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Electrically Tunable Optical Absorption in a Graphene-based Salisbury Screen

We demonstrate a graphene-based Salisbury screen consisting of a single layer of graphene placed in close proximity to a gold back reflector. The light absorption in the screen can be actively tuned by electrically gating the carrier density in the graphene layer with an ionic liquid/gel. The screen was designed to achieve maximum absorption at a target wavelength of 3.2 micrometer by using a 600 nm-thick, non-absorbing silica spacer layer. Spectroscopic reflectance measurements were performed in-situ as a function of gate bias. The changes in the reflectance spectra were analyzed using a Fresnel based transfer matrix model in which graphene was treated as an infinitesimally thin sheet with conductivity given by the Kubo formula. Temporal coupled mode theory was employed to analyze and intuitively understand the observed absorption changes in the Salisbury screen. We achieved ~ 6 % change in the optical absorption of graphene by tuning the applied gate bias from 0.8 V to 2.6 V, where 0.8 V corresponds to graphene's charge neutrality point.

significant attention for its unique electrical, optical and mechanical properties. [1][2][3][4] These include its ability to absorb 2.3 % of the incident light over a broad range of wavelengths, an extremely high charge carrier mobility on the order of ~200,000 cm 2 /Vs for suspended, high-quality graphene and an extraordinary intrinsic mechanical strength. [5][6] This makes graphene a promising candidate for many applications such as ultrafast photodetectors, modulators, solar cells and transparent electrodes. [7][8][9][10][11] Whereas the singlelayer-absorption is impressive, it is not strong enough for many optoelectronic applications as virtually all the light is transmitted. Moreover, for active devices such as electro-optical modulators and actively controlled thermal emitters, dynamic control over absorption is required as well. 12 In this work, we explore an electrically-tunable Salisbury screen device capable of achieving both increased absorption and active absorption modulation in a single graphene sheet.
Recently, there have been a number of excellent efforts directed at enhancing the optical absorption in graphene. For example, plasmonic nanostructures have been used to locally concentrate fields in this 2D material with the aim to increase the efficiency of graphene-based photodetectors. 13,14 Theoretically, complete light absorption in graphene has also been predicted under critical-coupling conditions by patterning it. 15 Integrating graphene with an optical waveguide has been employed to achieve a longer light-graphene interaction length. 16 Graphene microcavity photodetectors have also been demonstrated that produce increased absorption in graphene due to enhanced optical fields inside a high quality factor (Q) resonant cavity. 17 Here, we demonstrate a graphene-based Salisbury screen capable of boosting the absorption of infrared light in a graphene layer well beyond that of a suspended sheet. Furthermore, we show that we can actively tune the absorption in the graphene layer by electrical gating with an ionic gel. The original Salisbury 18 screen was invented by the American engineer Winfield Salisbury in 1952 and was employed in some of the first radar absorbent materials. 19 In its original implementation, a weakly absorbing layer of graphite (i.e. multi-layered graphene) was spaced from a metallic back reflector by a transparent spacer layer. It was shown that (for some target wavelength) the net reflection from the system can be made to vanish and unity absorption can be achieved. To first order, this occurs when the direct reflection from the absorbing layer and the light returning from the back reflector are equal in magnitude and opposite in sign.
For this to happen, the spacer layer thickness (t) has to be approximately equal to a quarter of the wavelength of the incident light in the spacer layer with refractive index n Spacer , i.e. t  /4n Spacer . In a second-order theory, multiple reflections between the screen and the reflector have to be accounted for.
When the mirror is a perfect electrical conductor (PEC) featuring a very high electrical conductivity, the spacer thickness should exactly equal one quarter of the targeted operation wavelength to maximize absorption. However, real metals at optical frequencies allow for some field penetration (up to a skin depth) and this gives rise to a reflection phase pick up that deviates from that of a perfect electrical conductor. As a result, a thinner spacer layer thickness can be used to achieve the destructive interference condition. The field penetration comes at the cost of some optical losses in the metal.
However, when a very strongly absorbing film like graphene is used in conjunction with a real, but highly conductive metal reflector, it is possible that most of the absorption takes place within the film as opposed to the metal. As a result, an active tuning of the absorption properties of the film can have a significant impact on the reflected signal. In this work, we combine experiment and theory to analyze the nature and magnitude of the absorption changes one can achieve with a graphene-based Salisbury screen device. Figure 1a shows a schematic of our proposed device configuration. It consists of a graphene sheet that is judiciously-spaced from a metallic back reflector by a transparent 600-nm-thick silicon dioxide (SiO 2 ) spacer layer. A 200-nm-thick gold (Au) film was used as the metal back reflector due to its high reflectance in the mid-infrared (IR) part of the electromagnetic spectrum. The entire stack was deposited on a silicon (Si) substrate by standard electron beam (e-beam) evaporation. The SiO 2 layer was produced by high density plasma enhanced chemical vapor deposition (HDPECVD). The thickness of this spacer layer was chosen such that an incident wave at a target wavelength of ~3.2 m produces a standing wave with a maximum in the electric field intensity at the location of the graphene sheet (Fig. 1b). This choice facilitates both strong light absorption and a relative insensitivity of the absorption to the exact position of the screen. The mid-IR spectral range around 3 m is of great importance for many applications, including IR vibrational spectroscopy and thermal radiation control. Commercially available CVD graphene (from ACS Material) was transferred onto the SiO 2 spacer. Using e-beam evaporation, large gold pads on the order of ~ 1 cm x 0.5 cm were then deposited to serve as source and drain contacts for electrical transport measurements on graphene. A larger, laterally-placed Au pad of approximately 2 cm x 1 cm was also deposited to electrically gate and control the carrier density of the graphene sheet with an ionic gel. This was followed by spin-coating a smooth, 4.5 m thick layer of the ionic gel, derived from the ionic liquid DEME-TFSI [N,N-diethyl-N-methyl-N-(2-methoxyethyl) ammonium bis(trifluoromethylsulfonyl) imide]. The ion gel has a high refractive index that is comparable to that of SiO 2 (n gel = 1.43). 20 As such it forms a low Q optical cavity together with the silica layer that facilitates resonant recirculation of the incident wave. For this reason, the presence of the ion gel layer can further enhance the light absorption in the graphene layer over a conventional screen that would have air above the conductive sheet. In this way the gel plays an important optical role in addition to its electrical role of gating the device.
The variation of the drain-source current through the graphene channel with the applied gate bias across the ion gel is shown in Fig. 1c. The measurements were performed using a semiconductor parameter analyzer (Agilent B1500). A constant drain-source voltage (V DS ) of 10 mV was applied while monitoring the resultant drain-source current (I DS ) as a function of the applied gate bias (V G ). Upon application of a gate bias, ionic charges accumulate at the ion gel/graphene and ion gel/gold pad interfaces. 21 This in turn causes the carrier density and hence the conductivity of graphene to change. A minimum in I DS occurs at a gate bias referred to as the Dirac voltage (V D ). This condition corresponds to the charge neutrality point (CNP) in graphene. 22  The electric double layers (EDLs) formed at the ion gel/graphene and ion gel/gold (Au) pad interfaces serve as capacitor structures with an approximate spacing between the "plates" of a few nanometers. 23 Physically, this effective distance is linked to the spacing of the ions in the gel and the mobile carriers in graphene or Au. We define a total double layer capacitance (C EDL ) as the geometric capacitance per unit area of the EDLs formed by the series combination of the Au/ion gel interfacial capacitance and graphene/ion gel interfacial capacitance. At first, one might think that these are the only capacitors at play in the system. However, due to the finite density of states of 2D conductors like graphene, such materials do not behave like the metallic plates of a conventional capacitor structure. Here, one needs to account for the substantial impact of band-filling/band-emptying upon charging/discharging of the 2D graphene 'plate' that features a small density-of-states compared to regular metals. To construct useful circuit models for such unusual capacitor plate materials, Luryi introduced the concept of a quantum capacitance (C Q ). 24 He found that one can take into account the band-filling/band-emptying with a second quantum capacitance placed in series to the usual geometric capacitance of a parallel plate capacitor. 25 where ω is the angular frequency, Γ is the scattering rate for the mobile carriers, k B is the Boltzmann constant and T is the temperature. The dependence of conductivity of a graphene sheet on wavelength is plotted in Fig. 1d  The spectral dependence of  can be understood by realizing that its magnitude is governed by two major contributions that dominate in different wavelength regimes. At longer wavelengths, the dominant contribution to the conductivity comes from the free-carrier response (i.e. intraband excitations). This contribution is described fairly well by the Drude model. At shorter wavelengths, the optical response is dominated by interband transitions and is independent of wavelength. 30 As a result, the conductivity approaches the well-known universal value of 60 µS at the shorter wavelengths. 31 It can be seen that an increase in the bias voltages causes the conductivity to decrease over the entire wavelength range of interest. The exact functional dependence of the conductivity on the applied bias is however different at each wavelength as each of the conductivity curves shows a 'swing' from a high to a low value at a photon energy E ph  2 E F . This swing is caused by the fact that a minimum amount of photon energy E ph  2 E F is required to stimulate an interband transition in graphene (as dictated by the state filling that is schematically depicted in the two band diagrams in Fig. 1d).
In order to theoretically predict the optical response of our graphene-based Salisbury screen in the infrared, a transfer matrix model 32 was used, wherein graphene was treated as an infinitesimally thin sheet with a conductivity given by Eq. Similar to the trends for graphene's conductivity (Fig. 1d), a gradual increase in the Fermi level first impacts the spectral reflectance at long wavelengths and then at shorter ones.
Next, we measured the dependence of the optical response of the fabricated graphene-based Salisbury absorber on gate bias. A Fourier Transform Infra-Red (FTIR) spectrometer was employed to measure the reflectance spectra. For practical applications, we are particularly interested in quantifying the ability to modulate the reflectance. To this end, we will analyze the normalized differential reflectance , which is proportional to the difference between the reflectance at a given Fermi energy level of interest (or applied gate bias) and the reflectance at the CNP given by R D . Based on I DS -V G measurements discussed earlier (Fig. 1c), the CNP for our devices was achieved at an applied bias of 0.8 Fig. 3a show measurements of the normalized differential reflectance at gate biases of 0. µm. This can be understood by noting that the change in reflectance with the applied gate bias can be expressed as a product of two contributions. One of them is optical in nature and is the change in reflectance for a given change in graphene's conductivity. The other is electrical in nature and quantifies the change in conductivity with a change in the applied voltage:

V. The dots in
The observed spectral dependence of the bias-induced reflectance changes can be understood from the spectral dependence of each of the two terms on the right side of Eq. (4). The changes ( ) can be calculated from the transfer matrix model. Figure 3b shows how the reflectance changes as the conductivity of the absorber layer is varied over a wide range of conductivity values. The plot highlights that the screen could have achieved unity absorption if only graphene had conductivity as high as 3 mS.
The inset shows that for typical conductivity values of graphene (0 µS to 100 µS), an almost linear dependence of the reflectance on conductivity is observed, with only a slight dependence on probe wavelengths. Fig. 3c plots the magnitude of ( ) versus the illumination wavelength. This quantity is largest when the illumination wavelength meets the Salisbury screen condition (  4tn Spacer ). This is expected as for this wavelength ( = 3.2 µm) the field is maximized at the location of the screen (Fig. 1b). To better understand the observed reflection changes for our graphene-based Salisbury screen, we employ coupled mode theory. 33 Coupled mode theory effectively hides some of the device complexity and thereby often affords a simple, basic intuition about the device operation. Following this approach, we treat our Salisbury screen as an asymmetric Fabry-Perot resonator as depicted schematically in Fig. 4a.
We consider a wave of amplitude s + , with frequency ω, incident on the resonator that can excite a resonator mode with amplitude a: where κ quantifies the degree of coupling between the resonator and the incident wave s + . The magnitudes of 1/τ i and 1/τ e represent the internal and external amplitude decay rates respectively and ω o is the resonant (angular) frequency. Assuming a steady state situation (da/dt = 0), one can use Eq. (4) to calculate the reflection coefficient for the structure: and hence find an expression for the reflectance: Each amplitude decay rate can be related to an optical quality factor: , and the total quality factor Q tot of the system can be found by inversely adding the relevant Q factors associated with different loss processes. The magnitude of Q tot measures the ratio of the stored energy in the cavity, E stored to the total power dissipated P tot from/in the cavity: .
In our model, graphene and gold are treated as dispersive media in the frequency range of our interest (IR). The silica and ion gel materials are assumed to have a constant permittivity in the IR. For a medium with constant permittivity, the average stored energy is defined as: where ϵ o is the permittivity of free space, ϵ is the relative permittivity of the medium and E is the electric field amplitude in the medium. The electric field intensity is integrated over volume V of the medium of relative permittivity ϵ. Gold is a dispersive medium and follows the Drude model in the considered spectral range. 34 The average energy stored for dispersive media obeying Drude model is given by: 35 where ϵ' is the real part of relative permittivity, ϵ'' is the imaginary part of the relative permittivity of the medium. The power dissipation (for both dispersive and dispersion-less media 36 ) is given by: Based on the coupled mode theory analysis, Q tot has contributions from both internal and external loss processes. The internal losses result from power absorbed in both graphene (P gr ) and the gold back reflector (P Au ). The external Q arises due to the optical power that leaks out of the cavity P rad . The total power loss in Eq. (8) is given by: , The total energy stored in the cavity is the sum of the energy stored in each layer of the resonator i.e.: , where E gr , E Au , E silica , E gel are the stored energy within graphene, gold, silica and ion gel layers respectively. Due to the high conductivity of the Au film in this spectral range, the magnitude of the power loss is very small compared to the radiation loss and loss in the graphene. As such, the electrically induced changes in the reflectance are effectively controlled by the changes in the loss within graphene. To understand the impact of the losses in graphene on Q tot , we next analyze the electrically-induced changes on the quality factor of graphene Q gr . Figure 4c shows the dependence of Q gr for the same resonance wavelengths and magnitudes of E F as in panel 4b. For E F = 0eV, the magnitude of Q gr again decreases by about a factor 2 from 340 to 160, which is reasonable given the virtually constant conductivity (i.e. absorption properties of graphene). Its value is significantly larger than Q tot , indicating that the optical losses in the graphene layer only contribute a small fraction to the total loss. This results in a relatively simple linear dependence of the reflectance from our screen at small values of  (Inset to Fig 3b). When a voltage is applied to raise the Fermi level in graphene, the conductivity of graphene is lowered (Fig. 1d), causing a rise in the magnitude of Q gr . The largest increase in Q gr from 309 to 1123 occurs at the wavelength of 4.17 µm corresponding to a maximum conductivity change. Based on our simulations this corresponds to an absorption change in graphene of ~6 %.
In conclusion, we have demonstrated a graphene-based Salisbury absorber that employs the Salisbury screen concept to enhance the absorption in graphene. The absorption in this planar absorber can be tuned by using a gate voltage. The reflectance changes within the absorber as a function of Fermi energy levels in graphene were modeled by a transfer matrix model and the experimental findings match well with the theoretical predictions. To relate the reflectance changes to the absorption within graphene and to understand the absorption mechanism, we made use of the temporal coupled mode theory. This theory explains the magnitude of the reflectance changes and why there is a simple linear dependence of the reflectance on the electrically-induced changes in graphene's conductivity. We achieved changes in the reflectance of up to ~3.3 % per volt with our design by varying the Fermi level in graphene. This shows the benefits of placing graphene in a Salisbury screen type configuration.

Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.