Wideband tunable mid-infrared cross polarization converter using rectangle-shape perforated graphene

The strong plasmonic response and wide electrostatic tunability of graphene make it a promising material for developing infrared optoelectronic components. In this paper, we present a mid-infrared wideband tunable cross polarization converter using periodically perforated graphene. The polarization converter consists of a metal ground plane, an insulator layer, and a rectangle-shape periodically perforated graphene sheet. By superimposing two localized surface plasmon modes, the polarization converter transforms a linear polarization to its cross polarization over a bandwidth as wide as ~5% of the central frequency (46.8THz) with a peak conversion ratio exceeding 90%. The polarization conversion performance is maintained over a wide range of incident angles up to 50°, and is highly tunable by electrostatic tuning of the graphene Fermi energy. Our proposed device enables the manipulation of light polarization for potential mid-infrared applications. ©2016 Optical Society of America OCIS codes: (310.6628) Subwavelength structures, nanostructures; (160.3918) Metamaterials; (230.5440) Polarization-selective devices; (130.3060) Infrared. References and links 1. J. Hu, J. Meyer, K. Richardson, and L. Shah, “Feature issue introduction: mid-IR photonic materials,” Opt. Mater. Express 3(9), 1571–1575 (2013). 2. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012). 3. Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012). 4. M. Z. Tidrow, W. A. Beck, W. W. Clark III, H. K. Pollehn, J. W. Little, N. K. Dhar, R. P. Leavitt, S. W. Kennerly, D. W. Beekman, A. C. Goldberg, and W. R. Dyer, “Device physics and focal plane array applications of QWIP and MCT,” Proc. SPIE 3629, 100–113 (1999). 5. G. Chen, A. 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Introduction
The presence of thermal radiation, molecular absorption and atmospheric window makes the mid-infrared an attractive regime for both fundamental and applied explorations.The mid-infrared is a well-suited spectral region to address technological challenges in sensing, spectroscopy, communication, and countermeasures [1].Tremendous progresses have been made in the past decades for mid-infrared components, especially on lasers [2,3] and detectors [4,5].In order to develop the mid-infrared technology to its full capacity, new device functionalities need to be developed, which depend critically on the material platforms.
Graphene is an emerging material with potential for advancing mid-infrared devices [6,7].As originated from its massless Dirac electrons, graphene is shown to exhibit a wide electrostatic tunability and a strong plasmonic response with relatively small loss [8,9], which makes it attractive for developing new device functionalities in the mid-infrared regime.On the basis of graphene plasmonic structures, a variety of mid-infrared components have been demonstrated in the past decade, including perfect absorbers [10][11][12][13], photodetectors [14,15], and modulators [16,17].Recently, interesting properties such as plasmonically induced transparency [18], tunable anomalous refraction [19] and optical polarization encoding [20] have also been proposed in graphene metasurfaces.In addition to these optoelectronic components, polarization converters are often needed.For example, in communication and spectroscopy, the ability to control polarization state is essential.Using metal nanostructures such as metallic nanoparticles [21][22][23][24][25][26], metallic nanoslots [27,28], and chiral metamaterials [29,30], researchers have demonstrated narrowband, multiband and broadband polarization converters, respectively.The polarization conversion in such devices has been shown to be related to the excitation of localized surface plasmon resonances.In this context, graphene plasmonic nanostructures also stand out as attractive candidates due to their electrostatic tunability [31], which in turn enables agility in altering polarization converters' working frequencies without readjusting the device geometry.H. Cheng et al. reported single-band tunable mid-infrared polarization converters using the L-shaped and cross-shaped graphene sheets, respectively [32,33].J. Ding et al. extended the polarization converter for dual-band operation by using L-shape perforated graphene sheets [34].These proposed polarization converters exhibit high polarization conversion ratios (PCRs) and a wide frequency tunability.However, they are all based on individual separate plasmonic resonances, and thus are limited in bandwidth.In this paper, we propose a high efficiency and wide-band graphene-based cross polarization converter, which is based on excitation of superimposed multiple plasmonic modes with well-defined phase relations, and is implementable in a simple structure of rectangle-shape perforated graphene.A bandwidth as wide as ~5% of the central frequency is found to be achievable in numerical simulations.

Structure design and simulation
The structure of our proposed polarization converter is sketched in Fig. 1(a).It consists of a metal ground plane, an insulator layer and a graphene sheet with periodic rectangle-shaped holes.The ground plane is made of a 100 nm thick gold, and the insulator layer is considered as a dielectric film with thickness of d = 1.1 µm.Figure 1(b) depicts one unit-cell of the array structure with the geometric parameters described in the caption, where p, L 1 , and L 2 represent the period, hole length, and hole width, respectively.The rectangular hole is oriented 45° from the x and y directions.The optical property of graphene is described in term of a two-dimensional conductivity as given by the well-known Kubo formula [35] where k B T indicates the thermal energy of 26 meV taken at room temperature, e is the electron charge,  is the reduced Plank constant, μ c is the Fermi energy, and τ is the electron scattering time typically taken as 0.5 ps [36].The first term of Eq. ( 1) represents the intraband contribution and the second term refers to the interband contribution.
The structure is modeled and simulated with the Ansys' HFSS solver in driven mode, which is based on the finite element method in frequency domain.The Au layer is described with a Drude model with a typical carrier concentration of 4.11 × 10 27 m −3 and a scattering time of 20 fs [37].The dielectric constant of the spacer layer is assumed to be 2.1 for simplicity like in [10] and [34].In reality, transparent materials such as ZnSe could be used for the spacer layer.The graphene is treated as a boundary condition with impedance defined by the conductivity as given in Eq. ( 1).Specifically, the surface resistance and reactance are given by the real part and imaginary part of 1/σ, respectively.This boundary modeling approach is more efficient in computation, and the results have been confirmed to agree with those obtained with the dielectric constant approach [36] according to our simulations.Floquet excitation port and periodic boundary condition were applied in the unit-cell, and the S parameters were used to calculate the complex reflection coefficients for both the cross-and co-polarized lights.

Results and discussions
The property of the polarization converter can be described with a general reflection matrix as [28] xx xy where the arbitrary element R lm represents the complex reflection coefficient of the reflected light linearly polarized in the l direction for incident excitation in the m direction.Due to the symmetry of our structure, we have R xx = R yy and R xy = R yx .In this study, we mainly analyze R xx and R yx by assuming an x-polarized incidence at the incident port without loss of generality.
The reflectance R xx and R yx as a function of frequency for the proposed structure is shown in Fig. 2(a), where the Fermi energy of graphene is taken as 1.0 eV.We can observe two overlapped reflection peaks in R yx at 46.4 THz and 47.4 THz, and the corresponding dips in R xx with small reflections.These features of R yx and R xx indicate a function of cross polarization conversion in the reflection mode.The polarization conversion ratio (PCR) can be defined as  In prior reported polarization converters using an L-shape perforated metal film or graphene sheet [23,34], it has been shown that the physical origin of the cross polarization conversion is related to two eigenmodes excited at two orthogonal incident polarizations along 45° and −45° counterclockwise from the positive x-axis direction, respectively.In order to gain physical insight of our wideband polarization conversion, we analyzed similar two eigenmodes.The incident polarization along 45° counterclockwise from the positive x-axis direction is defined as state A, and its orthogonal polarization along −45° counterclockwise from the positive x-axis direction is defined as state B. Figure 3(a) shows the reflection coefficients for these two states, i.e.R AA and R BB .The crossed terms R AB and R BA are negligibly small (not shown) indicating no polarization conversion for these two eigenmode states.It is seen that R AA and R BB exhibit resonances at 46.1 THz and 47.7 THz, respectively.The magnetic fields of these two resonant modes are plotted in Figs.3(c) and 3(d).These two modes exhibit a phase difference of about 180° over the band between 46.1 THz and 47.7 THz as shown in Fig. 3(b).This gives a clear picture of the polarization conversion in our structure.Namely, the incident x-polarization can be decomposed into two orthogonal components with polarizations along 45° and −45° counterclockwise from the positive x-axis direction, respectively.These two components excite the two eigenmodes in the states of A and B simultaneously.Due to the large permeability associated with the magnetic resonances [21], a near 180° phase difference is accumulated between the two components after reflection.The recombination of these two reflected components finally results in a polarization rotation by 90°over a wide bandwidth.It is worthy to note that the Fabry-Perot cavity defined by the spacer layer plays a critical role in the polarization conversion.Indeed, the two eigenmodes responsible for the polarization conversion can be considered as localized graphene resonances coupled to the Fabry-Perot cavity [38].Figures 4(a .Furthermore, the coupling to the Fabry-Perot cavity also changes the phase difference between the two eigenmodes (R AA and R BB ).As shown in Fig. 4(c), a near 180° phase difference is achievable over a wide band between 46.1 THz and 47.7 THz near the crossing conditions of d = 1.1µm and 3.3 µm, which therefore should be the optimal thicknesses for our proposed polarization converter.Figure 4(d) shows the PCRs of our polarization converter for different spacer thicknesses, which confirms the optimal thickness selected as d = 1.1 µm.To better understand the two superimposed modes in our rectangle-shape perforated graphene, we perform a couple of geometric parameter studies by varying the hole size.First we keep L 1 = 120 nm, and increase L 2 from 70 nm to 100 nm in a step of 10 nm.Second, we keep L 2 = 100 nm, and increase L 1 from 120 nm to 150 nm in a step of 10 nm.The corresponding PCRs for these two cases are plotted in Figs.5(a) and 5(b), respectively.It is seen from Fig. 5(a) that for each value of L 2 , there are two excited localized surface plasmon modes.As L 2 increases, the low-frequency mode blueshifts and the high-frequency mode redshifts.These two modes eventually merge to form our designed wide bandwidth at L 2 = 100 nm.Additionally, as seen from Fig. 5(b), as L 1 increases, the low-frequency mode redshifts and the high-frequency mode blueshifts, and these two modes gradually evolve into two separate bands.Taking together of these observations, we can see that the frequency of the low-frequency mode is proportional to L 2 and inversely proportional to L 1 , and the highfrequency mode exhibits the opposite characters with the resonant frequency proportional to L 1 and inversely proportional to L 2 .These modal behaviors with respect to the hole size are understandable from the field profiles as shown in Figs.2(c) and 2(d).For the low-frequency mode at 46.4 THz as shown in Fig. 2(c), the field maxima are mainly located along L 1 in graphene, thus the mode frequency is expected to be inversely proportional to L 1 , similar to the standing waves in a Fabry-Perot cavity.Additionally, the local maximum fields mainly reside between the corners of two neighboring rectangles, therefore as L 2 increases, the coupling between the corners of two neighboring rectangles becomes stronger and leads to a higher mode frequency, which is consistent with the observed behavior of the low-frequency mode.The high-frequency mode, as shown in Fig. 2(d), has its field maxima mainly distributed along L 2 in graphene, and therefore its frequency is inversely proportional to L 2 .Also an increasing L 1 would lead to a stronger coupling between two neighboring rectangles and thus result in a higher resonant frequency.These properties of mode shifts respect to the geometrical parameters form the basis of our proposed wide bandwidth device, which are different from the previously reported L-shape perforated graphene in [34], where the mode frequencies both redshift with increasing hole size.In addition, we also studied the effect of period on the device performance.Figure 6 shows the PCRs for different periods.As the period increases from 170 nm to 230 nm, the PCR redshifts in frequency.The optimal PCR value is obtained at a period of 190 nm.This dependence of PCR on the period is understandable as the spacing between neighboring holes changes so do the plasmonic resonant modes (i.e. standing waves).
For the polarization converter in reflection mode, operation with a wide range of incident angles is also desirable.Here, we examine the angular dependence of our polarization converter.Figure 7 shows the PCRs for an incident angle θ ranging from 0° to 60°.It is seen that the wideband operation is maintained over the angle range from 0° to 50° without much degradation in performance.This wide angle operation is another advantage over devices based on metal nanostructures.As an example, for the polarization converter based on slotted L-shaped metal antennas as reported in [28], its PCR bandwidth quickly degrades for incident angle larger than 30°.The less angular dependence of PCR in our device is related to the much smaller feature size of graphene.Usually, for the same resonant wavelength, the feature size of graphene plasmonic structure is several times smaller than the metal counterpart, which reduces the dependence on the incident angle.We next examine the tuning property of our cross polarization converter.The Femi energy of graphene can be tuned from about −1 eV to 1 eV by chemical doping or electrical gating [8], which suggests a great potential for tunable devices.Figure 8(a) shows the PCRs of our proposed device for different graphene Fermi energies.It is seen that the PCR is tunable over a wide range of frequencies from about 30 THz to 50 THz.As the graphene Fermi energy increases from 0.5 eV to 1.0 eV, the PCR maintains a wide bandwidth and increases in peak value from about 0.4 to 0.95.The higher PCRs with increasing Fermi energy are due to the fact that the graphene is becoming more metallic, whose strong plasmonic resonance results in a phase difference of the two reflected orthogonal components closer to 180°, thus leading to an enhanced PCR.This tuning property makes graphene-based cross polarization converters more attractive than the metal-based ones, since the tuning is realized by controlling the Fermi energy without adjusting the geometric parameters.Finally, it is noted that the electron scattering time of graphene could affect the performance of our proposed polarization converter.It has been reported in previous studies that the electron scattering time of graphene could vary within a wide range on the order of ps or sub-ps [36,39,40], depending on the film quality.Figure 8(b) shows the PCRs for different electron scattering times.For larger τ of more than 0.2 ps, the wide bandwidth is well maintained.However, for smaller τ of less than 0.2 ps, the PCRs degrade quickly with decreased peak values, and there is no effect of polarization conversion for small τ of 0.02 ps.This degrading of PCR with decreasing electron scattering time is due to the increased freecarrier loss in graphene, which causes a reduction in the reflected wave amplitudes and a deviation in phase difference between the two reflected orthogonal components.Therefore, a good quality of graphene sheet with relatively larger electron scattering time is beneficial to obtaining the wide bandwidth in our proposed polarization converter.

Conclusions
In conclusion, a wideband tunable mid-infrared cross polarization converter has been designed and theoretically demonstrated by using a three-layer structure with rectangle-shape perforated graphene sheet.Numerical simulations show that the designed polarization converter exhibits a PCR with FWHM bandwidth of ~5% of the central frequency, and peak value exceeding 90%.The wide bandwidth operation is attributed to the superposition of two eigenstate surface plasmon modes associated with the slot resonances, which are simultaneously excited by the incident polarization and have a near π phase shift.The polarization conversion performance is maintained over a wide range of incident angles up to 50°, and is highly tunable by electrostatic tuning of the graphene Fermi energy.Our proposed device holds the promise of controlling the light polarization for a wide range of applications such as mid-infrared sensing, spectroscopy and communication.By optimizing the graphene geometry for superimposing more plasmon modes, it is possible to achieve a broader bandwidth in tunable polarization converters.

Fig. 1 .
Fig. 1.(a) Schematic of the proposed cross polarization converter consisting of a rectangleshape perforated graphene sheet on top of a dielectric spacer layer backed with a metal ground plane.(b) Unit-cell of the structure with parameters of p = 190 nm, d = 1.1 µm, L 1 = 120 nm, and L 2 = 100 nm.
and is plotted in Fig.2(b).It is readily seen that the PCR exceeds 0.9 over a wide frequency band with overlapped two local maxima.The FWHM bandwidth of the PCR is 2.17 THz, about 5% of the central frequency.This wide bandwidth results from a superposition of two localized surface plasmon modes arising from the slot resonances.The magnetic field profiles of the two resonant modes at 46.4 THz and 47.4 THz are plotted in Figs.2(c) and 2(d), respectively.The fields are concentrated on the corners of each rectangular hole, indicative of a strong coupling between neighboring holes.To the best of our knowledge, such a wideband polarization conversion has not yet been reported for graphene-based polarization converters.

Fig. 2 .
Fig. 2. (a) Simulated reflectance and (b) PCR of the cross polarization converter.Magnetic field profile at the interface between graphene and air for the resonant mode at (c) 46.4 THz and (d) 47.4 THz.

Fig. 3 .
Fig. 3. (a) Simulated reflectance and (b) phase difference for the two eigenmodes with incident polarizations of 45° and −45° counterclockwise from the x-axis direction.Magnetic field profile at the interface between graphene and air for the resonant mode at (c) 46.1 THz and (d) 47.7 THz.
) and 4(b) show the calculated absorptions (1-|R AA | 2 and 1-|R BB | 2 ) of the two eigenmodes as a function of the dielectric thickness.The coupling of the localized resonant modes of the graphene slot with the Fabry-Perot resonances lead to crossing features and a periodical behavior as the dielectric thickness varies.Because the resonant frequencies of the two eigenmodes are designed to be very close, their crossing behaviors both occur around the spacer thickness of d = 1.1 µm and 3.3 µm as seen in Figs.4(a) and 4(b)

Fig. 4 .
Fig. 4. Simulated absorption of the eigenmode at 46.1 THz (a) and 47.7 THz (b), and (c) phase difference of the two eigenmodes as a function of the dielectric spacer thickness.(d) PCRs of the polarization converter for different dielectric spacer thicknesses.

Fig. 7 .
Fig. 7. Simulated PCRs of the structure for different incident angles.

Fig. 8 .
Fig. 8. Simulated PCRs of the structure for (a) different graphene Fermi energies and (b) different electron scattering times.