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Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range
Physica B ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Physica B journal homepage: www.elsevier.com/locate/physb
Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range Renxia Ning a,b, Shaobin Liu b,n, Haifeng Zhang b, Borui Bian b, Xiangkun Kong b a
College of Information Engineering, Huangshan University, Huangshan 245041,China Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 17 June 2014 Received in revised form 23 September 2014 Accepted 24 September 2014
Tunable absorption in periodic structure composed of graphene-based hyperbolic metamaterials (GHMMs) and isotropic medium is investigated by the transfer matrix method. The parallel part for relative permittivity of GHMMs consisting of monolayer graphene and conventional dielectric can be tuned by the chemical potential and dielectric layer thickness. The real part of the group index of GHMMs is insensitive to incident angle at the required frequency and the absorption of the periodic structure with GHMMs can be obtained nearly 100% at 22.4 terahertz (THz). The absorption peak of this frequency is almost uniform for both transverse electric (TE) and transverse magnetic (TE) polarizations. However, a new absorption peak can be observed incident angle is larger than 40 degree for TM polarization from 10 to 30 THz. The research results show that the absorption is insensitive to electromagnetic polarization at certain frequency. A new absorption peak can be found with TM polarization in low frequency region. These novel and effective GHMMs can replace metallic thin films as polarizing beam splitter for future optoelectronic applications. & 2014 Published by Elsevier B.V.
1. Introduction Graphene is a two-dimensional honeycomb structure with monolayer of carbon atom thickness, and is a type of gapless semiconductor [1–3]. Peculiar electronic properties have gained increasing interest from many researchers [4–9]. A single sheet of undoped graphene has single pass absorption of πα (2.3%), where α ¼e2/(ħc) is the quantum electrodynamics fine structure constant [10,11]. In many published works, researchers have focused on the absorption properties of graphene. Liu et al. [12] investigated absorption in graphene with resonant metal back reflector, which can be tuned by gate voltage with the terahertz (THz) spectra range. Peres et al. [13] studied the absorption of graphene on photonic crystal with the THz range, and they focused on the absorption can be enhanced by threefold with specific frequency range. Hashemi et al. [14] used metallic nanostructures to enhance light absorption in graphene by adjusting its structure. However, those results indicate that the absorption of graphene is still o50%. The low absorption is restricted in many applications, shch as photodetectors and saturable absorbers. Recently, perfect absorption of graphene has licited attention from researchers [15,16]. n
Corresponding author. E-mail address: [email protected] (S. Liu).
Previous results showed that the absorption is sensitive to electromagnetic polarization. However, the perfect absorption of polarization-insensitive graphene remains seldom studied. Hyperbolic metamaterials (HMMs) [17], namely anisotropic medium exhibiting hyperbolic shape of the dispersion relation, have been investigated on the THz [17], visible [18] and nearinfrared frequency regions [19]. A novel implementation of HMMs at far-infrared frequency range is composed of stacked graphene sheets separated by thin dielectric layers [19], which show that the GHMMs can become super absorbers for near-fields. HMMs can be designed into efficient and innovative absorbers which can enhance the decay rate of emitters near its surface [20]. The results can be applied to wide-angle absorption of the HMM structure. HMMs have various potential applications including negative refraction [21,22], optical waveguide [23] and imaging hyperlens [24]. To our knowledge, the perfect wide-angle absorption of HMMs has been rarely reported. We theoretically investigated the absorption of one-dimensional (1D) periodic structure of GHMMs. First, we discussed the refractive index of the structure of GHMMs with different chemical potentials and thickness of dielectric. The results may provide theoretical instructions for future optoelectronic applications of graphene. Second, a tunable absorption realized by 1D periodic structure composed of GHMMs and two kinds of isotropic dielectric is theoretically studied via transfer matrix method.
http://dx.doi.org/10.1016/j.physb.2014.09.038 0921-4526/& 2014 Published by Elsevier B.V.
Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
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Compared with Ref. [25], we present the different structures of the sheets as controlling parameters ranging from 10 THz to 30 THz. These results confirm the GHMMs mode absorption separation in optoelectronic devices, which are very favorable potential applications.
2. Theoretical model and numerical method 2.1. Graphene-based hyperbolic metamaterials For a graphene sheet, electromagnetic properties are described in terms of surface conductivity s that can be calculated as follows [26,27], σ = ie2μ/π ℏ2 (ω + i/τ), where, ω, ħ, e, μ, τ is radian frequency, Planck constant, charge of an electron, chemical potential, and phenomenological scattering rate, respectively. We assumed that the electronic band structure of a graphene sheet is unaffected by the neighboring, thus, the effective permittivity εg of graphene can be calculated as follow [28]: εg = 1 + iσ /ε0 ωtg , where tg is the thickness of graphene sheet, ε0 is the permittivity in the vacuum. First, we discussed the surface conductivity of the monolayer graphene. The dependence of real and imaginary parts of the s/s0 (s0 ¼e2/πħ, universal optical conductivity [29]) with the μ is plotted at τ ¼10 12 s, indicating that s/s0 is increased by μ with the required frequency range (Fig. 1). The conductivity of graphene is controlled by chemical potential, which suggests the potential applications of graphene in tunable metamaterials and metadevices (Fig. 1) [30]. Second, we analyzed the refractive index of the structure of GHMMs with different chemical potentials and dielectric thickness. Given that 1D geometric model composed of monolayer graphene and conventional dielectric, based on effective medium theory [31], the effective relative permittivity can be read as
Fig. 1. Variation of s with frequency of different μ of real part (a) and imaginary part (b).The black solid (red dash dot, blue dash dot) curves represent μ¼ 0.1 eV (0.2 eV, 0.3 eV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
Fig. 2. Real part of ε‖ with different frequencies and thicknesses of dielectric with μ¼0.1 eV, εC ¼2.25. Graphene-dielectric. Inset in schematic show a monolayer GHMM composed of graphene and dielectric.
[22,32]
⎡ ε∥ 0 0 ⎤ ⎥ ⎢ ε = ⎢ 0 ε∥ 0 ⎥ ⎥ ⎢ ⎣ 0 0 ε⊥ ⎦ ε∥ =
ε⊥ =
(1)
t g ε g + tC εC t g + tC
(2)
ε g εC (t g + tC ) εC t g + ε g tC
(3)
where ε‖ and ε⊥ are the parts of parallel and vertical relative permittivity, respectively. εC and tC are the dielectric permittivity and thickness, respectively. Figs. 2 and 3 show the real part of ε‖ for the different chemical potentials and thicknesses of dielectric as functions of frequency with εC ¼2.25. A hyperbolic dispersion is obtained for the entire frequency range under consideration, where the real part of ε‖ is negative whereas ε⊥ E εC has a positive real part [17]. Our results demonstrate that the frequency with effective refractive index equivalent to zero can be changed by varying chemical potentials μ and thicknesses of dielectric tC in the graphene-dielectric layered structure. The frequency of zero refractive index has blue shifted whereas the thickness of dielectric t C is increased with μ ¼0.1 eV (Fig. 2). The tuning of zero refractive index by increasing the chemical potential of graphene is plotted
Fig. 3. Real part of ε‖ with different frequencies and μ with thicknesses of dielectric for tC ¼30 nm.
Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
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Fig. 5. Schematic of the 1D periodic structure composed of tantalum pentoxide (A), silicon dioxide (B) and graphene-based hyperbolic metamaterials (M) under any incident angle.
infinite slab of material, transfer matrix method was used in our calculation [22,30,35,36].
3. Results and discussion We selected the composition parameters: dA ¼1 μm, dB ¼1 μm, μA ¼ μB ¼ μM ¼1. All materials data are previously obtained [15,37].
Fig. 4. Two dimensional map about (a) real and (b) imaginary parts of the group index of retraction for μ¼0.1 eV and tC ¼ 30 nm.
at tC ¼30 nm (Fig. 3). The critical ε‖ can be tuned by μ and tC, which also changed the frequency of absorption (Figs. 2 and 3). Considering the influence of incident angle θ, the effective phase and the group indices at low material absorption in anisotropic materials can be obtained from the Snell′s law as [33]
ε∥
) sin2θ
np =
ε∥ + (1 −
ng =
ε∥ ε⊥2 ε⊥ (1 − ) sin2θ − ε∥ ε∥ ε⊥
ε⊥
(4)
(5)
We investigated the group index of the GHMMs for frequency and incident angle. The dependence of ng on the frequency and incident angle for μ ¼ 0.1 eV and tC ¼30 nm is plotted in Fig. 4. With increasing incident angle, the real part of ng is positive and the imaginary part of ng is negative, which is usable for the design of negative refraction materials (Fig. 4) [22]. The group index substantially is unchanged as incident angle increased at 22.4 THz (Fig. 4). Hence, ng of the GHMMs is insensitive to incident angle, which offered intriguing application for electrically tunable spectral imaging [34]. Thus, we can design a periodic structure with GHMMs and investigate the absorption while changing incident angle and polarizations. 2.2. Tunable absorption of 1D periodic structure based-on HMMs We consider a 1D periodic structure composed of ordinary medium and GHMMs. Fig. 5 shows a schematic of oblique indent electromagnetic wave in a periodic structure composed of dielectric layers and hyperbolic metamaterials. We consider the periodic with the structure of (ABM)N, where A, B and M represent tantalum pentoxide, silicon dioxide and GHMMs, respectively. N is the number of periods. Considering the absorption as a function of frequency and incident angle for both polarizations for a half
Fig. 6. Absorption of GHMMs of μ¼ 0.1 eV, dA ¼ dB ¼1 um, tC ¼30 nm for (a) TE and (b) TM polarizations.
Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
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refractions are supported by GHMM for TM polarization at oblique incidence. Variation absorption of the TE and TM polarizations with different incident angles at 10–18 THz is plotted in Fig. 8. New absorption peak was found in TM polarization but never appeared in TE polarization (Fig. 8). This finding that the TM polarized waves can be absorbed, and TE polarized waves cannot be absorbed, when incident angle is larger than 40 degree with 10–16 THz. The results demonstrate some potential applications as polarization beam splitter for future optoelectronic devices.
4. Conclusion
Fig. 7. Two dimensional map of absorption for (a) TE and (b) TM polarizations with different frequencies and angles of incidence.
We proposed 1D periodic structure with GHMMs which is behavior of tunable absorption of mid-infrared frequency range. We derived the GHMM effective permittivity, which can be tuned by chemical potentials and thicknesses of dielectric. We discussed the effective group index of GHMMs, which is insensitive to incident angles. We also investigated the tunable absorption of the GHMMs of different polarizations and incident angles. Interestingly, in contrast to different polarization, the low frequency range of TM polarizations can be absorbed when angle of incidence is increased with 10–30 THz, whereas TE polarization cannot. The perfect absorption can be attained at 22.4 THz both TM and TE polarizations of incident angle less than 40 degree. The designed structure provides potential applications for absorption of beam splitting, and the perfect absorption can be achieved at the required frequency for both TE and TM polarizations.
Acknowledgements This work was supported by Chinese Specialized Research Fund for the Doctoral Program of Higher Education (grant No. 20123218110017), the Jiangsu Province Science Foundation (Grant No.BK2011727), Chinese Natural Science Foundation (Grant No.61307052), the Foundation of Aeronautical Science (No. 20121852030), the Fundamental Research Funds for the Central Universities (NO. NZ2013302), Youth Funding for Science & Technology Innovation in NUAA (NS2014039), Open Research Program in Jiangsu Key Laboratory of Meteorological Observation and Information Processing(Grant No.KDXS1207), Funding of Jiangsu Innovation Program for Graduate Education (CXZZ13_0166), Funding of HuangShan University Program for Scientific Research (2010xkj006), Funding of AnHui for Scientific Research (KJ2013B267).
Fig. 8. Absorption of 1D GHMMs versus polarizations with different incident angles from 9 THz to 18 THz.
References
The GHMM parameters are as follows: nC ¼ 1.5, tC ¼30 nm, μ ¼0.1 eV, N ¼ 9. The absorption spectra as a function of frequency with both polarizations for different incidence angle are plotted in Figs. 6 and 7. The absorption peaks are similar to different polarizations of incident angles at 22.4 THz. This finding demonstrates that the ng of the above-mentioned is insensitive for incident angle (Fig. 4(a)). However, the absorption peaks varied between the TM and TE polarizations at other frequency region (Fig. 6). A new absorption peak can be found when incident angle larger than 40 degree for TM polarization; this absorption peak has blue shifted while incident angle is increased, whereas the absorption peak at 22.4 THz has insignificantly changed (Figs. 6(a) and 7(a)). The results are consistent with Refs. [22,38]. This is due to negative
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Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
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Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range Renxia Ning a,b, Shaobin Liu b,n, Haifeng Zhang b, Borui Bian b, Xiangkun Kong b a
College of Information Engineering, Huangshan University, Huangshan 245041,China Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 17 June 2014 Received in revised form 23 September 2014 Accepted 24 September 2014
Tunable absorption in periodic structure composed of graphene-based hyperbolic metamaterials (GHMMs) and isotropic medium is investigated by the transfer matrix method. The parallel part for relative permittivity of GHMMs consisting of monolayer graphene and conventional dielectric can be tuned by the chemical potential and dielectric layer thickness. The real part of the group index of GHMMs is insensitive to incident angle at the required frequency and the absorption of the periodic structure with GHMMs can be obtained nearly 100% at 22.4 terahertz (THz). The absorption peak of this frequency is almost uniform for both transverse electric (TE) and transverse magnetic (TE) polarizations. However, a new absorption peak can be observed incident angle is larger than 40 degree for TM polarization from 10 to 30 THz. The research results show that the absorption is insensitive to electromagnetic polarization at certain frequency. A new absorption peak can be found with TM polarization in low frequency region. These novel and effective GHMMs can replace metallic thin films as polarizing beam splitter for future optoelectronic applications. & 2014 Published by Elsevier B.V.
1. Introduction Graphene is a two-dimensional honeycomb structure with monolayer of carbon atom thickness, and is a type of gapless semiconductor [1–3]. Peculiar electronic properties have gained increasing interest from many researchers [4–9]. A single sheet of undoped graphene has single pass absorption of πα (2.3%), where α ¼e2/(ħc) is the quantum electrodynamics fine structure constant [10,11]. In many published works, researchers have focused on the absorption properties of graphene. Liu et al. [12] investigated absorption in graphene with resonant metal back reflector, which can be tuned by gate voltage with the terahertz (THz) spectra range. Peres et al. [13] studied the absorption of graphene on photonic crystal with the THz range, and they focused on the absorption can be enhanced by threefold with specific frequency range. Hashemi et al. [14] used metallic nanostructures to enhance light absorption in graphene by adjusting its structure. However, those results indicate that the absorption of graphene is still o50%. The low absorption is restricted in many applications, shch as photodetectors and saturable absorbers. Recently, perfect absorption of graphene has licited attention from researchers [15,16]. n
Corresponding author. E-mail address: [email protected] (S. Liu).
Previous results showed that the absorption is sensitive to electromagnetic polarization. However, the perfect absorption of polarization-insensitive graphene remains seldom studied. Hyperbolic metamaterials (HMMs) [17], namely anisotropic medium exhibiting hyperbolic shape of the dispersion relation, have been investigated on the THz [17], visible [18] and nearinfrared frequency regions [19]. A novel implementation of HMMs at far-infrared frequency range is composed of stacked graphene sheets separated by thin dielectric layers [19], which show that the GHMMs can become super absorbers for near-fields. HMMs can be designed into efficient and innovative absorbers which can enhance the decay rate of emitters near its surface [20]. The results can be applied to wide-angle absorption of the HMM structure. HMMs have various potential applications including negative refraction [21,22], optical waveguide [23] and imaging hyperlens [24]. To our knowledge, the perfect wide-angle absorption of HMMs has been rarely reported. We theoretically investigated the absorption of one-dimensional (1D) periodic structure of GHMMs. First, we discussed the refractive index of the structure of GHMMs with different chemical potentials and thickness of dielectric. The results may provide theoretical instructions for future optoelectronic applications of graphene. Second, a tunable absorption realized by 1D periodic structure composed of GHMMs and two kinds of isotropic dielectric is theoretically studied via transfer matrix method.
http://dx.doi.org/10.1016/j.physb.2014.09.038 0921-4526/& 2014 Published by Elsevier B.V.
Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
Compared with Ref. [25], we present the different structures of the sheets as controlling parameters ranging from 10 THz to 30 THz. These results confirm the GHMMs mode absorption separation in optoelectronic devices, which are very favorable potential applications.
2. Theoretical model and numerical method 2.1. Graphene-based hyperbolic metamaterials For a graphene sheet, electromagnetic properties are described in terms of surface conductivity s that can be calculated as follows [26,27], σ = ie2μ/π ℏ2 (ω + i/τ), where, ω, ħ, e, μ, τ is radian frequency, Planck constant, charge of an electron, chemical potential, and phenomenological scattering rate, respectively. We assumed that the electronic band structure of a graphene sheet is unaffected by the neighboring, thus, the effective permittivity εg of graphene can be calculated as follow [28]: εg = 1 + iσ /ε0 ωtg , where tg is the thickness of graphene sheet, ε0 is the permittivity in the vacuum. First, we discussed the surface conductivity of the monolayer graphene. The dependence of real and imaginary parts of the s/s0 (s0 ¼e2/πħ, universal optical conductivity [29]) with the μ is plotted at τ ¼10 12 s, indicating that s/s0 is increased by μ with the required frequency range (Fig. 1). The conductivity of graphene is controlled by chemical potential, which suggests the potential applications of graphene in tunable metamaterials and metadevices (Fig. 1) [30]. Second, we analyzed the refractive index of the structure of GHMMs with different chemical potentials and dielectric thickness. Given that 1D geometric model composed of monolayer graphene and conventional dielectric, based on effective medium theory [31], the effective relative permittivity can be read as
Fig. 1. Variation of s with frequency of different μ of real part (a) and imaginary part (b).The black solid (red dash dot, blue dash dot) curves represent μ¼ 0.1 eV (0.2 eV, 0.3 eV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
Fig. 2. Real part of ε‖ with different frequencies and thicknesses of dielectric with μ¼0.1 eV, εC ¼2.25. Graphene-dielectric. Inset in schematic show a monolayer GHMM composed of graphene and dielectric.
[22,32]
⎡ ε∥ 0 0 ⎤ ⎥ ⎢ ε = ⎢ 0 ε∥ 0 ⎥ ⎥ ⎢ ⎣ 0 0 ε⊥ ⎦ ε∥ =
ε⊥ =
(1)
t g ε g + tC εC t g + tC
(2)
ε g εC (t g + tC ) εC t g + ε g tC
(3)
where ε‖ and ε⊥ are the parts of parallel and vertical relative permittivity, respectively. εC and tC are the dielectric permittivity and thickness, respectively. Figs. 2 and 3 show the real part of ε‖ for the different chemical potentials and thicknesses of dielectric as functions of frequency with εC ¼2.25. A hyperbolic dispersion is obtained for the entire frequency range under consideration, where the real part of ε‖ is negative whereas ε⊥ E εC has a positive real part [17]. Our results demonstrate that the frequency with effective refractive index equivalent to zero can be changed by varying chemical potentials μ and thicknesses of dielectric tC in the graphene-dielectric layered structure. The frequency of zero refractive index has blue shifted whereas the thickness of dielectric t C is increased with μ ¼0.1 eV (Fig. 2). The tuning of zero refractive index by increasing the chemical potential of graphene is plotted
Fig. 3. Real part of ε‖ with different frequencies and μ with thicknesses of dielectric for tC ¼30 nm.
Please cite this article as: R. Ning, et al., Physica B (2014), http://dx.doi.org/10.1016/j.physb.2014.09.038i
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Fig. 5. Schematic of the 1D periodic structure composed of tantalum pentoxide (A), silicon dioxide (B) and graphene-based hyperbolic metamaterials (M) under any incident angle.
infinite slab of material, transfer matrix method was used in our calculation [22,30,35,36].
3. Results and discussion We selected the composition parameters: dA ¼1 μm, dB ¼1 μm, μA ¼ μB ¼ μM ¼1. All materials data are previously obtained [15,37].
Fig. 4. Two dimensional map about (a) real and (b) imaginary parts of the group index of retraction for μ¼0.1 eV and tC ¼ 30 nm.
at tC ¼30 nm (Fig. 3). The critical ε‖ can be tuned by μ and tC, which also changed the frequency of absorption (Figs. 2 and 3). Considering the influence of incident angle θ, the effective phase and the group indices at low material absorption in anisotropic materials can be obtained from the Snell′s law as [33]
ε∥
) sin2θ
np =
ε∥ + (1 −
ng =
ε∥ ε⊥2 ε⊥ (1 − ) sin2θ − ε∥ ε∥ ε⊥
ε⊥
(4)
(5)
We investigated the group index of the GHMMs for frequency and incident angle. The dependence of ng on the frequency and incident angle for μ ¼ 0.1 eV and tC ¼30 nm is plotted in Fig. 4. With increasing incident angle, the real part of ng is positive and the imaginary part of ng is negative, which is usable for the design of negative refraction materials (Fig. 4) [22]. The group index substantially is unchanged as incident angle increased at 22.4 THz (Fig. 4). Hence, ng of the GHMMs is insensitive to incident angle, which offered intriguing application for electrically tunable spectral imaging [34]. Thus, we can design a periodic structure with GHMMs and investigate the absorption while changing incident angle and polarizations. 2.2. Tunable absorption of 1D periodic structure based-on HMMs We consider a 1D periodic structure composed of ordinary medium and GHMMs. Fig. 5 shows a schematic of oblique indent electromagnetic wave in a periodic structure composed of dielectric layers and hyperbolic metamaterials. We consider the periodic with the structure of (ABM)N, where A, B and M represent tantalum pentoxide, silicon dioxide and GHMMs, respectively. N is the number of periods. Considering the absorption as a function of frequency and incident angle for both polarizations for a half
Fig. 6. Absorption of GHMMs of μ¼ 0.1 eV, dA ¼ dB ¼1 um, tC ¼30 nm for (a) TE and (b) TM polarizations.
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refractions are supported by GHMM for TM polarization at oblique incidence. Variation absorption of the TE and TM polarizations with different incident angles at 10–18 THz is plotted in Fig. 8. New absorption peak was found in TM polarization but never appeared in TE polarization (Fig. 8). This finding that the TM polarized waves can be absorbed, and TE polarized waves cannot be absorbed, when incident angle is larger than 40 degree with 10–16 THz. The results demonstrate some potential applications as polarization beam splitter for future optoelectronic devices.
4. Conclusion
Fig. 7. Two dimensional map of absorption for (a) TE and (b) TM polarizations with different frequencies and angles of incidence.
We proposed 1D periodic structure with GHMMs which is behavior of tunable absorption of mid-infrared frequency range. We derived the GHMM effective permittivity, which can be tuned by chemical potentials and thicknesses of dielectric. We discussed the effective group index of GHMMs, which is insensitive to incident angles. We also investigated the tunable absorption of the GHMMs of different polarizations and incident angles. Interestingly, in contrast to different polarization, the low frequency range of TM polarizations can be absorbed when angle of incidence is increased with 10–30 THz, whereas TE polarization cannot. The perfect absorption can be attained at 22.4 THz both TM and TE polarizations of incident angle less than 40 degree. The designed structure provides potential applications for absorption of beam splitting, and the perfect absorption can be achieved at the required frequency for both TE and TM polarizations.
Acknowledgements This work was supported by Chinese Specialized Research Fund for the Doctoral Program of Higher Education (grant No. 20123218110017), the Jiangsu Province Science Foundation (Grant No.BK2011727), Chinese Natural Science Foundation (Grant No.61307052), the Foundation of Aeronautical Science (No. 20121852030), the Fundamental Research Funds for the Central Universities (NO. NZ2013302), Youth Funding for Science & Technology Innovation in NUAA (NS2014039), Open Research Program in Jiangsu Key Laboratory of Meteorological Observation and Information Processing(Grant No.KDXS1207), Funding of Jiangsu Innovation Program for Graduate Education (CXZZ13_0166), Funding of HuangShan University Program for Scientific Research (2010xkj006), Funding of AnHui for Scientific Research (KJ2013B267).
Fig. 8. Absorption of 1D GHMMs versus polarizations with different incident angles from 9 THz to 18 THz.
References
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