Abstract

Properly designed black phosphorus (BP) ribbons exhibit extreme anisotropic properties, which can be used to fabricate a high-efficiency transmitter or reflector depending on the linear polarization of excitation. In this study, we design a highly efficient and broad-angle polarization beam splitter (PBS) based on extremely anisotropic BP ribbons around the mid-infrared frequency region with an ultra-thin structure, and study its performance by using transfer matrix calculation and finite element simulation. In the broad frequency range of 80.4 terahertz - 85.0 terahertz (THz) and an wide angle range of more than 50°, the reflectivity and transmissivity of the designed PBS are both larger than 80% and the polarization extinction ratios are higher than 25.50 dB for s-polarization light and 20.40 dB for p- polarization light, respectively. Furthermore, the effect of incident angle and device parameters on the behavior of the proposed PBS is examined. Finally, we show that the operation frequency of this PBS can be tuned by the electron concentration of BP, which can facilitate some practical applications such as tunable polarization splitters or filters, and mid-infrared sensors.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2020 (1)

T. Liu, X. Jiang, H. Wang, Y. Liu, C. Zhou, and S. Xiao, “Tunable anisotropic absorption in monolayer black phosphorus using critical coupling,” Appl. Phys. Express 13(1), 012010 (2020).
[Crossref]

2019 (9)

D. Dong, Y. Liu, Y. Fan, Y. Fei, J. Li, and Y. Fu, “Tunable THz reflection-type polarizer based on monolayer phosphorene,” Appl. Opt. 58(35), 9643–9650 (2019).
[Crossref]

T. Liu, X. Jiang, C. Zhou, and S. Xiao, “Black phosphorus-based anisotropic absorption structure in the mid-infrared,” Opt. Express 27(20), 27618–27627 (2019).
[Crossref]

D. Dong, Y. Liu, Y. Fei, Y. Fan, J. Li, Y. Feng, and Y. Fu, “Designing a nearly perfect infrared absorber in monolayer black phosphorus,” Appl. Opt. 58(14), 3862 (2019).
[Crossref]

S. Xiao, T. Liu, L. Cheng, C. Zhou, X. Jiang, Z. Li, and C. Xu, “Tunable Anisotropic Absorption in Hyperbolic Metamaterials Based on Black Phosphorous/Dielectric Multilayer Structures,” J. Lightwave Technol. 37(13), 3290–3297 (2019).
[Crossref]

H. Zeng, Y. Zhang, F. Lan, S. Liang, L. Wang, T. Song, T. Zhang, Z. Shi, Z. Yang, X. Kang, X. Zhang, P. Mazumder, and D. M. Mittleman, “Terahertz Dual-Polarization Beam Splitter Via an Anisotropic Matrix Metasurface,” IEEE Trans. Terahertz Sci. Technol. 9(5), 491–497 (2019).
[Crossref]

Y. Guo, S. Wang, Y. Zhou, C. Chen, J. Zhu, R. Wang, and Y. Cai, “Broadband absorption enhancement of graphene in the ultraviolet range based on metal-dielectric-metal configuration,” J. Appl. Phys. 126(21), 213103 (2019).
[Crossref]

Y. Tian, J. Qiu, C. Liu, S. Tian, Z. Huang, and J. Wu, “Compact polarization beam splitter with a high extinction ratio over S + C + L band,” Opt. Express 27(2), 999–1009 (2019).
[Crossref]

Y. Lin, X. Liu, H. Chen, X. Guo, J. Pan, J. Yu, H. Zheng, H. Guan, H. Lu, Y. Zhong, Y. Chen, Y. Luo, W. Zhu, and Z. Chen, “Tunable asymmetric spin splitting by black phosphorus sandwiched epsilon-near-zero-metamaterial in the terahertz region,” Opt. Express 27(11), 15868–15879 (2019).
[Crossref]

Z. Liu, “Omnidirectional polarization beam splitter for white light,” Opt. Express 27(5), 7673–7684 (2019).
[Crossref]

2018 (9)

W. Shen, C. Hu, S. Huo, Z. Sun, S. Fan, J. Liu, and X. Hu, “Wavelength tunable polarizer based on layered black phosphorus on Si/SiO 2 substrate,” Opt. Lett. 43(6), 1255–1258 (2018).
[Crossref]

S. Saberi-Pouya, T. Vazifehshenas, M. Saleh, M. Farmanbar, and T. Salavati-fard, “Plasmon modes in monolayer and double-layer black phosphorus under applied uniaxial strain,” J. Appl. Phys. 123(17), 174301 (2018).
[Crossref]

L. Han, L. Wang, H. Xing, and X. Chen, “Active Tuning of Midinfrared Surface Plasmon Resonance and Its Hybridization in Black Phosphorus Sheet Array,” ACS Photonics 5(9), 3828–3837 (2018).
[Crossref]

Z. Song, Q. Chu, L. Ye, Y. Liu, C. Zhu, and Q. H. Liu, “High-performance polarization beam splitter based on anisotropic plasmonic nanostructures,” Appl. Phys. B 124(9), 177 (2018).
[Crossref]

A. Ozer, N. Yilmaz, H. Kocer, and H. Kurt, “Polarization-insensitive beam splitters using all-dielectric phase gradient metasurfaces at visible wavelengths,” Opt. Lett. 43(18), 4350–4353 (2018).
[Crossref]

Y. Cai and K.-D. Xu, “Tunable broadband terahertz absorber based on multilayer graphene-sandwiched plasmonic structure,” Opt. Express 26(24), 31693–31705 (2018).
[Crossref]

S. Shah, X. Lin, L. Shen, M. Renuka, B. Zhang, and H. Chen, “Interferenceless Polarization Splitting Through Nanoscale van der Waals Heterostructures,” Phys. Rev. Appl. 10(3), 034025 (2018).
[Crossref]

X. Luo, X. Zhai, L. Wang, and Q. Lin, “Enhanced dual-band absorption of molybdenum disulfide using a plasmonic perfect absorber,” Opt. Express 26(9), 11658–11666 (2018).
[Crossref]

W. Zheng, A. Nemilentsau, D. Lattery, P. Wang, T. Low, J. Zhu, and X. Wang, “Direct Investigation of the Birefringent Optical Properties of Black Phosphorus with Picosecond Interferometry,” Adv. Opt. Mater. 6(1), 1700831 (2018).
[Crossref]

2017 (5)

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]

Y. Zhou, M. Zhang, Z. Guo, L. Miao, S.-T. Han, Z. Wang, X. Zhang, H. Zhang, and Z. Peng, “Recent advances in black phosphorus-based photonics, electronics, sensors and energy devices,” Mater. Horiz. 4(6), 997–1019 (2017).
[Crossref]

H. Gao, M. Pu, X. Li, X. Ma, Z. Zhao, Y. Guo, and X. Luo, “Super-resolution imaging with a Bessel lens realized by a geometric metasurface,” Opt. Express 25(12), 13933–13943 (2017).
[Crossref]

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Plasmon canalization and tunneling over anisotropic metasurfaces,” Phys. Rev. B 96(7), 075436 (2017).
[Crossref]

Y. Liu and P. P. Ruden, “Temperature-dependent anisotropic charge-carrier mobility limited by ionized impurity scattering in thin-layer black phosphorus,” Phys. Rev. B 95(16), 165446 (2017).
[Crossref]

2016 (4)

J. He, Z. Xie, W. Sun, X. Wang, Y. Ji, S. Wang, Y. Lin, and Y. Zhang, “Terahertz Tunable Metasurface Lens Based on Vanadium Dioxide Phase Transition,” Plasmonics 11(5), 1285–1290 (2016).
[Crossref]

K. V. Sreekanth, M. ElKabbash, Y. Alapan, A. R. Rashed, U. A. Gurkan, and G. Strangi, “A multiband perfect absorber based on hyperbolic metamaterials,” Sci. Rep. 6(1), 26272 (2016).
[Crossref]

V. Eswaraiah, Q. Zeng, Y. Long, and Z. Liu, “Black Phosphorus Nanosheets: Synthesis, Characterization and Applications,” Small 12(26), 3480–3502 (2016).
[Crossref]

T. Zhang, X. Yin, L. Chen, and X. Li, “Ultra-compact polarization beam splitter utilizing a graphene-based asymmetrical directional coupler,” Opt. Lett. 41(2), 356–359 (2016).
[Crossref]

2015 (2)

Y. Cai, J. Zhu, and Q. H. Liu, “Tunable enhanced optical absorption of graphene using plasmonic perfect absorbers,” Appl. Phys. Lett. 106(4), 043105 (2015).
[Crossref]

A. Forouzmand and A. B. Yakovlev, “Electromagnetic Cloaking of a Finite Conducting Wedge With a Nanostructured Graphene Metasurface,” IEEE Trans. Antennas Propag. 63(5), 2191–2202 (2015).
[Crossref]

2014 (2)

T. Chen and S. He, “Frequency-tunable circular polarization beam splitter using a graphene-dielectric sub-wavelength film,” Opt. Express 22(16), 19748–19757 (2014).
[Crossref]

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]

2012 (2)

Y. Du, S.-G. Li, S. Liu, X.-P. Zhu, and X.-X. Zhang, “Polarization splitting filter characteristics of Au-filled high-birefringence photonic crystal fiber,” Appl. Phys. B 109(1), 65–74 (2012).
[Crossref]

B. Das, C. S. Yelleswarapu, and D. V. G. L. N. Rao, “Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter,” Opt. Commun. 285(24), 4954–4960 (2012).
[Crossref]

2010 (1)

S. N. Burokur, J.-P. Daniel, P. Ratajczak, and A. de Lustrac, “Tunable bilayered metasurface for frequency reconfigurable directive emissions,” Appl. Phys. Lett. 97(6), 064101 (2010).
[Crossref]

2008 (4)

O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express 16(9), 6736–6744 (2008).
[Crossref]

J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. 92(7), 071114 (2008).
[Crossref]

J.-B. Yang and X.-Y. Su, “Optical implementation of a polarization-independent bidirectional 3 × 3 optical switch,” Photon. Netw. Commun. 15(2), 153–158 (2008).
[Crossref]

J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. 92(7), 071114 (2008).
[Crossref]

2007 (2)

J. Feng and Z. Zhou, “Polarization beam splitter using a binary blazed grating coupler,” Opt. Lett. 32(12), 1662–1664 (2007).
[Crossref]

H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87(2), 283–287 (2007).
[Crossref]

2006 (1)

2005 (1)

2004 (1)

Y. W. Lee, J. Jung, and B. Lee, “Multiwavelength-Switchable SOA-Fiber Ring Laser Based on Polarization-Maintaining Fiber Loop Mirror and Polarization Beam Splitter,” IEEE Photonics Technol. Lett. 16(1), 54–56 (2004).
[Crossref]

2003 (1)

1980 (1)

P. Yeh, “optics of anisotropic layered media:a new 4 X 4 matrix algebra,” Surf. Sci. 96(1-3), 41–53 (1980).
[Crossref]

Alapan, Y.

K. V. Sreekanth, M. ElKabbash, Y. Alapan, A. R. Rashed, U. A. Gurkan, and G. Strangi, “A multiband perfect absorber based on hyperbolic metamaterials,” Sci. Rep. 6(1), 26272 (2016).
[Crossref]

Alù, A.

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Plasmon canalization and tunneling over anisotropic metasurfaces,” Phys. Rev. B 96(7), 075436 (2017).
[Crossref]

Azzam, R. M. A.

Beigang, R.

Burokur, S. N.

S. N. Burokur, J.-P. Daniel, P. Ratajczak, and A. de Lustrac, “Tunable bilayered metasurface for frequency reconfigurable directive emissions,” Appl. Phys. Lett. 97(6), 064101 (2010).
[Crossref]

Cai, Y.

Y. Guo, S. Wang, Y. Zhou, C. Chen, J. Zhu, R. Wang, and Y. Cai, “Broadband absorption enhancement of graphene in the ultraviolet range based on metal-dielectric-metal configuration,” J. Appl. Phys. 126(21), 213103 (2019).
[Crossref]

Y. Cai and K.-D. Xu, “Tunable broadband terahertz absorber based on multilayer graphene-sandwiched plasmonic structure,” Opt. Express 26(24), 31693–31705 (2018).
[Crossref]

Y. Cai, J. Zhu, and Q. H. Liu, “Tunable enhanced optical absorption of graphene using plasmonic perfect absorbers,” Appl. Phys. Lett. 106(4), 043105 (2015).
[Crossref]

Carvalho, A.

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]

Castro Neto, A. H.

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]

Chen, C.

Y. Guo, S. Wang, Y. Zhou, C. Chen, J. Zhu, R. Wang, and Y. Cai, “Broadband absorption enhancement of graphene in the ultraviolet range based on metal-dielectric-metal configuration,” J. Appl. Phys. 126(21), 213103 (2019).
[Crossref]

Chen, H.

Chen, L.

Chen, T.

Chen, X.

L. Han, L. Wang, H. Xing, and X. Chen, “Active Tuning of Midinfrared Surface Plasmon Resonance and Its Hybridization in Black Phosphorus Sheet Array,” ACS Photonics 5(9), 3828–3837 (2018).
[Crossref]

Chen, Y.

Y. Lin, X. Liu, H. Chen, X. Guo, J. Pan, J. Yu, H. Zheng, H. Guan, H. Lu, Y. Zhong, Y. Chen, Y. Luo, W. Zhu, and Z. Chen, “Tunable asymmetric spin splitting by black phosphorus sandwiched epsilon-near-zero-metamaterial in the terahertz region,” Opt. Express 27(11), 15868–15879 (2019).
[Crossref]

J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. 92(7), 071114 (2008).
[Crossref]

J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. 92(7), 071114 (2008).
[Crossref]

Chen, Z.

Cheng, L.

Chu, Q.

Z. Song, Q. Chu, L. Ye, Y. Liu, C. Zhu, and Q. H. Liu, “High-performance polarization beam splitter based on anisotropic plasmonic nanostructures,” Appl. Phys. B 124(9), 177 (2018).
[Crossref]

Correas-Serrano, D.

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz, “Plasmon canalization and tunneling over anisotropic metasurfaces,” Phys. Rev. B 96(7), 075436 (2017).
[Crossref]

Daniel, J.-P.

S. N. Burokur, J.-P. Daniel, P. Ratajczak, and A. de Lustrac, “Tunable bilayered metasurface for frequency reconfigurable directive emissions,” Appl. Phys. Lett. 97(6), 064101 (2010).
[Crossref]

Das, B.

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Zhang, M.

Y. Zhou, M. Zhang, Z. Guo, L. Miao, S.-T. Han, Z. Wang, X. Zhang, H. Zhang, and Z. Peng, “Recent advances in black phosphorus-based photonics, electronics, sensors and energy devices,” Mater. Horiz. 4(6), 997–1019 (2017).
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Y. Zhou, M. Zhang, Z. Guo, L. Miao, S.-T. Han, Z. Wang, X. Zhang, H. Zhang, and Z. Peng, “Recent advances in black phosphorus-based photonics, electronics, sensors and energy devices,” Mater. Horiz. 4(6), 997–1019 (2017).
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Zhang, X.-X.

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H. Zeng, Y. Zhang, F. Lan, S. Liang, L. Wang, T. Song, T. Zhang, Z. Shi, Z. Yang, X. Kang, X. Zhang, P. Mazumder, and D. M. Mittleman, “Terahertz Dual-Polarization Beam Splitter Via an Anisotropic Matrix Metasurface,” IEEE Trans. Terahertz Sci. Technol. 9(5), 491–497 (2019).
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Zhu, Z.

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).
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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic of phosphorene-assisted PBS. (b) A unit cell of the proposed PBS, the fixed unit cell period L is 40 nm, the W is the strip width. (c) An equivalent layer, where the conductivities along the AC and ZZ direction are $|\sigma _{\textrm{AC}}^{\textrm{eff}}|,|\sigma _{\textrm{ZZ}}^{\textrm{eff}}|$, respectively.
Fig. 2.
Fig. 2. Real (solid line) and imaginary (dashed line) parts of conductivity along with the armchair and zigzag directions of phosphorene for (a) monolayer BP and (b) metasurface composed of BP ribbons. (c) The anisotropic ratio of conductivity. (d) The permittivity of the equivalent layer.
Fig. 3.
Fig. 3. (a) Numerical and simulated results for the dependence of frequency on the reflectivity and transmissivity of the PBS when p-(s-) polarized light beam is incident at γ = 45°. (b) Dependence of incident angle of the p-(s-) polarized light beam on the reflectivity and transmissivity of PBS, where the operation frequency is 80.4 THz. (c) Reflectivity and transmission of PBS as a function of the frequency at γ = 45°, where ribbons of monolayer BP are not constructed. (d) Reflectivity and transmission as a function of the incident angle at the operation frequency of 80.4 THz, where ribbons of monolayer BP are not constructed.
Fig. 4.
Fig. 4. (a)/(b) the effective wave impedance of the vacuum and the anisotropic slab when the incident angle of the s- (p-) polarized light beam is 45°.
Fig. 5.
Fig. 5. (a) Normalized electrical field distribution of PBS (b) Normalized magnetic field distribution of PBS, in the (a) and (b), the incident angles are 20°,40°, and 60° when the frequency of the p-polarized light beam is 80.4 THz. (c) Normalized electrical field distribution of PBS (d) Normalized magnetic field distribution of PBS, in the (c) and (d), the operation frequencies are 75.0 THz, 83.0 THz, and 85.0 THz when the incident angle of the p-polarized light beam is 45°.
Fig. 6.
Fig. 6. (a)/(b) Reflectivity and transmissivity when the incident light is s-polarized. (c)/(d) Reflectivity and transmissivity when the incident light is p-polarized.
Fig. 7.
Fig. 7. (a)/(b) Reflectivity and transmissivity of PBS with the width of the BP ribbon set as 34 nm, 35 nm, and 36 nm for s-(p-) polarization, where the incident angle is 45°. (c)/(d) Reflectivity and transmissivity of PBS with the width of the BP ribbon set as 34 nm, 35 nm, and 36 nm for s-(p-) polarization, when the operation wavelength is 80.4 THz.
Fig. 8.
Fig. 8. (a)/(b) Reflectivity and transmissivity of PBS with the electron concentration ns set as 4×1013 cm−2, 5×1013 cm−2, and 6×1013 cm−2 for s-(p-) polarization when the incident angle is 45°. (c)/(d) Reflectivity and transmissivity of PBS with the electron concentration ns set as 4×1013 cm−2, 5×1013 cm−2, and 6×1013 cm−2 for s-(p-) polarization when the operation wavelength is 80.4 THz.

Tables (1)

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Table 1. Comparison of the PBS performance based on various 2D materials

Equations (11)

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σ j = i D j / ( π ( ω + i η / ) ) , j = AC,ZZ
D j = π e 2 n s / m j
ε j = ε r + i σ j / ( ω ε 0 d bp ) , j = AC,ZZ
C eff = ( 2 L ε 0 / π ) log [ 1 / sin π ( L W ) / ( 2 L ) ]
σ ZZ eff = ( W / L ) σ ZZ
σ AC eff = ( 1 / σ AC + i / ( ω C eff ) ) 1
( A s B s A p B p ) = ( M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ) ( C s 0 C P 0 )
R pp = | ( M 11 M 43 M 41 M 13 ) / ( M 11 M 33 M 13 M 31 ) | 2
T pp = | M 11 / ( M 11 M 33 M 13 M 31 ) | 2
R ss = | ( M 21 M 33 M 23 M 31 ) / ( M 11 M 33 M 13 M 31 ) | 2
T ss = | M 33 / ( M 11 M 33 M 13 M 31 ) | 2