Abstract

In terahertz (THz) photonics, there is an ongoing effort to develop thin, compact devices such as dielectric photonic crystal (PhC) slabs with desirable light–matter interactions. However, previous works in THz PhC slabs have been limited to rigid substrates with thicknesses ${\sim}100\,\,{\rm s}$ of micrometers. Dielectric PhC slabs have been shown to possess in-plane modes that are excited by external radiation to produce sharp guided-mode resonances with minimal absorption for applications in sensors, optics, and lasers. Here we confirm the existence of guided resonances in a membrane-type THz PhC slab with subwavelength (${\lambda _0}/6 {-} {\lambda _0}/12$) thicknesses of flexible dielectric polyimide films. The transmittance of the guided resonances was measured for different structural parameters of the unit cell. Furthermore, we exploited the flexibility of the samples to modulate the guided modes for a bend angle of $\theta \ge {5^ \circ }$, confirmed experimentally by the suppression of these modes. The mechanical flexibility of the device allows for an additional degree of freedom in system design for high-speed communications, soft wearable photonics, and implantable medical devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Communications-specific applications such as Wi-Fi enabled video calls, large data transfers, and entertainment streaming have pushed the bandwidth limits of non-optical components like copper wire, cable connections, etc. To achieve the higher bandwidths (${\ge} 100\;{\rm Gbit/s}$) required by the increased and future demand, researchers aim to develop new technologies designed to operate at terahertz (THz) frequencies. However, the majority of current devices and components are large and bulky with slow improvement for practical, compact THz platforms. The most popular candidates for planar, compact THz light manipulation are plasmonic metamaterials, subwavelength arrays of metallic resonators periodically distributed on a dielectric substrate. Applications of planar metamaterials include nonlinear enhancements [13], near-field focusing [4,5], and beam steering devices [6,7]. Additionally, due to the use of polyimide [810], polydimethylsiloxane (PDMS) [11] and carbon nanotube [12] substrates, THz metasurfaces are desirable for flexible photonics applications. But they are limited by intrinsic ohmic loss of metals at THz frequencies and requirements for fabrication of multilayer or composite structures.

To avoid the above limitations, photonic crystal (PhC) slabs have been employed to manipulate light–matter interaction with THz waves. In general, PhC slabs are two-dimensional (2D) planar devices composed of a dielectric material with an array of holes and periodicity in the range of the wavelength of interest. These planar 2D PhC slabs exhibit strong field confinement and interaction with THz waves with minimal absorption loss. In addition, the dielectric platforms of PhC slabs offer low-loss alternatives to metallic resonators.

As such, PhC slabs have been used to guide [13,14], filter [15,16], and enhance electric field distributions in small volumes [17,18]. Although light is usually confined within PhC slabs, certain guided modes can strongly couple with external radiation when they are normally incident to an in-plane resonance on the PhC surface. The in-plane mode, also described as the photonic band edge effect or the distributed feedback effect, can be utilized for lasing in PhCs [19,20]. Experimental demonstrations of the properties of 2D THz PhC slabs have been reported in silicon [2132] and GaAs [33] media. The majority of reported THz PhC slabs have thicknesses in the range of THz wavelength [2130,33] with a few demonstrations around 50 µm thickness [3133]. For thin samples originating from rigid crystals, the PhC slabs are fragile and difficult to handle.

In this Letter, we report the existence of guided-mode resonances supported by a flexible membrane-type PhC (both 50 and 25 µm thick) operating at THz frequencies. Experimental measurements of the fabricated device confirm the existence of guided resonances that couple the in-plane resonance of the PhC slab with external radiation. Systematic studies of these resonances with respect to different thicknesses and hole geometries are presented, and curvature-dependent spectral measurements show active tunability of the guided modes as a function of bend angle. As such, our results pave the way for a new, flexible medium for dielectric PhC slabs with subwavelength thickness. Furthermore, the mechanical robustness of the devices allows for applications in flexible photonics, including integration with future biomedical and communications platforms.

2. MATERIALS AND METHODS

A schematic of the unit cell is given in Fig. 1(a) for the flexible PhC slab with air holes of a specific diameter $d$, radius $r$, and period $a$ in a square lattice. Next, we calculated the first 10 bands of the photonic band structure using the MIT Photonic Bands (MPB) package [34] for a 2D PhC slab [Fig. 1(b)] with dielectric constant $\epsilon = 3.4$ and $r/a = 0.3$ and plotted for both TE and TM polarizations [Fig. 1(c)]. Unlike silicon (${n_{\rm Si}} \sim 3.418$ at 1 THz) or GaAs (${n_{\rm GaAs}} \sim 3.59$ at 1 THz) PhC slabs, no clear photonic bandgap is present in our samples made of Kapton polyimide (${n_K} \sim 1.843$). However, we observed and verified through spectrographic analysis guided resonances originating from the in-plane resonant mode of the PhC slab coupled to the external THz radiation in the direction normal to the PhC plane [Fig. 1(d)]. The in-plane resonance leaks out from the surface as a guided resonance as it is coupled to the radiation.

 figure: Fig. 1.

Fig. 1. Flexible 2D THz PhC slab. (a) Unit cell of the 2D PhC slab with air hole radius $r$, diameter $d$, and cell period a. (b) Band dispersion calculated for the PhC slab in (a) with $r/a = 0.3$ and $\epsilon = 3.4$. The TM mode is dashed, and the TE mode is solid. (c) Representation of the mechanism for supporting guided modes where the incident THz wave couples with the in-plane resonant mode of the PhC slab. (d) Optical images of the fabricated PhC slab and highly flexible Kapton film (top-right insert). Noticeable cracking on the surface of the slab is attributed to possible thermal expansion and contraction during the ICP etching process.

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Standard polyimide etch recipes reported in the literature are not applicable for Kapton films, which are uniquely synthesized for high temperature resistivity. To fabricate the air holes in our samples, we first patterned a titanium hard mask on the Kapton film, then dry etched with an inductively coupled plasma (ICP) etcher (Plasma-Pro 100 Cobra). The etching conditions are as follows: oxygen pressure of 20 mTorr, flow rate of 60 sccm, RF1 power at 75 W, and RF2 at power 1500 W with an approximate etch rate of ${\sim}1.05\;\unicode{x00B5} {\rm m/min}$. Then the titanium hard mask was removed with an etchant solution. A photo of a flexible Kapton polyimide film with an optical image of the PhC pattern on the sample is also shown [Fig. 1(d)].

Transmission measurements were performed with standard THz time-domain spectroscopy (THz-TDS) techniques. Two different experimental setups, at Rice and at Nanyang Technological University, were utilized to perform the measurements. The setups used output from a Ti:sapphire oscillator producing nearly (100–150 fs) pulses at 800 nm split into pump and probe beams. The pump and probe optical pulses served as generation and detection of the THz field in ZnTe crystals, respectively. The probe beam was delayed with respect to the pump beam using a delay stage, which in turn dictates the resolution of the system. Electric field amplitude and phase of the THz waveform are obtained by scanning the delay stage for a maximum resolution of 40 GHz. All measurements were done inside a box purged with dry air or nitrogen to remove excess water vapor. Numerical simulations were performed using a finite element method with periodic boundary conditions to emulate a 2D infinite array of unit cells. To ensure the accuracy of the simulations, the length scale of the mesh was set to ${\le} {\lambda _0}/10$ throughout the simulation domain, where ${\lambda _0}$ (600 µm) is the central wavelength of the incident radiation. The input and output ports were placed at $3{\lambda _0}$ from the PhC slab with open boundary conditions. In all numerical simulations, the permittivity value of $\epsilon = 3.4$ with the dielectric loss of 5% (tan $\delta = 0.05$) was applied for the dielectric Kapton layer.

3. RESULTS AND DISCUSSION

To study the behavior of the guided-mode resonances, we simulated (solid line) and measured (dotted line) the transmission of a 50 µm thick Kapton PhC slab with circular air holes of varying diameters [Fig. 2(a)]. Due to the periodicity of the unit cell (300 µm), such structures do not diffract normally incident THz radiation for frequencies less than 1 THz. The single guided resonance below 1 THz is observed between 0.9 and 1 THz in both experiment and simulation for all hole diameters. However, the experimental resonance has a larger linewidth compared to the simulations. The difference between the experiment and simulations is mainly due to finite sampling time, scattering losses, and possible disorder from slight imperfections or defects in the sample, which cause the experimental spectra to be dampened and inhomogeneously broadened. Recent measurements of comparable sharp resonances in the THz regime show a similar broadening in experiments for hole arrays in silicon slabs [35]. Unlike silicon PhC slabs with thicknesses ranging in the hundreds of micrometers [2126], Fabry–Perot oscillations are not observed in our sample.

 figure: Fig. 2.

Fig. 2. Transmission of the guided modes as a function of hole diameter for 50 µm thick sample. (a) Simulated (solid line) and measured (dashed line) transmission spectra for circular air holes of different diameters in a square lattice. The spectra are offset vertically for clarity. (b) The hole fill fraction (black) and effective refractive index (red) are also calculated for different ${ r}/{ a}$ values. (c) Shifts in frequency of the guided resonances are extracted from experiment and simulation for increasing ${ r}/{a}$ values. (d) The measured modulation depth of the ${d} = 160 \;{\unicode{x00B5}{\rm m}}$ sample (red) and ${d} = 180 \;{\unicode{x00B5}{\rm m}}$ (blue) are plotted in parallel with a measured ${Q}$-factor insert for ${d} = 160 \;{\unicode{x00B5}{\rm m}}$.

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To describe the dependence on hole geometry, Figs. 2(b) and 2(c) plot the fill fraction (FF) of the holes, the effective refractive index of the PhC slab (${n_{\rm eff}}$), and the frequency shift observed in the simulated and measured spectra as a function of $r/a$. The FF of the holes (${{\rm FF}_h}$) is calculated as ${(r/a)^2}$, while effective refractive index is determined from [21]

$${n_{\rm eff}} = \sqrt {( {{ \epsilon _K}*{{\rm FF}_K}} ) + ( {{ \epsilon _h}*{{\rm FF}_h}})} ,$$
where ${ \epsilon _K} = 3.4$ for Kapton film and ${ \epsilon _h} = 1$ for air holes, while the fill fraction of Kapton (${{\rm FF}_k})$ is given as $1 - {{\rm FF}_h}$. The calculated and measured resonances shift towards higher frequencies for about 50 GHz from ${r}/{a} = 0 . 23$ (${ d} = 140 \;{\unicode{x00B5}{\rm m}}$) to ${r}/{ a} = 0 . 3$ (${ d} = 180 \;{\unicode{x00B5}{\rm m}}$). These shifts are accompanied by increased FF of the holes (${\sim}12\%$) and lowered effective refractive index (${\sim}0.08$) of the PhC slabs. The variation of the refractive index that we obtained here is very promising for the development of future flexible THz photonic components based on polymide films, such as a flexible gradient index (GRIN) metalenses.

In order to quantify the resonances, modulation depth (MD) and quality factor (${Q}$ factor) from the guided modes are extracted in Fig. 2(d). ${Q}$ factor is defined as $Q = {f_i}/\Delta {f_i}$, where ${f_i}$ is the center frequency and $\Delta {f_i}$ is the full width at half-maximum (FWHM). The modulation depth is determined as ${\rm MD} = |({t_ {140} } - {t_i})/{t_ {140} }|$, where ${t_ {140} }$ is the transmission for ${d} = 140 \;{\unicode{x00B5}{\rm m}}$, and ${t_i}$ is the transmission for ${d} = 160$ and 180 µm, respectively. As shown in Fig. 2(d), the modulation depth of the PhC is gradually increased as the hole diameter is increased. Meanwhile, one can observe the ${ Q}$ factor linearly decreases as the hole diameter is increased. The measured modulation depth reaches a maximum value of about 85% around 0.95 THz, while the maximum measured ${Q}$ factor of the guided mode is about 11 when ${d} = 140 \;{\unicode{x00B5}{\rm m}}$.

The total ${Q}$ factor for our PhC device can be calculated from the following equation: $1/{Q_t} = 1/{Q_d} + 1/{Q_{\rm sw}}$, where ${Q_d}$ is the ${Q}$ factor due to dielectric losses and ${Q_{\rm sw}}$ is the ${Q}$ factor due to surface waves. For very thin substrates ($t \ll {\lambda _0}$), the loss due to surface waves, $1/{Q_{\rm sw}}$, is very small and can be neglected in calculation of the total ${Q}$ factor. This indicates that by reducing the thickness of the dielectric substrate, the ${Q}$ factor due to the surface waves can be improved, and as a result of that the total ${Q}$ factor of the device can be improved. Furthermore, the ${Q}$ factor due to dielectric losses can be improved by using low-loss materials. Hence, the total ${Q}$ factor is proportional to the substrate dielectric constant and inversely proportional to the substrate thickness.

To further analyze the guided modes, we reduced the thickness of the Kapton films to 25 µm (${\lambda _0}/12$) and fabricated PhC slabs with square holes in a square lattice [Fig. 3(a)]. Simulated and measured transmission amplitudes of the sample are plotted for varying hole diameters in Fig. 3(b). From the obtained results, the guided resonances that originate from periodic square holes and circular holes have very similar shape and linewidth for the same thickness. However, when the thickness is halved to 25 µm, the resonances exhibited extremely sharp dips compared to 50 µm. Indeed, a maximum measured ${Q}$ factor of about 31 is obtained when ${d} = 185 \;{\unicode{x00B5}{\rm m}}$ and linearly decreases as the hole’s diameter is increased. A maximum modulation depth of about 11.6% is observed for the guided resonance in measurements when ${d} = 185 \;{\unicode{x00B5}{\rm m}}$ with little modulation effect at the strong guided resonance frequency when ${d} = 190 \;{\unicode{x00B5}{\rm m}}$ [Fig. 3(d), dashed blue line]. Similar to the 50 µm sample, a minor frequency shift towards lower frequency is observed for decreasing hole diameters.

 figure: Fig. 3.

Fig. 3. Transmission of guided mode as a function of square hole diameter for 25 µm sample. (a) Unit cell of the PhC sample with parameters ${t} = 25 \;{\unicode{x00B5}{\rm m}}$, ${a} = 300 \;{\unicode{x00B5}{\rm m}}$, and variable diameter ${d}$. (b) Simulated (solid line) and measured (dotted line) transmission spectra for different diameters in a square lattice. The spectra are offset vertically for clarity. (c) Evolution of the ${Q}$ factor versus the hole diameter. Inset: optical microscope image of the fabricated PhC with square shaped air holes. (d) The frequency dependence of experimentally measured modulation depth for $d = 185\;\unicode{x00B5}{\rm m}$ and 190 µm.

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The use of flexible substrates provides an unprecedented route to achieve frequency agility and/or amplitude modulation of metadevices due to modifications in the profiles and the periodicities of the structures when the substrates are bended or stretched. Next, we take advantage of the flexibility of our samples through the demonstration of active modulation of guided-mode resonance (Fig. 4). To mimic the experiment for active tunability, curvature-dependent simulations were performed by using the appropriate bending angles with the entire curved device designed in full (not only the elementary cell). The responses of the PhC slabs are simulated for different bending angles with their corresponding experimental results in Fig. 4(b), where we taped the 25 µm sample with ${d} = 160 \;{\unicode{x00B5}{\rm m}}$ on curved surfaces of angles 5° and 10° as illustrated and shown in Fig. 4(a). The result of Fig. 4 shows a red-shift corresponding to an increase in propagation constant $\beta$ at angles further from normal incidence. Previous work on rigid SiNx PhC slabs in the visible and NIR attributed angular-dependent shifts to the empty lattice approximation [36]. This trend is supported by experimental measurements, where the resonance dip becomes very small with a red-shift from $\theta { = 0^ \circ }$ to $\theta { = 5^ \circ }$ with the complete disappearance at $\theta { = 10^ \circ }$. Another possible explanation of the red-shift of the guided mode is an increase of the periodicity along the $y$ axis (i.e., $a^\prime \gt a$), which is caused by the modification of the profile of the PhC upon bending as illustrated in Fig. 4(a). The observed strong sensitivity of the guided modes to the surface curvature of PhC slabs confirms an additional degree of freedom to tune the resonances previously not reported for rigid THz PhC slabs.

 figure: Fig. 4.

Fig. 4. Curvature-dependent transmission of the guided mode. (a) Top panel: the figure illustrates the setup of bent PhC sample. Bottom panel: image of the curved PhC sample showing an approximately determined bent angle of $\theta { = 10^ \circ }$. (b) Simulated (solid line) and measured (dotted line) transmission are plotted for the 25 µm thick sample with bending angles $\theta { = 0^ \circ }$, 5°, and 10°.

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4. CONCLUSION

To summarize, we have demonstrated the existence of the guided resonances in a membrane-type terahertz PhC slab from a flexible thin dielectric medium of Kapton polyimide films. The resonance originates from the coupling of the in-plane resonant mode on PhC plane to external radiation. The frequency positions of the resonances undergo a red-shift with increasing diameters of the air holes. For ultra-thin samples with subwavelength thickness (${\sim}{\lambda _0}/12$), the resonance dip is less pronounced and undergoes a red-shift from $\theta { = 0^ \circ }$ to $\theta { = 5^ \circ }$ with the complete disappearance at $\theta { = 10^ \circ }$. This allows for active tuning of the guided modes with respect to the curvature of the PhC slabs. The temperature resistance and the mechanical robustness of the Kapton films allow for easy integration of these PhC slabs into current microfabrication technology.

Funding

Air Force Office of Scientific Research (FA9550-16-1-0346); U.S. National Science Foundation (ECCS-1541959), (ECCS-1708315); Singapore Ministry of Education (MOE2016-T3-1-006); W. K. Keck Foundation.

Acknowledgment

T. A. S. acknowledges support from the CNS Scholars Program and C. K. acknowledges support in the form of the Just-Julian Graduate Research Assistantship. M. M. and R. S. acknowledge support from the Singapore Ministry of Education. J. K. acknowledges support by the U.S. National Science Foundation.

Disclosures

The authors declare no conflicts of interest.

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References

  • View by:

  1. H. Merbold, A. Bitzer, and T. Feurer, “Second harmonic generation based on strong field enhancement in nanostructured THz materials,” Opt. Express 19, 7262–7273 (2011).
    [Crossref]
  2. S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
    [Crossref]
  3. N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
    [Crossref]
  4. Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
    [Crossref]
  5. K. Guven and E. Ozbay, “Near field imaging in microwave regime using double layer split-ring resonator based metamaterial,” Opto-Electron. Rev. 14, 213 (2006).
    [Crossref]
  6. L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
    [Crossref]
  7. Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
    [Crossref]
  8. L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
    [Crossref]
  9. J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25, 32540–32549 (2017).
    [Crossref]
  10. R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
    [Crossref]
  11. J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
    [Crossref]
  12. J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
    [Crossref]
  13. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
    [Crossref]
  14. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [Crossref]
  15. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
    [Crossref]
  16. T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
    [Crossref]
  17. L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
    [Crossref]
  18. S. Mujumdar, A. F. Koenderink, R. Wuest, and V. Sandoghdar, “Nano-optomechanical characterization and manipulation of photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 13, 253–261 (2007).
    [Crossref]
  19. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
    [Crossref]
  20. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
    [Crossref]
  21. T. Prasad, V. L. Colvin, and D. M. Mittleman, “Dependence of guided resonances on the structural parameters of terahertz photonic crystal slabs,” J. Opt. Soc. Am. B 25, 633–644 (2008).
    [Crossref]
  22. T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy,” Opt. Express 15, 16954–16965 (2007).
    [Crossref]
  23. Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
    [Crossref]
  24. Z. Jian and D. M. Mittleman, “Broadband group-velocity anomaly in transmission through a terahertz photonic crystal slab,” Phys. Rev. B 73, 115118 (2006).
    [Crossref]
  25. Z. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
    [Crossref]
  26. R. Kakimi, M. Fujita, M. Nagai, M. Ashida, and T. Nagatsuma, “Capture of a terahertz wave in a photonic-crystal slab,” Nat. Photonics 8, 657–663 (2014).
    [Crossref]
  27. K. Tsuruda, M. Fujita, and T. Nagatsuma, “Extremely low-loss terahertz waveguide based on silicon photonic-crystal slab,” Opt. Express 23, 31977–31990 (2015).
    [Crossref]
  28. N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
    [Crossref]
  29. W. J. Otter, S. M. Hanham, N. M. Ridler, G. Marino, N. Klein, and S. Lucyszyn, “100 ghz ultra-high Q-factor photonic crystal resonators,” Sens. Actuators A 217, 151–159 (2014).
    [Crossref]
  30. M. Yata, M. Fujita, and T. Nagatsuma, “Photonic-crystal diplexers for terahertz-wave applications,” Opt. Express 24, 7835–7849 (2016).
    [Crossref]
  31. C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
    [Crossref]
  32. C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
    [Crossref]
  33. N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
    [Crossref]
  34. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref]
  35. Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
    [Crossref]
  36. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
    [Crossref]

2019 (1)

Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

2018 (3)

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
[Crossref]

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
[Crossref]

2017 (1)

2016 (1)

2015 (4)

K. Tsuruda, M. Fujita, and T. Nagatsuma, “Extremely low-loss terahertz waveguide based on silicon photonic-crystal slab,” Opt. Express 23, 31977–31990 (2015).
[Crossref]

L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
[Crossref]

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

2014 (3)

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

R. Kakimi, M. Fujita, M. Nagai, M. Ashida, and T. Nagatsuma, “Capture of a terahertz wave in a photonic-crystal slab,” Nat. Photonics 8, 657–663 (2014).
[Crossref]

W. J. Otter, S. M. Hanham, N. M. Ridler, G. Marino, N. Klein, and S. Lucyszyn, “100 ghz ultra-high Q-factor photonic crystal resonators,” Sens. Actuators A 217, 151–159 (2014).
[Crossref]

2013 (2)

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
[Crossref]

2011 (2)

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
[Crossref]

H. Merbold, A. Bitzer, and T. Feurer, “Second harmonic generation based on strong field enhancement in nanostructured THz materials,” Opt. Express 19, 7262–7273 (2011).
[Crossref]

2009 (1)

C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

2008 (1)

2007 (3)

T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy,” Opt. Express 15, 16954–16965 (2007).
[Crossref]

C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
[Crossref]

S. Mujumdar, A. F. Koenderink, R. Wuest, and V. Sandoghdar, “Nano-optomechanical characterization and manipulation of photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 13, 253–261 (2007).
[Crossref]

2006 (5)

K. Guven and E. Ozbay, “Near field imaging in microwave regime using double layer split-ring resonator based metamaterial,” Opto-Electron. Rev. 14, 213 (2006).
[Crossref]

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
[Crossref]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

Z. Jian and D. M. Mittleman, “Broadband group-velocity anomaly in transmission through a terahertz photonic crystal slab,” Phys. Rev. B 73, 115118 (2006).
[Crossref]

Z. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
[Crossref]

2005 (1)

Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
[Crossref]

2003 (1)

N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
[Crossref]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[Crossref]

2000 (1)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

1999 (1)

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[Crossref]

1998 (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

1996 (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Abbott, D.

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

Agha, I.

R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
[Crossref]

J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25, 32540–32549 (2017).
[Crossref]

Ahn, Y. H.

J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
[Crossref]

Ashida, M.

R. Kakimi, M. Fujita, M. Nagai, M. Ashida, and T. Nagatsuma, “Capture of a terahertz wave in a photonic-crystal slab,” Nat. Photonics 8, 657–663 (2014).
[Crossref]

Bagiante, S.

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

Bhaskaran, M.

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

Bitzer, A.

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

Brand, S.

T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Burrow, J. A.

R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
[Crossref]

J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25, 32540–32549 (2017).
[Crossref]

Chang, S.

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[Crossref]

Cluzel, B.

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
[Crossref]

Colvin, V. L.

Cong, L.

L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
[Crossref]

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

de Fornel, F.

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
[Crossref]

Dodabalapur, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[Crossref]

Dumas, C.

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
[Crossref]

Enderli, F.

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

Fabianska, J.

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

Fan, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Feurer, T.

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

H. Merbold, A. Bitzer, and T. Feurer, “Second harmonic generation based on strong field enhancement in nanostructured THz materials,” Opt. Express 19, 7262–7273 (2011).
[Crossref]

Fujita, M.

Fushman, I.

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
[Crossref]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

Gu, J.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Guven, K.

K. Guven and E. Ozbay, “Near field imaging in microwave regime using double layer split-ring resonator based metamaterial,” Opto-Electron. Rev. 14, 213 (2006).
[Crossref]

Han, J.

Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Hanham, S. M.

W. J. Otter, S. M. Hanham, N. M. Ridler, G. Marino, N. Klein, and S. Lucyszyn, “100 ghz ultra-high Q-factor photonic crystal resonators,” Sens. Actuators A 217, 151–159 (2014).
[Crossref]

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

Hong, J. T.

J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
[Crossref]

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
[Crossref]

Imada, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[Crossref]

In, S.

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
[Crossref]

Jeong, J.

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
[Crossref]

Jian, Z.

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J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
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J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
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J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
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N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
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C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
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N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
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K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
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J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
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Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
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A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
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J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
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A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
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S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Vuckovic, J.

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
[Crossref]

Wang, Q.

Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

Withayachumnankul, W.

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

Wuest, R.

S. Mujumdar, A. F. Koenderink, R. Wuest, and V. Sandoghdar, “Nano-optomechanical characterization and manipulation of photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 13, 253–261 (2007).
[Crossref]

Xu, N.

L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
[Crossref]

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Xu, Y.

Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

Yahiaoui, R.

R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
[Crossref]

J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25, 32540–32549 (2017).
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Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

Yata, M.

Yee, C.

C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
[Crossref]

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
[Crossref]

Yee, C. M.

C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

Yim, J. H.

J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
[Crossref]

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[Crossref]

Yue, W.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

Zhang, B.

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

Zhang, S.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

Zhang, W.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
[Crossref]

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Zhang, X.

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

Zhang, Y.

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

Zhao, X.

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

Zhu, X.

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

ACS Photon. (1)

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal terahertz field enhancement using split-ring resonators with a sub-10 nm gap,” ACS Photon. 5, 278–283 (2018).
[Crossref]

Adv. Funct. Mater. (1)

Q. Yang, S. Kruk, Y. Xu, Q. Wang, Y. K. Srivastava, K. Koshelev, I. Kravchenko, R. Singh, J. Han, Y. Kivshar, and I. Shadrivov, “Mie-resonant membrane Huygens’ metasurfaces,” Adv. Funct. Mater. 30, 1906851 (2019).
[Crossref]

Adv. Opt. Mater. (2)

Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3, 779–785 (2015).
[Crossref]

L. Cong, N. Xu, W. Zhang, and R. Singh, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry,” Adv. Opt. Mater. 3, 1176–1183 (2015).
[Crossref]

Appl. Phys. Lett. (7)

J. Li, C. M. Shah, W. Withayachumnankul, B. S.-Y. Ung, A. Mitchell, S. Sriram, M. Bhaskaran, S. Chang, and D. Abbott, “Mechanically tunable terahertz metamaterials,” Appl. Phys. Lett. 102, 121101 (2013).
[Crossref]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[Crossref]

C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
[Crossref]

C. M. Yee and M. S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[Crossref]

N. Jukam, C. Yee, M. S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006).
[Crossref]

Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
[Crossref]

N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Mujumdar, A. F. Koenderink, R. Wuest, and V. Sandoghdar, “Nano-optomechanical characterization and manipulation of photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 13, 253–261 (2007).
[Crossref]

J. Appl. Phys. (1)

Z. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
[Crossref]

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

J. Phys. Chem. Lett. (1)

J. T. Hong, D. J. Park, J. H. Yim, J. K. Park, J.-Y. Park, S. Lee, and Y. H. Ahn, “Dielectric constant engineering of single-walled carbon nanotube films for metamaterials and plasmonic devices,” J. Phys. Chem. Lett. 4, 3950–3957 (2013).
[Crossref]

Laser Photon. Rev. (1)

L. Cong, N. Xu, J. Gu, R. Singh, J. Han, and W. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photon. Rev. 8, 626–632 (2014).
[Crossref]

Microwave and Opt. Technol. Lett. (1)

Y. Liu, C. Liu, X. Jin, B. Zhang, Y. Zhang, X. Zhu, B. Su, and X. Zhao, “Beam steering by using a gradient refractive index metamaterial planar lens and a gradient phase metasurface planar lens,” Microwave and Opt. Technol. Lett. 60, 330–337 (2018).
[Crossref]

Nat. Photonics (1)

R. Kakimi, M. Fujita, M. Nagai, M. Ashida, and T. Nagatsuma, “Capture of a terahertz wave in a photonic-crystal slab,” Nat. Photonics 8, 657–663 (2014).
[Crossref]

Nature (2)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437–440 (2000).
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T. F. Krauss, R. M. D. L. Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
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Opt. Express (6)

Opto-Electron. Rev. (1)

K. Guven and E. Ozbay, “Near field imaging in microwave regime using double layer split-ring resonator based metamaterial,” Opto-Electron. Rev. 14, 213 (2006).
[Crossref]

Phys. Rev. B (4)

R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97, 155403 (2018).
[Crossref]

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B 83, 115326 (2011).
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K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

Z. Jian and D. M. Mittleman, “Broadband group-velocity anomaly in transmission through a terahertz photonic crystal slab,” Phys. Rev. B 73, 115118 (2006).
[Crossref]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[Crossref]

Sci. Rep. (1)

S. Bagiante, F. Enderli, J. Fabiańska, H. Sigg, and T. Feurer, “Giant electric field enhancement in split ring resonators featuring nanometer-sized gaps,” Sci. Rep. 5, 8051 (2015).
[Crossref]

Science (2)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293, 1123–1125 (2001).
[Crossref]

Sens. Actuators A (1)

W. J. Otter, S. M. Hanham, N. M. Ridler, G. Marino, N. Klein, and S. Lucyszyn, “100 ghz ultra-high Q-factor photonic crystal resonators,” Sens. Actuators A 217, 151–159 (2014).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Flexible 2D THz PhC slab. (a) Unit cell of the 2D PhC slab with air hole radius $r$, diameter $d$, and cell period a. (b) Band dispersion calculated for the PhC slab in (a) with $r/a = 0.3$ and $\epsilon = 3.4$. The TM mode is dashed, and the TE mode is solid. (c) Representation of the mechanism for supporting guided modes where the incident THz wave couples with the in-plane resonant mode of the PhC slab. (d) Optical images of the fabricated PhC slab and highly flexible Kapton film (top-right insert). Noticeable cracking on the surface of the slab is attributed to possible thermal expansion and contraction during the ICP etching process.
Fig. 2.
Fig. 2. Transmission of the guided modes as a function of hole diameter for 50 µm thick sample. (a) Simulated (solid line) and measured (dashed line) transmission spectra for circular air holes of different diameters in a square lattice. The spectra are offset vertically for clarity. (b) The hole fill fraction (black) and effective refractive index (red) are also calculated for different ${ r}/{ a}$ values. (c) Shifts in frequency of the guided resonances are extracted from experiment and simulation for increasing ${ r}/{a}$ values. (d) The measured modulation depth of the ${d} = 160 \;{\unicode{x00B5}{\rm m}}$ sample (red) and ${d} = 180 \;{\unicode{x00B5}{\rm m}}$ (blue) are plotted in parallel with a measured ${Q}$-factor insert for ${d} = 160 \;{\unicode{x00B5}{\rm m}}$.
Fig. 3.
Fig. 3. Transmission of guided mode as a function of square hole diameter for 25 µm sample. (a) Unit cell of the PhC sample with parameters ${t} = 25 \;{\unicode{x00B5}{\rm m}}$, ${a} = 300 \;{\unicode{x00B5}{\rm m}}$, and variable diameter ${d}$. (b) Simulated (solid line) and measured (dotted line) transmission spectra for different diameters in a square lattice. The spectra are offset vertically for clarity. (c) Evolution of the ${Q}$ factor versus the hole diameter. Inset: optical microscope image of the fabricated PhC with square shaped air holes. (d) The frequency dependence of experimentally measured modulation depth for $d = 185\;\unicode{x00B5}{\rm m}$ and 190 µm.
Fig. 4.
Fig. 4. Curvature-dependent transmission of the guided mode. (a) Top panel: the figure illustrates the setup of bent PhC sample. Bottom panel: image of the curved PhC sample showing an approximately determined bent angle of $\theta { = 10^ \circ }$. (b) Simulated (solid line) and measured (dotted line) transmission are plotted for the 25 µm thick sample with bending angles $\theta { = 0^ \circ }$, 5°, and 10°.

Equations (1)

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n e f f = ( ϵ K F F K ) + ( ϵ h F F h ) ,

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