Abstract

We report a high-resistivity silicon (HR-Si) prism coupled terahertz (THz) spoof surface plasmon polaritons (SSPPs) on flat subwavelength metasurface. Using a high refractive index prism as an external coupler, a more tightly confined SSPPs mode can be excited in a smaller resonant cavity, leading to strong light-matter interaction. Besides, theoretical analysis and experimental results have both indicated that the SSPPs resonance response to the filling patterns of analyte in the resonant cavity are quite different. In particular, we have found that the interaction between analyte and SSPPs wave can be maximized when the analyte filled with the whole resonant cavity and a higher sensitivity for THz sensing can be obtained. A high sensitivity varied from 0.31 THz/RIU to 0.85 THz/RIU is predicted. Furthermore, these SSPPs modes exhibit high Q-factor, and characteristic spectra of water caused by surface plasmon resonance (SPR) are observed, which is significant in promoting the THz-SPR sensing of polar liquids or aqueous analytes with THz metasurfaces.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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  7. R. Zhang, Q. Chen, K. Liu, Z. Chen, K. Li, X. Zhang, J. Xu, and E. Pickwell-MacPherson, “Terahertz Microfluidic Metamaterial Biosensor for Sensitive Detection of Small-Volume Liquid Samples,” IEEE Trans. Terahertz Sci. Technol. 9(2), 209–214 (2019).
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  11. Y. Huang, S. Zhong, Y. Shen, L. Yao, and D. Cui, “Graphene/Insulator Stack Based Ultrasensitive Terahertz Sensor with Surface Plasmon Resonance,” IEEE Photonics J. 9(6), 1–11 (2017).
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  14. L. Cong, S. Tan, R. Yahiaoui, F. Yan, W. Zhang, and R. Singh, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: a comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015).
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    [Crossref]
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    [Crossref]
  24. H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, “Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses,” Jpn. J. Appl. Phys. 43(10A), L1287–L1289 (2004).
    [Crossref]
  25. Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
    [Crossref]
  26. A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006).
    [Crossref]
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    [Crossref]
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    [Crossref]
  29. C. R. Williams, M. Misra, S. R. Andrews, and S. A. Maier, “Dual band terahertz waveguiding on a planar metal surface patterned with annular holes,” Appl. Phys. Lett. 96(1), 011101 (2010).
    [Crossref]
  30. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
    [Crossref]
  31. H. Yao and S. Zhong, “High-mode spoof spp of periodic metal grooves for ultra-sensitive terahertz sensing,” Opt. Express 22(21), 25149–25160 (2014).
    [Crossref]
  32. Y. Huang, S. Zhong, T. Shi, Y. Shen, and D. Cui, “Trapping waves with tunable prism-coupling terahertz metasurfaces absorber,” Opt. Express 27(18), 25647–25655 (2019).
    [Crossref]
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    [Crossref]
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    [Crossref]
  35. A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” Appl. Phys. A: Mater. Sci. Process. 100(2), 375–378 (2010).
    [Crossref]
  36. C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
    [Crossref]

2019 (3)

S. Zhong, “Progress in terahertz nondestructive testing: A review,” Front. Mech. Eng. 14(3), 273–281 (2019).
[Crossref]

R. Zhang, Q. Chen, K. Liu, Z. Chen, K. Li, X. Zhang, J. Xu, and E. Pickwell-MacPherson, “Terahertz Microfluidic Metamaterial Biosensor for Sensitive Detection of Small-Volume Liquid Samples,” IEEE Trans. Terahertz Sci. Technol. 9(2), 209–214 (2019).
[Crossref]

Y. Huang, S. Zhong, T. Shi, Y. Shen, and D. Cui, “Trapping waves with tunable prism-coupling terahertz metasurfaces absorber,” Opt. Express 27(18), 25647–25655 (2019).
[Crossref]

2018 (1)

Y. Huang, S. Zhong, Y. Shen, Y. Yu, and D. Cui, “Terahertz phase jumps for ultra-sensitive graphene plasmon sensing,” Nanoscale 10(47), 22466–22473 (2018).
[Crossref]

2017 (3)

H. Cheon, H. J. Yang, and J. H. Son, “Toward clinical cancer imaging using terahertz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–9 (2017).
[Crossref]

Y. Huang, S. Zhong, Y. Shen, L. Yao, and D. Cui, “Graphene/Insulator Stack Based Ultrasensitive Terahertz Sensor with Surface Plasmon Resonance,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

M. Islam, D. R. Chowdhury, A. Ahmad, and G. Kumar, “Terahertz Plasmonic Waveguide Based Thin Film Sensor,” J. Lightwave Technol. 35(23), 5215–5221 (2017).
[Crossref]

2016 (2)

M. Yin, S. Tang, and M. Tong, “The application of Terahertz spectroscopy to liquid petrochemicals detection: A review,” Appl. Spectrosc. Rev. 51(5), 379–396 (2016).
[Crossref]

X. Hu, G. Xu, L. Wen, H. Wang, Y. Zhao, Y. Zhang, D. R. S. Cumming, and Q. Chen, “Metamaterial absorber integrated microfluidic terahertz sensors,” Laser Photonics Rev. 10(6), 962–969 (2016).
[Crossref]

2015 (2)

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref]

L. Cong, S. Tan, R. Yahiaoui, F. Yan, W. Zhang, and R. Singh, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: a comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015).
[Crossref]

2014 (4)

R. Singh, W. Cao, I. Al-Naib, and L. Cong, “Ultrasensitive terahertz sensing with high-Q fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

C. Drexler, T. V. Shishkanova, C. Lange, S. N. Danilov, D. Weiss, S. D. Ganichev, and V. M. Mirsky, “Terahertz split-ring metamaterials as transducers for chemical sensors based on conducting polymers: a feasibility study with sensing of acidic and basic gases using polyaniline chemosensitive layer,” Microchim. Acta 181(15-16), 1857–1862 (2014).
[Crossref]

J. M. Jornet and I. F. Akyildiz, “Femtosecond-long pulse-based modulation for terahertz band communication in nanonetworks,” IEEE Trans. Commun. 62(5), 1742–1754 (2014).
[Crossref]

H. Yao and S. Zhong, “High-mode spoof spp of periodic metal grooves for ultra-sensitive terahertz sensing,” Opt. Express 22(21), 25149–25160 (2014).
[Crossref]

2013 (1)

B. Ng, J. Wu, S. M. Hanham, A. I. Fernández-Domínguez, N. Klein, Y. F. Liew, M. B. H. Breese, M. Hong, and S. A. Maier, “Spoof plasmon surfaces: a novel platform for THz sensing,” Adv. Opt. Mater. 1(8), 543–548 (2013).
[Crossref]

2012 (2)

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[Crossref]

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, “Metamaterial near-field sensor for deep-subwavelength thickness measurements and sensitive refractometry in the terahertz frequency range,” Appl. Phys. Lett. 100(22), 221101 (2012).
[Crossref]

2011 (1)

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated metal films,” New J. Phys. 13(3), 033024 (2011).
[Crossref]

2010 (3)

J. Liu, J. Dai, S. L. Chin, and X. C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4(9), 627–631 (2010).
[Crossref]

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” Appl. Phys. A: Mater. Sci. Process. 100(2), 375–378 (2010).
[Crossref]

C. R. Williams, M. Misra, S. R. Andrews, and S. A. Maier, “Dual band terahertz waveguiding on a planar metal surface patterned with annular holes,” Appl. Phys. Lett. 96(1), 011101 (2010).
[Crossref]

2008 (2)

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

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[Crossref]

2006 (2)

K. Siegrist, C. R. Bucher, I. Mandelbaum, A. R. Hight Walker, R. Balu, S. K. Gregurick, and D. F. Plusquellic, “High-resolution terahertz spectroscopy of crystalline trialanine: extreme sensitivity to beta-sheet structure and cocrystallized water,” J. Am. Chem. Soc. 128(17), 5764–5775 (2006).
[Crossref]

A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006).
[Crossref]

2005 (2)

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[Crossref]

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications-explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

2004 (2)

J. B. Pendry, L. Martínmoreno, and F. J. Garciavidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref]

H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, “Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses,” Jpn. J. Appl. Phys. 43(10A), L1287–L1289 (2004).
[Crossref]

2003 (2)

2002 (1)

M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. U. Jepsen, “Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy,” Biopolymers 67(4-5), 310–313 (2002).
[Crossref]

2001 (1)

1996 (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[Crossref]

1968 (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. A: Hadrons Nucl. 216(4), 398–410 (1968).
[Crossref]

Ahmad, A.

Akyildiz, I. F.

J. M. Jornet and I. F. Akyildiz, “Femtosecond-long pulse-based modulation for terahertz band communication in nanonetworks,” IEEE Trans. Commun. 62(5), 1742–1754 (2014).
[Crossref]

Al-Naib, I.

R. Singh, W. Cao, I. Al-Naib, and L. Cong, “Ultrasensitive terahertz sensing with high-Q fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Andrews, S. R.

C. R. Williams, M. Misra, S. R. Andrews, and S. A. Maier, “Dual band terahertz waveguiding on a planar metal surface patterned with annular holes,” Appl. Phys. Lett. 96(1), 011101 (2010).
[Crossref]

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

Azad, A. K.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref]

A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006).
[Crossref]

Balu, R.

K. Siegrist, C. R. Bucher, I. Mandelbaum, A. R. Hight Walker, R. Balu, S. K. Gregurick, and D. F. Plusquellic, “High-resolution terahertz spectroscopy of crystalline trialanine: extreme sensitivity to beta-sheet structure and cocrystallized water,” J. Am. Chem. Soc. 128(17), 5764–5775 (2006).
[Crossref]

Baraniuk, R. G.

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications-explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Barnes, W. L.

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

Beigang, R.

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, “Metamaterial near-field sensor for deep-subwavelength thickness measurements and sensitive refractometry in the terahertz frequency range,” Appl. Phys. Lett. 100(22), 221101 (2012).
[Crossref]

Breese, M. B. H.

B. Ng, J. Wu, S. M. Hanham, A. I. Fernández-Domínguez, N. Klein, Y. F. Liew, M. B. H. Breese, M. Hong, and S. A. Maier, “Spoof plasmon surfaces: a novel platform for THz sensing,” Adv. Opt. Mater. 1(8), 543–548 (2013).
[Crossref]

Bucher, C. R.

K. Siegrist, C. R. Bucher, I. Mandelbaum, A. R. Hight Walker, R. Balu, S. K. Gregurick, and D. F. Plusquellic, “High-resolution terahertz spectroscopy of crystalline trialanine: extreme sensitivity to beta-sheet structure and cocrystallized water,” J. Am. Chem. Soc. 128(17), 5764–5775 (2006).
[Crossref]

Cao, W.

R. Singh, W. Cao, I. Al-Naib, and L. Cong, “Ultrasensitive terahertz sensing with high-Q fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Chen, Q.

R. Zhang, Q. Chen, K. Liu, Z. Chen, K. Li, X. Zhang, J. Xu, and E. Pickwell-MacPherson, “Terahertz Microfluidic Metamaterial Biosensor for Sensitive Detection of Small-Volume Liquid Samples,” IEEE Trans. Terahertz Sci. Technol. 9(2), 209–214 (2019).
[Crossref]

X. Hu, G. Xu, L. Wen, H. Wang, Y. Zhao, Y. Zhang, D. R. S. Cumming, and Q. Chen, “Metamaterial absorber integrated microfluidic terahertz sensors,” Laser Photonics Rev. 10(6), 962–969 (2016).
[Crossref]

Chen, Z.

R. Zhang, Q. Chen, K. Liu, Z. Chen, K. Li, X. Zhang, J. Xu, and E. Pickwell-MacPherson, “Terahertz Microfluidic Metamaterial Biosensor for Sensitive Detection of Small-Volume Liquid Samples,” IEEE Trans. Terahertz Sci. Technol. 9(2), 209–214 (2019).
[Crossref]

Cheon, H.

H. Cheon, H. J. Yang, and J. H. Son, “Toward clinical cancer imaging using terahertz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–9 (2017).
[Crossref]

Chin, S. L.

J. Liu, J. Dai, S. L. Chin, and X. C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4(9), 627–631 (2010).
[Crossref]

Chowdhury, D. R.

Cong, L.

L. Cong, S. Tan, R. Yahiaoui, F. Yan, W. Zhang, and R. Singh, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: a comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015).
[Crossref]

R. Singh, W. Cao, I. Al-Naib, and L. Cong, “Ultrasensitive terahertz sensing with high-Q fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Coutaz, J. L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[Crossref]

Cui, A.

G. Kumar, S. Pandey, A. Cui, and A. Nahata, “Planar plasmonic terahertz waveguides based on periodically corrugated metal films,” New J. Phys. 13(3), 033024 (2011).
[Crossref]

Cui, D.

Y. Huang, S. Zhong, T. Shi, Y. Shen, and D. Cui, “Trapping waves with tunable prism-coupling terahertz metasurfaces absorber,” Opt. Express 27(18), 25647–25655 (2019).
[Crossref]

Y. Huang, S. Zhong, Y. Shen, Y. Yu, and D. Cui, “Terahertz phase jumps for ultra-sensitive graphene plasmon sensing,” Nanoscale 10(47), 22466–22473 (2018).
[Crossref]

Y. Huang, S. Zhong, Y. Shen, L. Yao, and D. Cui, “Graphene/Insulator Stack Based Ultrasensitive Terahertz Sensor with Surface Plasmon Resonance,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

Cumming, D. R. S.

X. Hu, G. Xu, L. Wen, H. Wang, Y. Zhao, Y. Zhang, D. R. S. Cumming, and Q. Chen, “Metamaterial absorber integrated microfluidic terahertz sensors,” Laser Photonics Rev. 10(6), 962–969 (2016).
[Crossref]

Dai, J.

J. Liu, J. Dai, S. L. Chin, and X. C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photonics 4(9), 627–631 (2010).
[Crossref]

A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006).
[Crossref]

Danilov, S. N.

C. Drexler, T. V. Shishkanova, C. Lange, S. N. Danilov, D. Weiss, S. D. Ganichev, and V. M. Mirsky, “Terahertz split-ring metamaterials as transducers for chemical sensors based on conducting polymers: a feasibility study with sensing of acidic and basic gases using polyaniline chemosensitive layer,” Microchim. Acta 181(15-16), 1857–1862 (2014).
[Crossref]

Dereux, A.

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

Dorney, T. D.

Drexler, C.

C. Drexler, T. V. Shishkanova, C. Lange, S. N. Danilov, D. Weiss, S. D. Ganichev, and V. M. Mirsky, “Terahertz split-ring metamaterials as transducers for chemical sensors based on conducting polymers: a feasibility study with sensing of acidic and basic gases using polyaniline chemosensitive layer,” Microchim. Acta 181(15-16), 1857–1862 (2014).
[Crossref]

Durach, M.

A. Rusina, M. Durach, and M. I. Stockman, “Theory of spoof plasmons in real metals,” Appl. Phys. A: Mater. Sci. Process. 100(2), 375–378 (2010).
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Figures (9)

Fig. 1.
Fig. 1. (a) Exciting SSPPs on subwavelength trapezoidal grooves metasurface with the HR-Si prism based Otto configuration; (b) Optical microscopy image of the fabricated metasurface with a period of p = 60 µm, top width of wt = 31 µm, bottom width of wb = 21 µm and depth of h = 90 µm.
Fig. 2.
Fig. 2. (a) Experimentally measured transmission spectra of silicon wafers with different resistivity. The inset shows the time-domain waveforms from THz-TDS transmission measurement of silicon wafers with different resistivity ρSi. (b) Real and imaginary part of dielectric permittivity of silicon wafers (ɛ1 and ɛ2) with different resistivity. The inset shows the penetration depth of the evanescent wave Lp created by the HR-Si (ρSi = 10k Ohm·cm) prism and PE prism at prism-air interface, respectively.
Fig. 3.
Fig. 3. SSPPs dispersion curves for corrugated metallic metasurfaces in the Brillioun zone. The blue solid line is the vacuum light, and the dotted and double dot-dash line are the parallel wavevector k for PE and HR-Si prism, respectively. The dot-dash and dash curve shows the effective medium approximation model calculation for rectangular shape grooves, and green points indicate the FEM calculation with COMSOL software for trapezoidal shape grooves. The insets show the electric field distributions for the unit cell of the trapezoidal grooves at different wavevector k.
Fig. 4.
Fig. 4. SSPPs dispersion curves for two different filling patterns of water: filled in the grooves, and filled in the gap and grooves. The scatter data are the experimental results.
Fig. 5.
Fig. 5. Theoretical resonance frequency as a function of the refractive index for two different filling patterns of materials. The inset shows the absolute gradient of the resonance frequency curves, i.e., sensitivity Sn.
Fig. 6.
Fig. 6. Simulated reflectivity spectra for two different prisms using COMSOL software. The insets show the electric field and the time-average energy density distributions for the unit cell of the trapezoidal grooves.
Fig. 7.
Fig. 7. Experimental time-domain waveforms (a), reflected spectra (b), and reflectivity spectra (c) from the measurement of free-space coupling between THz radiation and SSPPs at different coupling gaps g. The experimental time-domain waveforms are shifted for visual clarity.
Fig. 8.
Fig. 8. Experimental time-domain waveforms (a), reflected spectra (b), and reflectivity spectra (c) for two different filling patterns of water: filled in the grooves, and filled in the gap and grooves at their optimum SPR condition. The experimental time-domain waveform is shifted for visual clarity. Experimental reflectivity spectra (d) for two different filling patterns of gasoline: filled in the grooves, and filled in the gap and grooves at their optimum SPR condition.
Fig. 9.
Fig. 9. (a) The variation of simulated resonance frequency versus refractive index of analyte for different analyte quantity (normalized to the volume of groove) and their corresponding linear fitting curves. (b) The variation of sensitivity versus analyte quantity. The insets show the 2D unit cell of the variation of analyte quantity.

Equations (9)

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E sam ( ω ) / E sam ( ω ) E ref ( ω ) E ref ( ω ) = A e i ϕ ,
T   ( ω )  =  | A ( ω ) | 2 ,
n ( ω ) = ( ϕ ( ω ) c ) / ( ϕ ( ω ) c ) ( ω d ) ( ω d ) + 1 ,
α ( ω )  =  2 κ ( ω ) ω / 2 κ ( ω ) ω c c = ( 2 / 2 d d ) ln [ ( 4 n ( ω ) ) / ( 4 n ( ω ) ) ( A ( ω ) ( n ( ω ) + 1 ) 2 ) ( A ( ω ) ( n ( ω ) + 1 ) 2 ) ] ,
ε 1 + i ε 2  =  ( n ( ω ) + i κ ( ω ) ) 2 .
L p = c / c ( ω ( n p sin θ in ) 2 ( n d ) 2 ) ( ω ( n p sin θ in ) 2 ( n d ) 2 ) .
k SSPPs = ( ε d k 0 2 + ( ( w eff ε d ) / ( w eff ε d ) ( p ε g ) ( p ε g ) ) 2 k g 2 tan 2 ( k g h ) ) 1 / 1 2 2 ,
k  =  n p ( ω / c ) sin θ in  =  k SSPPs .
R = | E sam ( ω ) / E sam ( ω ) E ref ( ω ) E ref ( ω ) | 2 .

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