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Metamaterial terahertz switch based on split-ring resonator embedded with photoconductive silicon XINWANG LIU, HONGJUN LIU,* QIBING SUN,
AND
NAN HUANG
State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Science, Xi’an 710119, China *Corresponding author: [email protected] Received 9 December 2014; revised 13 March 2015; accepted 13 March 2015; posted 18 March 2015 (Doc. ID 229120); published 9 April 2015
In this paper, a metamaterial terahertz (THz) switch based on a split-ring resonator embedded with photoconductive silicon is presented and numerically investigated. Simulation results show that the switch works at two different resonant modes with different pump light powers and that the response time of the switch is less than 1 ps. By defining the switching window as the frequency range where the transmission magnitude of the ON state is one order of magnitude higher than the OFF state, a switching window ranging from 1.26 to 1.49 THz is obtained. The large modulation depth of the switch is due to the large separations of the maximum and minimum transmissions, which are 0.89 and 0.01, respectively. Particularly, the switch is frequency tunable by changing the thickness and permittivity of the dielectric layer. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (050.6624) Subwavelength structures; (040.2235) Far infrared or terahertz. http://dx.doi.org/10.1364/AO.54.003478
1. INTRODUCTION Metamaterials are artificially designed subwavelength periodic structures that can achieve properties that may not be found in nature. Due to their unique electromagnetic resonant properties, considerable attention has been attracted to the applications of metamaterials in the terahertz (THz) and optical frequency ranges, including negative refractive index components [1], perfect absorbers [2], and invisibility cloaking [3]. The periodic unit cell of a metamaterial, called a meta-atom, is one of the most important characteristics in designing metamaterials for THz applications. In most cases the building blocks of meta-atoms are micrometer-scale split-ring resonators (SRRs), which exhibit anisotropic properties depending on the polarization property of the incident waves. By properly designing the structural dimensions and the geometrical arrangement, many THz metamaterial functional devices can be obtained. These include detectors, modulators, filters, polarizers, and switches. In particular, active THz metamaterials controlled by external stimuli via microelectromechanical systems, photoexcitation [4,5], electric bias [6], magnetic field [7], pressure [8], and temperature [9], are intense subjects now, as they are capable of dynamic and flexible modulation of THz waves. In recent years, many studies have been carried out on the THz switch. A series of THz metamaterial switches has been proposed, including THz photonic crystal switching [10], carbon nanotube metamaterial-based THz optical switching [11–13], 1559-128X/15/113478-06$15/0$15.00 © 2015 Optical Society of America
THz photoconductive switching with nanostructured vanadium dioxide film [14,15], and THz photoconductive switching based on silicon [16–19]. With respect to the photoconductive THz switch embedded with silicon, the conductivity of the silicon can be controlled by an external pump light, leading to a modulation of the metamaterial resonant frequency and strength. In addition to an optical pump source, an external voltage can also be used to excite photocarriers and dynamically change the conductivity of silicon. In this paper, we investigate a metamaterial THz switch based on an asymmetrical split-ring resonator (ASRR) [20] embedded with silicon. The switch works at different resonant modes when the conductivity of silicon varies with different pump power densities. Therefore, a switching window ranging from 1.26 to 1.49 THz is obtained, where the transmittance of the ON state is one order of magnitude higher than that of the OFF state. In addition, the response time of the switch is less than 1 ps. Furthermore, the position and width of the switching window can be tuned by changing the permittivity and thickness of the dielectric layer. 2. STRUCTURE AND PRINCIPLES The conductivity of silicon is tunable by changing the power density of the incident pump light. Based on this photoinduced characteristic, a metamaterial THz switch is designed. The unit cell of the switch is schematically shown in Fig. 1, where the
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Fig. 1. Schematic of the switch. (a) Plane view of the unit cell. (b) Perspective view of the unit cell. The electric field of the incident THz wave is oriented along the x direction.
plane view and perspective view are both depicted. The unit cell has a simplified structure that consists of an ASRR, photoconductive silicon, and a polyimide layer. The ASRR has two different gaps, with the silicon embedded in the left gap, but not the right. It should be noticed that two beams of light are incident on the switch. One beam of light is the normally incident THz pulses with the electrical field parallel to the split gap of the ASRR. The other is an obliquely incident near-infrared (∼800 nm) pump beam with ∼100 fs pulse duration that is used to photoexcite the silicon. The pump pulses are a few picoseconds prior to the arrival of the THz pulses, ensuring a quasisteady state for the charge carriers in the silicon. To maximize photoexcitation uniformity, the pump laser beam is expanded to ∼8 mm diameter, larger than the THz forcal spot (∼3 mm in diameter). The complex dielectric constant of gold is modeled at THz frequencies using the Drude model with plasma frequency ωp 1.37 × 1016 rad∕s and damping constant γ c 3.95 × 1013 rad∕s [21]. The blue region refers to the polyimide layer, which is modeled with a frequency independent permittivity of 2.88 0.09i [22]. The photoconductive silicon is simulated with εSi 11.7 and a pump power dependent conductivity σ Si . The unit cell repeats in the x and y directions forming an ASRR array with period p 50 μm. The outer square length (a) of the ASRR is 40 μm, and the width (w) is 3 μm. Since the resonant frequency is related to the gap dimension, we optimized those two gaps (g 1 , g 2 ) to be 4 and 12 μm, respectively. The thicknesses of the gold layer (t) and the polyimide layer (d ) are 0.5 and 5.3 μm, respectively. An inductive-capacitive (LC) circuit model [23,24] can be used to extend our understanding of the interaction between the THz waves and the switch. The incident THz waves interact with the ASRR, forming a circular current at the surface of the ASRR. The flow of the circular current induces an inductance L, which scales as the effective area enclosed by the ASRR. The capacitance C of the split ring can be calculated as C εA∕g, where A is the effective cross section of the ring, ε is the effective permittivity within the gap, and g is the gap dimension. ωp LC−1∕2 determines the resonant frequency, and the L∕C ratio determines the resonance width. 3. SIMULATION RESULTS AND DISCUSSION A numerical simulation was carried out to analyze the resonant properties of the switch when the silicon had different
conductivities. In practical applications, the upper limit of silicon conductivity can be assumed to be an order of 105 S∕m [19]. This value can be reached if an incident pump power of 1 W optically excites a photocarrier density n ∼ 1018 cm−3 . Figure 2 shows the transmission spectra from 0 to 2 THz for the silicon with different conductivities, which was obtained using the finite difference time domain (FDTD) method. The higher-order resonances at higher frequencies are not discussed here for lack of relevance. The blue rectangle region refers to the switching window, where the transmission for σ Si 1 × 105 S∕m is one order of magnitude higher than the transmission for σ Si 1 S∕m. The switching window ranges from 1.26 to 1.49 THz with maximum and minimum transmissions of 0.89 and 0.01, respectively. One can see that the switch has two resonant frequencies for the silicon without illumination. The resonant frequencies are 0.98 and 1.68 THz, corresponding to the transmissions of 0.01 and 0.11, respectively. There is a transmission peak of 0.89 at 1.35 THz between those two absorption resonances. However, the switch only has a single resonance when the silicon conductivity is 1 × 105 S∕m. The resonant frequency is 1.39 THz, and the transmittance is approximately 0.01. Thus, the switch is at the ON state when σ Si 1 S∕m (no pump light), and at the OFF state when
Fig. 2. Transmission spectra of the switch when silicon has different conductivities. The blue rectangle region ranging from 1.26 to 1.49 THz represents the switching window.
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Fig. 3. (a) Dependence of the pump power on the silicon conductivity. (b) Carrier density as a function of pump pulse delay time. The inset lists the parameters of the pump pulses.
σ Si 1 × 105 S∕m. Based on the photoconductivity-induced mode-switching effect [18], this device can work as a metamaterial THz switch. Since the dynamic response of the switch is determined by the variation of the silicon conductivities, the dependence of the pump power on the conductivity was investigated. The calculated results are shown in Fig. 3(a). It is found that the conductivity is proportional to the pump power. In our assumption, a pump power of 1 mW corresponds to a fluence of 2 μJ∕cm2 resulting in a photogenerated carrier density n ∼ 5 × 1015 cm−3 . However, at higher power, the conductivity should not be proportional to the pump power due to the influence of some physical processes. On the one hand, the carrier–carrier scattering resulting from a large carrier density saturates the conductivity [19]. On the other hand, the probability of a multiphoton process is enhanced with the increase of pump power, which causes the quantum efficiency to vary from 1 to 0.5. Nevertheless, our assumption that the maximum conductivity can reach to 1000 S/cm is feasible and reasonable if practical application is taken into account. This can be confirmed by the experimental results in Ref. [16]. A simulation of carrier generation in silicon was performed by solving the carrier rate equation [25] dN 1 − RαI 1 − R2 βI 2 N − ; 2E photon dt E photon τ0
(1)
where N is the carrier density, R is the surface reflection, and α and β refer to the absorption coefficient and two-photon
absorption coefficient, respectively. E photon is the single-photon energy, and τ0 is the carrier transmission time. The input pump pulse has a Gaussian profile I I 0 exp−2t∕τp 2 , where τp is the pulsewidth. In the simulation, τ0 2 ps, R 0.33, α 5.02 × 103 cm−1 , β 2 cm∕GW, E photon 2.49 × 10−19 J, and τp 100 fs [25]. Additionally, we set the pump power to 1 W (corresponding to a fluence of 2 mJ∕cm2 ). Equation (1) can be solved by using the four-order Runge–Kutta method, and the numerical results are depicted in Fig. 3(b). Figure 3(b) shows that the carrier density quickly reaches 8 × 1018 cm−3 in less than 0.2 ps. Then, it begins to slowly drop due to carrier recombination. After about 10 ps, a few free carriers exist in the silicon. This photocarrier lifetime of approximately 10 ps is ideal to demonstrate ultrafast THz metamaterial switching due to the picosecond duration of the THz pulses [5]. The time domain spectra for σ Si 1 S∕m and σ Si 1 × 105 S∕m were computed using the FDTD method, and the results are presented in Fig. 4. For a THz input pulse with a Gaussian profile, the red line and the blue line refer to the reflection wave output and the transmission wave output, respectively. When the silicon conductivity is fixed, we define the response time of the switching as the delay time between when the transmission wave reaches its maximum magnitude and the input THz wave reaches its maximum magnitude. As one can see in Figs. 4(a) and 4(b), the response times τ1 and τ2 are both less than 1 ps. For clarity, the common logarithm ratios of transmittance at the ON state to the OFF state were computed as a function of
Fig. 4. Time domain spectra for (a) σ Si 1 S∕m and (b) σ Si 1 × 105 S∕m. The red line and the blue line refer to the transmission wave output and the reflection wave output, respectively. τ1 and τ2 represent the response times of the switching.
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Fig. 5. Logarithmic spectra were obtained via taking the common logarithm for the ratio of the ON state transmission to the OFF state transmission. The switching windows are tunable by changing (a) permittivity and (b) thickness of the dielectric layer. The red dashed line refers to the threshold of the switch.
the dielectric permittivity and thickness. As one can see in Fig. 5, the switching window is tuned by varying the permittivity and thickness. The red dashed line represents the threshold of the switch, which is defined as log10 T on ∕T off 1. Confining the thickness to d 5.3 μm, the optimal working frequencies, corresponding to the maximum logarithmic values, shift from 1.45 to 1.30 THz with increasing permittivity. If the permittivity is set to ε 2.88, the optimal working frequencies shift from 1.61 to 1.39 THz by changing the thickness. However, the switching window almost remains the same when the thickness is larger than 5 μm. Thus, the switch is frequency tunable by changing the permittivity and thickness of the dielectric layer. Figure 6 illustrates the electric field and current distribution for cases with no pump illumination (σ Si 1 S∕m) and heavy photodoping (σ Si 1 × 105 S∕m) at their respective resonant frequencies. Obviously, those three resonant frequencies belong to different resonant modes. With different pump power densities, the variation of the silicon conductivity induces a
mode-switching effect [18]. The incident THz wave energy concentrates within the gaps to build a closed loop for the circular current, leading to resonance enhancement of the electric field in the vicinity of the gaps. As Figs. 6(a) and 6(b) show, the electric field enhancement of the left gap is larger than that of the right gap due to the smaller size of the left gap. Meanwhile, the current at the left half-SRR is stronger than at the right accordingly [20]. It is clear that the resonance at 0.98 THz is induced by the LC resonance. However, as the surface current distribution shows in Fig. 6(d), three disconnected currents distribute on the left split ring, which corresponds to the third-order resonance. But for the right split ring, there is only one current corresponding to the LC resonance. Thus, the resonance at 1.68 THz is induced by coupling between the third-order resonance of the left SRR and the LC resonance of the right SRR. When the silicon conductivity reaches an order of 105 S∕m (gold conductivity is 4.09 × 107 S∕m), it can be treated as a metal. Therefore, Fig. 6(e) shows that the left gap is short-circuited and the electric field
Fig. 6. Electric field and current distribution at different resonant frequencies. (a), (b) Electric field and surface current at 0.98 THz for σ Si 1 S∕m. (c), (d) Electric field and surface current at 1.68 THz for σ Si 1 S∕m. (e), (f) Electric field and surface current at 1.39 THz for σ Si 1 × 105 S∕m (photosensitive silicon is not shown here). The arrows indicate the direction of current.
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Fig. 7. (a) S21 parameters of the switch at the ON state and the OFF state for silicon with conductivity σ 1 S∕m and σ 1 × 105 S∕m, respectively. Also plotted are the S21 parameters of Model I and Model II. (b) Model I. (c) Model II.
only exists within the right gap. In this case, the effective capacitance is only determined by the right gap [26]. As Fig. 6(f) shows, the left SRR has the dipole resonance and the right SRR has the LC resonance. Thus, similar to the resonance at 0.98 THz, the transmission minimum at 1.39 THz is caused by the resonant coupling. In order to further understand the physical mechanism of the mode-switching effect, the S21 parameters at the ON/OFF states and two models without embedded silicon are depicted in Fig. 7. As one can see, these two models well describe the transmission spectra shape of the switch at different resonant modes except for a small discrepancy in resonant frequencies and magnitudes. The shift is less than several tens of gigahertz in the resonant frequency and can be explained by the change of the dielectric environment in the gapparea. ffiffiffiffiffiffiffi According to the formulas C εA∕g and f res 1∕ LC , the effective capacitance C increases when the silicon is embedded in the small gap of Model I, resulting in a blueshift of the resonant frequency [27]. Thus, it is reasonable to analyze the ON state and the OFF state using Model I and Model II, respectively. Model I has two different gaps, while Model II has only the right gap. The other structural parameters of those two models are the same as the switch. It is obvious that Model I and Model II have different effective capacitances and inductances. Figure 7(a) shows that there are three resonant points for the ON state. The resonance f on1 corresponding to 0.98 THz comes from the LC resonance. In contrast, the resonance f on2 at 1.68 THz, as we discussed above, is the combined result of the third-order resonance and the LC resonance. For the switch in the OFF state, f off 1 at 1.39 THz is caused by the coupling of the dipole resonance and the LC resonance. Both resonances, f off 2 and f on3 corresponding to 2.60 and 2.70 THz, are induced by the hybridization of higher-order resonances. This is confirmed by the circulating current distributions (not shown). With the increase of pump light power, the LC resonance and the third-order resonance of the left SRR disappear. At the same time, the increasing photoexcited free
carrier density of silicon causes the resonance of the left gap to short-circuit [4,16]. Hence, as Model II shows, the left SRR becomes a closed-ring resonator, from which the dipole resonance arises. 4. CONCLUSIONS We have proposed and numerically investigated a metamaterial THz switch based on an ASRR embedded with photoconductive silicon. The switch has a simplified structure and a fast response time, which is less than 1 ps. By changing the pump power density, the conductivity of silicon can be made to vary from 1 S/m to 1 × 105 S∕m, switching the device from the ON state to the OFF state. A switching window ranging from 1.26 to 1.49 THz is obtained for which the ON state transmittance is one order of magnitude higher than the OFF state transmittance. Particularly, the position and width of the switching window can be tuned by changing the thickness and permittivity of the dielectric layer. National Natural Science Foundation of China (NSFC) (61178023, 61275134). REFERENCES 1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). 2. J. Grant, Y. Ma, S. Saha, A. Khalid, and D. R. S. Cumming, “Polarization insensitive, broadband terahertz metamaterial absorber,” Opt. Lett. 36, 3476–3478 (2011). 3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). 4. J.-M. Manceau, N.-H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: blueshift tunability and broadband phase modulation,” Appl. Phys. Lett. 96, 021111 (2010). 5. H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Tavlor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
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17. M. A. Khorrami and S. El-Ghazaly, “Design and analysis of a siliconbased terahertz plasmonic switch,” Opt. Express 21, 25452–25466 (2013). 18. N.-H. Shen, M. Kafesaki, T. Koschny, Z. Lei, E. N. Economou, and C. M. Soukoulis, “Broadband blueshift tunable metamaterials and dual-band switches,” Phys. Rev. B 79, 161102(R) (2009). 19. H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz meta-materials,” Nat. Photonics 2, 295–298 (2008). 20. Z. C. Chen, M. H. Hong, C. S. Lim, N. R. Han, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of large-area asymmetric split ring resonator metamaterials and its structural tuning for terahertz resonance,” Appl. Phys. Lett. 96, 181101 (2010). 21. M. Amin, M. Farhat, and H. Bagci, ˇ “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3, 2105 (2013). 22. H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: design, fabrication, and characterization,” Phys. Rev. B 78, 241103(R) (2008). 23. L. Fu, H. Schweizer, H. Guo, N. Liu, and H. Giessen, “Analysis of metamaterials using transmission line models,” Appl. Phys. B 86, 425–429 (2007). 24. A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92, 011119 (2008). 25. B. Huttner, “Ultrashort pulse damage of semiconductor,” in Ninth International Conference on Nonlinear Optics of Liquid and Photorefractive Crystals (2004), pp. 493–500. 26. W. J. Padilla and A. J. Taylor, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006). 27. S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4, 4988 (2013).
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Vol. 54, No. 11 / April 10 2015 / Applied Optics
Metamaterial terahertz switch based on split-ring resonator embedded with photoconductive silicon XINWANG LIU, HONGJUN LIU,* QIBING SUN,
AND
NAN HUANG
State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Science, Xi’an 710119, China *Corresponding author: [email protected] Received 9 December 2014; revised 13 March 2015; accepted 13 March 2015; posted 18 March 2015 (Doc. ID 229120); published 9 April 2015
In this paper, a metamaterial terahertz (THz) switch based on a split-ring resonator embedded with photoconductive silicon is presented and numerically investigated. Simulation results show that the switch works at two different resonant modes with different pump light powers and that the response time of the switch is less than 1 ps. By defining the switching window as the frequency range where the transmission magnitude of the ON state is one order of magnitude higher than the OFF state, a switching window ranging from 1.26 to 1.49 THz is obtained. The large modulation depth of the switch is due to the large separations of the maximum and minimum transmissions, which are 0.89 and 0.01, respectively. Particularly, the switch is frequency tunable by changing the thickness and permittivity of the dielectric layer. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (050.6624) Subwavelength structures; (040.2235) Far infrared or terahertz. http://dx.doi.org/10.1364/AO.54.003478
1. INTRODUCTION Metamaterials are artificially designed subwavelength periodic structures that can achieve properties that may not be found in nature. Due to their unique electromagnetic resonant properties, considerable attention has been attracted to the applications of metamaterials in the terahertz (THz) and optical frequency ranges, including negative refractive index components [1], perfect absorbers [2], and invisibility cloaking [3]. The periodic unit cell of a metamaterial, called a meta-atom, is one of the most important characteristics in designing metamaterials for THz applications. In most cases the building blocks of meta-atoms are micrometer-scale split-ring resonators (SRRs), which exhibit anisotropic properties depending on the polarization property of the incident waves. By properly designing the structural dimensions and the geometrical arrangement, many THz metamaterial functional devices can be obtained. These include detectors, modulators, filters, polarizers, and switches. In particular, active THz metamaterials controlled by external stimuli via microelectromechanical systems, photoexcitation [4,5], electric bias [6], magnetic field [7], pressure [8], and temperature [9], are intense subjects now, as they are capable of dynamic and flexible modulation of THz waves. In recent years, many studies have been carried out on the THz switch. A series of THz metamaterial switches has been proposed, including THz photonic crystal switching [10], carbon nanotube metamaterial-based THz optical switching [11–13], 1559-128X/15/113478-06$15/0$15.00 © 2015 Optical Society of America
THz photoconductive switching with nanostructured vanadium dioxide film [14,15], and THz photoconductive switching based on silicon [16–19]. With respect to the photoconductive THz switch embedded with silicon, the conductivity of the silicon can be controlled by an external pump light, leading to a modulation of the metamaterial resonant frequency and strength. In addition to an optical pump source, an external voltage can also be used to excite photocarriers and dynamically change the conductivity of silicon. In this paper, we investigate a metamaterial THz switch based on an asymmetrical split-ring resonator (ASRR) [20] embedded with silicon. The switch works at different resonant modes when the conductivity of silicon varies with different pump power densities. Therefore, a switching window ranging from 1.26 to 1.49 THz is obtained, where the transmittance of the ON state is one order of magnitude higher than that of the OFF state. In addition, the response time of the switch is less than 1 ps. Furthermore, the position and width of the switching window can be tuned by changing the permittivity and thickness of the dielectric layer. 2. STRUCTURE AND PRINCIPLES The conductivity of silicon is tunable by changing the power density of the incident pump light. Based on this photoinduced characteristic, a metamaterial THz switch is designed. The unit cell of the switch is schematically shown in Fig. 1, where the
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Fig. 1. Schematic of the switch. (a) Plane view of the unit cell. (b) Perspective view of the unit cell. The electric field of the incident THz wave is oriented along the x direction.
plane view and perspective view are both depicted. The unit cell has a simplified structure that consists of an ASRR, photoconductive silicon, and a polyimide layer. The ASRR has two different gaps, with the silicon embedded in the left gap, but not the right. It should be noticed that two beams of light are incident on the switch. One beam of light is the normally incident THz pulses with the electrical field parallel to the split gap of the ASRR. The other is an obliquely incident near-infrared (∼800 nm) pump beam with ∼100 fs pulse duration that is used to photoexcite the silicon. The pump pulses are a few picoseconds prior to the arrival of the THz pulses, ensuring a quasisteady state for the charge carriers in the silicon. To maximize photoexcitation uniformity, the pump laser beam is expanded to ∼8 mm diameter, larger than the THz forcal spot (∼3 mm in diameter). The complex dielectric constant of gold is modeled at THz frequencies using the Drude model with plasma frequency ωp 1.37 × 1016 rad∕s and damping constant γ c 3.95 × 1013 rad∕s [21]. The blue region refers to the polyimide layer, which is modeled with a frequency independent permittivity of 2.88 0.09i [22]. The photoconductive silicon is simulated with εSi 11.7 and a pump power dependent conductivity σ Si . The unit cell repeats in the x and y directions forming an ASRR array with period p 50 μm. The outer square length (a) of the ASRR is 40 μm, and the width (w) is 3 μm. Since the resonant frequency is related to the gap dimension, we optimized those two gaps (g 1 , g 2 ) to be 4 and 12 μm, respectively. The thicknesses of the gold layer (t) and the polyimide layer (d ) are 0.5 and 5.3 μm, respectively. An inductive-capacitive (LC) circuit model [23,24] can be used to extend our understanding of the interaction between the THz waves and the switch. The incident THz waves interact with the ASRR, forming a circular current at the surface of the ASRR. The flow of the circular current induces an inductance L, which scales as the effective area enclosed by the ASRR. The capacitance C of the split ring can be calculated as C εA∕g, where A is the effective cross section of the ring, ε is the effective permittivity within the gap, and g is the gap dimension. ωp LC−1∕2 determines the resonant frequency, and the L∕C ratio determines the resonance width. 3. SIMULATION RESULTS AND DISCUSSION A numerical simulation was carried out to analyze the resonant properties of the switch when the silicon had different
conductivities. In practical applications, the upper limit of silicon conductivity can be assumed to be an order of 105 S∕m [19]. This value can be reached if an incident pump power of 1 W optically excites a photocarrier density n ∼ 1018 cm−3 . Figure 2 shows the transmission spectra from 0 to 2 THz for the silicon with different conductivities, which was obtained using the finite difference time domain (FDTD) method. The higher-order resonances at higher frequencies are not discussed here for lack of relevance. The blue rectangle region refers to the switching window, where the transmission for σ Si 1 × 105 S∕m is one order of magnitude higher than the transmission for σ Si 1 S∕m. The switching window ranges from 1.26 to 1.49 THz with maximum and minimum transmissions of 0.89 and 0.01, respectively. One can see that the switch has two resonant frequencies for the silicon without illumination. The resonant frequencies are 0.98 and 1.68 THz, corresponding to the transmissions of 0.01 and 0.11, respectively. There is a transmission peak of 0.89 at 1.35 THz between those two absorption resonances. However, the switch only has a single resonance when the silicon conductivity is 1 × 105 S∕m. The resonant frequency is 1.39 THz, and the transmittance is approximately 0.01. Thus, the switch is at the ON state when σ Si 1 S∕m (no pump light), and at the OFF state when
Fig. 2. Transmission spectra of the switch when silicon has different conductivities. The blue rectangle region ranging from 1.26 to 1.49 THz represents the switching window.
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Fig. 3. (a) Dependence of the pump power on the silicon conductivity. (b) Carrier density as a function of pump pulse delay time. The inset lists the parameters of the pump pulses.
σ Si 1 × 105 S∕m. Based on the photoconductivity-induced mode-switching effect [18], this device can work as a metamaterial THz switch. Since the dynamic response of the switch is determined by the variation of the silicon conductivities, the dependence of the pump power on the conductivity was investigated. The calculated results are shown in Fig. 3(a). It is found that the conductivity is proportional to the pump power. In our assumption, a pump power of 1 mW corresponds to a fluence of 2 μJ∕cm2 resulting in a photogenerated carrier density n ∼ 5 × 1015 cm−3 . However, at higher power, the conductivity should not be proportional to the pump power due to the influence of some physical processes. On the one hand, the carrier–carrier scattering resulting from a large carrier density saturates the conductivity [19]. On the other hand, the probability of a multiphoton process is enhanced with the increase of pump power, which causes the quantum efficiency to vary from 1 to 0.5. Nevertheless, our assumption that the maximum conductivity can reach to 1000 S/cm is feasible and reasonable if practical application is taken into account. This can be confirmed by the experimental results in Ref. [16]. A simulation of carrier generation in silicon was performed by solving the carrier rate equation [25] dN 1 − RαI 1 − R2 βI 2 N − ; 2E photon dt E photon τ0
(1)
where N is the carrier density, R is the surface reflection, and α and β refer to the absorption coefficient and two-photon
absorption coefficient, respectively. E photon is the single-photon energy, and τ0 is the carrier transmission time. The input pump pulse has a Gaussian profile I I 0 exp−2t∕τp 2 , where τp is the pulsewidth. In the simulation, τ0 2 ps, R 0.33, α 5.02 × 103 cm−1 , β 2 cm∕GW, E photon 2.49 × 10−19 J, and τp 100 fs [25]. Additionally, we set the pump power to 1 W (corresponding to a fluence of 2 mJ∕cm2 ). Equation (1) can be solved by using the four-order Runge–Kutta method, and the numerical results are depicted in Fig. 3(b). Figure 3(b) shows that the carrier density quickly reaches 8 × 1018 cm−3 in less than 0.2 ps. Then, it begins to slowly drop due to carrier recombination. After about 10 ps, a few free carriers exist in the silicon. This photocarrier lifetime of approximately 10 ps is ideal to demonstrate ultrafast THz metamaterial switching due to the picosecond duration of the THz pulses [5]. The time domain spectra for σ Si 1 S∕m and σ Si 1 × 105 S∕m were computed using the FDTD method, and the results are presented in Fig. 4. For a THz input pulse with a Gaussian profile, the red line and the blue line refer to the reflection wave output and the transmission wave output, respectively. When the silicon conductivity is fixed, we define the response time of the switching as the delay time between when the transmission wave reaches its maximum magnitude and the input THz wave reaches its maximum magnitude. As one can see in Figs. 4(a) and 4(b), the response times τ1 and τ2 are both less than 1 ps. For clarity, the common logarithm ratios of transmittance at the ON state to the OFF state were computed as a function of
Fig. 4. Time domain spectra for (a) σ Si 1 S∕m and (b) σ Si 1 × 105 S∕m. The red line and the blue line refer to the transmission wave output and the reflection wave output, respectively. τ1 and τ2 represent the response times of the switching.
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Fig. 5. Logarithmic spectra were obtained via taking the common logarithm for the ratio of the ON state transmission to the OFF state transmission. The switching windows are tunable by changing (a) permittivity and (b) thickness of the dielectric layer. The red dashed line refers to the threshold of the switch.
the dielectric permittivity and thickness. As one can see in Fig. 5, the switching window is tuned by varying the permittivity and thickness. The red dashed line represents the threshold of the switch, which is defined as log10 T on ∕T off 1. Confining the thickness to d 5.3 μm, the optimal working frequencies, corresponding to the maximum logarithmic values, shift from 1.45 to 1.30 THz with increasing permittivity. If the permittivity is set to ε 2.88, the optimal working frequencies shift from 1.61 to 1.39 THz by changing the thickness. However, the switching window almost remains the same when the thickness is larger than 5 μm. Thus, the switch is frequency tunable by changing the permittivity and thickness of the dielectric layer. Figure 6 illustrates the electric field and current distribution for cases with no pump illumination (σ Si 1 S∕m) and heavy photodoping (σ Si 1 × 105 S∕m) at their respective resonant frequencies. Obviously, those three resonant frequencies belong to different resonant modes. With different pump power densities, the variation of the silicon conductivity induces a
mode-switching effect [18]. The incident THz wave energy concentrates within the gaps to build a closed loop for the circular current, leading to resonance enhancement of the electric field in the vicinity of the gaps. As Figs. 6(a) and 6(b) show, the electric field enhancement of the left gap is larger than that of the right gap due to the smaller size of the left gap. Meanwhile, the current at the left half-SRR is stronger than at the right accordingly [20]. It is clear that the resonance at 0.98 THz is induced by the LC resonance. However, as the surface current distribution shows in Fig. 6(d), three disconnected currents distribute on the left split ring, which corresponds to the third-order resonance. But for the right split ring, there is only one current corresponding to the LC resonance. Thus, the resonance at 1.68 THz is induced by coupling between the third-order resonance of the left SRR and the LC resonance of the right SRR. When the silicon conductivity reaches an order of 105 S∕m (gold conductivity is 4.09 × 107 S∕m), it can be treated as a metal. Therefore, Fig. 6(e) shows that the left gap is short-circuited and the electric field
Fig. 6. Electric field and current distribution at different resonant frequencies. (a), (b) Electric field and surface current at 0.98 THz for σ Si 1 S∕m. (c), (d) Electric field and surface current at 1.68 THz for σ Si 1 S∕m. (e), (f) Electric field and surface current at 1.39 THz for σ Si 1 × 105 S∕m (photosensitive silicon is not shown here). The arrows indicate the direction of current.
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Fig. 7. (a) S21 parameters of the switch at the ON state and the OFF state for silicon with conductivity σ 1 S∕m and σ 1 × 105 S∕m, respectively. Also plotted are the S21 parameters of Model I and Model II. (b) Model I. (c) Model II.
only exists within the right gap. In this case, the effective capacitance is only determined by the right gap [26]. As Fig. 6(f) shows, the left SRR has the dipole resonance and the right SRR has the LC resonance. Thus, similar to the resonance at 0.98 THz, the transmission minimum at 1.39 THz is caused by the resonant coupling. In order to further understand the physical mechanism of the mode-switching effect, the S21 parameters at the ON/OFF states and two models without embedded silicon are depicted in Fig. 7. As one can see, these two models well describe the transmission spectra shape of the switch at different resonant modes except for a small discrepancy in resonant frequencies and magnitudes. The shift is less than several tens of gigahertz in the resonant frequency and can be explained by the change of the dielectric environment in the gapparea. ffiffiffiffiffiffiffi According to the formulas C εA∕g and f res 1∕ LC , the effective capacitance C increases when the silicon is embedded in the small gap of Model I, resulting in a blueshift of the resonant frequency [27]. Thus, it is reasonable to analyze the ON state and the OFF state using Model I and Model II, respectively. Model I has two different gaps, while Model II has only the right gap. The other structural parameters of those two models are the same as the switch. It is obvious that Model I and Model II have different effective capacitances and inductances. Figure 7(a) shows that there are three resonant points for the ON state. The resonance f on1 corresponding to 0.98 THz comes from the LC resonance. In contrast, the resonance f on2 at 1.68 THz, as we discussed above, is the combined result of the third-order resonance and the LC resonance. For the switch in the OFF state, f off 1 at 1.39 THz is caused by the coupling of the dipole resonance and the LC resonance. Both resonances, f off 2 and f on3 corresponding to 2.60 and 2.70 THz, are induced by the hybridization of higher-order resonances. This is confirmed by the circulating current distributions (not shown). With the increase of pump light power, the LC resonance and the third-order resonance of the left SRR disappear. At the same time, the increasing photoexcited free
carrier density of silicon causes the resonance of the left gap to short-circuit [4,16]. Hence, as Model II shows, the left SRR becomes a closed-ring resonator, from which the dipole resonance arises. 4. CONCLUSIONS We have proposed and numerically investigated a metamaterial THz switch based on an ASRR embedded with photoconductive silicon. The switch has a simplified structure and a fast response time, which is less than 1 ps. By changing the pump power density, the conductivity of silicon can be made to vary from 1 S/m to 1 × 105 S∕m, switching the device from the ON state to the OFF state. A switching window ranging from 1.26 to 1.49 THz is obtained for which the ON state transmittance is one order of magnitude higher than the OFF state transmittance. Particularly, the position and width of the switching window can be tuned by changing the thickness and permittivity of the dielectric layer. National Natural Science Foundation of China (NSFC) (61178023, 61275134). REFERENCES 1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). 2. J. Grant, Y. Ma, S. Saha, A. Khalid, and D. R. S. Cumming, “Polarization insensitive, broadband terahertz metamaterial absorber,” Opt. Lett. 36, 3476–3478 (2011). 3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). 4. J.-M. Manceau, N.-H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: blueshift tunability and broadband phase modulation,” Appl. Phys. Lett. 96, 021111 (2010). 5. H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Tavlor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32, 1620–1622 (2007).
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