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Dynamic metasurface based cavity structures for enhanced absorption and phase modulation Muhammad Tayyab Nouman, Ji hyun hwang, Mohd Faiyaz, Gyejung Lee, Do Young Noh, and Jae-Hyung Jang ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01014 • Publication Date (Web): 04 Dec 2018 Downloaded from http://pubs.acs.org on December 4, 2018
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Dynamic metasurface based cavity structures for enhanced absorption and phase modulation M. Tayyab Nouman1, Ji-Hyun Hwang1, Mohd. Faiyaz2, Gyejung Lee1, Do-Young Noh2 and JaeHyung Jang*. 1School
of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, 1 Oryongdong Buk-gu, Gwangju 500-712, South Korea. 2Department
of Physics and Photon Science, Gwangju Institute of Science and Technology, 1 Oryongdong Buk-gu, Gwangju 500-712, South Korea. KEYWORDS: Dynamic metasurface, Metasurface optical cavity, Terahertz, Phase modulator, Perfect absorption modulator. ABSTRACT: Metasurface based optical cavity structures consist of a metallic metasurface realized on top of a dielectric slab backed with a metal plane. Such structures have been employed in the design of optical devices such as flat lenses, wave plates and holograms at frequencies from microwave to mid-infrared. Recently, such structures with dynamically reconfigurable optical characteristics have been explored for electrically tunable optical absorption and reflection phase modulation. To date, absorption modulation and phase modulation have been realized with large insertion loss. In this work, we employ an analytical approach based on transmission line theory where the metasurface is represented by a surface admittance. We extend the above approach for the design and analysis of under and over coupled resonance regimes in metasurface cavity structure. This enables a mutual design of cavity thickness and individual metasurface for large amplitude or phase modulation. A dynamic metasurface based optical cavity is experimentally demonstrated at THz frequencies where the dynamic metasurface consists of metallic resonators embedded with thin film vanadium dioxide patches. By driving insulator to metal transition in vanadium dioxide, the THz optical response of the metasurface based cavity structure is modulated. The fabricated device exhibits perfect absorption modulation and reflection phase modulation up to 180°. The reported results demonstrate the potential of such structures for realizing novel devices such as tunable holograms, high-efficiency modulators and frequency tunable filters at THz. The analytical approach presented here can be applied for analysis and design of metasurface cavity structures based on other material systems at frequencies ranging from THz to mid-infrared.
Metasurface based optical cavity structures consist of a metallic metasurface backed by a metal plane. Also known as metal insulator metal (MIM) resonators or gap plasmon resonators, 1, 2 these structures have the ability to realize any reflection phase from 0° to 360°. Due to their ultrathin compact form and monolithic integration capability with active devices, they are highly appealing for various optical devices. They have been used for realizing devices such as absorbers, 3 wave plates, 4 flat lenses, 5 focusing reflectors for THz vertical cavity surface emitting lasers (VCSELs), 6 holograms 7 and so forth. By augmenting dynamically reconfigurable characteristics to such devices, their application scope can be greatly extended. Recently, metasurface cavity structures exhibiting dynamically reconfigurable optical characteristics have been explored to realize electrically tunable perfect optical absorption and reflection phase modulation. Tunable perfect absorption has been reported at mid-infrared using graphene based metasurfaces. 8, 9 Reflection phase modulation has been
demonstrated using graphene and indium-tin-oxide (ITO) based metasurfaces at mid-infrared and nearinfrared wavelengths. 10-13 At THz frequency, graphene based MIM resonator metasurfaces have been reported for realizing reflection phase and polarization modulation. 14 A maximum phase modulation of 243° at THz frequency was demonstrated, but its reflectance level was limited to 1~34% only during phase modulation.14 To date, the devices for the absorption and phase modulation suffer from large insertion loss. Previously, the reflection characteristics of such structures have been explained using coupled mode theory (CMT). 15 Based on CMT, the reflection coefficient of the metasurface cavity near the resonance ωo, was described using Eq. (1) given below, 10 ( abs ) i ( o ) (1) ( ) rad ( rad abs ) i ( o ) Here γrad and γabs denote the radiation rate and absorption rate for the metasurface cavity resonator,
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which in turn depend on geometrical or material properties of the structure. For γabs > γrad, the metasurface cavity resonator is said to be under-coupled and its reflection phase range is limited between 90° to 270° around the resonance frequency. For γabs < γrad, the resonator is over-coupled and its reflection phase range covers full 0° to 360° around the resonance frequency. 10 The above model has been used in some of the previous works to justify the observed reflection phase characteristics. However, the γabs and γrad, used in the above model, can only be calculated for simple metasurface geometries. Full wave electromagnetic (EM) simulations are typically required to evaluate whether the realized resonant response will be under-coupled or overcoupled. Additionally, the above model does not predict the resonance frequency of the metasurface cavity structure. An alternative model for describing the reflection characteristics of metasurface cavity structures, based on transmission line theory has also been reported previously. 9, 16 It involves representing the metasurface by an equivalent surface admittance, ym and has been used to design perfect absorption response in metasurface cavity structures. Here, we leverage the above approach to design metasurface cavity structures for large reflection phase modulation along with low insertion loss. In this approach, first, the surface admittance, ym, of the individual metasurface is extracted from its reflection response. Based on the metasurface susceptance (imaginary part of ym), the thickness of the metasurface cavity structure required to realize resonance can be directly calculated. More importantly, based on the metasurface conductance (real part of ym) we can predict whether the realized cavity resonance would be undercoupled, over-coupled, or critically-coupled. Based on the above model, individual metasurface response can be optimized for a given cavity thickness and vice versa. The surface admittance based approach offers new utility and insights that are not available in the previous approach. It enables design of metasurface cavity thickness without relying on full wave EM simulations. It distinctly shows that high efficiency phase modulation, i.e. phase modulation with large reflection amplitude, can be realized by designing the metasurface having conductance much greater than 1 or much smaller than 1. Additionally, it allows design of frequency tunable filter that has not been considered before both theoretically or experimentally. We then demonstrate a dynamic metasurface based optical cavity structure. The dynamic metasurface is realized by using metallic resonators embedded with thin film vanadium dioxide (VO2) patches. By driving insulator to metal transition (IMT) in VO2, the THz reflection response of the metasurface based cavity structure is modulated. The fabricated device exhibits an absorption modulation depth of 90% with a very low insertion loss of 0.7 dB. Reflection phase modulation from 0° to 180° is demonstrated while maintaining the reflectance as high as 10~ 65% during phase modulation. The above results represent 10 times improved insertion
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loss while having comparable absorption and phase modulation compared to the existing state of the art. 14 The analytical approach based on transmission line theory presented here allows a mutual design of individual metasurface and cavity thickness, which has not been possible for the CMT approach that does not allow a systematic design of metasurface cavity structure.
THEORY An example metasurface based optical cavity structure consisting of a cross-shaped resonator metasurface on a polyimide substrate having back metal plane is shown in Fig. 1(a). The individual metasurface structure without the back metal plane is shown in Fig. 1(b). If the metasurface, located at the boundary of two media, has a thickness much smaller than the operating wavelength, it can be modeled as an equivalent shunt admittance. 17, 18 On this basis, the metasurface based cavity structure (Fig. 1(a)) can be described by the equivalent transmission line circuit model shown in Fig. 1(c). Also, the individual metasurface, shown in Fig. 1(b) can be described by the equivalent circuit model shown in Fig. 1(d). The equivalent circuit in Fig. 1(d) is valid given the substrate is semi-infinite, a condition that can be appropriately mimicked in the experiment (See supporting information for details). The normalized input admittance, yin, of the above circuit is given in Eq. (2),
yin ( ) ym ( ) nsub
(2)
Here, ym represents the effective surface admittance of the metasurface normalized with respect to the free space admittance, Yo. The input admittance, yin, is related to the reflection coefficient, Г, as follows. 1 yin ( ) (3) ( ) 1 yin ( ) By inverting Eq. (3) and substituting in Eq. (2), Eq. (4) can be obtained, 1 nsub (1 nsub )( ) (4) ym ( ) 1 ( ) If we know the reflection coefficient, Г, of the individual metasurface, we can extract the metasurface admittance, ym, by using Eq. (4). It can then be used to analyze the overall metasurface cavity structure. The back metal in the metasurface cavity structure acts as a short circuit, 19 which results in a purely imaginary susceptance, ysc, given as Eq. (5).
ysc ( ) jnsub cot l , 2 nsub
(5)
The above susceptance is in parallel with metasurface admittance, ym, as shown in Fig. 1(c). Here, β is the propagation constant in the substrate and l is the thickness of the substrate. The normalized input admittance, yin, seen at the input of equivalent circuit in Fig. 1(c) is hence given as follows.
yin ( ) ym ( ) ysc ( )
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g m ( ) jbm ( ) jnsub cot l
(6)
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Figure 1. Reflection characteristics of the metasurface based optical cavity structures. (a) Schematic of cross resonator metasurface based optical cavity. (b) Schematic of individual cross resonator metasurface. (c) & (d) Transmission line equivalent circuit models for metasurface optical cavity and the individual metasurface. (e) Reflection characteristics of the cross resonator metasurface. R=|Г|2 (f) Metasurface admittance and short circuit susceptance for l=198 μm. (g) Calculated reflectance and reflection phase results for metasurface cavity with l=198 μm. (h) Complex reflection coefficient of the metasurface cavity plotted on admittance chart to illustrate the resonance coupling states. (i) Metasurface admittance and short circuit susceptance for l=181 μm and, 150 μm. (j) & (k) EM simulation results for metasurface cavity with l=181 μm and l=150 μm, respectively.
Here, gm(ω) and bm(ω) are the real and imaginary parts of the metasurface admittance, ym(ω), referred to as metasurface conductance and susceptance, respectively. Using Eq. (6) and Eq. (3), the reflection response of the metasurface cavity is expressed as a function of individual metasurface admittance, ym, and the cavity thickness, l. We now illustrate the application of above model. Figure 1(e) shows reflectance, R, and reflection phase of an individual cross resonator metasurface, obtained using full wave electromagnetic (EM) simulations under normal incidence. (Simulation details are provided in supporting information). The metasurface is designed to resonate at a frequency of 0.6 THz. Using Eq. (4), the normalized surface admittance, ym=gm + jbm, is evaluated and is shown in Fig. 1(f). The figure also shows inverted short circuit susceptance (-1× ysc), corresponding to a substrate thickness, l, of 198 μm which intersects metasurface susceptance, bm, at 0.76 THz. This represents the point where the total input admittance becomes purely real according to Eq. (6) and a resonance occurs. The reflection coefficient, Г, of the metasurface cavity structure, calculated using Eq. (3), is shown in Fig. 1(g). It is in full agreement with reflection coefficient obtained via EM simulation of cross metasurface based cavity structure, verifying the above behavior. (See supporting information for simulation details).
In Fig. 1(h), Γ is plotted on an admittance chart (black curve) at frequencies ranging from 0.68 THz to 0.78 THz around the resonance frequency. The plot reveals an interesting behavior. The locus of Γ is similar with a constant conductance circle corresponding to gm = 2. (Note that the metasurface conductance, gm, is 2 at the resonance frequency of 0.76 THz.) It is because the gm variation is much smaller than the overall susceptance variation around the resonance frequency. It has important implication for the reflection amplitude and phase characteristics of the metasurface based cavity structure. As shown in Fig. 1(h), if the value of gm at the resonance frequency is greater than or equal to one, the locus of reflection coefficients (black and red curves) is limited to the 2nd and 3rd quadrant in Г plane. As a result, the reflection phase range around resonance is limited to 180±90°. If the value of gm is less than one, the locus of reflection coefficient (blue) covers all four quadrants in Г plane and reflection phase exhibits full coverage from 0° to 360°. These resonance characteristics have originally been studied in microwave resonators coupled to transmission lines. 19 In the case of gm1, are referred to as critically-coupled and under-coupled, respectively. In the case of gm=1, Γ moves along the unity conductance circle and results in zero reflection at the resonance frequency. 20 In the above example, the short circuit
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Figure 2. (a) Schematic description of the dynamic metasurface and resonator dimensions. l1 = 5 μm, l2 = 20 μm, l3 = 60 μm, l4 = 6 μm, w1 = 100 μm, w2 = 50 μm, w3 = 6 μm. (b) Top view of the metasurface unit cell. (c) Transmission line equivalent circuit for the individual metasurface. (d) Reflection coefficient of the individual dynamic metasurface plotted on an admittance chart from 0.30 to 0.60 THz, at different applied bias current. (e) & (f) Reflectance R and reflection phase ϕ of the individual metasurface at different applied bias current. (g) & (h) Metasurface conductance gm(ω) and susceptance bm(ω).
admittance, ysc, intersects metasurface susceptance, bm, at 0.76 THz, where gm is 2, representing an under-coupled resonance state. However, by changing the cavity thickness, the intersection point of ysc and bm can be controlled to achieve the desired coupling state. The appropriate cavity thickness, l, required to realize a resonance at the design frequency, ωo, can be calculated from the metasurface susceptance, bm, using Eq. (7) (See Supporting information, for details).
l (o )
n c tan 1 ( sub ) nsub o bm (o )
(7)
Figure 1(i) shows the metasurface admittance ym, along with short circuit susceptance, ysc, for the two different cavity thicknesses of l=181 μm and l=150 μm. For l=181 μm, the bm and ysc curves intersect at 0.81 THz where gm is 1, resulting in the critically-coupled resonance state. It is verified by the corresponding EM simulation results in Fig. 1(j), exhibiting the same resonance frequency of 0.81 THz as well as zero reflection. For l=150 um, the intersection takes place at 0.94 THz where gm is smaller than 1, resulting in the over-coupled resonance state. Fig. 1(k) shows the corresponding EM simulated reflectance which verifies the resonance at 0.94 THz and reflection phase covering 0° to 360°. The reflection coefficients obtained for the above two cases are also plotted on the admittance chart in Fig. 1(h), at frequency range around their resonance frequencies. It clearly illustrates the behavior of reflection phase characteristics determined by under-coupled, critically-coupled and over-coupled resonance states. The amplitude of the reflection coefficient at resonance is governed by the value of gm at resonance. For gm much greater than 1 or smaller than 1, the reflection coefficient is quite large and the resonator is said to be highly under-coupled or over-coupled, respectively. The model, presented above, provides an intuitive and flexible approach for designing the
resonance frequency as well as coupling states. As shown in Fig. 1(f), in case of individual metasurface, gm1 at frequencies close to the resonance frequency. Therefore, to realize a metasurface cavity with over-coupled resonance state, the individual metasurface should be away from resonance having gm1. The resonance coupling states and reflection phase characteristics can thus be modulated if the individual metasurface can be dynamically switched in and out of resonance. We now present a dynamic metasurface based optical cavity structure. First, the design of the individual dynamic metasurface and its reflection characteristics are described. After that, the reflection characteristics of the overall metasurface optical cavity are presented, along with these amplitude and phase modulation results.
DYNAMIC METASURFACE CAVITY Figure 2(a) shows a schematic description of the individual metasurface. It consists of pairs of cut wires located between horizontal grating wires. VO2 thin film patches, having a thickness of 1 μm, are placed underneath the cut wires that are connected to top or bottom grating wire. The grating wires are alternatively connected to the left and right bias pads, placed at the periphery of the main device, as shown in the Fig. 2(a). The applied bias current flowing across the VO2 patches leads to an IMT in VO2, triggered by the Joule heating. 21 The metasurface is realized on a c-plane sapphire substrate having a thickness of 430 μm. The polarization of the incident THz wave is perpendicular to the wire gratings. The dynamic reflection response of the device is realized by using VO2 to vary the equivalent capacitance
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in metasurface unit cell. As shown in Fig. 2(b), the equivalent capacitance of the unit cell is determined by the series combination of the two capacitances C1 and C2. The capacitance C1 results from the gap between cut wires and the capacitance C2 originates from the gap between top and bottom grating wires of the unit cells in the same column. An IMT in VO2 shorts the capacitance C1, changing the equivalent capacitance from series combination of C1 and C2 to just C2. It causes an increased capacitance resulting in a downward shift of the metasurface resonance frequency. 22 The reflection characteristics of the metasurface are measured using THz-time domain spectroscopy (THzTDS) setup based on linearly polarized photoconductive antennas. 23 Using the setup, complete THz pulses through the sample were measured and Fourier transformed to obtain the amplitude and phase response of the device. (Details regarding the fabrication and characterization are provided in supporting information). During the measurement, the primary THz pulse reflected from the metasurface is followed by the secondary pulses caused by multiple reflections in the finite substrate. In our measurement, only the primary pulse was kept while the secondary pulses were ignored. This mimics measuring the metasurface realized on a semi-infinite substrate, which permits using Eq. (4) to calculate the admittance of metasurface only. Figure 2(e) shows the measured reflectance characteristics. At the applied current lower than 90 mA, the metasurface exhibits resonance at 0.52 THz. Increasing the current to 190 mA results in a gradual transition of VO2 from the insulator to the metallic state. It causes a resonance frequency shift from 0.52 to 0.35 THz. Figure 2(f) shows the reflection phase characteristics of the metasurface. At a fixed current, the reflection phase lies in the vicinity of 180° and crosses 180° at the resonance frequency. By changing the applied bias current from 90mA to 190 mA, a maximum phase modulation of 21° is achieved at 0.47 THz. The limited amplitude and phase modulation realized above can be understood from the equivalent transmission line circuit shown in Fig. 2(c). As shown in the figure, the real part of the total input admittance is given by the sum of metasurface conductance and substrate characteristic admittance. Since substrate characteristic admittance is always greater than or equal to one, the real part of the total input admittance is always greater than 1. Therefore the individual metasurface is always under-coupled. It is clearly shown in the admittance chart in Fig 2(d). Due to undercoupling, the reflection phase is limited to around 180°. Furthermore, the individual metasurfaces cannot achieve perfect absorption of free space waves because the real part of total input admittance must be equal to one for critical-coupling and perfect absorption. With the reflection amplitudes and phases measured above, the normalized effective surface admittances of the metasurface are extracted using Eq. (4). Figures 2(g) and 2(h) show the extracted metasurface conductance, gm, and susceptance, bm, respectively. With these admittance
values, the reflection response of the metasurface cavity structure can be calculated using Eq. (3) and Eq. (6). The metasurface admittance can also be calculated by using the equivalent circuit of the metasurface unit cell (Supporting information section number 3) instead of extracting it from the measured or simulated results.
Figure 3. (a) Schematic description of dynamic metasurface cavity having thickness l=430 μm. (b) Metasurface susceptance curves along with short circuit susceptance, ysc, for l=430 μm. (c) & (d) Reflection phase ϕ and Reflectance, R, of the metasurface cavity calculated using the transmission line model. (e) & (f) Reflection phase ϕ and Reflectance, R, of the metasurface cavity measured using THz-TDS.
Figure 3(a) shows the metasurface cavity structure having a substrate thickness of 430 μm. The calculated reflectance and phase response of the metasurface cavity structure are shown in Fig. 3(d) and 3(c), respectively. The measured response of the metasurface cavity structure obtained using THz-TDS (see supporting information for characterization details) is shown in Figs. 3(e) and 3(f). As shown in the figures, fairly good agreement is observed for both reflectance and phase characteristics even though the position of the resonance frequencies in the measured results is slightly higher than those in the calculated results. As shown in Fig. 3(f), the cavity structure exhibits multiple resonances. The resonance frequencies and reflectance amplitudes at resonance depend on the applied current. The position and displacement of the resonance frequencies are satisfactorily explained by observing the frequency points where the short circuit admittance, ysc, curve intersects with metasurface susceptance, bm, curve. At these frequencies where the two curves intersect, the total input susceptance is zero, representing the resonance
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points. As shown in Fig. 3(b), ysc intersects bm at 0.26 THz for the applied bias current of 90 mA. As the applied current is changed to 190 mA, this intersection frequency point moves to 0.24 THz and the resonance frequency observed in the reflectance spectra also moves to 0.24 THz. The intersection frequency points at 0.36 THz and 0.47 THz are shifted to 0. 45 THz and 0.54 THz, respectively. Consequently, the resonance frequencies exhibit the same shifting. On the basis of above results, the above cavity structure is shown to function as a dynamically tunable filter. The amount of resonance frequency shift is governed by the change in metasurface susceptance and slope of ysc curve. In the above case, the maximum resonance frequency shift amounts to 0.08 THz (from 0.45 THz to 0.54 THz). The amount of frequency shift can be further enhanced by decreasing the cavity thickness which will decrease the slope of the ysc curve. (The supporting calculation results are provided in supporting information)
Figure. 4. (a) Metasurface conductance curves at 90 mA and 190 mA. (b) Admittance smith chart, showing reflection coefficient, Г, of the metasurface cavity structure, from 0.24 to 0.30 THz. (c) Reflectance, R=|Г|2, of the metasurface cavity measured using THz-TDS. (d) Modulation depth as a function of frequency.
We now analyze the reflectance modulation characteristics of the presented device. Fig. 4 (c) shows metasurface cavity reflectance from 0.24 to 0.4 THz while Fig. 4(a) shows individual metasurface conductance gm for the same frequency range. At 90 mA, the metasurface conductance, gm, is close to one. Therefore, the resonances realized at 0.28 THz and 0.38 THz are in critically-coupled states and the corresponding reflectance values are close to zero. As the current is increased to 190 mA, the conductance values become much larger than 1, the resonances move to a highly under-coupled state, and the reflectance becomes very high. Fig. 4(b) shows the reflection coefficient, Г, from 0.24 to 0.30 THz, plotted on the admittance Smith chart, which clearly illustrates the critically-coupled and undercoupled resonance states at 90 mA and 190 mA respectively. In Fig. 4(d), we plot reflectance modulation
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depth defined as 1-Rmax/Rmin. Modulation depth as high as 97% is realized at 0.28 THz while having an insertion loss of 2 dB, where the insertion loss is defined as 10log(Rmax). 8 At 0.38 THz, the modulation depth of 90% is realized with an insertion loss as low as 0.7 dB. Since there is no transmission in the present case, the absorption, A, is related to reflectance simply by A=1-R. The absorption modulation depth is thus equal to reflection modulation depth. Previously, absorption modulation depth of 96% has been reported with an insertion loss of 1.55 dB. 9 The present device exhibits improved insertion loss while having similar levels of modulation depth.
Fig. 5. (a) Metasurface conductance curves at different values of applied current. (b) & (c) Measured reflectance, R, and Reflection phase ϕ of the metasurface cavity. (d) Admittance smith chart, showing reflection coefficient, Г, of the metasurface cavity structure, from 0.5 to 0.55 THz, for different applied current levels. (e) Reflection coefficient, Г, variation at 0.525 THz, 0.53 THz and 0.535 THz, while the current is varied from 90 to 190 mA.
We now discuss the phase modulation characteristics of the device. As shown previously, the metasurface conductance values are greater than or equal to one for all the applied current levels at the frequencies between 0.2 and 0.5 THz, resulting in all the resonances in this frequency range to be critically-coupled or undercoupled. Therefore, as shown in Fig. 3(e), the corresponding phase around the resonance is limited to 180±50°. As a result, no significant phase modulation is observed between 0.2 to 0.5 THz. However, significant phase modulation is observed at 0.53 THz. Fig. 5 show the metasurface conductance (gm), metasurface cavity reflectance, and reflection phase from 0.48 to 0.58 THz. At 0.53 THz, gm changes from 10 to less than 1 when the current increases from 90 to 190 mA. Consequently, the resonance at 0.53 THz moves from under-coupled to over-coupled state, which is illustrated in the admittance Smith chart in Fig. 5(d). The change from under-coupled to over-coupled state results in large amplitude and phase modulation around the resonance frequency, as shown in Figures 5(b) and 5(c). The reflectance continuously
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decreases as the current is increased from 90 to 150 mA. It increases again as the current is increased from 150 to 190 mA, along with a large jump in the reflection phase, due to the transition from under-coupled to over-coupled state. As shown in Fig. 5(e), 180° to 90° and 180° to 270° phase modulation occurs at 0.525 and 0.535 THz, respectively. At 0.53 THz, 180° to 0° phase modulation is observed when the applied current is increased from 90 to 190 mA. By appropriately designing the anisotropic response of the cavity, this phase modulation may be employed to realize dynamic circular polarizers and polarization rotators. The 180° phase modulation at 0.53 THz is achieved while maintaining high reflectance level of 10~65%. Previously, the gate controlled graphene metasurface exhibiting the maximum phase modulation of 243° has been reported, but its reflectance is limited only to 1~34%. 14 The improved reflectance level achieved here can be ascribed to the change of resonance state from highly under-coupled state to over-coupled state, which is enabled by the large modulation range of metasurface conductance. Realizing continuous phase modulation along with constant reflectance is more desirable. However, it does not seem to be achievable in the present case since the phase modulation is enabled by the modulation of conductance from greater than 1 to less than 1, and the reflectance levels get smaller as the conductance value gets close to 1. Nonetheless, It has been shown that functional metasurface devices for dynamic beam steering and beam shaping can be realized if both the 0° and 180° phase states are achieved while high reflectance is maintained. 24 Even though the achieved reflectance level is limited to 12% when the reflection phase is 180° for the present metasurface cavity structure, it can be further increased by improving the quality factor of the metasurface resonance. As the quality factor of the metasurface resonance increases, the metasurface conductance decreases and the reflectance level increases. The simulation results, presented in the Supporting Information, show that stronger metasurface resonance results in reflectance as high as 55% for both 0° and 180° phase. Continuous phase modulation from 0° to 180° while maintaining high reflectance may be realized in devices that operate in highly over-coupled state and their tuning elements are purely reactive. In such a case, the locus of the reflection coefficient is close to the unit circle of the admittance chart, implying the high reflectance level. Realizing such purely reactive tuning elements has been very difficult especially at the high frequency bands such as THz and IR. Previously, it has been shown that the switching time of VO2 depends on the mechanism of insulator to metal transition (IMT) 25 in VO2. Switching time as short as 2 ns has been reported in VO2 devices featuring electric field assisted IMT. 26 For the VO2 devices operated by the thermally driven transition, as is the case of the present device, the switching speed of the device depends on multiple factors such as the total VO2 area, thermal coefficient of the substrate and the overall heat
dissipation capability of the device. Typical switching time of this type of devices is reported to be in millisecond range. 27 The maximum power consumed by the present device is about 140 mW. It includes the power dissipated in the bias pads and the metallic wires forming the metasurface. The power consumption can be further decreased by reducing the total VO2 area and corresponding thermal mass of the device. In summary, metasurface based optical cavity structures, which consist of a metallic metasurface on a metal plane backed dielectric slab are investigated. An analytical model for the design and analysis of the above structures was presented. The model was based on transmission line theory where the metasurface is represented by a surface admittance. It was demonstrated that the desired resonance frequency of the metasurface cavity structure can be realized by appropriately controlling the thickness of the substrate. The resonance coupling states and the reflection phase characteristics are governed by the metasurface conductance. A dynamic metasurface based optical cavity is experimentally demonstrated at THz frequencies where the dynamic metasurface consisted of metallic resonators embedded with thin film vanadium dioxide (VO2) patches. The designed dynamic metasurface has tunable conductance from much larger than one to smaller than one. It enabled overall metasurface cavity structure to undergo resonance coupling state change from strongly under-coupled to critically-coupled or over-coupled state. It results in a large amplitude or phase modulation. An absorption modulation depth of 90% was demonstrated with an insertion loss of 0.7 dB at 0.38 THz. Reflection phase modulation of 0° to 180° was demonstrated at 0.53 THz while maintaining reflectance level between 10~65% during the phase modulation. The results presented here demonstrate the potential of dynamic metasurface cavity structures for realizing switchable holograms, polarizers, high efficiency modulators and tunable filters. The analytical approach provided here can be applied for analysis and design of metasurface cavity based on other material systems at frequencies ranging from THz to mid infrared.
ASSOCIATED CONTENT Supporting Information. “This material is available free of charge via the Internet at http://pubs.acs.org.” Electromagnetic simulation details of the individual metasurface and metasurface cavity, Metasurface cavity thickness design, Metasurface admittance calculation, Fabrication and characterization details of metasurface cavity device, Depth optimization for frequency tunable filters, VO2 optical conductivity characterization, I-V characteristics of VO2 metasurface device, Full wave electromagnetic simulations of the metasurface cavity structure.
AUTHOR INFORMATION Corresponding Author
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[email protected]. Author Contributions
M.T. Nouman carried out the metasurface design and simulation. M. Faiyaz carried out VO2 thin film growth. J.H. Hwang and M.T. Nouman fabricated the metasurface devices. M.T. Nouman and G. Lee carried out the measurements. J.H. Jang supervised the work. The manuscript was written through contributions of all authors. Funding Sources
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT and Future Planning) (No. 2017R1A2B3004049). Notes
The authors declare no competing financial interests.
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For Table of Contents (TOC) use only Dynamic metasurface based cavity structures for enhanced absorption and phase modulation M. Tayyab Nouman, Ji-Hyun Hwang, Mohd. Faiyaz, Gyejung Lee, Do-Young Noh and Jae-Hyung Jang.
TOC:
Dynamic metasurface cavity structures (top left figure) enable amplitude and phase modulation of incident waves. Their response is modeled using a transmission line equivalent circuit (bottom left figure). By varying the applied bias current to the device, reflection phase is modulated from 0° to 180° at 0.53 THz (bottom right figure). This phase modulation capability can enable realization of compact, energy efficient dynamic wave front shaping devices.
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