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This paper demonstrates a new type of frequency tunable polarization selective surface operating at low THz, which is devised by utilizing the unique features of graphene. The device is comprised of an infinite array of identical unit cells in three layers. Multiple graphene dipoles are placed on the top and bottom layers to form the vertical and horizontal electric field filters. Using this new configuration, the proposed device exhibits reflection for the incident Left-Hand-Circular-Polarization (LHCP) waves and becomes transparent to the incoming Right-Hand-Circular-Polarization (RHCP) waves. The excited localized surface plasmonic resonance mode on the graphene based unit cells significantly reduces the physical dimension of the device. The unit cell dimension of the proposed design is in the order of 0.18 wavelengths in comparison to conventional metallic structures, where it is of order a half a wavelength. In the full wave analysis, the graphene based polarization selective surfaces exhibit an isolation of 21 dB for LHCP waves and a transmission loss of around 5.1 dB for waves with RHCP characteristics. The performance has also been examined under oblique incidence. The results fully verify that the proposed planar device operates properly for incident angles up to 40°. The tuning effect of the described device is investigated by varying the chemical potentials of graphene. Significant frequency reconfiguration capability is achieved in the isolation of LHCP incident waves, and meanwhile, for RHCP incidence, the transmission rate remains reasonably high.
© 2015 Optical Society of America
1. Introduction
Polarization selective surfaces [1] are engineered meta-surfaces, which function as spatial filters for electromagnetic waves of different polarizations, mostly at microwave frequency bands. These surfaces transmit pre-defined polarized waves and block other polarization components. Of all the polarization related meta-surfaces, the circular polarization selective surfaces (CPSS) [1–4] have attracted most attention due to their potential for satellite communication antennas such as reflect arrays [5]. Typical Left-Hand-Circularly-Polarized selective surfaces (LHCPSS) are defined to transmit right-hand polarized waves and to filter out the left-hand polarization components of the incoming waves. To achieve the circular polarization filtering purpose, the first LHCPSS is configured in [1] using two orthogonal dipoles and a half wavelength transmission line in the vertical direction, which occupies a lot of space in practical operation. These resonant dipoles have been optimized in [2,3] to reduce the profile of the three-dimensional structures. Also the work presented in [4] has successfully removed the vertical transmission line and has simplified the CPSS into two-dimensional surfaces, which enables the CPSS to be manufactured using planar structures i.e. microstrip substrates. However, the propagation characteristics of the CPSS need further study for the higher frequencies of operation in the THz spectrum, as well as frequency tuning for broadband applications. THz polarizers have recently been implemented using wire grids [6], nanotubes [7] and liquid crystals [8] according to current literature. However, these devices are either made from bulky materials or lack frequency tuning capabilities.
Recent progress in graphene research has introduced a radically new approach to produce polarization selective devices in the THz range. This planar one atom thick carbon film possesses impressive mechanical and flexibility properties, exceptional optical transparency, as well as tunable sheet resistance via external biasing [9,10]. These properties of graphene can potentially lead to novel technologies for new generation devices such as optical modulators [11], plasmonic devices [12–15], photoconductive antennas [16], hyper-lenses [17], cloaks [18] and absorbers [19] in the THz spectrum. Moreover, various THz polarizers have been proposed using graphene materials, which possess broad bandwidth [20,21] and frequency tunable characteristics [22]. However, the graphene based optical polarizers presented in [19–21] were developed using bulk substrate materials. Further investigation is required to obtain planar polarization selective devices with a minimal profile, which may be applied to future wireless communication at THz such as described in [23].
In this paper, new types of planar polarization selective surfaces based on tunable graphene materials and operating at 1.12 THz are presented. The plasmonic resonance [12–14] of graphene strips is utilized to replace metallic dipoles in the conventional design [4]. The utilized graphene strips dramatically reduce the overall dimension of the proposed CPSS. Meanwhile, the decreased unit cell dimension offers better spatial filtering capabilities for THz waves, which normally possess very narrow beam widths. The tunability of the graphene sheet impedance is also used in the research to enhance the CPSS broadband operation for THz waves.
2. Graphene characterization
As regards electromagnetic wave propagation analyses a graphene membrane is an infinitesimally thin, two-dimensional material characterized by surface impedance. Principally, the sheet impedance of graphene is determined by the intra-band and inter-band contributions of surface conductivity, which are defined as σinter and σintra respectively. As illustrated in [24], these two types of sheet conductivities are given by:
Where Γ = 1/2τ, μc represent the collision frequency and chemical potential of the graphene material respectively; τ, ω, T are defined as the relaxation time of graphene, operating frequency and room temperature.The sheet impedance of the graphene is fully characterized when all these parameters are determined. The total conductivity of the graphene is determined then as σtotal = σintra + σinter. The sheet impedance is then finalized via Zs = 1/ σtotal and both the resistance and reactance may exist in the final Zs format due to the complex formation of Eqs. (1) and (2).
In order to fully illustrate typical sheet resistance and reactance of the graphene at low THz, the sheet impedance curves versus frequency are plotted in Fig. 1 assuming a collision frequency (Γ) of 0.66 meV (τ = 0.5 ps) and variable chemical potential values under the guideline of the graphene material characteristics stated in [24] assuming room temperature operation. According to Fig. 1, both the real and imaginary values of the graphene are significant in the THz regime and they vary accordingly when higher chemical potential values are applied to the material. In addition, the negative imaginary value of the conductivity reflects that the graphene sheet possesses inductive surface impedance.
Another distinct advantage of graphene sheets over their metallic counterparts is the dimension of its local surface plasmonic resonances [12–15] at low THz frequencies. The reduced size of the resonant structures resulting from inherent graphene surface plasmon resonances [25–27] is an obvious advantage to minimize the profile of the THz devices. The work presented in [26] and [27] has demonstrated that a patterned graphene sheet possesses plasmonic resonance dimensions much smaller than λ/10 (approximately at λ/20) under periodic boundary conditions, in an operational band below 2 THz.
3. Graphene based polarization selective surfaces design
The proposed graphene polarizer is based upon conventional designs using conductive materials proposed in [2,3] and the planar revisions stated in [4] to stop the LHCP incoming waves and pass the RHCP waves at THz frequencies. It consists of two layers of graphene strips formed as arrays, each with a period L fixed at 48 μm, which is equivalent to around 0.18 wavelengths for the central operating frequency of 1.12 THz. An L shaped metallic strip is placed in between two layers of graphene strips, separated by dielectric substrates with thickness t equivalent to 25 μm and dielectric constant of 2.33, which is used to guide and couple the vertically induced current into the horizontal direction. The vertical and horizontal arms of the metallic L shaped strip have the same length of 43 μm and width of 4.3 μm. The length of and the width of the L strip form the main factors to obtain the coupling effect between the top and bottom layers. In the L shaped design, the optimized resonance behavior as well as high transmission efficiency between vertical and horizontal arms must be considered.
On the top layer, 12 identical graphene strips are vertically oriented to function as the vertical polarized wave filter. The strip length a is fixed at 20 μm and the width b is 5.8μm. The space between adjacent elements g is 4 μm. Another identical set of graphene strips is placed horizontally on the bottom layer. The dimensions of these graphene strips are selected to obtain optimized plasmon resonances based on information in reference [26] and [27]. The overall size of the unit cell is determined to accommodate these Graphene strips as well as the L shaped trace.
Compared to conventional polarization selective surfaces [4], which require unit cell sizes to be approximately half a wavelength, the proposed graphene device significantly reduces each unit element by up to 60%, owing to the plasmonic resonance of the graphene in the THz band. This allows more graphene strips to be packed in a limited aperture and it leads to the increase of angular bandwidth for graphene polarizers.
Principally, the vertical and horizontal dipole arrays in the device are utilized to reflect the vertically and horizontally polarized electromagnetic waves respectively. The L shaped metallic strip in the middle layer transfers the induced current flow from the vertical direction into the horizontal direction and at the same time a 90° phase delay is obtained to reflect the LHCP waves [1–4]. On the bottom layer of the device, the horizontal dipoles have a high electric field concentration for the incident LHCP waves due to the strong resonance behaviours. However the RHCP waves are transparent to the reflection mechanism due to the L trace phase delay misalignment for the RHCP waves. Under these electromagnetic wave manipulations, the LHCP waves are mostly reflected by multilayer structure. A small proportion of the LHCP waves are also absorbed by the resonance dipoles due to the lossy characteristics of graphene. This reflection and the absorption capability for the proposed device is expressed as a LHCP wave isolation capability in the performance analysis (see Fig. 2). Numerically, this parameter is expressed as [4]:
where Pout (LHCP) and Pin (LHCP) is the transmitted and input power level of the LHCP waves respectively.
However, due to the phase delay orientation mismatch for the RHCP waves, the reflection mechanism is not met for the RHCP waves. Therefore, the RHCP waves may transmit through the three layer surface configuration with minimum intervention. The loss associated with the RHCP waves transmission for the discussed device is calculated via the RHCP waves’ output and input power level differences when the proposed device is used [4]:
where Pout (RHCP) and Pin (RHCP) are the transmitted and input power levels of the LHCP waves.The isolation and transmission loss parameters may be assessed via the S21 parameter in the scattering matrix. A minus sign needs to be added to S21 to determine the value of these parameters according to the IEEE definition of the S parameters and the transmission loss.
4. Results and discussions
4.1 Full wave analysis
This investigation focuses on the numerical analysis of the presented graphene configured polarization selective surfaces operating in the low THz spectrum at 1.12 THz. Ideally, the presented device is assumed to block out all the LHCP waves incident on the vertical graphene dipole surfaces and the incoming RHCP components may transmit through the full structure with minimal losses. The substrate between the graphene patches and L trace is Duroid 5870 with a dielectric constant 2.33 and dissipation factor 0.0012. According to the operating principle stated in section 3, both the vertical graphene strips on the top layer and the horizontal graphene dipoles on the bottom must remain in the plasmonic resonance state in order to filter the LHCP waves at the operating frequency to achieve the design specification properly. Analytical simulation is arranged to verify the operational characteristics and performance output of the proposed device. Full wave simulation is executed in the CST Microwave studio environment under periodic boundary conditions, in which a two dimensional array of infinite identical elements is formed. Two sets of polarization waves namely the LHCP waves and RHCP waves are assumed to impinge on the device for electromagnetic transmission analysis. It is worth mentioning that the non-locality effect may improve the accuracy of the graphene plasmonic resonance predictions at high THz. However, this effect is not included in the paper because the wavelength associated in the analysis is significantly larger than the wavelength threshold, under which the non-locality factor may affect the performance.
The electric field distribution at the bottom graphene layer is shown in Fig. 3(a) for LHCP waves and Fig. 3(b) for RHCP waves at the central operating frequency of 1.12 THz. It may be easily shown from Fig. 3(a) that higher electric fields concentrate at the edge of the graphene strips, which confirm that a strong resonance mode exists for the LHCP incident at 1.12 THz. Meanwhile, a much weaker electric field density for the graphene strip is seen in Fig. 3(b) under the same field density scale for the incident RHCP waves case. The comparison between Fig. 3(a) and Fig. 3(b) illustrates that the LHCP waves have strong resonance interaction with the prescribed graphene based polarization selective surfaces, which are transparent to the incoming RHCP waves at the same time. The numerical results of the proposed polarization selective surfaces are expressed in terms of LHCP isolation in Fig. 3(c) and RHCP transmission loss in Fig. 3(d), in order to assess the performance of the design. An isolation of around 20.8 dB is illustrated at the central operating frequency of 1.12 THz verifying the extremely high blockage effect of the graphene based polarization selective device for the LHCP waves, which, in fact, is even slightly better (2 dB) than that of their metal counterparts in [4] in the microwave band. A low transmission loss of 5.1 dB is observed in Fig. 3(d) for the RHCP wave. This phenomenon reflects that the prescribed device is almost transparent to the incident RHCP waves, although the transmission loss value is slightly higher (2.1 dB) than the metal polarizer used in [4] in the microwave band, due to the absorption of the graphene materials introduced by the higher sheet resistance characteristic.
Fig. 3 The performances of the proposed polarization selective surfaces (a) electric field distribution in bottom layer for LHCP waves incidence, (b) electric field distribution in bottom layer for RHCP waves incidence, (c) isolation curve for LHCP waves, (d) transmission loss curve for RHCP waves.
Based on the performance analyses above, the discussed polarization selective surfaces configured by graphene materials are able to block the incoming LHCP electromagnetic waves and at the same time transmit any incident RHCP waves through the device. The prescribed polarization selective surfaces offer a direct solution to obtain purified RHCP waves for wireless communication at low THz.
4.2 Oblique incident wave analysis
The feasibility of the proposed polarization selective surfaces in terms of different incident angles has also been conducted in this work. The purpose of this is to demonstrate that the proposed device is also fully operational under various incident angles. Under the periodic boundary conditions in this investigation, circularly polarized waves of incident angles of 0°, 10°, 20°, 30° and 40° are assumed to impinge on the unit cells of the proposed device.
Figure 4 demonstrates the performances of the proposed devices for oblique incident angles for both the RHCP wave transmission loss and LHCP wave isolation. Figure 4(a) illustrates clearly that the isolation resonance frequency of the device remains almost constant at 1.12THz although a very small shift to 1.15 THz is seen when the incident angle increases to 40°. When the incident angle is varied, the peak isolation value of the device fluctuates from 22 dB to 27 dB. This phenomenon reflects that the majority power of the LHCP waves is reflected or absorbed at the operating frequency. Meanwhile, the transmission loss of the proposed device against different incident angles is presented in Fig. 4(b). The transmission loss curves illustrate that the transmission loss of the polarization selective surfaces fluctuates from 5.1 dB to 5.3 dB, when the incident angle of the incoming electromagnetic waves is increased up to 40°. The low transmission loss variations of around 0.2 dB for the different incident angles confirm that the proposed prototype is highly insensitive to variable incident angles. This advanced capability demonstrates that the presented device is suitable for oblique incident applications in wireless communications at THz frequencies.
Fig. 4 Oblique incident analysis results (a) isolation curve for LHCP waves, (b) transmission loss curve for RHCP waves.
4.3 Frequency reconfigurable investigations
The frequency reconfigurable capability of the proposed device is due to the impedance tuning characteristics of the graphene material, that is, the sheet resistance and reactance of the planar graphene is variable when external electric biasing is applied to the material. The negative sheet conductance of this planar material defines inductive sheet impedance characteristics. Therefore, the tuning of the chemical potential of the graphene practically changes the inductive impedance of the graphene dipoles and the operating frequency of these strips can be varied, according to L-C circuit resonance.
In this investigation, the graphene material is assumed to be biased between a chemical potential of 0.09 eV and 0.18 eV when Γ is fixed at 0.66 meV according to the biasing range availability and the Γ parameter analysis illustrated in [24]. This arrangement is equivalent to the sheet impedance varying between 186.4 + j 641.7 Ω/square and 94.7 + 326.2 Ω/square. Practically, this external biasing condition may be achieved using straight copper strip in a unit cell environment, as shown in Fig. 5. The line width should be narrow to avoid unwanted electromagnetic waves interacting with the graphene patches. An external DC is applied between top and bottom strips to supply voltages.
The transmission loss and isolation performances of the proposed polarization selective surfaces are presented in Fig. 6,when the chemical potential of the graphene material is varied. It may be observed clearly that the resonances of the isolation curves vary according to the different chemical potential values.
Fig. 6 Frequency tunable analysis for the proposed polarization selective surfaces: (a) isolation curve for LHCP waves, (b) transmission loss curve for RHCP waves.
The operating frequency of the proposed LHCP selective surfaces is shifted between 1.02 THz and 1.22 THz with the peak isolation fluctuation between 12 dB to 38 dB, confirming that the majority of LHCP waves are still blocked by the proposed device when the chemical potential of the graphene is varied. Meanwhile, the quality factor of the isolation resonance is enlarged if the chemical potential of the device is increased. These phenomena agree well with the series resonance circuit analysis, where operating frequency and quality factor is determined as and . The higher the chemical potential is, the smaller the parasitic sheet inductance of the graphene strips will be. Hence, this leads to higher operating frequency and quality factor.
Figure 6(b) illustrates that the transmission loss for the incoming RHCP waves remain low when the sheet impedance of the proposed graphene device is tuned. The minimum transmission loss of 2.7 dB is observed at an operating frequency of 1.2 THz when the chemical potential is 0.18 eV. The highest transmission loss of 5 dB is introduced due to the weaker resonance behaviour associated with graphene with a chemical potential value 0.09eV at a frequency of 1.02 THz. Overall, the low transmission loss results verify that a large proportion of incoming RHCP waves is transmitted through the proposed polarization selective surfaces effectively when the chemical potential of the planar graphene is varied.
5. Conclusion
We have demonstrated a conceptual design of frequency-tunable polarization selective surfaces configured with patterned graphene sheets, which selectively rejects LHCP and passes RHCP electromagnetic waves at low THz frequencies. The introduction of graphene into the device simplified the proposed THz polarizer into a planar structure. The surface plasmonic resonance of the graphene has significantly reduced the dimension of the resonance patches in the unit cell. Although the use of the copper based L trace limits the miniaturization of the unit cell, the dimension of the proposed polarization selective surfaces is still reduced to around 0.18λ, which is much smaller than the λ/2 dimension of their copper counterparts in [4]. The smaller grid cell size increases the wave selection accuracy level for THz communication, as more cells of the proposed device may be used to filter the narrow beam width LHCP waves at THz frequencies. The tunable characteristics of the graphene sheet impedance also enable the frequency reconfiguration of the proposed planar polarizer, thus enabling switching capability in the THz spectrum.
In the performance analysis, the LHCP selective surfaces have been observed to possess a maximum transmission loss of 5dB for RHCP waves and isolation capability of around 21 dB for LHCP waves. In the oblique incidence analysis of the circularly polarized waves, a transmission loss fluctuation of around 0.1dB has been observed for oblique angles up to 40°. At the same time, the isolation of the LHCP waves is slightly improved to 25 dB when the angle of incidence is increased. The frequency reconfigurable capability of the proposed planar polarizer has also been verified in this work. The peak isolation performance is variable between 1.0 THz to 1.2 THz and the transmission loss remain below 5 dB when the chemical potential is switched between 0.09 eV and 0.18 eV, assuming the external biasing of the planar graphene materials is varied accordingly.
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