Abstract

We analyze the interaction of electromagnetic waves with double-layered subwavelength metallic slits on a dielectric substrate. This structure allows efficient transmission of an incident TM-polarized electromagnetic wave into the dielectric substrate, due to the presence of surface modes which couple the incident wave to the TEM waveguide modes supported by the subwavelength metallic slits. Our study shows that electromagnetic transmission through double-layered subwavelength metallic slits is strongly geometry dependent. Based on this observation, a terahertz modulation scheme is presented which, compared to existing terahertz modulator solutions, has the promise of significant enhancement in modulation index over a broad range of terahertz frequencies.

©2011 Optical Society of America

1. Introduction

Terahertz imaging and spectroscopy systems have attracted a growing interest because of their emerging applications in medical diagnosis, material characterization, security screening, and the pharmaceutical industry. While a great deal of attention has been given to the development of high performance terahertz sources and detectors, very few studies have been conducted on the realization of efficient passive terahertz components such as terahertz spatial beam modulators. Terahertz spatial beam modulators capable of controlling the transmission/reflection of an incident terahertz wave allow encoding information in a terahertz communication system [1,2]. Additionally, two dimensional arrays of terahertz spatial beam modulators enable manipulating the terahertz wave front to achieve real time beam steering. They can be also used to realize single-pixel terahertz imaging and spectroscopy systems based on compressive sensing [3,4].

In spite of their numerous applications, terahertz spatial beam modulators capable of offering large modulation bandwidth, large modulation index, low signal attenuation and high modulation speed are not available. Existing designs for modulators in the optical and infrared regime, which use Fabry-Perot filters [5], liquid crystals [6], magneto-optic effects, quantum well structures [7,8], or deformable mirrors, do not operate efficiently at terahertz frequencies because of the lack of materials with the desired properties at terahertz frequencies and the practical difficulties in scaling device dimensions to efficiently operate at terahertz frequencies. Moreover, demonstrated terahertz modulators based on semiconducting structures offer modulation index of a few percent and usually require cryogenic temperatures [9,10]. On the other hand, metamaterials are promising candidates for realizing high-performance terahertz spatial beam modulators. This is because their spectral response can be engineered by their geometry, rather than being limited by characteristics of the existing materials at terahertz frequencies. The use of metamaterials has been previously demonstrated for realizing narrowband terahertz band-pass filters and modulators [1118]. However, the reported metamaterial-based terahertz modulator designs offer limited modulation bandwidth and modulation index and introduce considerable signal attenuation.

To address the performance limitations of existing terahertz modulators, we present a terahertz modulation scheme using reconfigurable double-layered subwavelength metallic slits. Our theoretical analysis of electromagnetic wave interaction with double-layered subwavelength metallic slits shows that the electromagnetic transmission through double-layered subwavelength metallic slits is strongly geometry dependent. Based on this observation, a terahertz modulation scheme is presented which, compared to existing terahertz modulator solutions, has the promise of significant enhancement in modulation index over a broad range of terahertz frequencies.

2. Electromagnetic interaction with double-layered subwavelength metallic slits

Figure 1 illustrates the cross-sectional view of the double-layered subwavelength metallic slits studied in this work. Because of the two-dimensional geometry of the metallic slits, their interaction with electromagnetic waves is strongly polarization dependent. For a TE polarized electromagnetic excitation (the electric field in y direction), the metallic electrodes support only evanescent modes. For a TM polarized electromagnetic excitation (magnetic field in y direction), in addition to the evanescent modes, the sub-wavelength slab waveguides formed by metallic electrodes also support TEM electromagnetic guided modes at wavelengths larger than the slit periodicity, d. Therefore, efficient electromagnetic power transmission into the substrate can be achieved [19,20]. In this section, the transmissivity of a TM-polarized incident electromagnetic wave into the substrate, as a function of slit geometry (a1, a2, h1, h2, d, s) and electromagnetic wavelength is analytically derived.

 figure: Fig. 1

Fig. 1 Schematic view of double-layered subwavelength metallic slits studied in this paper

Download Full Size | PPT Slide | PDF

For a normally incident TM-polarized electromagnetic excitation, the magnetic fields in region 1 (z0), 3 (h1zh1s), and 5 (zh1h2s) are calculated as:

H˜y(1)=pu1,peiαpzeiGpx+r1,peiαpzeiGpx
H˜y(3)=pu3,peiαp(z+h1+s)eiGpx+r3,peiαp(z+h1+s)eiGpx
H˜y(5)=ptpeiαpsub(z+h1+h2+s)eiGpx
where, u 1, p and u 3, p are the amplitudes of the forward-propagating p th diffraction mode on the two layers of subwavelength metallic slits, r 1, p and r 3, p are the amplitudes of the backward-propagating p th diffraction mode from the top of the two layers of subwavelength metallic slits, tp is the amplitude of the transmitted p th diffraction mode into the substrate, Gp = 2πp/d is the parallel momentum along the metal surface, k = ω/c is the momentum of the incident wave, αp=k2Gp2 is the momentum of electromagnetic wave in z direction, εsub is the substrate permittivity, ksub=ω/cεsub/ε0 is the electromagnetic momentum in the substrate, αpsub=ksub2Gp2 is the z component of electromagnetic momentum in the substrate. The electric field in region 1, 3, and 5 has components in x and z direction which are calculated using Maxwell’s equation×H˜=εE˜t (E˜x=1jωεH˜yz, E˜z=1jωεH˜yx), where the time dependence of ejωt is assumed.
E˜x(1)=pαpωε0u1,peiαpzeiGpxαpωε0r1,peiαpzeiGpx
E˜x(3)=pαpωε0u3,peiαp(z+h1+s)eiGpxαpωε0r3,peiαp(z+h1+s)eiGpx
E˜x(5)=pαpsubωεsubtpeiαpsub(z+h1+h2+s)eiGpx
The magnetic fields in region 2 (0zh1) and 4 (h1zh1s) are calculated as:
H˜y(2)=u2eikzr2eik(z+h1)
H˜y(4)=u4eik(z+h1+s)r4eik(z+h1+h2+s)
Assuming the slit width (d-a) and height (h) is much larger than the metal skin depth, the corresponding x component of electric fields in region 2 and 4 are calculated using Maxwell’s equation:
E˜x(2)=kωε0u2eikzkωε0r2eik(z+h1)
E˜x(4)=kωε0u4eik(z+h1+s)kωε0r4eik(z+h1+h2+s)
Boundary condition (continuity of tangential field components) at z = 0, z = -h 1, z = -h 1-s, and z = -h 1- h 2 -s is used to find the transmissivity of an incident TM-polarized electromagnetic wave into the substrate:

At z = 0,H˜(1)=H˜(2)and E˜(1)=E˜(2):

pu1,peiGpx+r1,peiGpx=u2+r2eikh1
pαpωε0u1,peiGpxαpωε0r1,peiGpx=kωε0u2kωε0r2eikh1

At z = -h 1,H˜(2)=H˜(3)and E˜(2)=E˜(3):

pu3,peiαpseiGpx+r3,peiαpseiGpx=u2eikh1+r2
pαpωε0u3,peiαpseiGpxαpωε0r3,peiαpseiGpx=kωε0u2eikh1kωε0r2

At z = -h 1-s,H˜(3)=H˜(4)and E˜(3)=E˜(4):

pu3,peiGpx+r3,peiGpx=u4+r4eikh2
pαpωε0u3,peiGpxαpωε0r3,peiGpx=kωε0u4kωε0r4eikh2

At z = -h 1-h 2-s,H˜(4)=H˜(5)and E˜(4)=E˜(5):

ptpeiGpx=u4eikh2+r4
pαpsubωεsubtpeiGpx=kωε0u4eikh2kωε0r4
By integrating both sides of Eq. (11), 13 over one of the top metallic slits and integrating both sides of Eq. (15), 17 over one of the bottom metallic slits:
p(u1,p+r1,p)gp1=u2+r2eikh1
p(u3,peiαps+r3,peiαps)gp1=u2eikh1+r2
p(u3,p+r3,p)gp2eiGpd/2=u4+r4eikh2
ptpgp2eiGpd/2=u4eikh2+r4
where, gp1=sin(Gpa1/2)Gpa1/2 and gp2=sin(Gpa2/2)Gpa2/2.

Also, by multiplying both sides of Eq. (12), 14, 16, and 18 by eGp'xand integrating over one period of metallic slits the next set of boundary conditions can be calculated. It should be noted that electric field at the boundary of metal and air are calculated using the metal surface impedance η (E˜x=ηH˜y).

αpωε0(u1,pr1,p)=a1dgp1kωε0(u2r2eikh1)+η(δ0,p+r1,p)
αpωε0(u3,peiαpsr3,peiαps)=a1dgp1kωε0(u2eikh1r2)+η(u3,peiαps+r3,peiαps)
αpωε0(u3,pr3,p)=a2dgp2eiGpd/2kωε0(u4r4eikh2)+η(u3,p+r3,p)
αpsubωεsubtp=a2dgp2eiGpd/2kωε0(u4eikh2r4)+ηtp
By eliminating the variables r1,p, u3,p, r3,p, u2,r2,u4and r4, the transmission amplitude tpfor the p th diffraction order is calculated. It should be noted that for an obliquely incident TM-polarized electromagnetic wave, the transmission amplitude for the p th diffraction order is calculated by modifying the electromagnetic momentum along the metallic slit surface, Gp = kx + 2πp/d, where kx is the incident electromagnetic momentum along the x axis.

The zeroth order diffraction mode is the only diffraction mode contributing to the electromagnetic power transfer to substrate since higher order diffraction modes are evanescent. Therefore, the subwavelength metallic slit geometric parameters (a1, a2, h1, h2, d, s) are chosen to enable high transmission of the zeroth order diffraction mode, t 0, into the substrate over the desired electromagnetic frequency range. Figures 2a , 2b, and 2c illustrate the estimated power transmission spectrum of a normally incident TM-polarized electromagnetic wave through the discussed double-layered subwavelength metallic slits into the substrate and as a function of slit geometry. The plots show that for very thin slits (h 1, h 2 << λ), the maximum transmission into the substrate is limited by reflections at substrate-air interface to4εsubε0(εsub+ε0)2.

 figure: Fig. 2

Fig. 2 Power transmission spectrum of a TM-polarized electromagnetic wave normally incident on a double-layered array of subwavelength metallic slits into the substrate and as a function of slit geometry. The results indicate that for thin metallic slits (h 1, h 2 << λ), the maximum power transmissivity is determined by reflections at the substrate-air interface. Maximum transmissivity can be achieved over a broad frequency range for deep subwavelength slits (d << λ). For similar geometric parameters (a 1, a 2, d, s, h 2, h 2 << λ), a more broadband transmission spectrum can be achieved for a) lower aspect ratio slits, b) larger spacing between double-layered metallic slits, c) thicker metallic slits, d, e, and f) power transmission spectrum of the structures analyzed in part a, b, and c calculated by the finite element method (COMSOL package).

Download Full Size | PPT Slide | PDF

The results indicate that very broad transmission bandwidths can be achieved by using deep subwavelength metallic slits (d << λ) and the transmission bandwidth can be further enhanced by use of lower aspect ratio slits (d/a1 and d/a2), larger spacing between the two subwavelength metallic slits (s), and thicker metallic slits (h 1, h 2). Figures 2d, 2e, and 2f show the calculated power transmission spectrum of the normally incident TM-polarized electromagnetic wave by the finite element method (COMSOL package), which closely match the presented analytical results.

Figure 3a shows the power density distribution of a normally incident TM-polarized electromagnetic wave along a double-layered array of subwavelength metallic slits on a silicon substrate at 0.066c/d frequency (c: speed of light) for a1 = 0.5d, a2 = 0.3d, h1 = 0.25d, h2 = 0.025d, s = 0.15d. The power density is calculated by the finite element method (COMSOL package) and by using perfect lossless metallic slits. The electromagnetic power flux along the discussed double-layered array of subwavelength metallic slits (Fig. 3b) illustrates the surface waves excited on top of the periodic arrays of subwavelength metallic slits that excite TEM slab waveguide modes in the subwavelength slits to achieve efficient power transmission into the substrate.

 figure: Fig. 3

Fig. 3 Contour plot of the power density distribution (a) and power flux (b) of a normally incident TM-polarized electromagnetic wave along a periodic arrangement of double-layered subwavelength metallic slits on a silicon substrate, calculated by the finite element method (COMSOL package). The analyzed geometry is (a1 = 0.5d, a2 = 0.3d, h1 = 0.25d, h2 = 0.025d, s = 0.15d) and the electromagnetic frequency is 0.066c/d. Red arrows represent the electromagnetic power flow direction and illustrate how the electromagnetic propagation direction is bent on top of the metallic slits to excite the TEM slab waveguide modes and achieve a high transmission through the metallic slits.

Download Full Size | PPT Slide | PDF

3. Terahertz modulation based on reconfigurable subwavelength metallic slits

Figure 4 illustrates the schematic diagram of the proposed terahertz modulator based on reconfigurable double-layered subwavelength metallic slits. The modulator consists of one layer of subwavelength metallic slits fabricated on a high resistivity silicon substrate. A second layer of subwavelength metallic slits is a part of a miro-electromechanical actuator suspended on top of the first subwavelength metallic slit layer. The miro-electromechanical actuator is designed to allow moving the suspended subwavelength metallic slit layer to physically touch the stationary subwavelength metallic slit layer on silicon substrate. The TM-polarized terahertz wave to be modulated is incident on top of the suspended subwavelength metallic slits.

 figure: Fig. 4

Fig. 4 Schematic diagram and operation concept of the presented terahertz beam modulator based on reconfigurable double-layered subwavelength metallic slits.

Download Full Size | PPT Slide | PDF

As discussed in the previous section, the metallic slit geometry can be specifically designed to allow efficient transmission (up to 70% determined by silicon permittivity relative to air) of the incident TM-polarized terahertz wave into the silicon substrate. In other words, by employing deep subwavelength slit periodicity (d) and low slit aspect ratio (d/a1 and d/a2) efficient terahertz transmission can be maintained over a frequency bandwidth of several THz.

The silicon substrate is mounted on a high resistivity silicon lens to collimate and couple the transmitted terahertz wave out of the device. Transmission loss of terahertz waves through high resistivity silicon is negligible (absorption coefficient less than 0.1 cm−1 for 0.1-2THz frequency range) [21]. Due to the power reflection at the silicon-air interface on the lens spherical face, at least 3dB insertion loss is expected for the discussed terahertz modulator. One way to prevent the 50% power reduction is removing silicon substrate in the modulator active area to have both subwavelength metallic slit layers suspended, but this will reduce device reliability.

The operation concept of the presented terahertz modulator is as follows. During the modulation ‘ON’ state, the moving subwavelength metallic slit layer is suspended on top of the stationary metallic slit layer. This allows low-loss transmission of a TM-polarized incident terahertz wave over a broad range of terahertz frequencies. During the modulation ‘OFF’ state, the micro-electromechanical actuator moves the suspended subwavelength metallic slit layer to physically touch the stationary metallic slit layer on top of the silicon substrate. This blocks the transmission of the incident terahertz wave if the metal thicknesses are much larger than the metal skin depth (few tens of nanometers for most metals at terahertz frequency range).

Figure 5 shows the performance of a terahertz modulator based on reconfigurable double-layered subwavelength metallic slits designed for efficient operation over a frequency bandwidth of more than 2THz. Metallic slits are made up of Au and fabricated on a silicon substrate with a1 = 10μm, a2 = 6μm, h1 = 5μm, h2 = 0.5μm, d = 20μm, s = 1.5μm. While the frequency-dependent permittivity of Au is defined by the Drude model, power transmission is calculated by the finite element method (COMSOL package). Due to the reflections at the silicon-air interfaces, a maximum power transmissivity of 50% is achieved during the modulator ‘ON’ state. The power transmissivity is blocked during the modulation ‘OFF’ state, offering a modulation index of 100% over a frequency bandwidth of more than 2THz (Fig. 5a). In practical applications, where direct metal-to-metal contact can reduce device lifetime, an intermediate dielectric layer with a thickness less than metal skin depth can cover the stationary subwavelength metallic slits, without a significant effect on the modulator performance. As shown in Fig. 5a, lower modulation index can be achieved at low terahertz frequencies if the metal skin depth is comparable with the intermediate dielectric thickness. Figure 5b shows the power transmission of a TM-polarized terahertz wave through the analyzed modulator with no intermediate dielectric covering the stationary metallic slit array, as a function of the air-gap size between the two subwavelength metallic slit layers. Results show a very steep dependence of power transmission as a function of the air-gap size, indicating that the designed terahertz modulator is mostly suitable for operation in the digital ON-OFF regime. The presented theoretical analysis of electromagnetic wave interaction with double-layered subwavelength metallic slits considers an infinite number of subwavelength metallic slits. However, a finite number of slits will be used for practical realization of the proposed terahertz modulators. To confirm the validity of the presented analytical model, we have analyzed the performance of the designed terahertz modulator with a finite number of metallic slits by the finite element method and observed negligible deviation from the predictions of the analytical model for down to five metallic slits in each layer.

 figure: Fig. 5

Fig. 5 a) Power transmission spectrum of a TM-polarized terahertz wave normally incident on a terahertz modulator based on double-layered subwavelength metallic slits fabricated on a silicon substrate with (a1 = 10μm, a2 = 6μm, h1 = 5μm, h2 = 0.5μm, d = 20μm, s = 1.5μm) during modulation ‘ON’ and ‘OFF’ modes. For an intermediate dielectric with a thickness much smaller than metal skin depth, up to 100% modulation index can be achieved. b) Power transmission through the analyzed modulator with no intermediate dielectric covering the stationary metallic slit array, as a function of the air-gap size between the two subwavelength metallic slit layers.

Download Full Size | PPT Slide | PDF

Integration of the suspended subwavelength metallic slit layer with a micro-electromechanical actuator capable of moving in the normal direction relative to the silicon substrate enables development of a fully integrated terahertz spatial beam modulator based on the presented scheme [22,23]. Integrated terahertz spatial beam modulators fabricated in large two-dimensional arrays can be used in high resolution single pixel terahertz cameras based on compressive sensing. The high polarization sensitivity of the discussed terahertz spatial beam modulators offers an additional degree of freedom to implement a variety of different terahertz imaging modalities based on compressive sensing. The results of a fully integrated terahertz spatial beam modulator based on reconfigurable double-layered subwavelength metallic slits will be presented in following publications.

Acknowledgements

The authors gratefully acknowledge the financial support from National Science Foundation Sensor and Sensing Systems division (Award #1030270). Also, the authors wish to acknowledge Prof. Jung Tsung Shen, Department of Electrical and Systems Engineering, Washington University, St. Louis, for discussions and contributions to this work.

References and links

1. T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004). [CrossRef]  

2. C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008). [CrossRef]  

3. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008). [CrossRef]  

4. G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002). [CrossRef]  

5. H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006). [CrossRef]  

6. R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, “Liquid crystal based electrically switchable Bragg structure for THz waves,” Opt. Express 17(9), 7377–7382 (2009). [CrossRef]   [PubMed]  

7. D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008). [CrossRef]   [PubMed]  

8. P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007). [CrossRef]  

9. T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004). [CrossRef]  

10. R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000). [CrossRef]  

11. J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002). [CrossRef]  

12. T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004). [CrossRef]  

13. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006). [CrossRef]   [PubMed]  

14. W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009). [CrossRef]  

15. H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007). [CrossRef]   [PubMed]  

16. H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef]   [PubMed]  

17. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]  

18. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef]   [PubMed]  

19. J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004). [CrossRef]  

20. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef]   [PubMed]  

21. D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). [CrossRef]  

22. D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003). [CrossRef]  

23. I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005). [CrossRef]  

References

  • View by:

  1. T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
    [Crossref]
  2. C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
    [Crossref]
  3. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
    [Crossref]
  4. G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
    [Crossref]
  5. H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
    [Crossref]
  6. R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, “Liquid crystal based electrically switchable Bragg structure for THz waves,” Opt. Express 17(9), 7377–7382 (2009).
    [Crossref] [PubMed]
  7. D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008).
    [Crossref] [PubMed]
  8. P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
    [Crossref]
  9. T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
    [Crossref]
  10. R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
    [Crossref]
  11. J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
    [Crossref]
  12. T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
    [Crossref]
  13. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
    [Crossref] [PubMed]
  14. W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
    [Crossref]
  15. H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
    [Crossref] [PubMed]
  16. H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
    [Crossref] [PubMed]
  17. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
    [Crossref]
  18. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
    [Crossref] [PubMed]
  19. J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004).
    [Crossref]
  20. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
    [Crossref] [PubMed]
  21. D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990).
    [Crossref]
  22. D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
    [Crossref]
  23. I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
    [Crossref]

2009 (3)

R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, “Liquid crystal based electrically switchable Bragg structure for THz waves,” Opt. Express 17(9), 7377–7382 (2009).
[Crossref] [PubMed]

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

2008 (3)

D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008).
[Crossref] [PubMed]

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

2007 (2)

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
[Crossref] [PubMed]

2006 (3)

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

2005 (2)

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

2004 (5)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004).
[Crossref]

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

2003 (1)

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

2002 (2)

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

2000 (1)

R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
[Crossref]

1990 (1)

Averitt, R. D.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
[Crossref] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Azad, A. K.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Baek, S.-H.

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

Baker, C.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Bank, S. R.

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Brener, I.

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

Chan, W. L.

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Chen, H.-T.

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Cho, I.-J.

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

Cich, M. J.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

Cooke, D. G.

Cumming, D. R. S.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Dawson, P.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

Drysdale, T. D.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Exter, M.

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Fattinger, C.

Gianvittorio, J. P.

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

Gossard, A. C.

Gregory, I. S.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Grischkowsky, D.

Hein, G.

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Hsieh, C.-F.

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

Jastrow, C.

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

Jepsen, P. U.

Judy, J.

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

Kadlec, F.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

Katehi, L. B.

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

Keiding, S.

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Kersting, R.

R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
[Crossref]

Kleine-Ostmann, T.

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

Koch, M.

R. Wilk, N. Vieweg, O. Kopschinski, and M. Koch, “Liquid crystal based electrically switchable Bragg structure for THz waves,” Opt. Express 17(9), 7377–7382 (2009).
[Crossref] [PubMed]

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

Kopschinski, O.

Kürner, T.

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

Kužel, P.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

Lammel, G.

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Linfield, E. H.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Mittleman, D. M.

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Münter, K.

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

Pacheco, S. P.

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

Padilla, W. J.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Pan, C.-L.

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

Pan, R.-P.

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

Panaitov, G.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Peroulis, D.

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

Petzelt, J.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

Pierz, K.

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

Piesiewicz, R.

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

Platzman, P. M.

J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004).
[Crossref]

Rahmat-Samii, Y.

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

Renaud, P.

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

Sarabandi, K.

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

Schiesser, S.

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

Schubert, J.

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

Schweizer, S.

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004).
[Crossref]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Song, T.

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

Strasser, G.

R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
[Crossref]

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

Tang, T.-T.

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

Taylor, A. J.

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices,” Opt. Lett. 32(12), 1620–1622 (2007).
[Crossref] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Tribe, W. R.

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

Unterrainer, K.

R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
[Crossref]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Vieweg, N.

Wilk, R.

Wu, H.-Y.

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Yoon, E.

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

Zendejas, J.

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Zide, J. M.

Appl. Phys. Lett. (5)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

P. Kužel, F. Kadlec, J. Petzelt, J. Schubert, and G. Panaitov, “Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range,” Appl. Phys. Lett. 91(23), 232911 (2007).
[Crossref]

T. Kleine-Ostmann, P. Dawson, K. Pierz, G. Hein, and M. Koch, “Room-temperature operation of an electrically driven terahertz modulator,” Appl. Phys. Lett. 84(18), 3555–3557 (2004).
[Crossref]

T. D. Drysdale, I. S. Gregory, C. Baker, E. H. Linfield, W. R. Tribe, and D. R. S. Cumming, “Transmittance of a tunable filter at terahertz frequencies,” Appl. Phys. Lett. 85(22), 5173–5175 (2004).
[Crossref]

W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94(21), 215311 (2009).
[Crossref]

Electron. Lett. (4)

R. Kersting, G. Strasser, and K. Unterrainer, “Terahertz phase modulator,” Electron. Lett. 36(13), 1156–1158 (2000).
[Crossref]

J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” Electron. Lett. 38(25), 1627 (2002).
[Crossref]

T. Kleine-Ostmann, K. Pierz, G. Hein, P. Dawson, and M. Koch, “Audio signal transmission over THz communication channel using semiconductor modulator,” Electron. Lett. 40(2), 124 (2004).
[Crossref]

C. Jastrow, K. Münter, R. Piesiewicz, T. Kürner, M. Koch, and T. Kleine-Ostmann, “300 GHz Transmission System,” Electron. Lett. 44(3), 213 (2008).
[Crossref]

IEEE Photon. Technol. Lett. (1)

H.-Y. Wu, C.-F. Hsieh, T.-T. Tang, R.-P. Pan, and C.-L. Pan, “Electrically tunable room-temperature 2 liquid crystal terahertz phase shifter,” IEEE Photon. Technol. Lett. 18(14), 1488–1490 (2006).
[Crossref]

IEEE Trans. Microw. Theory Tech. (2)

D. Peroulis, S. P. Pacheco, K. Sarabandi, and L. B. Katehi, “Electromechanical Considerations in Developing Low-Voltage RF MEMS Switches,” IEEE Trans. Microw. Theory Tech. 51(1), 259–270 (2003).
[Crossref]

I.-J. Cho, T. Song, S.-H. Baek, and E. Yoon, “A Low-Voltage and Low-Power RF MEMS Series and Shunt Switches Actuated by Combination of Electromagnetic and Electrostatic Forces,” IEEE Trans. Microw. Theory Tech. 53(7), 2450–2457 (2005).
[Crossref]

J. Microelectromech. Syst. (1)

G. Lammel, S. Schweizer, S. Schiesser, and P. Renaud, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” J. Microelectromech. Syst. 11(6), 815–828 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

J. T. Shen and P. M. Platzman, “Properties of a one-dimensional metallophotonic crystal,” Phys. Rev. B 70(3), 035101 (2004).
[Crossref]

Phys. Rev. Lett. (2)

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Science (1)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Schematic view of double-layered subwavelength metallic slits studied in this paper
Fig. 2
Fig. 2 Power transmission spectrum of a TM-polarized electromagnetic wave normally incident on a double-layered array of subwavelength metallic slits into the substrate and as a function of slit geometry. The results indicate that for thin metallic slits (h 1, h 2 << λ), the maximum power transmissivity is determined by reflections at the substrate-air interface. Maximum transmissivity can be achieved over a broad frequency range for deep subwavelength slits (d << λ). For similar geometric parameters (a 1, a 2, d, s, h 2, h 2 << λ), a more broadband transmission spectrum can be achieved for a) lower aspect ratio slits, b) larger spacing between double-layered metallic slits, c) thicker metallic slits, d, e, and f) power transmission spectrum of the structures analyzed in part a, b, and c calculated by the finite element method (COMSOL package).
Fig. 3
Fig. 3 Contour plot of the power density distribution (a) and power flux (b) of a normally incident TM-polarized electromagnetic wave along a periodic arrangement of double-layered subwavelength metallic slits on a silicon substrate, calculated by the finite element method (COMSOL package). The analyzed geometry is (a1 = 0.5d, a2 = 0.3d, h1 = 0.25d, h2 = 0.025d, s = 0.15d) and the electromagnetic frequency is 0.066c/d. Red arrows represent the electromagnetic power flow direction and illustrate how the electromagnetic propagation direction is bent on top of the metallic slits to excite the TEM slab waveguide modes and achieve a high transmission through the metallic slits.
Fig. 4
Fig. 4 Schematic diagram and operation concept of the presented terahertz beam modulator based on reconfigurable double-layered subwavelength metallic slits.
Fig. 5
Fig. 5 a) Power transmission spectrum of a TM-polarized terahertz wave normally incident on a terahertz modulator based on double-layered subwavelength metallic slits fabricated on a silicon substrate with (a1 = 10μm, a2 = 6μm, h1 = 5μm, h2 = 0.5μm, d = 20μm, s = 1.5μm) during modulation ‘ON’ and ‘OFF’ modes. For an intermediate dielectric with a thickness much smaller than metal skin depth, up to 100% modulation index can be achieved. b) Power transmission through the analyzed modulator with no intermediate dielectric covering the stationary metallic slit array, as a function of the air-gap size between the two subwavelength metallic slit layers.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

H ˜ y ( 1 ) = p u 1 , p e i α p z e i G p x + r 1 , p e i α p z e i G p x
H ˜ y ( 3 ) = p u 3 , p e i α p ( z + h 1 + s ) e i G p x + r 3 , p e i α p ( z + h 1 + s ) e i G p x
H ˜ y ( 5 ) = p t p e i α p s u b ( z + h 1 + h 2 + s ) e i G p x
E ˜ x ( 1 ) = p α p ω ε 0 u 1 , p e i α p z e i G p x α p ω ε 0 r 1 , p e i α p z e i G p x
E ˜ x ( 3 ) = p α p ω ε 0 u 3 , p e i α p ( z + h 1 + s ) e i G p x α p ω ε 0 r 3 , p e i α p ( z + h 1 + s ) e i G p x
E ˜ x ( 5 ) = p α p s u b ω ε s u b t p e i α p s u b ( z + h 1 + h 2 + s ) e i G p x
H ˜ y ( 2 ) = u 2 e i k z r 2 e i k ( z + h 1 )
H ˜ y ( 4 ) = u 4 e i k ( z + h 1 + s ) r 4 e i k ( z + h 1 + h 2 + s )
E ˜ x ( 2 ) = k ω ε 0 u 2 e i k z k ω ε 0 r 2 e i k ( z + h 1 )
E ˜ x ( 4 ) = k ω ε 0 u 4 e i k ( z + h 1 + s ) k ω ε 0 r 4 e i k ( z + h 1 + h 2 + s )
p u 1 , p e i G p x + r 1 , p e i G p x = u 2 + r 2 e i k h 1
p α p ω ε 0 u 1 , p e i G p x α p ω ε 0 r 1 , p e i G p x = k ω ε 0 u 2 k ω ε 0 r 2 e i k h 1
p u 3 , p e i α p s e i G p x + r 3 , p e i α p s e i G p x = u 2 e i k h 1 + r 2
p α p ω ε 0 u 3 , p e i α p s e i G p x α p ω ε 0 r 3 , p e i α p s e i G p x = k ω ε 0 u 2 e i k h 1 k ω ε 0 r 2
p u 3 , p e i G p x + r 3 , p e i G p x = u 4 + r 4 e i k h 2
p α p ω ε 0 u 3 , p e i G p x α p ω ε 0 r 3 , p e i G p x = k ω ε 0 u 4 k ω ε 0 r 4 e i k h 2
p t p e i G p x = u 4 e i k h 2 + r 4
p α p s u b ω ε s u b t p e i G p x = k ω ε 0 u 4 e i k h 2 k ω ε 0 r 4
p ( u 1 , p + r 1 , p ) g p 1 = u 2 + r 2 e i k h 1
p ( u 3 , p e i α p s + r 3 , p e i α p s ) g p 1 = u 2 e i k h 1 + r 2
p ( u 3 , p + r 3 , p ) g p 2 e i G p d / 2 = u 4 + r 4 e i k h 2
p t p g p 2 e i G p d / 2 = u 4 e i k h 2 + r 4
α p ω ε 0 ( u 1 , p r 1 , p ) = a 1 d g p 1 k ω ε 0 ( u 2 r 2 e i k h 1 ) + η ( δ 0 , p + r 1 , p )
α p ω ε 0 ( u 3 , p e i α p s r 3 , p e i α p s ) = a 1 d g p 1 k ω ε 0 ( u 2 e i k h 1 r 2 ) + η ( u 3 , p e i α p s + r 3 , p e i α p s )
α p ω ε 0 ( u 3 , p r 3 , p ) = a 2 d g p 2 e i G p d / 2 k ω ε 0 ( u 4 r 4 e i k h 2 ) + η ( u 3 , p + r 3 , p )
α p s u b ω ε s u b t p = a 2 d g p 2 e i G p d / 2 k ω ε 0 ( u 4 e i k h 2 r 4 ) + η t p

Metrics