Tunable multichannel absorber composed of graphene and doped periodic structures

Optics Communications 383 (2017) 391–396

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Tunable multichannel absorber composed of graphene and doped periodic structures Xiang-kun Kong a,b,n, Xiang-zhu Shi a, Jin-jun Mo c, Yun-tuan Fang d, Xin-lei Chen a, Shao-bin Liu a a Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China c College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China d School of Computer Science and Telecommunication Engineering, Jiangsu University, Zhenjiang 212013, China

art ic l e i nf o

a b s t r a c t

Article history: Received 6 July 2016 Received in revised form 30 August 2016 Accepted 18 September 2016

A new design for a tunable multichannel compact absorber, which is achieved by using an asymmetric photonic crystal with graphene monolayers, is theoretically proposed. The graphene monolayers are periodically embedded into the first and last dielectric layers. The absorption, reflection, and transmission spectra of the absorber are studied numerically. A perfect absorption channel is achieved because of impedance matching, and channel number can be modulated by changing periodic number. The characteristic properties of the absorption channel depend on graphene conductivity, which can be controlled via the gate voltage. The proposed structure works as a perfect absorber that is independent from polarization. It has potential applications in the design of multichannel filters, thermal detectors, and electromagnetic wave energy collectors. & 2016 Elsevier B.V. All rights reserved.

Keywords: Absorber Graphene Photonic crystal Transfer matrix method

1. Introduction As a type of artificial material, one-dimensional (1D) photonic crystals (PCs) with a periodic arrangement of refractive index have attracted considerable attention for the past few years because of their capability to create a range of forbidden frequencies known as photonic band gap (PBG) [1]. PBGs have many interesting and attractive applications in optical filters [2], reflectors [3], and nonlinear diodes [4], as well as in fabricating PC waveguides [5,6]. Different materials have been used to dynamically control the transmittance spectrum of a PC. The electromagnetic (EM) properties of PCs, which are composed of metals [7,8], plasma [9,10], metamaterials [11,12], and superconductor elements [13,14], have been investigated. These materials have an advantage given that their permittivity can be transformed by an external magnetic field, outside voltage, or temperature. Consequently, the EM properties of devices with PCs, including tunable elements, can be adjusted. Graphene, as a planar atomic layer of carbon atoms arranged in a honeycomb lattice, is actually a type of semiconductor [15–17]. In n Corresponding author at: Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China E-mail address: [email protected] (X.-k. Kong).

http://dx.doi.org/10.1016/j.optcom.2016.09.038 0030-4018/& 2016 Elsevier B.V. All rights reserved.

addition to distinct properties such as high charge carrier mobility, electronic energy spectrum without a gap between the conduction and valence bands, and frequency independent absorption of EM radiation [18–20], another superiority of graphene is that its carrier concentration can be electrically modulated within a wide frequency range by altering outside gate voltage. Given these unique characteristics, 1D graphene-based PCs have been investigated extensively. Madani et al. [21] focused on transmission properties in a 1D PC with graphene monolayers. A new type of omnidirectional PBG in the THz region, which was nearly insensitive to polarization, was theoretically analyzed. Zhang et al. [22] investigated strong second-harmonic generation from bilayer graphene embedded into 1D PC. Naggar [23] focused on the properties of a tunable THz omnidirectional PBG by periodically introducing graphene sheets into the first layer of a conventional 1D PC. Entezar [24] and Zhang [25] researched on the optical properties of a defective 1D PC with graphene monolayers and Fibonacci quasi-periodic graphene PCs, respectively. Photonic applications, such as multi-peak or broadband absorbers, were proposed by Miloua [26] and Ning [27]. However, However, polarization-independent absorbers with tunable multichannels and high absorption characteristics are rarely reported. In the current study, a tunable multichannel compact absorber produced using an asymmetric PC with graphene monolayers is theoretically investigated. The absorber has a compact structure,

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and the absorption channel can be dynamically modulated within the THz range. We research on the effects of parameters, such as the number of PCs, the chemical potential, and the distance between the graphene sheets, on the optical response of the structure. The possibility to achieve a polarization-independent and tunable multichannel perfect absorber is discussed.

2

R= r =

T = t2 =

m11η0 + m12η0ηn + 1 − m21 − m22η0

2

,

m11η0 + m12η0ηn + 1 + m21 + m22η0

(5)

2

2η0 m11η0 + m12η0ηn + 1 + m21 + m22η0

, (6)

2. Theoretical model and method

(7)

A = 1 − T − R. A schematic cross-sectional view of the absorber is shown in Fig. 1 as follows: GC (BA)N (AB )N CG′, where G and G′ are composed of graphene sheets separated by thin dielectric layers. A and B are dielectric layers with low and high dielectric constants εA and εB , respectively; N is the periodic number of the structure; and layer C is the same material as layer A but with a different thickness. The frequency-dependent effective permittivity, εG, G ′, of the grapheme sheets separated by dielectric layers with a dielectric constant εd and a thickness d is given by the Kubo formula as follows [24]:

σg (ω)

εG, G = εd + i ′ ωε0d

(1)

where the surface conductivity σg (ω) of the graphene sheet can be written as the sum of the intraband and interband electron transition contributions as [23]

σg (ω) = σgint ra(ω) + σgint er (ω)

(2)

where

σgint ra(ω) =

e2 i ⎡ 16kBT μ ⎤ ⎢ log(2 cosh( ))⎥ 2kBT ⎦ 4ℏ 2π ⎣ ℏω

σgint er (ω) =

e2 ⎡ 1 1 ℏω − 2μ ⎢ + arctan 4ℏ ⎣ 2 π 2kBT −

⎤⎤ i ⎡ (ℏω + 2μ)2 ⎢ log( )⎥⎥ 2π ⎣ (ℏω − 2μ)2 + (2kBT )2 ⎦⎦

(3)

(4)

In Eq. (4), e is the charge of the electron, ℏ is the Planck constant, ω is the radian frequency, kB is the Boltzmann constant, T is the temperature (K), and μ is the chemical potential that can be controlled via the gate voltage. The well-known transfer matrix method has been used to obtain reflection, transmission, and absorption [28,29] as follows:

where m11, m12, m21, and m22 are the elements of the total transfer matrix

⎞ ⎛ i − sin δl ⎟ ⎜ cos δl η M = [MGMC (MBMA) (MAMB ) MC MG ′] = ∏ ⎜ ⎟ l l = 1 ⎜ −iη sin δ cos δl ⎟⎠ ⎝ l l n

N

N

(8)

When different polarizations are considered, ηl = εl / μl 1 − (sin2θ /εlμl ) for the TE wave and ηl = μl / εl 1 − (sin2θ /εlμl ) for the TM wave. η0 and ηn + 1 are defined as the corresponding η parameters of the incidence and exit media (air in this study), respectively.

3. Numerical results and discussion In this study, a tunable multichannel perfect absorber with an asymmetric PC that contains graphene monolayers and doped periodic structures within the THz frequency range is theoretically investigated. Layers G and G′ are graphene–SiO2 systems made up of thin SiO2 films deposited on epitaxially grown graphene monolayers. The permittivity of SiO2 is set to εd ¼5.07. [30]. The permittivity of the graphene–SiO2 multilayer εG, G is calculated ′ according to Eq. (1), and μ = 0.2 eV and T ¼300 K are assumed during the calculation of the surface conductivity of graphene. Layers A and B are assumed to be SiO2 and silicon with a permittivity of εA ¼5.07 and εB ¼ 10.9, respectively. The thickness values da ¼ 9.2 mm and db ¼6.3 mm are set to satisfy nada = nbdb . dc ¼5 mm, dG ¼ 10 mm, and dG ′ ¼25 mm are selected to investigate the performance of the device within the THz frequency range. All of the aforementioned structure parameters are selected to achieve the perfect absorption process shown in Fig. 2(a), which fulfill the requirement of the impedance matching method [31]. When only the simplest structure GCBAABCG′ is considered, a channel with nearly zero transmission and zero reflection but

Fig. 1. Schematic diagram of the absorber with the structure GC (BA)N (AB )N CG′, in which layers G and G′ are composed of graphene sheets separated by thin dielectric layers.

X.-k. Kong et al. / Optics Communications 383 (2017) 391–396

(a)

(b)

1.0 R T A

0.8

393

200 H E

150 100

E&H(a.u.)

A&T&R

50

0.6 0.4

0 -50

-100 -150

0.2 0.0 3.50

-200 -250

3.55

3.60

3.65

3.70

3.75

0

3.80

10

20

Frequency(THz)

30 40 Z axis(µ m)

50

60

70

Fig. 2. (a) Absorption (A), reflection (R), and transmission (T) spectra of the absorber of the absorber. (b) Electric (E) and magnetic (H) field distributions in the multichannel absorber at frequency 3.65 THz.

1.0 N=1 N=2 N=3

0.8 0.6

A

perfect absorption at a frequency of 3.65 THz exists based on the tunneling conditions at normal incidence [32,33]. Furthermore, impedance ZG can be deduced using the impedance matching method [31], in which the effective index neff = (nada + nbdb + nc dc ) /(da + db + dc )for the multilayer CBAABC used to determine ZCBAABC . The last layer G′ dissipates nearly all of the EM wave energy. To verify this assumption, the field distributions at a frequency of 3.65 THz are displayed in Fig. 2(b). As shown in the figure, the electric field presents an anti-symmetric distribution in the proposed structure and gradually decreases within the last graphene dielectric multilayer medium.. Subsequently, narrow multichannel absorption for the proposed structure, which consists of an asymmetric PC with graphene monolayers, is exhibited. Fig. 3 shows the effect of periodic number N on the number of absorption channels. Evidently, when the periodic number increases, the number of absorption channels increases accordingly. The proposed structure displays a broadband absorption spectrum because of the coupling of evanescent waves. When N = 3, three absorption channels located at 2.53, 2.83, and 3.64 GHz exist. The optical characteristics of graphene sheets are known to depend on their conductivity σg (ω), which can be controlled via the gate voltage by modulating the chemical potential. Thus, by introducing graphene sheets into the dielectric layers, the position of the absorption channels can be tuned. As shown in Fig. 4, we investigate the dependence of the absorption channel on the chemical potential μ under normal incidence condition. This phenomenon appears as color maps of the absorption versus the chemical potential and the frequency of TE and TM waves. Notably, the absorptions are similar at normal incidence. The position of absorption moves to a higher frequency range, which is associated with a decreasing peak, as the chemical potential increases. The full width at half maximum (FWHM) of the absorption channel becomes narrower as frequency increases. It nearly vanishes when μ approaches 0.3 eV. Thus, we can conclude that the frequency of absorption highly depends on the chemical potential of the graphene monolayers. Furthermore, the number of graphene monolayers that are periodically embedded into layers G and G′ can assist in designing the proposed multichannel absorber. Fig. 5 shows the dependence of absorption, transmission, and reflection on the distance between the graphene monolayers. The spectra of the absorption,

0.4 0.2 0.0 2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

Frequency(THz) Fig. 3. Effect of periodic number N on the channel number of the absorber.

transmission, and reflection of the structure GCBAABCG′ at different values of d ¼0.2, 0.3, and 0.4 μm are shown in Figs. 5(a)–(c), respectively. As illustrated in Fig. 5, the increase in d is associated with the decrease in absorption channel width and a shift in its center frequency toward the lower region from 3.65 to 3.46 GHz. Moreover, when the spacing between the graphene sheets increases from 0.2 μm to 0.4 μm, the peak absorption declines swiftly from nearly 1 to 0.42, whereas reflection and transmission increase.. These results are attributed to the variation in the effective dielectric constant of layer G and the decrease in the number of graphene sheets. On the basis of the Kubo formula, thickness d can affect the value of effective permittivity εG, G , which directly in′ fluences tunneling conditions at normal incidence. Meanwhile, thickness d can affect the number of graphene sheets if the thickness of layers G and G′ is fixed. Evidently, the EM wave energy will be transmitted throughout the entire structure if the number of graphene sheets is insufficient. We then discuss the change in thickness of the graphene dielectric multilayers G and G′ as a function of absorption in Fig. 6. As illustrated in Fig. 6(a), the absorption peak initially increases to nearly 100% and then decreases with the increase in dG because of reflection. At an optimal dG = 10 μm , a nearly perfect absorption

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X.-k. Kong et al. / Optics Communications 383 (2017) 391–396

Fig. 4. Color map of the absorption for the structure GCBAABCG′ at normal incidence. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

1.0 0.5

A&T&R

0.0 1.0 0.5

R T A d=0.2um

(a)

R T A d=0.3um

(b)

0.0 1.0

0.5

0.0

3.2

R T A d=0.4um

3.3

(c)

3.4

3.5

3.6

3.7

resonant frequency remains the same. Therefore, the thickness of dG ′ ¼15 μm is the optimized value. To study the dependence of absorption on the incident angle, the color maps of absorption versus the frequency and the incident angle are shown in Fig. 7. When the incident angle is less than 40°, the perfect absorption peak is similar for both polarizations. The position of the absorption frequency for TE waves moves faster to a higher value of approximately 3.98 THz with the increase in the incident angle. By contrast, that for TM waves moves slowly to a lower value of approximately 3.89 THz. This property is highly similar to the PBGs created using graphene dielectric nanolayers [24]. Unlike in TM mode, the absorption peak in TE mode slightly decreases when the incident angle is larger than 60°. Therefore, the proposed structure is a good option for a directional perfect absorber that is independent from polarization.

3.8

Frequency(THz) Fig. 5. Absorption, reflection, and transmission spectra of the absorber at different distances of the graphene sheets (a) d ¼0.2 μm, (b) d ¼ 0.3 μm, and (c) d¼ 0.4 μm.

accompanied by a relatively narrow FWHM is achieved. As shown in Fig. 6(b), the resonant frequency initially increases with dG ′. When dG ′ = 15 μm corresponds to the perfect absorption, the

4. Conclusion A new design for a compact absorber with an asymmetric 1D PC that contains graphene sheets has been proposed. Graphene monolayers have been periodically embedded into the first and last dielectric layers. The absorption, reflection, and transmission spectra of the absorber have been studied numerically, and the

Fig. 6. Absorption map of the absorber with structure GCBAABCG′ (a) A(f , dG ) and (b) A(f , dG ′) .

X.-k. Kong et al. / Optics Communications 383 (2017) 391–396

395

Fig. 7. Absorption map of the absorber with structure GCBAABCG′ (a) A(f , dG ) and (b) A(f , dG ′).

tunable multichannel perfect absorption characteristics are displayed. The number of absorption channels can be adjusted by changing the periodic number of dielectric layers A and B. Another advantage of the proposed structure is that graphene conductivity can be controlled by the gate voltage by modulating the chemical potential, which provides a flexible method to tune the absorption channel. Moreover, the proposed structure can be used as a polarization-independent directional compact absorber, which has possible applications in the design of multichannel filters, thermal detectors, and EM wave energy collectors.

Acknowledgment This work was supported by the supports from the Fundamental Research Funds for the Central Universities (Grant No. NJ20160008), Chinese Natural Science Foundation (Grant No. 61471368), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20150757) and the Open Research Program in China's State Key Laboratory of Millimeter Waves (Grant No. K201609).

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