Open Access
Add to BibSonomy
Abstract
As one of the most significant 2D materials, black phosphorus (BP) offers a promising way to manipulate the polarization state of light due to its in-plane anisotropy, however, reconfigurable polarization manipulation is still challenging in simple BP structure. Here, we propose a multilayer metamaterial with twisted BP nanostructures and numerically study its circular dichroism (CD) and circular birefringence (CB) responses. The dependences of the circular polarization responses in the twisted BP metamaterial have been fully investigated on geometrical and material parameters. The giant tunability enables the twisted BP nanostructure to be attractive for constructing BP-based metamaterials devices, such as polarizers, biosensors and modulators.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
An object has chirality that cannot be superimposed upon its mirror image by in-plane rotation or translation. Chiral materials may exhibit different optical responses to right- and left- circularly polarized light (RCP and LCP), known as chiroptical effect [1]. Optical activity is one of the important chiroptical effects, manifesting itself as circular dichroism (CD) and circular birefringence (CB) in lossy chiral materials. CD is defined as different transmission/absorption of circularly polarized waves while CB is able to rotate the polarization plane of linearly polarized light. By detecting different responses of circularly polarized light, chiral materials can be recognized and analyzed. However, chiroptical effects in natural materials are very weak, thus the corresponding optical devices are bulky in order to enhance the interaction between chiral material and circularly polarized light. The advent of various artificial structures offers an opportunity realize strong chiroptical responses, such as chiral nanostructures [2], photonic crystals [3], two-dimensional (2D) materials [4,5], and metamaterials [6–8]. Besides, chiroptical response can be enhanced not only in intrinsically chiral structures but also in achiral structures, which is termed as extrinsic chirality [9]. In contrast to intrinsic chiral structures, extrinsic chiroptical response can be obtained by breaking symmetry of the whole system containing achiral structure and incident direction of light [10–12].
Since the discovery of graphene, 2D materials have attracted much attention from broad scientific community and industries [13–18]. With their atomic-scale thickness and excellent optoelectronic properties, 2D materials including graphene, transition metal dichalcogenides (TMDCs) and black phosphorus (BP), provide a powerful platform to achieve novel nanophotonic devices in the infrared and visible bands, such as field-effect transistor [16], photodetector [19–21], and ultrafast laser [22,23]. Such 2D materials possess abundant electronic band properties that are tailored by several methods, such as doping synthesis, heterostructures and the number of stacked layers, and exhibit many intriguing phenomena, for instance, superconductivity [24,25], anisotropic moiré optical transitions [26], and strain-engineered perfect absorption [27]. Among 2D materials, monolayer BP has received lots of interests due to its outstanding optical, mechanical, thermal, and high optical absorption [28–32]. BP is flexible and can be mechanically exfoliated the same as graphene. BP exhibits a layer-dependent direct band gap ranging from ∼ 0.3 eV (bulk) to ∼ 1.4 eV (monolayer) in contrast to zero band gap in graphene and only a direct band gap of ∼1.8 eV (monolayer) in MoS2 [33]. The flexible band gap in BP can fill the gap between graphene and TMDCs. The extensive investigation of BP brings many outstanding applications such as spectrometer [17], phosphorene heterostructures [26], polarization-dependent epsilon-near-zero behavior [34], electro-optic polarization conversion [35], polarimeters [36] and anisotropic plasmons [37]. More importantly, intrinsic in-plane anisotropy has been used to realize many polarization-dependent nanophotonic phenomena [34–41]. Gate-switchable transport and optical linear dichroism have been demonstrated in a 90° twisted bilayer BP structure based first-principles calculations [42]. Liu et al reported a large and tunable optical rotation effect in twisted black phosphorus, in which the polarization-plane rotation (PORA) can be engineered by the twist angle and BP thickness and is up to 0.49° per atomic layer [43]. Optical activity due to extrinsic chirality has been numerically studied in unpatterned [11,44] and patterned monolayer black phosphorus [45], in which polarization responses can be tailored by angles of incidence or the Fermi level of BP. Besides the bandgap modulation, intraband optical conductivity in BP can be modulated by the charge density in a two-dimensional electron gas and the polarization-dependent epsilon-near-zero behavior has been observed, offering an opportunity for active polarization-sensitive IR metasurfaces [34]. Moreover, an hBN/tri-layer BP/hBN structure has been integrated into Fabry-Pérot cavity for achieving reconfigurable polarization conversion in the telecommunication band [35], in which the large electrically controlled birefringence of tri-layer BP enables polarization conversion across nearly half the Poincaré sphere via spectral tuning. Fiber-integrated polarimeters have been experimentally realized based on van der Waals stacks that are composed of one Bi2Se3 layer (power calibration), two BP layers and three hBN layers (encapsulation) [36]. Importantly, two anisotropic BP layers are twisted in order to enable precise polarization sensing and polarimetric imaging. Recently, twisted BP/α-MoO3 stacks have been proposed to construct optical elements with arbitrary Jones matrices and theoretically investigated for polarization manipulation via the designs of rotators, pseudorotators, symmetric and ambidextrous polarizers [46], but the accurate control of material and geometrical parameters such as thickness and twist angle of BP and α-MoO3, the layer spacing, and the chemical potential in BP is required.
Although several polarizations have been investigated using the anisotropic properties of BP, there are few studies on chiroptical responses in simple twisted BP nanostructures. The structured BP may offer more opportunities to manipulate the polarization state of light and the operation wavelength can be easily engineered to anywhere in far-infrared range. In this work, we propose a twisted multilayer metamaterial consisting of cascaded BP squares with dielectric spacers. The dependences of the twisted BP metamaterial on geometry and material parameters are fully investigated. With the scheme of stacking anisotropic BP material, it is expected to realize reconfigurable polarization devices and the work provides a new way for actively manipulating the polarization state of light in emerging photonic applications.
2. Results and discussion
2D BP material with in-plane anisotropy exhibits the ability to manipulate the polarization state of light [34–41]. Traditional anisotropic nanostructures have been stacked with a twist angle to realize broadband circular polarizers [7], which mainly depends on strong, resonant anisotropy at the metasurface level rather than intrinsic chirality. In order to achieve polarization counterpart of 2D BP materials, here we develop multi-layer twisted BP metamaterial to tailor the propagation of circularly polarized light. BP layer is much thinner than that of gold nanorod, thus compact polarization devices may be readily realized. In addition, anisotropic properties of BP can be easily utilized to obtain chiroptical response by the twist arrangement. The schematic diagram of the multilayered metamaterial is shown in Fig. 1(a), which is composed of a dielectric and monolayer BP stack. The square lattice consists of structured square BP patterned on the dielectric layer. In order to realize strong response of multi-layered BP metamaterial to circularly polarized light, a twist angle between two adjacent BP layers is inevitably introduced. For modelling simplicity, the twist angle between different adjacent layers is identical and is labelled by θ. The twist angle and anisotropic crystal structure of the BP layer are illustrated in Fig. 1(b) and Fig. 1(c), respectively. The armchair direction of the first BP layer (i.e. the bottom layer) is the same as the x axis. The armchair directions of the second to fifth layers are oriented at θ, 2θ, 3θ, 4θ, respectively. Circularly polarized light is normally incident on twisted BP metamaterial. The optimized geometrical parameters are as follows: the thicknesses of the dielectric layers are d1 = d2 = 150 nm and h1 = h2 = h3 = h4= 2 µm, the period is p = 300 nm and the BP square width is w = 285 nm. When the layer number of the BP is changed, the thicknesses of the top, bottom and spacer layers are kept unchanged. The refractive index of the dielectric is taken to be 2. For the monolayer BP, the optical conductivity can be calculated from Kubo formula by employing ab initio calculations [47]. In our simulation, a simple semiclassical Drude model is used to describe the optical characteristics of monolayer BP [48]. The conductivity is calculated as follows
Fig. 1. Schematic of the proposed metamaterial consisting of five-layer twisted monolayer BPs. (a) 3D illustration of multilayer twisted chiral metamaterial under illumination of circularly polarized light. The geometrical parameters are d1 = d2 = 150 nm, h1 = h2 = h3 = h4= 2 µm. The armchair direction of the first BP layer is the same as the x axis. There is a twist angle θ between the armchair directions of two adjacent BP layers. The armchair directions of the second to fifth layers are oriented at θ, 2θ, 3θ, 4θ, respectively. (b) Illustration of the twist angle θ. θ represents the angle between the armchair direction of the first layer and the x-axis. (c) Anisotropic crystal structure of monolayer BP.
Here, j denotes the x or y direction, Dj is the Drude weight and mj is the electron effective mass with the armchair and zigzag direction, mx ≈ 0.15 m0, my ≈ 0.7 m0 (m0 is the static electron mass). Here the electron doping concentration is set as n = 3 × 1013 cm−2 that can be tuned by chemical or electrostatic doping [29]. Next, the permittivity of monolayer BP can be represented by a diagonal matrix
Fig. 2. (a) Simulated transmittance spectra of five-layer twisted BP metamaterial. (b) Circular dichroism and circular birefringence spectra of five-layer twisted BP metamaterial. The twist angle is θ = 20°.
The transmission matrix can be determined by relating incident electric field Ein to the transmitted electric field Etr for circularly polarized light. The formula can be defined as Emtr = tmnEnin (m = + or −, n = + or –) from Jones matrix, in which “+” and “−” denote right-handed circularly polarized light (RCP) and left- handed circularly polarized light (LCP), respectively. The intensity transmittance could be calculated as Tmn = |tmn|2. The magnitude difference Δ = T++ − T−−is a measure of CD, and the phase difference $\Phi $= arg(t++) − arg(t−−) is a measure of CB from the definition [10]. The transmittance properties of five-layer twisted BP metamaterial have been studied in the wavelength range from 15 to 95 µm for normally incident circularly polarized light, in which the twist angle is θ = 20°. In Fig. 2(a), there is an obvious difference between T++ and T− − while two cross-polarization conversion T + - and T-+ are identical and very weak. In Fig. 2(b), the CD and CB spectra indicate the strong response of the BP metamaterial to incident circularly polarized light, resulting from the rotation arrangement of the BP layers. Three resonant CD values are -12.2%, 17.5%, and -4.3%, the corresponding wavelength are 31.7 µm, 41.4 µm and 65.8 µm respectively. In the wavelength range of 20-80 µm, the twisted BP metamaterial differently responses to RCP and LCP waves. The CD spectrum is accompanied by resonant CB one. The CB can reach -18.1° around 36.4 µm. The simulation results in Fig. 2 reveal chiroptical response of the proposed multilayer metamaterial.
Since the twisted BP metamaterial is multi-layered, it is necessary to investigate how the layer number of the BP affects electromagnetic responses to incident circularly polarized light. N represents the number of cascading layers of BP in Fig. 3(a) and Fig. 3(b). When the layer number N of the BP varies, the period, the width of the BP square, and thicknesses of the dielectric layers remain unchanged and the twist angle is still θ = 20°. When the layer number of the BP varies in the range of 3 to 7, both CD and CB spectra experience an obvious change in Fig. 3(a) and Fig. 3(b). As the metamaterial consists of 5 BP layers, the resonant CD values are relatively larger and fewer or more BP layers lead to a weak CD response. Increasing the layer number of the BP results in more pronounced CB phenomenon. The peaks of the CD and CB spectra are slightly shifted as the layer number N of the BP varies. Considering relatively simple configuration, twisted 5-layer BP metamaterial is adopted to study how geometrical parameters impact on CD and CB responses. For incident circularly polarized light, the remarkable responses of the metamaterial depend on the twist spatial arrangement of anisotropic BP blocks rather than intrinsic chirality. The relative rotation of the anisotropy direction in BP bring about chiroptical response that is similar to chiral metamaterial. Different CD and CB responses are produced when increasing the twist angle from 10° to 30° by 5° step, as illustrated in Fig. 3(c) and Fig. 3(d). The twist angle leads to the changes of both CD and CB spectra, not only resonant frequencies but also peak values. In Fig. 3(c), there are two large resonance peaks that are strongly dictated by the twist angle. The optimal CD and CB spectra can be achieved in Fig. 3(c) and Fig. 3(d) when the twist angle is θ = 20°.
Fig. 3. (a)-(b) Simulated CD and CB spectra of twisted metamaterial for different BP layers. (c)-(d) Simulated CD and CB spectra of twisted 5-layer BP metamaterial for different twist angle θ.
Compared with unstructured BP layer, structured BP array offers more flexibilities to engineer the working wavelength of metamaterial via changing it geometrical parameters. The dependences of the CD and CB properties on structured parameters will be investigated next. Figure 4 depicts the CD and CB spectra of 5-layer BP metamaterial with changing the metamaterial period and width of the BP, in which the duty ratio k is defined as the width of the BP square over the period of the metamaterial (k = w/p). In Fig. 4(a) and Fig. 4(b), the twist angle and the duty ratio are fixed as θ = 20° and k = 0.95. When the period of the metamaterial varies from 100 to 500 nm, the width of the BP square correspondingly varies from 95 to 475 nm. As the period is changed, the peak values of the CD and CB spectra vary in the ranges of 12.8% to 17.5% and -16.3° to -18.4°, respectively. The spectra profiles are slightly broader for a large period. Importantly, the resonance peak positions are largely moved and the shift exceeds 20 µm as the period increases. Besides the period, BP's duty ratio k also has a significant impact on the chiroptical response. The effects of the duty ratio on the CD and CB spectra of the 5-layer metamaterial are illustrated in Fig. 4(c) and Fig. 4(d), respectively. When the duty ration varies from 0.75 to 0.95, the twist angle and the period are fixed as θ = 20° and p = 300 nm, respectively. Compared with the period, the duty ratio has a stronger impact on responses of the BP metamaterial to circularly polarized light. The peak value of the CD spectra increases from 5.8% to 17.5% when the duty ratio k is changed from 0.75 to 0.95, and the corresponding resonant peak wavelength changes from 31.3 µm to 41.8 µm. As the duty ratio increases, the peak value of the CB spectra is changed from -3.2° to -18.1° and the corresponding resonance wavelength is changed from 27.4 µm to 36.4 µm. Therefore, appropriate geometry design of the BP square with a fixed duty ratio is a good choice to alter the operation wavelength of the polarization device.
Fig. 4. (a)-(b) Simulated CD spectra and CB spectra of twisted 5-layer BP metamaterial with various periods. The twist angle and the duty ration are fixed as θ = 20° and k = 0.95. (c)-(d) Simulated CD spectra and CB spectra of twisted five-layer BP metamaterial with various duty ratios. The twist angle and the period are fixed as θ = 20° and p = 300 nm.
Tunable polarization control is highly promising in metamaterials with 2D materials [5,11,34,35,44]. The electron doping concentration can be readily explored to tailor responses of 5-layer BP metamaterial, allowing new possibility for reconfigurable polarization components. The electron doping concentration level can be tailored by different chemical or electrostatic doping [11,34,35]. When the electron doping concentration is considered, the geometry of the twisted 5-layer BP metamaterial remains unchanged. The twist angle, the period and the width of the BP square are fixed as θ = 20°, p = 300 nm and w = 285 nm (k = 0.95). Figure 5 depicts CD and CB characteristics of the BP metamaterial with varying electron doping concentration levels from 1 × 1013 cm-2 to 9 × 1013 cm-2. The increasing electron concentration level leads to enhanced CD and CB responses and spectrum shifts of the BP metamaterial. In Fig. 5(a), the positive resonance peak of the CD spectra is increased from 3.3% to 29.4%, while the corresponding resonant wavelength shifts from 70 to 24 µm. In Fig. 5(b), the negative maximum value of the CB spectra is enhanced from 0° to 87.1°. It is noted that there are weak CD and CB responses when the electron doping concentration is n = 1 × 1013 cm-2, while the CD and CB spectra are much more significant as the electron doping concentration is increased to n = 9 × 1013 cm-2. As the electron doping concentration increases, the optical rotation continues to increase, the resonance peaks blueshift, and the widths of the resonances are slightly suppressed. The absorption and reflection of the structure will be affected by a rise in electron concentration. Modulating the electron doping concentration of the BP nanostructure, reconfigurable BP-based polarization devices seems to be accessible.
Fig. 5. Simulated (a) CD spectra and (b) CB spectra of twisted five-layer BP metamaterial with different concentration levels. The twist angle, the period and the width of the BP square are fixed as θ = 20°, p = 300 nm and w = 285 nm.
Besides geometrical and material parameters such as the twist angle, the metamaterial period and the electron doping concentration level, the angular dependence of the performance of the BP-based metamaterial also deserves to be studied. The elevation angle is defined as β and the azimuth angle α is the rotation angle of the whole metamaterial with respect to the x-direction, as displayed in Fig. 6(a). The electron doping concentration, the twist angle, the period and the width of the BP square are fixed as n = 3 × 1013 cm−2, θ = 20°, p = 300 nm and w = 285 nm. Two cases will be discussed. One is that the elevation angle varies when the azimuth angle is α = 0. The other is that the azimuth angle varies when the elevation angle is β = 40°. It can be seen that when the elevation angle is less than 60°, the CD and CB spectra of the twisted 5-layer BP metamaterial almost remain unchanged in both resonant frequencies and strengths as shown in Fig. 6(b) and Fig. 6(c). In Fig. 6(b), two maximum CD values are about 17.5% and -12.5% at the wavelengths 41.5 µm and 31.7 µm, respectively. At grazing incidence, the CD spectra gradually decrease to zero. In Fig. 6(c), as the elevation angle increases, the CB peak value remains unchanged at 37 µm that lies in between two CD passbands. Figure 6(d) and Fig. 6(e) show the CD and CB spectra when the azimuth angle is in the range from 0° to 360° at a fixed elevation angle of β = 40°. Obviously, the CD and CB spectra are periodically manipulated by the variation of the azimuth angle. When the azimuth angle is changed, peak values of both CD and CB alternatively emerge in different passbands. Similar to the results in Fig. 6(b) and Fig. 6(c), the CD and CB spectra are also kept unmoved. According to the aforementioned results, the properties of the twisted 5-layer BP metamaterial are robust to both the elevation angle and the azimuth angle within a broad range.
Fig. 6. Angular dependence of chiroptical responses in the twisted BP metamaterial. (a) Schematic diagram of multilayer metamaterial at oblique incidence. The azimuth and elevation angles are marked by α and β. (b)-(c) CD spectra and CB spectra of the twisted BP metamaterial with varied elevation angle β when the azimuth angle α is fixed at 0°. (d)-(e) CD spectra and CB spectra of the twisted BP metamaterial with varied azimuth angle α from 0° to 360° when the elevation angle is β = 40°, the doping concentration is n = 3 × 1013 cm−2. The twist angle, the period and the width of the BP square are fixed as θ = 20°, p = 300 nm and w = 285 nm.
3. Conclusions
In conclusion, we have proposed and numerically investigated optical responses of a multilayered metamaterial with twisted BP squares to circularly polarized light. The simulation results show that the twist arrangement of anisotropic structured BP layer enables the metamaterial to differently response to incident RCP and LCP light. The twisted metamaterial with structured BP squares offers an opportunity to manipulate its CD and CB responses via changing the period and the width of the BP square. When the geometrical parameters of the BP square vary, the spectrum shift exceeding 20 µm makes the BP metamaterial work in different wavelength ranges. More importantly, the electron doping concentration level of the BP material could flexibly tailor CD and CB responses of the twisted BP metamaterial. It is noted that the CB reaches up to 87.1° as the electron doping concentration is increased to n = 9 × 1013 cm-2. The work may be helpful to realize various circular polarization devices. The proposed multilayered metamaterial could be directly integrated into optical devices due to its simple geometry structure and will bring more possibilities to realize tunable polarization devices.
Funding
National Natural Science Foundation of China (62275061, 62175049); Natural Science Foundation of Heilongjiang Province (ZD2020F002); 111 Project (B13015); Fundamental Research Funds for the Central Universities (3072021CFT2501, 3072022CF2505, 3072022TS2509).
Acknowledgment
We thank Prof. Huifeng Ma in State Key Laboratory of Millimeter Waves of Southeast University for simulation support.
Disclosures
The authors declare no conflicts of interest regarding this article.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. Z. Wang, F. Cheng, T. Winsor, and Y. Liu, “Optical chiral metamaterials: a review of the fundamentals, fabrication methods and applications,” Nanotechnology 27(41), 412001 (2016). [CrossRef]
2. Y. Luo, C. Chi, M. Jiang, R. Li, S. Zu, Y. Li, and Z. Fang, “Plasmonic chiral nanostructures: chiroptical effects and applications,” Adv. Opt. Mater. 5(16), 1700040 (2017). [CrossRef]
3. Y. Chen, W. Chen, X. Kong, D. Wu, J. Chu, and C.-W. Qiu, “Can weak chirality induce strong coupling between resonant states?” Phys. Rev. Lett. 128(14), 146102 (2022). [CrossRef]
4. O. V. Kotov and Y. E. Lozovik, “Enhanced optical activity in hyperbolic metasurfaces,” Phys. Rev. B 96(23), 235403 (2017). [CrossRef]
5. T. Stauber, T. Low, and G. Gómez-Santos, “Chiral response of twisted bilayer graphene,” Phys. Rev. Lett. 120(4), 046801 (2018). [CrossRef]
6. S. Zhang, J. Zhou, Y.-S. Park, J. Rho, R. Singh, S. Nam, A. K. Azad, H.-T. Chen, X. Yin, A. J. Taylor, and X. Zhang, “Photoinduced handedness switching in terahertz chiral metamolecules,” Nat. Commun. 3(1), 942 (2012). [CrossRef]
7. Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3(1), 870 (2012). [CrossRef]
8. X. Yin, M. Schäferling, A.-K. U. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015). [CrossRef]
9. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008). [CrossRef]
10. E. Plum, X.-X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009). [CrossRef]
11. Q. Hong, W. Xu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Optical activity in monolayer black phosphorus due to extrinsic chirality,” Opt. Lett. 44(7), 1774 (2019). [CrossRef]
12. J. Wu, X. Xu, X. Su, S. Zhao, C. Wu, Y. Sun, Y. Li, F. Wu, Z. Guo, H. Jiang, and H. Chen, “Observation of giant extrinsic chirality empowered by quasi-bound states in the continuum,” Phys. Rev. Appl. 16(6), 064018 (2021). [CrossRef]
13. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef]
14. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102(30), 10451–10453 (2005). [CrossRef]
15. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8(3), 902–907 (2008). [CrossRef]
16. L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, “Black phosphorus field-effect transistors,” Nat. Nanotechnol. 9(5), 372–377 (2014). [CrossRef]
17. S. Yuan, D. Naveh, K. Watanabe, T. Taniguchi, and F. Xia, “A wavelength-scale black phosphorus spectrometer,” Nat. Photonics 15(8), 601–607 (2021). [CrossRef]
18. C.-J. Kim, A. Sánchez-Castillo, Z. Ziegler, Y. Ogawa, C. Noguez, and J. Park, “Chiral atomically thin films,” Nat. Nanotechnol. 11(6), 520–524 (2016). [CrossRef]
19. F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009). [CrossRef]
20. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010). [CrossRef]
21. X. Chen, X. Lu, B. Deng, O. Sinai, Y. Shao, C. Li, S. Yuan, V. Tran, K. Watanabe, T. Taniguchi, D. Naveh, L. Yang, and F. Xia, “Widely tunable black phosphorus mid-infrared photodetector,” Nat. Commun. 8(1), 1672 (2017). [CrossRef]
22. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010). [CrossRef]
23. M. Zhang, Q. Wu, F. Zhang, L. Chen, X. Jin, Y. Hu, Z. Zheng, and H. Zhang, “2D black phosphorus saturable absorbers for ultrafast photonics,” Adv. Opt. Mater. 7(1), 1800224 (2019). [CrossRef]
24. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018). [CrossRef]
25. M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363(6431), 1059–1064 (2019). [CrossRef]
26. S. Zhao, E. Wang, E. A. Üzer, S. Guo, R. Qi, J. Tan, K. Watanabe, T. Taniguchi, T. Nilges, P. Gao, Y. Zhang, H.-M. Cheng, B. Liu, X. Zou, and F. Wang, “Anisotropic moiré optical transitions in twisted monolayer/bilayer phosphorene heterostructures,” Nat. Commun. 12(1), 3947 (2021). [CrossRef]
27. M. Alidoust, K. Halterman, D. Pan, M. Willatzen, and J. Akola, “Strain-engineered widely tunable perfect absorption angle in black phosphorus from first principles,” Phys. Rev. B 102(11), 115307 (2020). [CrossRef]
28. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, “Phosphorene: an unexplored 2D semiconductor with a high hole mobility,” ACS Nano 8(4), 4033–4041 (2014). [CrossRef]
29. T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. H. Castro Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B 90(7), 075434 (2014). [CrossRef]
30. V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B 89(23), 235319 (2014). [CrossRef]
31. L. Li, J. Kim, C. Jin, G. J. Ye, D. Y. Qiu, F. H. da Jornada, Z. Shi, L. Chen, Z. Zhang, F. Yang, K. Watanabe, T. Taniguchi, W. Ren, S. G. Louie, X. H. Chen, Y. Zhang, and F. Wang, “Direct observation of the layer-dependent electronic structure in phosphorene,” Nat. Nanotechnol. 12(1), 21–25 (2017). [CrossRef]
32. G. Zhang, S. Huang, F. Wang, and H. Yan, “Layer-dependent electronic and optical properties of 2D black phosphorus: Fundamentals and Engineering,” Laser Photonics Rev. 15(6), 2000399 (2021). [CrossRef]
33. B. Deng, V. Tran, Y. Xie, H. Jiang, C. Li, Q. Guo, X. Wang, H. Tian, S. J. Koester, H. Wang, J. J. Cha, Q. Xia, L. Yang, and F. Xia, “Efficient electrical control of thin-film black phosphorus bandgap,” Nat. Commun. 8(1), 14474 (2017). [CrossRef]
34. S. Biswas, W. S. Whitney, M. Y. Grajower, K. Watanabe, T. Taniguchi, H. A. Bechtel, G. R. Rossman, and H. A. Atwater, “Tunable intraband optical conductivity and polarization-dependent epsilon-near-zero behavior in black phosphorus,” Sci. Adv. 7(2), eabd4623 (2021). [CrossRef]
35. S. Biswas, M. Y. Grajower, K. Watanabe, T. Taniguchi, and H. A. Atwater, “Broadband electro-optic polarization conversion with atomically thin black phosphorus,” Science 374(6566), 448–453 (2021). [CrossRef]
36. Y. Xiong, Y. Wang, R. Zhu, H. Xu, C. Wu, J. Chen, Y. Ma, Y. Liu, Y. Chen, K. Watanabe, T. Taniguchi, M. Shi, X. Chen, Y. Lu, P. Zhan, Y. Hao, and F. Xu, “Twisted black phosphorus–based van der Waals stacks for fiber-integrated polarimeters,” Sci. Adv. 8(18), eabo0375 (2022). [CrossRef]
37. Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016). [CrossRef]
38. F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017). [CrossRef]
39. J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018). [CrossRef]
40. Y. M. Qing, H. F. Ma, and T. J. Cui, “Tailoring anisotropic perfect absorption in monolayer black phosphorus by critical coupling at terahertz frequencies,” Opt. Express 26(25), 32442–32450 (2018). [CrossRef]
41. X.-G. Gao, X.-K. Li, W. Xin, X.-D. Chen, Z.-B. Liu, and J.-G. Tian, “Fabrication, optical properties, and applications of twisted two-dimensional materials,” Nanophotonics 9(7), 1717–1742 (2020). [CrossRef]
42. T. Cao, Z. Li, D. Y. Qiu, and S. G. Louie, “Gate switchable transport and optical anisotropy in 90° twisted bilayer black phosphorus,” Nano Lett. 16(9), 5542–5546 (2016). [CrossRef]
43. S.-Y. Wang, K.-X. Huang, Q.-Q. Guo, H.-W. Guo, J.-G. Tian, and Z.-B. Liu, “Tunable optical rotation in twisted black phosphorus,” J. Phys. Chem. Lett. 12(19), 4755–4761 (2021). [CrossRef]
44. Y. Zeng, J. Xu, W. Xiao, Z. Yang, H. Chen, H. Chen, Y. Liu, and Y. Liu, “Giant 2D-chiroptical response in an achiral metasurface integrated with black phosphorus,” Opt. Express 30(5), 8266–8274 (2022). [CrossRef]
45. M. Sun, Y. Wang, H. Hu, H. Zhang, W. Li, B. Lv, Z. Zhu, C. Guan, and J. Shi, “Optical properties and dynamic extrinsic chirality of structured monolayer black phosphorus,” Front. Mater. 9, (2022).
46. K. Khaliji, L. Martín-Moreno, P. Avouris, S.-H. Oh, and T. Low, “Twisted two-dimensional material stacks for polarization optics,” Phys. Rev. Lett. 128(19), 193902 (2022). [CrossRef]
47. A. S. Rodin, A. Carvalho, and A. H. Castro Neto, “Strain-induced gap modification in black phosphorus,” Phys. Rev. Lett. 112(17), 176801 (2014). [CrossRef]
48. T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014). [CrossRef]
