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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 11340–11350
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Terahertz plasmonic waveguide based on metal rod arrays for nanofilm sensing

Borwen You, Chien-Chun Peng, Jia-Shing Jhang, Hungh-Hsuan Chen, Chin-Ping Yu, Wei-Chih Lai, Tze-An Liu, Jin-Long Peng, and Ja-Yu Lu  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 11340-11350 (2014)
http://dx.doi.org/10.1364/OE.22.011340


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Abstract

A high-aspect-ratio metallic rod array is demonstrated to generate and propagate highly confined terahertz (THz) surface plasmonic waves under end-fire excitation. The transverse modal power distribution and spectral properties of the bound THz plasmonic wave are characterized in two metallic rod arrays with different periods and in two configurations with and without attaching a subwavelength superstrate. The integrated metallic rod array–based waveguide can be used to sense the various thin films deposited on the polypropylene superstrate based on the phase-sensitive mechanism. The sensor exhibits different phase detection sensitivities depending on the modal power immersed in the air gaps between the metallic rods. Deep-subwavelength SiO2 and ZnO nanofilms with an optical path difference of 252 nm, which is equivalent to λ/3968 at 0.300 THz, are used as analytes to test the integrated plasmonic waveguide. Analysis of the refractive index and thickness of molecular membranes indicates that the metallic rod array–based THz waveguide can integrate various biochip platforms for minute molecular detection, which is extremely less than the coherent length of THz waves.

© 2014 Optical Society of America

1. Introduction

Terahertz (THz) sensing has attracted considerable attention in recent years because THz radiation can be used for the noninvasive and label-free detection of diverse materials based on the molecular fingerprints of analytes, such as metals, polar molecules, and bio/chemical materials. However, THz sensing is not applicable for minute materials or ultra-thin films because the ultra-small optical path difference (OPD), which depends on the physical thickness and refractive index differences of analytes, is almost impossible to resolve using the traditional THz spectroscopic system [1

1. H.-B. Liu, G. Plopper, S. Earley, Y. Chen, B. Ferguson, and X.-C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron. 22(6), 1075–1080 (2007). [CrossRef] [PubMed]

]. Surface plasmon (SP) technology has undergone tremendous development; surface plasmon polaritons (SPPs) facilitate THz nanofilm sensing. SP waves excited by electromagnetic waves are resonant oscillations of conduction electrons at the metal–dielectric interface. Compared with the optical plasma frequency of metals, the plasmon frequency of semiconductors is located only at the THz frequency range; it depends on the carrier concentrations and is derived from the Drude model [2

2. M. C. Schaafsma and J. G. Rivas, “Semiconductor plasmonic crystals: active control of THz extinction,” Semicond. Sci. Technol. 28(12), 124003 (2013). [CrossRef]

]. Hence, a semiconductor surface can act as a THz plasmonic waveguide that supports bound THz SP waves for micrometer-thick film sensing [3

3. T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008). [CrossRef]

]. Another way to effectively support bound THz SP waves is to use metamaterials or spoof surface plasmon polaritons (SSPPs) from various patterned metal surfaces to generate strongly localized and enhanced fields [4

4. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

]. The frequencies of the generated SSPPs can be adjusted from optical to microwave frequency ranges according to the sizes and shapes of the artificial metal. In addition, the effective propagation constants of SSPPs are influenced by the geometric parameters of a metal. Thus, the field confinement ability of SSPPs can be altered [5

5. L. Shen, X. Chen, and T.-J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]

]. The highly confined and enhanced electromagnetic field is sensitive to the surrounding dielectric materials. It can surpass the diffraction limit of the electromagnetic field and route photons on a nano-scale circuit to realize system-on-a-chip [6

6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

8

8. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

] and near-field molecular/nanofilm sensing [9

9. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]

11

11. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

].

An integrated optical waveguide can be used for bio-chemical sensing applications. This waveguide sensor is composed of three main layers: waveguide, superstrate, and sensing analytes [12

12. R. E. Kunz and K. Cottier, “Optimizing integrated optical chips for label-free (bio-)chemical sensing,” Anal. Bioanal. Chem. 384(1), 180–190 (2006). [CrossRef] [PubMed]

, 13

13. P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17(8), R93–R116 (2006). [CrossRef]

]. The sensing mechanism of an integrated optical waveguide sensor is based on the evanescent field or decay length of waveguide modes strongly affected by the sensing layer, which may be constituted by bulk, thin film, or particle analytes. The detection sensitivity is significantly affected by the decay length of the evanescent waveguide mode, which is determined by the refractive indexes and thicknesses of the waveguide and superstrate layers. By analogy, the detection sensitivity of the SP sensor based on the metamaterial or textured metal surface can be optimized by adjusting the geometrical parameters of the metamaterial, which is equivalent to optimize the SSPP’s decay length.

In this presentation, we combine the concepts of integrated optical waveguide and textured metal surface to demonstrate a THz plasmonic waveguide sensor composed of metallic rod arrays (MRAs). According to the sensing scheme of SSPPs, the MRA-based plasmonic waveguide can effectively excite and support the THz SP waves to sensitively detect nanometer-thick thin films based on the phase-sensitive mechanism. MRAs, fabricated through bottom-up microstereolithography for a certain period, change the decay length of evanescent waveguide modes at the air–MRA interfaces by adjusting the air gaps between the metallic rods. A 100 µm-thick polypropylene (PP) film superstrate is top conjugated with the MRAs, forming an integrated THz plasmonic waveguide, to load various dielectric nanofilms for sensing. The phase detection sensitivity, which is dependent on the thickness of the PP superstrate, is also experimentally characterized by analyzing the THz electric field waveforms and the corresponding power spectra for the MRA plasmonic waveguides integrated with PP superstrates of different thicknesses. SiO2 and ZnO nanofilms (thickness: 300 nm) deposited on a 100 µm-thick PP superstrate are used as analytes. The nanofilms are successfully recognized by the integrated MRA waveguide sensor, where the OPD is 252 nm, which is equivalent to λ/3968 at 0.300 THz. The MRA-based waveguide sensor can potentially integrate various biochip platforms for the highly sensitive detection of molecular membranes with different thicknesses and refractive indices based on the sensing modality.

2. THz plasmonic waveguide based on MRAs

Figures 2(a)
Fig. 2 Measured transmittance of (a) 420 µm- and (b) 620 µm-Λ MRAs.
and 2(b) show the normalized transmission spectra (i.e. transmittance) of the 420 µm- and 620 µm-Λ MRA waveguides, respectively. The spectra were obtained through THz time-domain spectroscopy [19

19. B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, and C.-L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 96(5), 051105 (2010). [CrossRef]

] and through comparison of the THz transmitted powers with and without an MRA device. Two transmission bands are found in both MRA structures within the spectral range of 0.1 THz to 0.6 THz. However, the transmittance of transmission band measured from the 620 µm-Λ MRA is obviously higher than that of the transmission band measured from the 420 µm-Λ MRA because of the high air-filling ratio among the rods. The rejection bands of the two MRAs within the spectral range of 0.1 THz to 0.6 THz are caused by the destructive interference of multiple reflections among the metal rods when THz waves transmit through the 30 arrays of the MRA waveguide. The central frequency of the rejection band is consistent with the Bragg frequency calculated from c/2nΛ, where c, n, and Λ are the light speed in vacuum, effective refractive index, and period of MRA, respectively. As shown in Fig. 2(a), the rejection band for the 420 µm-Λ MRA ranges from 0.284 THz to 0.425 THz, which corresponds to a 141 GHz bandwidth. As shown in Fig. 2(b), the rejection band for the 620 µm-Λ MRA ranges from 0.240 THz to 0.270 THz. These values are consistent with the results calculated using the finite-difference time-domain (FDTD) method.

3. Superstrate-integrated MRA waveguides

4. Nanofilm detection based on a phase-sensitive mechanism

Basing on the sensitivity analysis in Fig. 9(e), we choose the 620 µm-Λ MRA waveguide integrated with a 100 µm-thick PP superstrate for nanofilm sensing. In this experiment, SiO2 and ZnO nanofilms sputter coated on the 100 µm-thick PP superstrate are prepared as standard samples to confirm the nanofilm-sensing capability of the MRA structure. Three samples each with an area of 9 mm × 18 mm are prepared on the same PP superstrate for continuous measurement by just moving the integrated position of the superstrate on the MRA waveguide to avoid inaccurate phase measurement induced by thickness variation in a superstrate. The three sample areas on one PP superstrate are the SiO2 nanofilm, ZnO nanofilm, and blank space. The thicknesses of the two dielectric nanofilms controlled by sputter coating are both 300 nm. The films are used to observe the refractive index–induced OPD in the sensing application. Figure 10(a)
Fig. 10 (a) Electric field oscillations of THz waves passing through a 620 µm-Λ MRA waveguide integrated in a 100 µm-thick PP substrate with and without nanofilm coating. (b) Detected phase retardations induced by SiO2 and ZnO nanofilms.
shows the propagation of THz electric field oscillations through the integrated MRA waveguide loaded with and without a nanofilm. The electric field oscillations in the duration of 25 ps to 70 ps are apparently distinct for the three waveforms. These results show that the SiO2 and ZnO films can be recognized based on their different refractive indices, which are 1.95 and 2.79, respectively, at 0.300 THz [22

22. W. Chen, S. Kirihara, and Y. Miyamoto, “Fabrication and measurement of micro three-dimensional photonic crystals of SiO2 ceramic for terahertz wave applications,” J. Am. Ceram. Soc. 90(7), 2078–2081 (2007). [CrossRef]

, 23

23. A. K. Azad, J. Han, and W. Zhang, “Terahertz dielectric properties of high-resistivity single-crystal ZnO,” Appl. Phys. Lett. 88(2), 021103 (2006). [CrossRef]

]. Figure 10(b) shows the theoretical and measured transmittances of the blank device, as well as the phase retardations, induced by the two nanofilms. The measured phase retardation is obtained by comparing the measured phases of the integrated MRA loaded with and without a nano film [Fig. 10(b)]. Different nanofilms can be identified by using the integrated MRA waveguide based on the phase retardation in the transmission band of 0.300 THz to 0.450 THz. Otherwise, the phase retardation in the rejection bands at 0.200 THz to 0.300 THz and 0.450 THz to 0.550 THz is considerably chaotic without repeatable response in the sensing measurement. The phase retardations for sensing the SiO2 and ZnO nanofilms are apparently distinct because of the large OPD (approximately 252 nm) between the two nanofilms. Basing on the phase detection resolution of 0.39 rad in our THz time–domain spectroscopy system and the proportional relation between the phase retardation and thickness variation (Fig. 9), we find that the minimum detectable OPD for nanofilm sensing at 0.300 THz is reduced to approximately 64 nm, which corresponds to λ/15702. When the operation electromagnetic frequency increases to 0.400 THz, the OPD resolution is further decreased to 21 nm, which corresponds to λ/35714. This result can be attributed to the increase in detection sensitivity with increasing frequency (Fig. 9).

5. Conclusion

Acknowledgment

This work was supported by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 100-2221-E-006 −174 -MY3) of Taiwan.

References and links

1.

H.-B. Liu, G. Plopper, S. Earley, Y. Chen, B. Ferguson, and X.-C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron. 22(6), 1075–1080 (2007). [CrossRef] [PubMed]

2.

M. C. Schaafsma and J. G. Rivas, “Semiconductor plasmonic crystals: active control of THz extinction,” Semicond. Sci. Technol. 28(12), 124003 (2013). [CrossRef]

3.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008). [CrossRef]

4.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]

5.

L. Shen, X. Chen, and T.-J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]

6.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

7.

J.-T. Kim, J.-J. Ju, S. Park, M.-S. Kim, S.-K. Park, and M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16(17), 13133–13138 (2008). [CrossRef] [PubMed]

8.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

9.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]

10.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

11.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

12.

R. E. Kunz and K. Cottier, “Optimizing integrated optical chips for label-free (bio-)chemical sensing,” Anal. Bioanal. Chem. 384(1), 180–190 (2006). [CrossRef] [PubMed]

13.

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17(8), R93–R116 (2006). [CrossRef]

14.

A. Mazhorova, J. F. Gu, A. Dupuis, M. Peccianti, O. Tsuneyuki, R. Morandotti, H. Minamide, M. Tang, Y. Wang, H. Ito, and M. Skorobogatiy, “Composite THz materials using aligned metallic and semiconductor microwires, experiments and interpretation,” Opt. Express 18(24), 24632–24647 (2010). [CrossRef] [PubMed]

15.

B. You, J.-Y. Lu, T.-A. Liu, and J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21(18), 21087–21096 (2013). [CrossRef] [PubMed]

16.

J.-W. Choi, R. Wicker, S.-H. Lee, K.-H. Choi, C.-S. Ha, and I. Chung, “Fabrication of 3D biocompatible / biodegradable micro-scaffolds using dynamic mask projection microstereolithography,” J. Mater. Process. Technol. 209(15-16), 5494–5503 (2009). [CrossRef]

17.

M. Farsari, F. Claret-Tournier, S. Huang, C. R. Chatwin, D. M. Budgett, P. M. Birch, R. C. D. Young, and J. D. Richardson, “A novel high-accuracy microstereolithography method employing an adaptive electro-optic mask,” J. Mater. Process. Technol. 107(1-3), 167–172 (2000). [CrossRef]

18.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1120 (1983). [CrossRef] [PubMed]

19.

B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, and C.-L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 96(5), 051105 (2010). [CrossRef]

20.

J. M. Khosrofian and B. A. Garetz, “Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt. 22(21), 3406–3410 (1983). [CrossRef] [PubMed]

21.

Bahaa, E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (New York, Wiley, 1991), Chap. 7.

22.

W. Chen, S. Kirihara, and Y. Miyamoto, “Fabrication and measurement of micro three-dimensional photonic crystals of SiO2 ceramic for terahertz wave applications,” J. Am. Ceram. Soc. 90(7), 2078–2081 (2007). [CrossRef]

23.

A. K. Azad, J. Han, and W. Zhang, “Terahertz dielectric properties of high-resistivity single-crystal ZnO,” Appl. Phys. Lett. 88(2), 021103 (2006). [CrossRef]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7400) Optical devices : Waveguides, slab
(310.2785) Thin films : Guided wave applications
(160.3918) Materials : Metamaterials
(300.6495) Spectroscopy : Spectroscopy, teraherz
(050.6875) Diffraction and gratings : Three-dimensional fabrication

ToC Category:
Terahertz Optics

History
Original Manuscript: March 10, 2014
Revised Manuscript: April 22, 2014
Manuscript Accepted: April 28, 2014
Published: May 2, 2014

Virtual Issues
Vol. 9, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Borwen You, Chien-Chun Peng, Jia-Shing Jhang, Hungh-Hsuan Chen, Chin-Ping Yu, Wei-Chih Lai, Tze-An Liu, Jin-Long Peng, and Ja-Yu Lu, "Terahertz plasmonic waveguide based on metal rod arrays for nanofilm sensing," Opt. Express 22, 11340-11350 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-11340


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References

  1. H.-B. Liu, G. Plopper, S. Earley, Y. Chen, B. Ferguson, X.-C. Zhang, “Sensing minute changes in biological cell monolayers with THz differential time-domain spectroscopy,” Biosens. Bioelectron. 22(6), 1075–1080 (2007). [CrossRef] [PubMed]
  2. M. C. Schaafsma, J. G. Rivas, “Semiconductor plasmonic crystals: active control of THz extinction,” Semicond. Sci. Technol. 28(12), 124003 (2013). [CrossRef]
  3. T. H. Isaac, W. L. Barnes, E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008). [CrossRef]
  4. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008). [CrossRef]
  5. L. Shen, X. Chen, T.-J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008). [CrossRef] [PubMed]
  6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
  7. J.-T. Kim, J.-J. Ju, S. Park, M.-S. Kim, S.-K. Park, M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16(17), 13133–13138 (2008). [CrossRef] [PubMed]
  8. R. Zia, J. A. Schuller, A. Chandran, M. L. Brongersma, “Plasmonics the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]
  9. S. Lal, S. Link, N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]
  10. D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
  11. W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  12. R. E. Kunz, K. Cottier, “Optimizing integrated optical chips for label-free (bio-)chemical sensing,” Anal. Bioanal. Chem. 384(1), 180–190 (2006). [CrossRef] [PubMed]
  13. P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17(8), R93–R116 (2006). [CrossRef]
  14. A. Mazhorova, J. F. Gu, A. Dupuis, M. Peccianti, O. Tsuneyuki, R. Morandotti, H. Minamide, M. Tang, Y. Wang, H. Ito, M. Skorobogatiy, “Composite THz materials using aligned metallic and semiconductor microwires, experiments and interpretation,” Opt. Express 18(24), 24632–24647 (2010). [CrossRef] [PubMed]
  15. B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, “Hybrid terahertz plasmonic waveguide for sensing applications,” Opt. Express 21(18), 21087–21096 (2013). [CrossRef] [PubMed]
  16. J.-W. Choi, R. Wicker, S.-H. Lee, K.-H. Choi, C.-S. Ha, I. Chung, “Fabrication of 3D biocompatible / biodegradable micro-scaffolds using dynamic mask projection microstereolithography,” J. Mater. Process. Technol. 209(15-16), 5494–5503 (2009). [CrossRef]
  17. M. Farsari, F. Claret-Tournier, S. Huang, C. R. Chatwin, D. M. Budgett, P. M. Birch, R. C. D. Young, J. D. Richardson, “A novel high-accuracy microstereolithography method employing an adaptive electro-optic mask,” J. Mater. Process. Technol. 107(1-3), 167–172 (2000). [CrossRef]
  18. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1120 (1983). [CrossRef] [PubMed]
  19. B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, C.-L. Pan, “Subwavelength plastic wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 96(5), 051105 (2010). [CrossRef]
  20. J. M. Khosrofian, B. A. Garetz, “Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data,” Appl. Opt. 22(21), 3406–3410 (1983). [CrossRef] [PubMed]
  21. Bahaa, E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (New York, Wiley, 1991), Chap. 7.
  22. W. Chen, S. Kirihara, Y. Miyamoto, “Fabrication and measurement of micro three-dimensional photonic crystals of SiO2 ceramic for terahertz wave applications,” J. Am. Ceram. Soc. 90(7), 2078–2081 (2007). [CrossRef]
  23. A. K. Azad, J. Han, W. Zhang, “Terahertz dielectric properties of high-resistivity single-crystal ZnO,” Appl. Phys. Lett. 88(2), 021103 (2006). [CrossRef]

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