Frequency-tunable and functionality- switchable ... - OSA Publishing

Vol. 7, No. 12 | 1 Dec 2017 | OPTICAL MATERIALS EXPRESS 4277

Frequency-tunable and functionalityswitchable polarization device using silicon strip array integrated with a graphene sheet HUAN JIANG,1 WENYU ZHAO,1 AND YONGYUAN JIANG1,2,3,4,* 1

Institute of Modern Optics, Department of physics, Harbin Institute of Technology, Harbin 150001, China 2 Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin 150001, China 3 Key Laboratory of Micro-Nano Optoelectronic Information System of Ministry of Industry and Information Technology, Harbin 150001, China 4 Collaborative Innovation Center of Extreme Optics, Taiyuan 030006, Shanxi, China *[email protected]

Abstract: We propose a frequency-tunable and functionality-switchable polarization conversion device in transmission mode by integrating a silicon strip array with a graphene sheet in the mid-infrared region. High cross-polarization transmission, together with the dynamic frequency shift, contributes to a frequency-tunable half-wave plate working from 17.6 to 17.8 THz. Simultaneously, the device can act as a switchable polarizer to selectively generate co- or cross-polarized light by combining the frequency-tunability and a sharp xshape polarization transmission caused by hybrid Mie resonances. Furthermore, this graphene-based metasurface also realizes continuous 180-degree phase modulation by electrically controlling graphene. The transmitted frequency-tunable and functionalityswitchable device with simple-shape inclusions achieves multiple polarization conversions for both linearly and circularly polarized light without refabricating the geometric parameters, which represents a significant advance compared with previously reported counterparts. © 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (130.0130) Integrated optics; (130.5440) Polarization-selective devices.

References and links 1.

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#308846 Journal © 2017

https://doi.org/10.1364/OME.7.004277 Received 9 Oct 2017; revised 2 Nov 2017; accepted 2 Nov 2017; published 8 Nov 2017


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1. Introduction Polarization is an inherent characteristic of electromagnetic waves and holds the freedom to light propagation and optical information processing. The ability to control the polarization of light has great importance for practical applications in sensing, analytical chemistry, biology, imaging, astronavigation, high-precision measurement and so on. The traditional methods to control polarization is through bulky birefringent crystals or anisotropy materials, while these schemes are not compatible with dynamic and compact on-chip applications [1]. Fortunately, metamaterials, the artificial composite structures, open a new way to manipulate polarization with the advantage of ultrathin nanostructures. Polarization devices based on metamaterials, i.e. polarization converters, polarizers, polarization sensors and polarization filters, have been achieved from microwave to visible light relying on the structures of split ring [2], U-shaped metallic nanoparticles [3] L-shaped [4], apertures [5], multilayer coupled grating [6], and helix [7]. However, most of these devices suffer from large Ohmic losses and complicatedshape inclusions for lack of magnetic responses naturally. Therefore, dielectric materials [8, 9] supporting electric and magnetic resonances become good candidates to simplify the constructions. On the other hand, to meet the requirement of dynamic polarization manipulations, some tunable devices based on phase-changed materials [10–12] and graphene [13–17] have been proposed recently. However, most of these graphene-based devices are limited in reflection mode and hold the tunability in working frequency but not functions. Here, we numerically demonstrate a frequency-tunable and functionality-switchable device using a simple-shape array to modulate the polarization of transmitted light in the mid-infrared spectrum. First, a half-wave plate was obtained by exciting Mie multipole resonances in silicon strip array, and then the electrical frequency-tunability of half-wave plate is achieved by covering a graphene sheet on the dielectric silicon strip array. In addition, a switchable polarizer for both linearly and circularly polarized light is realized due to the combination of the x-shape polarization


transmission and frequency-tunability. The multifunctional polarizer selectively transmits coor cross-polarized light by switching the gate voltage applied on graphene. Furthermore, this graphene-based silicon strip array also achieves continuous phase modulation between coand cross-polarized transmitted light in 17.85 THz from 90 to 270 degrees. The proposed graphene-based metasurface with simple construction opens exciting possibilities to achieve dynamic polarization modulation and its further development in both frequency-tunable and functionality-switchable polarization devices. 2. A tunable half-wave plate 2.1. Hybrid Mie multipole resonances and x-shape polarization transmission

Fig. 1. (a) The silicon strip array in CST Microwave Studio. (b) A unit cell of silicon array, a = 10 μm, b = 4 μm, and d = 7 μm. (c) Polarization transmission coefficients of silicon strip array. (d) The scattered intensities of electric dipole ( I p ), magnetic dipole ( I M ), electric quadrupole ( I Qe ), and magnetic quadrupole ( I Qm ) resonances.

To obtain a tunable half-wave plate, Mie multipole resonances are excited in the silicon strip array to get high cross-polarization and low co-polarization transmission. Due to the characteristics of electric and magnetic resonances in dielectric materials, we choose silicon strip as a basic unit cell. Then, we further optimize the silicon strip array and get the final structure. Figure 1(b) schematically depicts a unit cell of our strip array, where the strip is rotated anticlockwise 45 degrees along the x direction. The refractive index of silicon is 3.45 in the mid-infrared range [18], while the surrounding media is assumed to be air (n = 1) in our simulation. Polarization transmission coefficients are calculated using the frequency domain solver of CST Microwave Studio, which is based on frequency-domain finite integration technology. Figure 1(a) shows the array in CST Microwave Studio, where the pink box is the simulation region, and the top of pink box is the port named “Zmax” acting as a source and the bottom of pink box is the port named “Zmin” acting as a detector. The periodic boundary of unit cell is applied in x and y directions, and open for the z-direction in the environment of free space. Figure 1(c) shows the co- and cross-polarized transmission coefficients of normal incident linearly polarized, left circularly polarized (LCP) and right circularly polarized


(RCP) light, where tco represents co-polarization transmission coefficient of x-to-x, y-to-y, RCP-to-RCP or LCP-to-LCP light, and tcross represents cross-polarization transmission coefficient of x-to-y, y-to-x, RCP-to-LCP or LCP-to-RCP light. The co-polarized transmission is higher than the cross-polarized one from 16.8 to 17.45 THz, while the transmission difference reverses from 17.55 to 18 THz. The cross-polarization transmission coefficient is above 0.8 and the co-polarization one is below 0.2 from 17.58 to 17.68 THz. The reverse of the polarization transmission difference in two adjacent regions constructs a sharp x-shape curve of polarization transmission. The x-shape polarization transmission curve will play a constructive role in engineering switchable polarizer, which can be interpreted by hybrid Mie multipole resonances. In order to show the contribution of multipole modes quantitatively, the radiated powers of multipole resonances were calculated according to the general multipole scattering theory [9]:  1  3 electric dipole moment : P = Jd r, iω 

(1)

 1   3 magnetic dipole moment : M = (r × J )d r, 2c 

(2)

electric quadrupole moment : Qαβ =

1 2   [ra J β + rβ Jα − r ⋅ J δαβ ]d 3 r,  3 i 2ω

magnetic quadrupole moment : M αβ =

( )

  1 [ r×J  3c

(

)

α

  rβ + r × J

(

)

β

rα ]d 3 r,

(3) (4)

  where c is the speed of light in the vacuum, J is the volume current density in a unit cell, r is the displacement vector from the origin to point (x, y, z) in a Cartesian coordinate system, and α , β =x, y, z . Therefore, the decomposed far-field scattered power by these multipole moments can be calculated from the induced currents [8] as  2  2 2 2 I p = 2ω 4 P 3c 3 , I M = 2ω 4 M 3c3 , I Qe = ω 6  Qαβ 5c 5 , and I Qm = ω 6  M αβ 40c5 .

As shown in Fig. 1(d), the electric dipole resonance marked in blue dash line is responsible for high cross-polarization transmission coefficient, which means electric dipole resonance converts the polarization of incident light into its cross direction. While the superposition of the electric dipole, magnetic dipole and electric quadrupole resonances keeps high copolarization transmission from 16.8 to 17.45 THz. The small dip of cross-polarization transmission in 17.52 THz mainly results from magnetic dipole resonance (red dash line) and electric quadrupole resonance (green dash line). While other multipole resonance modes, i.e. near-zero magnetic quadrupole, contribute little to the polarization transmission spectrum. In a word, the hybrid modes of electric dipole, magnetic dipole and electric quadrupole resonances are dominant in the x-shape polarization transmission. In the right part of the x-shape curve from 17.58 to 17.68 THz, incident linearly or circularly polarized wave is largely converted into its cross-polarization state, while the same polarized wave is almost blocked, which demonstrates the function of a half-wave plate. Besides the difference in polarization transmission, Fig. 2 shows 180-degree phase difference between co- and cross-polarized transmitted light near 17.6 THz, which further manifests half-wave plate’s function for both linearly and circularly polarized light. The near-unity 2 2 2 polarization conversion rate ( PCR = tcross  tco + tcross  ) [19] in Fig. 2 shows the good   performance of our half-wave plate in polarization conversion.


Fig. 2. The polarization conversion rate (PCR) of the proposed half-wave plate and the phase difference between co- and cross-polarized transmitted waves.

2.2. Frequency-tunability and a tunable half-wave plate

Fig. 3. (a) The graphene-based metasurface consists of silicon strip array covered with a graphene sheet, (b) Co- and (c) cross-polarization transmission coefficients with different graphene’s Fermi energies.

Next, we add the frequency-tunability to the half-wave plate by covering a graphene sheet on the silicon strip array as shown in Fig. 3(a). Graphene, an atom-thick sheet with twodimensionally arranged carbon atoms, is regarded as an anisotropic material with different conductivities in- and out-of-plane [20, 21]. The in-plane conductivity is calculated using Random Phase Approximation [22, 23],  ω 2e 2ωT i σ (ω ) = log  2 cos h  F −1 π  ω + iτ   2ωT

  ω' ω  −H  H    e 2   ω  2ω ∞  2  2   d ω ' H   + i  + π 0 ω 2 − ω '2    4   2      (5)


where H (ω ) = sin h(ω ωT ) [ cos h(ωF ωT ) + cos h(ω ωT ) ] ,

ωF = EF  , ωT = κ BT  , ω is

angular frequency of the incident light, e and κ B are the charge of an electron and Boltzmann constant, and  = h / 2π represents the reduced Planck constant. In our simulation, we assume temperature T = 300 K, relaxation time τ = 1 ps and Fermi energy EF ranges from 0 to 1.5 eV. Graphene is modeled as an anisotropic material with out-of-plane (z direction) dielectric constant 2.25 and in-plane (x-y plane) permittivity derived from ε (ω ) = 1 + iσ (ω ) ωε 0 t [24], where ε 0 represents the permittivity in the vacuum, t = 1 nm is the thickness of graphene. Here graphene sheet is treated as an anisotropic thin layer, which is verified in experiment [25]. Figures 3(b) and 3(c) show co- and cross-polarized transmission coefficients with various Fermi energies. A blue shift appears with the increase of Fermi energy from 0 to 1.2 eV, demonstrating the dependence of spectral position on graphene’s Fermi energy. The changes in resonant frequency can be interpreted by the perturbation theory [24, 26]       dV [(Δμ ⋅ H 0 ) ⋅ H 0* + (Δε ⋅ E0 ) ⋅ E0* ]  ΔWm + ΔWe Δω (6) =− V =−  *  * ω0 Wm + We  dV (μ ⋅ H 0 ⋅ H 0 + ε ⋅ E0 ⋅ E0 ) V

  where ω0 is resonant angular frequency, E0 and H 0 are the unperturbed electric and    magnetic fields whose complex conjugates are represented by E0* and H 0* . Moreover, Δε  and Δμ are the changes in dielectric permittivity and magnetic permeability regarded as the material perturbation, We and Wm are the total electric and magnetic energies. The value of  ∆ω relies on not only the material perturbation caused by graphene Δε , but also the local  enhancement of optical fields generated by dielectric array E0 . Different Fermi energies related with various conductivities result in different disturbed fields in silicon array. These different disturbed fields affect the multipole resonances at various degrees when the dielectric microstructures are fabricated close to graphene sheet, causing the shift of response frequency. The cross-polarization transmission maintains 0.8 with small fluctuation after applying different Fermi energies in graphene sheet from 17.58 to 17.84 THz in Fig. 3(c). A small blue shift of working frequency in Figs. 3(b) and 3(c) demonstrate the frequencytunability of a half-wave plate. Actually, large-area graphene can be grown by a chemical vapor deposition (CVD) process and transferred onto the silicon array. Fermi energy of graphene can be easily adjusted with a field effect transistor structure [27], where the change of 0.1 eV is achieved with a bias voltage of a few voltages. Therefore, we can effectively switch the response wavelength for the half-wave plate from 17.58 to 17.84 THz by electrically controlling graphene.

3. Functionality-switchable polarizer

Besides a tunable half-wave plate, we achieve a switchable polarizer using the same structure as the former one in Fig. 3(a). The sharp x-shape curve of polarization transmission and the tunability of frequency bring the graphene-based metasurface a new function as switchable polarizer. Figure 4(a) shows the polarization transmission coefficients of the switchable polarizer with Fermi energies of 0 and 1.2 eV, tij represents the transmitted coefficient of j-toi polarized light, and i(j)-polarized light represent x-polarized, y-polarized, LCP or RCP waves. When j-polarized light illuminates, the cross-polarized transmission coefficient with 0 eV (blue line) and the co-polarized transmission coefficient with 1.2 eV (red line) are above 0.8 from 17.55 to 17.62 THz, while the co-polarized transmission coefficient with 0 eV (black


line) and the cross-polarized transmission coefficient with 1.2 eV (pink line) are below 0.2 in the blue rectangle marked region. The big difference between co- and cross-polarization transmission results in a high-efficiency and switchable polarizer. The polarization selectivity of transmitted light means that we can highly choose the transmitted polarization state between i- or j-polarization by applying 0 or 1.2 eV Fermi energy.

Fig. 4. (a) Polarization transmission coefficients of a switchable polarizer both for linearly and circular polarized light. (b) PSR of i(j)-polarized light with EF of 0(1.2) eV, the inset shows the enlarged drawing of PSRs.

To value the switchable polarizer, the polarization suppression ratios (PSR) with Fermi energies of 0 and 1.5 eV is shown in Fig. 4(b). Blue line represents the ratio of the transmitted light intensity of i-polarized light to j-polarized light with the Fermi energy of 0 eV (PSRi) and the ratio of the transmitted light intensity of j-polarized light to i-polarized light with 1.2 eV (PSRj) is marked by the red line. Even though taking no account of the maximum value in 17.53 THz, PSRi with 0 eV in inset (blue line) is about 15, which means that the proposed metasurface converts most of the incident linearly and circularly polarized light into its crosspolarized light. The PSR of j-polarized light (red line) is about 20 as shown in the inset of Fig. 4(b), which represents a major advance compared with the previously reported polarization device [15]. The high PSR verifies the function to keep co-polarized transmitted light effectively by applying 1.2 eV Fermi energy. Thus, we achieve a switchable polarizer both for linearly and circularly polarized light by dynamically adjusting graphene’s Fermi energy between 0 eV and 1.2 eV in a fixed graphene-based structure.

Fig. 5. The multiple functions of the electrically controlled switchable polarizer for linear (a) and circular (b) polarized light.

For understanding the switchable functions vividly, Fig. 5 shows multiple polarization conversions for incident linearly and circularly polarized light. First, taking linearly polarized light as an example in Fig. 5(a), our graphene-based metasurface can generate x- or ypolarized light by choosing 0 eV or 1.2 eV Fermi energy. The polarized direction of the incident linearly light rotates 90 degrees without external field (0 eV), which is consistent


with function of the half-wave plate discussed above. Moreover, although the structure with 1.2 eV holds the same polarization as the incident wave, the electrical manipulation compared with the conventional way of mechanical demolition possesses significant potentials for integrated devices. Similarly, for the case of circularly polarized light incidence in Fig. 5(b), RCP and LCP waves can be selectively attained by actively controlling Fermi energy. Therefore, we realize a switchable polarizer for linearly and circularly polarized waves from 17.55 to 17.65 THz. Due to the low efficiency of terahertz source, the polarization device with high transmission efficiency is highly desired. The proposed device makes great progress in transmission efficiency when compared with the reported transmitted crosspolarized device [16]. 4. Multifunctional polarization converter

Fig. 6. (a) Co- and (b) cross-polarization transmission coefficients with the Fermi energies of 0, 0.6 and 1.5 eV. (c) The phase differences of co- and cross-polarized transmitted light with the Fermi energies of 0, 0.6 and 1.5 eV in 17.85 THz.

Except a tunable half-wave plate and switchable polarizer, the graphene-covered strip array also holds the function of phase modulation. Figures 6(a) and 6(b) present the evolution of the polarization transmission coefficients of the multifunctional polarization converter with different Fermi energies. The phase differences of co- and cross-polarized transmitted light ranges from 90 to 270 degrees corresponding to EF from 0 to 1.5 eV in 17.85 THz as shown in Fig. 6(c), which means the array could convert linearly polarized light into LCP, crosspolarized and RCP light by choosing different Fermi energies among 0, 0.6, 1.5 eV. In addition, due to the continuous adjustment of Fermi energy, Fig. 6(c) predicts the generation of arbitrary elliptical polarization states from LCP to RCP for an incident linearly polarized light by realizing continuous phase difference from 90 to 270 degrees. Though the transmission efficiency does not reach unity and the transmitted light is not pure RCP or LCP light, the continuous polarization-tunability by electrically gating graphene rather than changing their geometry parameters is a major advantage compared to previously reported single-functional devices.


5. Summary and conclusion

In summary, we numerically achieve transmitted multifunctional polarization conversion via simple construction in mid-infrared region. Silicon strip array acts as a half-wave plate due to the excitation of hybrid Mie multipole resonances. After covering a graphene sheet on the silicon array, the working waveband can be shifted from 17.58 to 17.84 THz by applying different Fermi energies. Simultaneously, the x-shape curve of polarization transmission encountering the dynamic shift of response wavelength brings a switchable polarizer, which could selectively pass co- or cross-polarized light in the waveband of 17.55 to 17.62 THz. In addition, the graphene-based metasurface also achieves continuous polarization evolution from LCP to RCP in 17.85 THz. Significantly, the simple design for the dynamic control of polarization conversion without any mechanical stretch or rotation will be beneficial for its further practical applications in manipulating the polarization state of waves and exploring polarization-sensitive devices. Funding

National Natural Science Foundation of China (NSFC) (51176041).