most previous works in our study.
Table 1. Comparison of the previous studies based on microrings and our study.
3. Conclusion
We propose an on-chip ultracompact multimode vortex beam emitter, which overcomes the constraint relationship between the emitter size and number of OAM modes utilizing vertical modes in large-aspect-ratio Si waveguides. We designed four-mode and five-mode vortex beam emitters maintaining the same radius of 1.5 µm and demonstrated the effectiveness of the design through simulations. Compared to most previous work, our design permits more OAM mode emission at an ultracompact size, which can fully exploit the advantages of on-chip OAM communication. The results show the immense potential of vertical modes in on-chip optical systems and further research can be conducted for structure fabrication by multiple aligned electron beam lithography (EBL) and reactive ion etching (RIE), as well as explore other applications utilizing vertical modes in PICs. In addition, it has been previously demonstrated that such microring-based vortex beam emitters can be used as on-chip OAM modes (de )multiplexers [21]. Therefore, our design also has potential for on-chip OAM mode (de)multiplexing. Even though the bandwidth of the designed emitter is only about 5 nm, it can be possible to achieve multimode OAM emission at different wavelengths by ingenious design of coinciding multiple resonant wavelengths of different modes [21] or adopting a structure similar to concentric rings [59], thus making it compatible with wavelength division multiplexing (WDM). As a potential scheme for on-chip OAM communication, our design combines the advantages of multimode OAM emission and ultracompact size, and is expected to further advance the integration level of on-chip optical interconnection.
Funding
National Key Research and Development Program of China (2022YFF0604802); National Natural Science Foundation of China (61621001, 61925504, 6201101335, 62020106009, 62192770, 62192772); Science and Technology Commission of Shanghai Municipality (17JC1400800, 20JC1414600, 21JC1406100); “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education (17SG22); Shanghai Municipal Education Commission (2021SHZDZX0100); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflict 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.
References
1. M. Smit, K. Williams, and J. Van Der Tol, “Past, present, and future of inp-based photonic integration,” APL Photonics 4(5), 050901 (2019). [CrossRef]
2. W. Bogaerts, D. Pérez, J. Capmany, D. A. Miller, J. Poon, D. Englund, F. Morichetti, and A. Melloni, “Programmable photonic circuits,” Nature 586(7828), 207–216 (2020). [CrossRef]
3. X. Chen, M. M. Milosevic, S. Stanković, S. Reynolds, T. D. Bucio, K. Li, D. J. Thomson, F. Gardes, and G. T. Reed, “The emergence of silicon photonics as a flexible technology platform,” in Proceedings of the IEEE, (IEEE, 2018), pp. 2101–2116.
4. X. Cao, S. Zheng, Y. Long, Z. Ruan, Y. Luo, and J. Wang, “Mesh-structure-enabled programmable multitask photonic signal processor on a silicon chip,” ACS Photonics 7(10), 2658–2675 (2020). [CrossRef]
5. J. Wu, G. Yue, W. Chen, Z. Xing, J. Wang, W. R. Wong, Z. Cheng, S. Y. Set, G. Senthil Murugan, X. Wang, and T. Liu, “On-chip optical gas sensors based on group-iv materials,” ACS Photonics 7(11), 2923–2940 (2020). [CrossRef]
6. W. Liu, G. Chen, Y. Wang, X. Feng, Y. Xie, Y. Huang, and H. Yang, “Exploration of electrical and novel optical chip-to-chip interconnects,” IEEE Des. Test 31(5), 28–35 (2014). [CrossRef]
7. R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S.-Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” in Proceedings of the IEEE, (IEEE, 2008), pp. 230–247.
8. M.-K. Chin, C.-W. Lee, S.-Y. Lee, and S. Darmawan, “High-index-contrast waveguides and devices,” Appl. Opt. 44(15), 3077–3086 (2005). [CrossRef]
9. P. Guo, W. Hou, L. Guo, X. Zhang, Z. Ning, and M. S. Obaidat, “Design for architecture and router of 3d free-space optical network-on-chip,” in 2018 IEEE International Conference on Communications (ICC), (IEEE, 2018), pp. 1–6.
10. Q. Zhang, J. Ni, and C.-W. Qiu, “Vortex 4.0 on chip,” Light: Sci. Appl. 9(1), 103 (2020). [CrossRef]
11. L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
12. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
13. I. B. Djordjevic, “Deep-space and near-earth optical communications by coded orbital angular momentum (oam) modulation,” Opt. Express 19(15), 14277–14289 (2011). [CrossRef]
14. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. Lavery, M. Tur, S. Ramachandran, A. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015). [CrossRef]
15. J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4(5), B14–B28 (2016). [CrossRef]
16. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef]
17. L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light: Sci. Appl. 8(1), 27 (2019). [CrossRef]
18. S. Yu, “Potentials and challenges of using orbital angular momentum communications in optical interconnects,” Opt. Express 23(3), 3075–3087 (2015). [CrossRef]
19. J. Wang, J. Liu, S. Li, Y. Zhao, J. Du, and L. Zhu, “Orbital angular momentum and beyond in free-space optical communications,” Nanophotonics 11(4), 645–680 (2022). [CrossRef]
20. D. Zhang, X. Feng, and Y. Huang, “Encoding and decoding of orbital angular momentum for wireless optical interconnects on chip,” Opt. Express 20(24), 26986–26995 (2012). [CrossRef]
21. S. Li, Z. Nong, X. Wu, W. Yu, M. He, C. Klitis, Y. Zhu, S. Gao, J. Liu, Z. Li, L. Liu, M. Sorel, S. Yu, and X. Cai, “Orbital angular momentum vector modes (de) multiplexer based on multimode micro-ring,” Opt. Express 26(23), 29895–29905 (2018). [CrossRef]
22. Z. Xie, T. Lei, F. Li, H. Qiu, Z. Zhang, H. Wang, C. Min, L. Du, Z. Li, and X. Yuan, “Ultra-broadband on-chip twisted light emitter for optical communications,” Light: Sci. Appl. 7(4), 18001 (2018). [CrossRef]
23. M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]
24. H. Ren, G. Briere, X. Fang, P. Ni, R. Sawant, S. Héron, S. Chenot, S. Vézian, B. Damilano, V. Brändli, S. A. Maier, and P. Genevet, “Metasurface orbital angular momentum holography,” Nat. Commun. 10(1), 2986 (2019). [CrossRef]
25. H. Yang, Z. Xie, H. He, Q. Zhang, and X. Yuan, “A perspective on twisted light from on-chip devices,” APL Photonics 6(11), 110901 (2021). [CrossRef]
26. H. Ren and S. A. Maier, “Nanophotonic materials for twisted-light manipulation,” Advanced Materials p. 2106692 (2021).
27. Y. Jiang, Y. Cao, and X. Feng, “Progress in integrated devices for optical vortex emission,” J. Phys. D: Appl. Phys. 53(30), 303002 (2020). [CrossRef]
28. X. Wang, Z. Nie, Y. Liang, J. Wang, T. Li, and B. Jia, “Recent advances on optical vortex generation,” Nanophotonics 7(9), 1533–1556 (2018). [CrossRef]
29. D. M. Fatkhiev, M. A. Butt, E. P. Grakhova, R. V. Kutluyarov, I. V. Stepanov, N. L. Kazanskiy, S. N. Khonina, V. S. Lyubopytov, and A. K. Sultanov, “Recent advances in generation and detection of orbital angular momentum optical beams-a review,” Sensors 21(15), 4988 (2021). [CrossRef]
30. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012). [CrossRef]
31. Y. Wang, P. Zhao, X. Feng, Y. Xu, K. Cui, F. Liu, W. Zhang, and Y. Huang, “Integrated photonic emitter with a wide switching range of orbital angular momentum modes,” Sci. Rep. 6(1), 1–9 (2016). [CrossRef]
32. Q. Xiao, C. Klitis, S. Li, Y. Chen, X. Cai, M. Sorel, and S. Yu, “Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings,” Opt. Express 24(4), 3168–3176 (2016). [CrossRef]
33. Z. Shao, J. Zhu, Y. Zhang, Y. Chen, and S. Yu, “On-chip switchable radially and azimuthally polarized vortex beam generation,” Opt. Lett. 43(6), 1263–1266 (2018). [CrossRef]
34. S. Li, Y. Ding, X. Guan, H. Tan, Z. Nong, L. Wang, L. Liu, L. Zhou, C. Yang, K. Yvind, L. K. Oxenløwe, S. Yu, and X. Cai, “Compact high-efficiency vortex beam emitter based on a silicon photonics micro-ring,” Opt. Lett. 43(6), 1319–1322 (2018). [CrossRef]
35. I. V. Stepanov, D. M. Fatkhiev, V. S. Lyubopytov, R. V. Kutluyarov, E. P. Grakhova, N. Neumann, S. N. Khonina, and A. K. Sultanov, “Wavelength-tunable vortex beam emitter based on silicon micro-ring with pn depletion diode,” Sensors 22(3), 929 (2022). [CrossRef]
36. Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, “Tunable topological charge vortex microlaser,” Science 368(6492), 760–763 (2020). [CrossRef]
37. P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353(6298), 464–467 (2016). [CrossRef]
38. N. Carlon Zambon, P. St-Jean, M. Milićević, A. Lemaître, A. Harouri, L. Le Gratiet, O. Bleu, D. Solnyshkov, G. Malpuech, I. Sagnes, S. Ravets, A. Amo, and J. Bloch, “Optically controlling the emission chirality of microlasers,” Nat. Photonics 13(4), 283–288 (2019). [CrossRef]
39. B. Chen, Y. Wei, T. Zhao, S. Liu, R. Su, B. Yao, Y. Yu, J. Liu, and X. Wang, “Bright solid-state sources for single photons with orbital angular momentum,” Nat. Nanotechnol. 16(3), 302–307 (2021). [CrossRef]
40. J. Zhang, C. Sun, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, Y. Luo, Y. Xiao, C. Yu, T. Tanemura, Y. Nakano, S. Li, X. Cai, and S. Yu, “An inp-based vortex beam emitter with monolithically integrated laser,” Nat. Commun. 9(1), 1–6 (2018). [CrossRef]
41. N. Zhou, S. Zheng, X. Cao, Y. Zhao, S. Gao, Y. Zhu, M. He, X. Cai, and J. Wang, “Ultra-compact broadband polarization diversity orbital angular momentum generator with 3.6× 3.6 µm2 footprint,” Sci. Adv. 5(5), eaau9593 (2019). [CrossRef]
42. Y. Guo, M. Pu, Z. Zhao, Y. Wang, J. Jin, P. Gao, X. Li, X. Ma, and X. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016). [CrossRef]
43. W. E. Hayenga, M. Parto, J. Ren, F. O. Wu, M. P. Hokmabadi, C. Wolff, R. El-Ganainy, N. A. Mortensen, D. N. Christodoulides, and M. Khajavikhan, “Direct generation of tunable orbital angular momentum beams in microring lasers with broadband exceptional points,” ACS Photonics 6(8), 1895–1901 (2019). [CrossRef]
44. U. Stella, T. Grosjean, N. De Leo, L. Boarino, P. Munzert, J. R. Lakowicz, and E. Descrovi, “Vortex beam generation by spin-orbit interaction with bloch surface waves,” ACS Photonics 7(3), 774–783 (2020). [CrossRef]
45. K. G. Cognée, H. M. Doeleman, P. Lalanne, and A. F. Koenderink, “Generation of pure oam beams with a single state of polarization by antenna-decorated microdisk resonators,” ACS Photonics 7(11), 3049–3060 (2020). [CrossRef]
46. Z. Zhang, H. Zhao, D. G. Pires, X. Qiao, Z. Gao, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, “Ultrafast control of fractional orbital angular momentum of microlaser emissions,” Light: Sci. Appl. 9(1), 179 (2020). [CrossRef]
47. D. Wang, F. Liu, T. Liu, S. Sun, Q. He, and L. Zhou, “Efficient generation of complex vectorial optical fields with metasurfaces,” Light: Sci. Appl. 10(1), 67 (2021). [CrossRef]
48. Y. Meng, Y. Chen, L. Lu, Y. Ding, A. Cusano, J. A. Fan, Q. Hu, K. Wang, Z. Xie, Z. Liu, Y. Yang, Q. Liu, M. Gong, Q. Xiao, S. Sun, M. Zhang, X. Yuan, and X. Ni, “Optical meta-waveguides for integrated photonics and beyond,” Light: Sci. Appl. 10(1), 235 (2021). [CrossRef]
49. X. Guo, Y. Ding, X. Chen, Y. Duan, and X. Ni, “Molding free-space light with guided wave–driven metasurfaces,” Sci. Adv. 6(29), eabb4142 (2020). [CrossRef]
50. Y. Meng, Z. Liu, Z. Xie, R. Wang, T. Qi, F. Hu, H. Kim, Q. Xiao, X. Fu, Q. Wu, S.-H. Bae, M. Gong, and X. Yuan, “Versatile on-chip light coupling and (de) multiplexing from arbitrary polarizations to controlled waveguide modes using an integrated dielectric metasurface,” Photonics Res. 8(4), 564–576 (2020). [CrossRef]
51. E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969). [CrossRef]
52. Q. Wang and S.-T. Ho, “Ultracompact tm-pass silicon nanophotonic waveguide polarizer and design,” IEEE Photonics J. 2(1), 49–56 (2010). [CrossRef]
53. D. Dai, “Multimode optical waveguide enabling microbends with low inter-mode crosstalk for mode-multiplexed optical interconnects,” Opt. Express 22(22), 27524–27534 (2014). [CrossRef]
54. L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “Wdm-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014). [CrossRef]
55. C. Sun, J. Zhang, B. Xiong, J. Wang, Z. Hao, L. Wang, Y. Han, H. Li, and Y. Luo, “Analysis of oam mode purity of integrated optical vortex beam emitters,” IEEE Photonics J. 9, 1–7 (2017). [CrossRef]
56. K. Cheng, Z. Wei, Y. Fan, X. Zhang, C. Wu, and H. Li, “Realizing broadband transparency via manipulating the hybrid coupling modes in metasurfaces for high-efficiency metalens,” Adv. Opt. Mater. 7(15), 1900016 (2019). [CrossRef]
57. T. He, T. Liu, S. Xiao, Z. Wei, Z. Wang, L. Zhou, and X. Cheng, “Perfect anomalous reflectors at optical frequencies,” Sci. Adv. 8(9), eabk3381 (2022). [CrossRef]
58. L. Ferrari, J. S. Smalley, H. Qian, A. Tanaka, D. Lu, S. Dayeh, Y. Fainman, and Z. Liu, “Design and analysis of blue ingan/gan plasmonic led for high-speed, high-efficiency optical communications,” ACS Photonics 5(9), 3557–3564 (2018). [CrossRef]
59. N. Zhang, M. Scaffardi, C. Klitis, M. N. Malik, V. Toccafondo, F. Fresi, J. Zhu, X. Cai, S. Yu, A. Bogoni, and M. Sorel, “Large-scale integrated reconfigurable orbital angular momentum mode multiplexer,” https://arxiv.org/abs/2008.00680 (2020).
