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Enhancement of THz absorption in monolayer graphene for light at Brewster angle incidence
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Physics Letters A ••• (••••) ••••••
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Enhancement of THz absorption in monolayer graphene for light at Brewster angle incidence Jun Wu Department of Physics, Zhejiang University of Science and Technology, Hangzhou, 310023, China
a r t i c l e
i n f o
Article history: Received 19 May 2019 Received in revised form 29 July 2019 Accepted 16 September 2019 Available online xxxx Communicated by A. Eisfeld Keywords: Graphene Brewster angle Guided mode resonance Spectrum selective absorption
a b s t r a c t The enhancement of absorption in graphene for light at Brewster angle incidence is investigated. It is achieved by placing a graphene on a resonant Brewster filter that incorporating a spacer layer. The absorber presents above 50% absorption at resonance, which is attributed to the excitation of guided mode resonances. The electromagnetic field intensity distributions are illustrated to intuitively confirm the physical mechanism of such phenomenon. Moreover, the influence of geometric parameters on absorption is investigated to provide a useful guidance for practical fabrication. Besides, it is found that the absorption properties not only can be controlled by adjusting the incident angle but also can be dynamically tuned by changing the Fermi level. Last, the graphene absorption can be easily extended to multichannel by only an increase in the thickness of spacer. The results open new avenues for combining graphene with general guided mode resonance structure to enable novel optoelectronics device applications. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In the past few years, Terahertz (THz) technology has attracted tremendous research interests due to its growing applications on communications, medical imaging, sensing and security [1–4]. Though increased research efforts have been made to investigate THz phenomena, high-performance terahertz devices are still lacking. Among these, THz absorbers are highly desirable due to their potential applications in high-resolution terahertz imaging, detecting, sensing and modulation for security and biomedicine [5–8]. Therefore, enhancement of THz wave absorption is the key factor in the realization of THz properties. In the past decade, metamaterials and metasurfaces have been employed to develop THz absorbers [9–11]. However, the absorbers proposed above, are static which can not be dynamically tuned in a wide frequency range. Fortunately, graphene, as a two-dimensional form of carbon with the atoms arranged in a honeycomb lattice, was considered as a viable candidate in realizing tunable THz absorbers because of its extraordinary electric, optical, mechanical and thermal properties [12–14]. At THz frequency, graphene surface plasmon polaritons can be excited, which exhibits extreme field confinement to the interface and low damping losses compared to the typical surface plasmon polaritons on metal surface [15,16]. More importantly, its conductivity can be tuned by means
E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2019.125994 0375-9601/© 2019 Elsevier B.V. All rights reserved.
of external gate voltages, which makes graphene-based devices flexible tunable without re-fabricating a new structure [17]. To enable these properties for application in perfect absorbers [18–22], modulators [23,24], optical polarization encoding [25], asymmetric transmission [26], biosensors [27], photodetectors [28], and plasmonic waveguides [29], a key issue that must be addressed is to enhance absorption in graphene monolayer, since the lightgraphene interaction is extreme weak due to the ultrathin thickness of graphene. To address this problem, different kinds of structures have been proposed, such as depositing a graphene monolayer on a dielectric spacer supported by a metallic layer [30], combining graphene with cross-shaped metallic resonator [31], graphene-based one-dimensional photonic crystals [32], based on graphene-SiO2 -Si-dielectrics-metallic ground plane structures [33], a tunable multichannel absorber based on graphene circular rings structure [34], realizing multichannel tunable perfect absorption with metal-distributed Bragg reflector [35]. Though nearly perfect absorption has been achieved in mixed metallic-graphene structures [30,31,33,34], some of the energy are absorbed by the metallic layer. A scheme for enhancement of light absorption in monolayer graphene based on Brewster filter was proposed in ref. [36]. However, the Brewster grating is composed of different materials with high and low refractive indices, which is disadvantages for real fabrication. In this work, the enhancement of absorption in graphene monolayer with guided mode resonances (GMRs) effect is investigated. It is achieved by placing a monolayer graphene on a reso-
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monochromatic plane wave incident from the air have incident angle θ . In the THz frequency range, the complex surface conductivity of graphene can be described by means of the following Drude-like expression [38,39]:
σ (ω ) =
Fig. 1. Schematic diagram of the proposed graphene absorber. d is the period of dielectric grating; h and w are the corresponding thickness and width, respectively; h f is the thickness of absentee layer.
e2 E f
2. Design and results The representation of the proposed graphene absorber is shown in Fig. 1, which consists of a monolayer graphene deposited on a resonant waveguide-grating Brewster filter that incorporating an absentee layer. The concept of resonant Brewster filter incorporating an absentee layer was proposed by group of R. Magnusson in 2002 [37]. It contains a dielectric grating and a substrate separated by a dielectric spacer. Such Brewster filter exhibits an angular resonance located at the Brewster angle with sideband reflectance suppressed by application of a half-wavelength absentee spacer [37]. The structure is characterized by the periodic interval d, the width w and the thickness h of grating, the thickness h f of the dielectric spacer and the graphene monolayer. The refractive indices of grating and dielectric spacer are nh = 1.78 and n f = 1.78, respectively. In addition, a dielectric slab with a refractive index of 1.45 is employed as a semi-infinite substrate for practical fabrication. A TM polarization (with magnetic field parallel to y-direction)
(1)
Here, E f and τ are the Fermi energy level and the carrier relaxation time, respectively; h¯ is the reduced Planck’s constant, e is the elementary charge, ω is the angular frequency. In this work, the relaxation time is fixed as τ = 1.0 ps. The Fermi energy level is initially selected as E f = 0.3 eV and its influence on absorption properties will be investigated latter. In our simulation, the monolayer graphene is considered as a thin layer of thickness h g = 0.34 nm with a permittivity:
εg = 1 + nant waveguide-grating Brewster filter that incorporating an absentee layer. The electromagnetic field intensity distributions at resonant frequency are plotted to intuitively confirm the physical mechanism of such enhanced absorption phenomenon. Next, the influences of different factors, such as geometric parameters and incident angle, on the absorption properties are investigated in detail to provide a useful guidance for practical applications. Lastly, the influence of Fermi level on the absorption spectra is investigated, so as to demonstrate the tunability of the proposed structure.
i
π h¯ 2 ω + i τ −1
i σ (ω)
ε0 ωh g
(2)
where ε0 is the relative permittivity of vacuum. The method of rigorous coupled-wave analysis (RCWA) [40, 41] is employed to calculate the absorption A, which was obtained by employing A = 1 − R − T , where R is the reflection, and T is the transmission. With some computational efforts, we obtain the structure parameters of the designed absorber, which is shown as follows: d = 18 μm, w = 9.9 μm, h = 2.1 μm, and h f = 13.5 μm. A TM polarization light is incident at Brewster angle, which is θ = 55.1◦ calculated by employing thin film theory [42]. The calculated absorption, reflection and transmission spectra for TM polarization under Brewster angle incidence are shown in Fig. 2(a). Clearly, a resonant peak with about 53.62% absorption is observed at the frequency of 7.13 THz. And the reflection and transmission are very low at the resonant frequency. Moreover, the frequency bandwidth is about 0.0055 THz (ν ) with a quality factor ( Q = ν /ν , ν is the resonant frequency) of about 1300, which exhibits an ultranarrow absorption profile. Fig. 2(b) shows the absorption response of the monolayer graphene as a function of incident angle at the frequency of 7.13 THz. It is found that a resonant absorption peak with low sideband is achieved at the Brewster angle and linewidth of angle is about 0.25◦ , showing an ultranarrow angle linewidth. To intuitively disclose the potential physical mechanism of such enhanced absorption behavior, we show the electromagnetic field intensity distributions at the resonant frequency in Fig. 3. As shown in Fig. 3(a), the magnetic field is strongly enhanced and concentrated mostly in the spacer. In addition, it presents a clear standing wave profile along x-direction, which is a typical feature of a guided mode. Thus, when a TM polarization light is incident
Fig. 2. (a) The simulated absorption, reflection and transmission spectra for TM polarization wave under Brewster angle incidence; (b) absorption versus angle of incidence at frequency of 7.13 THz.
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Fig. 3. (a) Normalized magnetic field intensity distributions of | H y / H 0 |2 ; (b) electric field intensity distributions of | E |2 . The regions enclosed by the white dash line are the dielectric grating and the region enclosed by the black dash line is the spacer. A monolayer graphene is deposited on the dielectric grating and it can not be displayed due to its ultrathin thickness. The origin of the z-axis is located at a surface 5 μm below the spacer. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
Fig. 4. Graphene absorption as a function of incident angle and (a) duty cycle f , (b) the grating thickness and (c) the spacer thickness at the operating frequency of 7.13 THz.
at Brewster angle, guided mode resonance is excited at the spacer. At the same time, the electric field is strongly enhanced at the top surface of the grating where graphene monolayer is coated, as illustrated in Fig. 3(b). Such strongly enhanced electric field will boost the absorption in graphene, as the time-averaged power loss density is calculated by [43]: d P loss /dV = 1/2ε0 ωIm(ω)| E |2 , where ω is the angular frequency, Im(ε) denotes the imaginary part of relative permittivity, and E is the electric field. The enhanced absorption in graphene monolayer is attributed to the general GMRs excited in the spacer by magnetic field. 3. Discussion Typically, the GMR is sensitive to the variation of geometric parameters, which correspondingly leads to the change of absorption peak. Thus, the geometry tolerance should be controlled in a certain range during the fabrication process of this device. To provide a useful guidance for practical fabrication, we investigate the influence of geometric parameters on the graphene absorption, which is shown in Fig. 4. Fig. 4(a) shows the absorption as a function of incident angle and duty cycle ( f = w /d). It can be seen that increasing f from 0.2 to 0.95 results in the shift of resonant angle from 56◦ to 53.8◦ , and the peak absorption is fluctuant with the variation of f . Overall, the influence of f on the absorption performance is small. From Fig. 4(b), we can see that the resonant absorption at Brewster angle is almost unchanged when increasing h from 2.0 μm to 2.2 μm. However, the absorption angle shifts almost linearly with the variation of h f . Such phenomenon is attributed to the GMRs excited in the spacer, which results in a larger shift of absorption angle with the change of h f . The ab-
Fig. 5. Graphene absorption as a function of frequency and incident angle.
sorption angle of the proposed structure has less sensitivity to the grating parameters and changes linearly with the spacer thickness, which reduces the fabrication difficult as the spacer thickness is easier to control than the grating parameters during producing process. Thus our structure is superior to the scheme proposed in ref. [36], where the absorption angle is more sensitive to the variation of grating parameters. For an absorber, the absorbance should be remained high for a wide range of incident angles. To investigate the angular sensitivity, we show the absorption as functions of incident angle and frequency in Fig. 5. Clearly, the resonant frequency exhibits redshift with the increase of the incident angle and the absorbance is also changed accordingly. Such behavior is attributed to the GMRs, which is sensitive to the variation of incident angle. This feature
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Fig. 6. Graphene absorption for different Fermi level with the variation of (a) frequency for light at Brewster angle incidence, (b) incident angle at operating frequency of 7.13 THz.
For practical fabrication, the resonant waveguide-grating Brewster filter can be easily fabricated by the traditional lithography. Then, a commercial CVD-grown monolayer graphene can be directly transferred onto the filter by conventional wet-base transfer method. Beside, as stated above, the absorption properties can be remained with large geometric parameter tolerance. Both of which will benefit the real application. 4. Conclusions
Fig. 7. Absorption spectra for h f = 32 μm.
makes the designed absorber can be regarded as a thermal emitter with a high directivity [44]. Subsequently, we discuss the manipulation of light absorption by adjusting the Fermi level of monolayer graphene. In practical application, to turn the Fermi level of graphene, two electrodes can be fabricated by thermal deposition, one was on graphene and the other one was on the absentee layer for the gate voltage. The simulated graphene absorption for different Fermi levels with the variation of frequency for light at Brewster angle incidence and of incident angle at operating frequency of 7.13 THz are presented in Figs. 6(a) and 6(b), respectively. As shown in Fig. 6(a), when the Fermi level increases from 0.2 eV to 0.4 eV, the absorption spectra experiences a blueshift. In addition, with the Fermi level deviating from the optimized value, the peak absorption reduces accordingly. From Fig. 6(b), it is found that the absorption angle increases with the increase of Fermi level, which exhibits a similar trend as the variation of absorption spectra. Therefore, the absorption properties of the proposed absorber can be flexibly tunable by adjusting the Fermi level without re-fabricating the device, which is particular attractive for real applications. Though a single-band graphene absorber is investigated in this work, it can be easily extended to a multichannel absorber by adjusting the physical dimensional. For this purpose, we show the absorption spectra for h f = 32 μm in Fig. 7, where other geometric parameters are the same as before. Clearly, two resonant absorption peaks are observed at frequencies 6.6525 THz and 7.2415 THz, with the corresponding absorbance above 40%. As guided mode resonance is excited in the spacer, increasing the thickness of spacer will generate additional guided modes, leading to the realization of multichannel absorption in graphene monolayer. This feature is particular fascinating as the absorption channels can be easily extended without re-optimizing the geometric parameters.
In summary, a tunable THz graphene absorber for light at Brewster angle incidence is proposed and investigated. It consists of a monolayer graphene on a resonant waveguide-grating Brewster filter that incorporating a spacer layer. A resonant peak with absorption above 50% is achieved, which is attributed to the excitation of GMRs in the spacer layer. Moreover, it is found that the absorption properties can be remained with large geometric parameter tolerance, which will benefit the real fabrication. More importantly, the absorption performance not only can be manipulated by changing the incident angle without re-optimizing the geometric parameters but also can be flexibly tunable by adjusting the Fermi level without re-fabricating the device, which is particular attractive for real applications. We also found that the graphene absorption can be easily extended to multichannel by increasing the space thickness. The conclusions points to a new opportunity to combine graphene with general guided mode resonances structure to enable novel optoelectronics device applications in the field of THz devices. Acknowledgements The authors acknowledge the support of National Natural Science Foundation of China (61405217). References [1] G.P. Williams, Filling the THz gap-high power sources and applications, Rep. Prog. Phys. 69 (2) (2006) 301–326. [2] M. Tonouchi, Cutting-edge terahertz technology, Nat. Photonics 1 (2) (2007) 97–105. [3] P.U. Jepsen, D.G. Cooke, M. Koch, Terahertz spectroscopy and imaging-modern techniques and applications, Laser Photonics Rev. 5 (2011) 124–166. [4] J. Federici, L. Moeller, Review of terahertz and subterahertz wireless communications, J. Appl. Phys. 107 (11) (2010) 111101. [5] J. Wang, J. Gou, W. Li, Preparation of room temperature terahertz detector with lithium tantalate crystal and thin film, AIP Adv. 4 (2014) 97–105. [6] M. Diem, T. Koschny, C.M. Soukoulis, Wide-angle perfect absorber/thermal emitter in the terahertz regime, Phys. Rev. B, Condens. Matter 79 (2008) 033101. [7] R. Yahiaoui, et al., Multispectral terahertz sensing with highly flexible ultrathin metamaterial absorber, J. Appl. Phys. 118 (2015) 083103. [8] S. Savo, D. Shrekenhamer, W.J. Padilla, Liquid crystal metamaterial absorber spatial light modulator for THz applications, Adv. Opt. Mater. 2 (2014) 275–279.
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[m5G; v1.261; Prn:24/09/2019; 15:38] P.1 (1-5)
Physics Letters A ••• (••••) ••••••
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Enhancement of THz absorption in monolayer graphene for light at Brewster angle incidence Jun Wu Department of Physics, Zhejiang University of Science and Technology, Hangzhou, 310023, China
a r t i c l e
i n f o
Article history: Received 19 May 2019 Received in revised form 29 July 2019 Accepted 16 September 2019 Available online xxxx Communicated by A. Eisfeld Keywords: Graphene Brewster angle Guided mode resonance Spectrum selective absorption
a b s t r a c t The enhancement of absorption in graphene for light at Brewster angle incidence is investigated. It is achieved by placing a graphene on a resonant Brewster filter that incorporating a spacer layer. The absorber presents above 50% absorption at resonance, which is attributed to the excitation of guided mode resonances. The electromagnetic field intensity distributions are illustrated to intuitively confirm the physical mechanism of such phenomenon. Moreover, the influence of geometric parameters on absorption is investigated to provide a useful guidance for practical fabrication. Besides, it is found that the absorption properties not only can be controlled by adjusting the incident angle but also can be dynamically tuned by changing the Fermi level. Last, the graphene absorption can be easily extended to multichannel by only an increase in the thickness of spacer. The results open new avenues for combining graphene with general guided mode resonance structure to enable novel optoelectronics device applications. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In the past few years, Terahertz (THz) technology has attracted tremendous research interests due to its growing applications on communications, medical imaging, sensing and security [1–4]. Though increased research efforts have been made to investigate THz phenomena, high-performance terahertz devices are still lacking. Among these, THz absorbers are highly desirable due to their potential applications in high-resolution terahertz imaging, detecting, sensing and modulation for security and biomedicine [5–8]. Therefore, enhancement of THz wave absorption is the key factor in the realization of THz properties. In the past decade, metamaterials and metasurfaces have been employed to develop THz absorbers [9–11]. However, the absorbers proposed above, are static which can not be dynamically tuned in a wide frequency range. Fortunately, graphene, as a two-dimensional form of carbon with the atoms arranged in a honeycomb lattice, was considered as a viable candidate in realizing tunable THz absorbers because of its extraordinary electric, optical, mechanical and thermal properties [12–14]. At THz frequency, graphene surface plasmon polaritons can be excited, which exhibits extreme field confinement to the interface and low damping losses compared to the typical surface plasmon polaritons on metal surface [15,16]. More importantly, its conductivity can be tuned by means
E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2019.125994 0375-9601/© 2019 Elsevier B.V. All rights reserved.
of external gate voltages, which makes graphene-based devices flexible tunable without re-fabricating a new structure [17]. To enable these properties for application in perfect absorbers [18–22], modulators [23,24], optical polarization encoding [25], asymmetric transmission [26], biosensors [27], photodetectors [28], and plasmonic waveguides [29], a key issue that must be addressed is to enhance absorption in graphene monolayer, since the lightgraphene interaction is extreme weak due to the ultrathin thickness of graphene. To address this problem, different kinds of structures have been proposed, such as depositing a graphene monolayer on a dielectric spacer supported by a metallic layer [30], combining graphene with cross-shaped metallic resonator [31], graphene-based one-dimensional photonic crystals [32], based on graphene-SiO2 -Si-dielectrics-metallic ground plane structures [33], a tunable multichannel absorber based on graphene circular rings structure [34], realizing multichannel tunable perfect absorption with metal-distributed Bragg reflector [35]. Though nearly perfect absorption has been achieved in mixed metallic-graphene structures [30,31,33,34], some of the energy are absorbed by the metallic layer. A scheme for enhancement of light absorption in monolayer graphene based on Brewster filter was proposed in ref. [36]. However, the Brewster grating is composed of different materials with high and low refractive indices, which is disadvantages for real fabrication. In this work, the enhancement of absorption in graphene monolayer with guided mode resonances (GMRs) effect is investigated. It is achieved by placing a monolayer graphene on a reso-
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monochromatic plane wave incident from the air have incident angle θ . In the THz frequency range, the complex surface conductivity of graphene can be described by means of the following Drude-like expression [38,39]:
σ (ω ) =
Fig. 1. Schematic diagram of the proposed graphene absorber. d is the period of dielectric grating; h and w are the corresponding thickness and width, respectively; h f is the thickness of absentee layer.
e2 E f
2. Design and results The representation of the proposed graphene absorber is shown in Fig. 1, which consists of a monolayer graphene deposited on a resonant waveguide-grating Brewster filter that incorporating an absentee layer. The concept of resonant Brewster filter incorporating an absentee layer was proposed by group of R. Magnusson in 2002 [37]. It contains a dielectric grating and a substrate separated by a dielectric spacer. Such Brewster filter exhibits an angular resonance located at the Brewster angle with sideband reflectance suppressed by application of a half-wavelength absentee spacer [37]. The structure is characterized by the periodic interval d, the width w and the thickness h of grating, the thickness h f of the dielectric spacer and the graphene monolayer. The refractive indices of grating and dielectric spacer are nh = 1.78 and n f = 1.78, respectively. In addition, a dielectric slab with a refractive index of 1.45 is employed as a semi-infinite substrate for practical fabrication. A TM polarization (with magnetic field parallel to y-direction)
(1)
Here, E f and τ are the Fermi energy level and the carrier relaxation time, respectively; h¯ is the reduced Planck’s constant, e is the elementary charge, ω is the angular frequency. In this work, the relaxation time is fixed as τ = 1.0 ps. The Fermi energy level is initially selected as E f = 0.3 eV and its influence on absorption properties will be investigated latter. In our simulation, the monolayer graphene is considered as a thin layer of thickness h g = 0.34 nm with a permittivity:
εg = 1 + nant waveguide-grating Brewster filter that incorporating an absentee layer. The electromagnetic field intensity distributions at resonant frequency are plotted to intuitively confirm the physical mechanism of such enhanced absorption phenomenon. Next, the influences of different factors, such as geometric parameters and incident angle, on the absorption properties are investigated in detail to provide a useful guidance for practical applications. Lastly, the influence of Fermi level on the absorption spectra is investigated, so as to demonstrate the tunability of the proposed structure.
i
π h¯ 2 ω + i τ −1
i σ (ω)
ε0 ωh g
(2)
where ε0 is the relative permittivity of vacuum. The method of rigorous coupled-wave analysis (RCWA) [40, 41] is employed to calculate the absorption A, which was obtained by employing A = 1 − R − T , where R is the reflection, and T is the transmission. With some computational efforts, we obtain the structure parameters of the designed absorber, which is shown as follows: d = 18 μm, w = 9.9 μm, h = 2.1 μm, and h f = 13.5 μm. A TM polarization light is incident at Brewster angle, which is θ = 55.1◦ calculated by employing thin film theory [42]. The calculated absorption, reflection and transmission spectra for TM polarization under Brewster angle incidence are shown in Fig. 2(a). Clearly, a resonant peak with about 53.62% absorption is observed at the frequency of 7.13 THz. And the reflection and transmission are very low at the resonant frequency. Moreover, the frequency bandwidth is about 0.0055 THz (ν ) with a quality factor ( Q = ν /ν , ν is the resonant frequency) of about 1300, which exhibits an ultranarrow absorption profile. Fig. 2(b) shows the absorption response of the monolayer graphene as a function of incident angle at the frequency of 7.13 THz. It is found that a resonant absorption peak with low sideband is achieved at the Brewster angle and linewidth of angle is about 0.25◦ , showing an ultranarrow angle linewidth. To intuitively disclose the potential physical mechanism of such enhanced absorption behavior, we show the electromagnetic field intensity distributions at the resonant frequency in Fig. 3. As shown in Fig. 3(a), the magnetic field is strongly enhanced and concentrated mostly in the spacer. In addition, it presents a clear standing wave profile along x-direction, which is a typical feature of a guided mode. Thus, when a TM polarization light is incident
Fig. 2. (a) The simulated absorption, reflection and transmission spectra for TM polarization wave under Brewster angle incidence; (b) absorption versus angle of incidence at frequency of 7.13 THz.
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Fig. 3. (a) Normalized magnetic field intensity distributions of | H y / H 0 |2 ; (b) electric field intensity distributions of | E |2 . The regions enclosed by the white dash line are the dielectric grating and the region enclosed by the black dash line is the spacer. A monolayer graphene is deposited on the dielectric grating and it can not be displayed due to its ultrathin thickness. The origin of the z-axis is located at a surface 5 μm below the spacer. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
Fig. 4. Graphene absorption as a function of incident angle and (a) duty cycle f , (b) the grating thickness and (c) the spacer thickness at the operating frequency of 7.13 THz.
at Brewster angle, guided mode resonance is excited at the spacer. At the same time, the electric field is strongly enhanced at the top surface of the grating where graphene monolayer is coated, as illustrated in Fig. 3(b). Such strongly enhanced electric field will boost the absorption in graphene, as the time-averaged power loss density is calculated by [43]: d P loss /dV = 1/2ε0 ωIm(ω)| E |2 , where ω is the angular frequency, Im(ε) denotes the imaginary part of relative permittivity, and E is the electric field. The enhanced absorption in graphene monolayer is attributed to the general GMRs excited in the spacer by magnetic field. 3. Discussion Typically, the GMR is sensitive to the variation of geometric parameters, which correspondingly leads to the change of absorption peak. Thus, the geometry tolerance should be controlled in a certain range during the fabrication process of this device. To provide a useful guidance for practical fabrication, we investigate the influence of geometric parameters on the graphene absorption, which is shown in Fig. 4. Fig. 4(a) shows the absorption as a function of incident angle and duty cycle ( f = w /d). It can be seen that increasing f from 0.2 to 0.95 results in the shift of resonant angle from 56◦ to 53.8◦ , and the peak absorption is fluctuant with the variation of f . Overall, the influence of f on the absorption performance is small. From Fig. 4(b), we can see that the resonant absorption at Brewster angle is almost unchanged when increasing h from 2.0 μm to 2.2 μm. However, the absorption angle shifts almost linearly with the variation of h f . Such phenomenon is attributed to the GMRs excited in the spacer, which results in a larger shift of absorption angle with the change of h f . The ab-
Fig. 5. Graphene absorption as a function of frequency and incident angle.
sorption angle of the proposed structure has less sensitivity to the grating parameters and changes linearly with the spacer thickness, which reduces the fabrication difficult as the spacer thickness is easier to control than the grating parameters during producing process. Thus our structure is superior to the scheme proposed in ref. [36], where the absorption angle is more sensitive to the variation of grating parameters. For an absorber, the absorbance should be remained high for a wide range of incident angles. To investigate the angular sensitivity, we show the absorption as functions of incident angle and frequency in Fig. 5. Clearly, the resonant frequency exhibits redshift with the increase of the incident angle and the absorbance is also changed accordingly. Such behavior is attributed to the GMRs, which is sensitive to the variation of incident angle. This feature
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Fig. 6. Graphene absorption for different Fermi level with the variation of (a) frequency for light at Brewster angle incidence, (b) incident angle at operating frequency of 7.13 THz.
For practical fabrication, the resonant waveguide-grating Brewster filter can be easily fabricated by the traditional lithography. Then, a commercial CVD-grown monolayer graphene can be directly transferred onto the filter by conventional wet-base transfer method. Beside, as stated above, the absorption properties can be remained with large geometric parameter tolerance. Both of which will benefit the real application. 4. Conclusions
Fig. 7. Absorption spectra for h f = 32 μm.
makes the designed absorber can be regarded as a thermal emitter with a high directivity [44]. Subsequently, we discuss the manipulation of light absorption by adjusting the Fermi level of monolayer graphene. In practical application, to turn the Fermi level of graphene, two electrodes can be fabricated by thermal deposition, one was on graphene and the other one was on the absentee layer for the gate voltage. The simulated graphene absorption for different Fermi levels with the variation of frequency for light at Brewster angle incidence and of incident angle at operating frequency of 7.13 THz are presented in Figs. 6(a) and 6(b), respectively. As shown in Fig. 6(a), when the Fermi level increases from 0.2 eV to 0.4 eV, the absorption spectra experiences a blueshift. In addition, with the Fermi level deviating from the optimized value, the peak absorption reduces accordingly. From Fig. 6(b), it is found that the absorption angle increases with the increase of Fermi level, which exhibits a similar trend as the variation of absorption spectra. Therefore, the absorption properties of the proposed absorber can be flexibly tunable by adjusting the Fermi level without re-fabricating the device, which is particular attractive for real applications. Though a single-band graphene absorber is investigated in this work, it can be easily extended to a multichannel absorber by adjusting the physical dimensional. For this purpose, we show the absorption spectra for h f = 32 μm in Fig. 7, where other geometric parameters are the same as before. Clearly, two resonant absorption peaks are observed at frequencies 6.6525 THz and 7.2415 THz, with the corresponding absorbance above 40%. As guided mode resonance is excited in the spacer, increasing the thickness of spacer will generate additional guided modes, leading to the realization of multichannel absorption in graphene monolayer. This feature is particular fascinating as the absorption channels can be easily extended without re-optimizing the geometric parameters.
In summary, a tunable THz graphene absorber for light at Brewster angle incidence is proposed and investigated. It consists of a monolayer graphene on a resonant waveguide-grating Brewster filter that incorporating a spacer layer. A resonant peak with absorption above 50% is achieved, which is attributed to the excitation of GMRs in the spacer layer. Moreover, it is found that the absorption properties can be remained with large geometric parameter tolerance, which will benefit the real fabrication. More importantly, the absorption performance not only can be manipulated by changing the incident angle without re-optimizing the geometric parameters but also can be flexibly tunable by adjusting the Fermi level without re-fabricating the device, which is particular attractive for real applications. We also found that the graphene absorption can be easily extended to multichannel by increasing the space thickness. The conclusions points to a new opportunity to combine graphene with general guided mode resonances structure to enable novel optoelectronics device applications in the field of THz devices. Acknowledgements The authors acknowledge the support of National Natural Science Foundation of China (61405217). References [1] G.P. Williams, Filling the THz gap-high power sources and applications, Rep. Prog. Phys. 69 (2) (2006) 301–326. [2] M. Tonouchi, Cutting-edge terahertz technology, Nat. Photonics 1 (2) (2007) 97–105. [3] P.U. Jepsen, D.G. Cooke, M. Koch, Terahertz spectroscopy and imaging-modern techniques and applications, Laser Photonics Rev. 5 (2011) 124–166. [4] J. Federici, L. Moeller, Review of terahertz and subterahertz wireless communications, J. Appl. Phys. 107 (11) (2010) 111101. [5] J. Wang, J. Gou, W. Li, Preparation of room temperature terahertz detector with lithium tantalate crystal and thin film, AIP Adv. 4 (2014) 97–105. [6] M. Diem, T. Koschny, C.M. Soukoulis, Wide-angle perfect absorber/thermal emitter in the terahertz regime, Phys. Rev. B, Condens. Matter 79 (2008) 033101. [7] R. Yahiaoui, et al., Multispectral terahertz sensing with highly flexible ultrathin metamaterial absorber, J. Appl. Phys. 118 (2015) 083103. [8] S. Savo, D. Shrekenhamer, W.J. Padilla, Liquid crystal metamaterial absorber spatial light modulator for THz applications, Adv. Opt. Mater. 2 (2014) 275–279.
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