Abstract

This paper describes the design and numerical simulation of a two-dimensional comb-shaped graphene structure. Based on the principle of using the simplest possible design for the intended function of the bandpass filter, the proposed structure includes one graphene nanoribbon (GNR) and several lateral GNRs vertically placed near the main GNR. The transmission characteristics of the bandpass filter can be tuned by adjusting geometric parameters, or, by adjusting the chemical potential of graphene. These control approaches are, together, more convenient for tunability than a conventional metallic structure. It can be observed that by increasing the gate voltage, the length or width of the periodic part, one can move the peak of the transmission spectrum towards smaller wavelengths. We believe that the presented structure will be useful for optical integrated components and other compact optical devices in the future.

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

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References

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    [Crossref]
  4. A. Tavousi, A. Rostami, G. Rostami, and M. Dolatyari, “3-D Numerical Analysis of Smith-Purcell-Based Terahertz Wave Radiation Excited by Effective Surface Plasmon,” J. Lightwave Technol. 33(22), 4640–4647 (2015).
    [Crossref]
  5. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (1)

2017 (1)

M. Janfaza, M. A. Mansouri-Birjandi, and A. Tavousi, “Tunable plasmonic band-pass filter based on Fabry-Perot graphene nanoribbons,” Appl. Phys. B 123(10), 262 (2017).
[Crossref]

2015 (3)

2014 (2)

C. Zeng, J. Guo, and X. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry-Pérot microcavity,” Appl. Phys. Lett. 105(12), 121103 (2014).
[Crossref]

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

2013 (4)

2012 (3)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

T.-T. Yeh, S. Genovesi, A. Monorchio, E. Prati, F. Costa, T.-Y. Huang, and T.-J. Yen, “Ultra-broad and sharp-transition bandpass terahertz filters by hybridizing multiple resonances mode in monolithic metamaterials,” Opt. Express 20(7), 7580–7589 (2012).
[Crossref]

2011 (2)

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

2009 (3)

2008 (2)

X.-S. Lin and X.-G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008).
[Crossref]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

2006 (1)

P. Bhattacharyya, P. K. Basu, H. Saha, and S. Basu, “Fast Response Methane Sensor Based on Pd(Ag)/ZnO/Zn MIM Structure,” Sens. Lett. 4(4), 371–376 (2006).
[Crossref]

2005 (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005).
[Crossref]

Alú, A.

P. Chen, C. Argyropoulos, and A. Alú, “Terahertz Antenna Phase Shifters Using Integrally-Gated Graphene Transmission-Lines,” IEEE Trans. Antennas Propag. 61(4), 1528–1537 (2013).
[Crossref]

Argyropoulos, C.

P. Chen, C. Argyropoulos, and A. Alú, “Terahertz Antenna Phase Shifters Using Integrally-Gated Graphene Transmission-Lines,” IEEE Trans. Antennas Propag. 61(4), 1528–1537 (2013).
[Crossref]

Baghban, H.

A. Rostami, H. Rasooli, and H. Baghban, Terahertz Technology: Fundamentals and Applications, Lecture Notes in Electrical Engineering (Springer-Verlag, 2011).

Basu, P. K.

P. Bhattacharyya, P. K. Basu, H. Saha, and S. Basu, “Fast Response Methane Sensor Based on Pd(Ag)/ZnO/Zn MIM Structure,” Sens. Lett. 4(4), 371–376 (2006).
[Crossref]

Basu, S.

P. Bhattacharyya, P. K. Basu, H. Saha, and S. Basu, “Fast Response Methane Sensor Based on Pd(Ag)/ZnO/Zn MIM Structure,” Sens. Lett. 4(4), 371–376 (2006).
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Bhattacharyya, P.

P. Bhattacharyya, P. K. Basu, H. Saha, and S. Basu, “Fast Response Methane Sensor Based on Pd(Ag)/ZnO/Zn MIM Structure,” Sens. Lett. 4(4), 371–376 (2006).
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Chen, P.

P. Chen, C. Argyropoulos, and A. Alú, “Terahertz Antenna Phase Shifters Using Integrally-Gated Graphene Transmission-Lines,” IEEE Trans. Antennas Propag. 61(4), 1528–1537 (2013).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

Costa, F.

Dolatyari, M.

García de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

García-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” in Nanoscience and Technology: A Collection of Reviews from Nature Journals, (World Scientific, 2010), pp. 11–19.

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Genovesi, S.

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Gómez-Díaz, J. S.

Gu, J.

Guinea, F.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

Guo, J.

C. Zeng, J. Guo, and X. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry-Pérot microcavity,” Appl. Phys. Lett. 105(12), 121103 (2014).
[Crossref]

Han, J.

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

He, M.

He, S.

He, Y.

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Huang, T.-Y.

Huang, X. G.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

Huang, X.-G.

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Janfaza, M.

A. Tavousi, M. A. Mansouri-Birjandi, and M. Janfaza, “Optoelectronic application of graphene nanoribbon for mid-infrared bandpass filtering,” Appl. Opt. 57(20), 5800–5805 (2018).
[Crossref]

M. Janfaza, M. A. Mansouri-Birjandi, and A. Tavousi, “Tunable plasmonic band-pass filter based on Fabry-Perot graphene nanoribbons,” Appl. Phys. B 123(10), 262 (2017).
[Crossref]

Jiang, X.

Jin, X.-P.

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Kong, F.

Koppens, F. H. L.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

Lao, J.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

Li, K.

Li, W.

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Lin, X.-S.

Liu, X.

C. Zeng, J. Guo, and X. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry-Pérot microcavity,” Appl. Phys. Lett. 105(12), 121103 (2014).
[Crossref]

Lu, X.

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

Mansouri-Birjandi, M. A.

A. Tavousi, M. A. Mansouri-Birjandi, and M. Janfaza, “Optoelectronic application of graphene nanoribbon for mid-infrared bandpass filtering,” Appl. Opt. 57(20), 5800–5805 (2018).
[Crossref]

M. Janfaza, M. A. Mansouri-Birjandi, and A. Tavousi, “Tunable plasmonic band-pass filter based on Fabry-Perot graphene nanoribbons,” Appl. Phys. B 123(10), 262 (2017).
[Crossref]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005).
[Crossref]

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Martín-Moreno, L.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

Monorchio, A.

Nikitin, A. Y.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” in Nanoscience and Technology: A Collection of Reviews from Nature Journals, (World Scientific, 2010), pp. 11–19.

Perruisseau-Carrier, J.

Prati, E.

Rasooli, H.

A. Rostami, H. Rasooli, and H. Baghban, Terahertz Technology: Fundamentals and Applications, Lecture Notes in Electrical Engineering (Springer-Verlag, 2011).

Rostami, A.

A. Tavousi, A. Rostami, G. Rostami, and M. Dolatyari, “3-D Numerical Analysis of Smith-Purcell-Based Terahertz Wave Radiation Excited by Effective Surface Plasmon,” J. Lightwave Technol. 33(22), 4640–4647 (2015).
[Crossref]

A. Rostami, H. Rasooli, and H. Baghban, Terahertz Technology: Fundamentals and Applications, Lecture Notes in Electrical Engineering (Springer-Verlag, 2011).

Rostami, G.

Saha, H.

P. Bhattacharyya, P. K. Basu, H. Saha, and S. Basu, “Fast Response Methane Sensor Based on Pd(Ag)/ZnO/Zn MIM Structure,” Sens. Lett. 4(4), 371–376 (2006).
[Crossref]

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Sheng, S.

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Tao, J.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

Q. Zhang, X.-G. Huang, X.-S. Lin, J. Tao, and X.-P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express 17(9), 7549–7554 (2009).
[Crossref]

Tavousi, A.

Teng, J.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

Wang, B.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Wang, L.

Wang, Q. J.

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

Xing, Q.

Yeh, T.-T.

Yen, T.-J.

Yuan, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005).
[Crossref]

Zeng, C.

C. Zeng, J. Guo, and X. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry-Pérot microcavity,” Appl. Phys. Lett. 105(12), 121103 (2014).
[Crossref]

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Zhang, Q.

Zhang, W.

Zhang, X.

S. He, X. Zhang, and Y. He, “Graphene nano-ribbon waveguides of record-small mode area and ultra-high effective refractive indices for future VLSI,” Opt. Express 21(25), 30664–30673 (2013).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Zhuang, H.

ACS Nano (1)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

M. Janfaza, M. A. Mansouri-Birjandi, and A. Tavousi, “Tunable plasmonic band-pass filter based on Fabry-Perot graphene nanoribbons,” Appl. Phys. B 123(10), 262 (2017).
[Crossref]

Appl. Phys. Lett. (2)

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

C. Zeng, J. Guo, and X. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated Fabry-Pérot microcavity,” Appl. Phys. Lett. 105(12), 121103 (2014).
[Crossref]

IEEE Trans. Antennas Propag. (1)

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Figures (9)

Fig. 1.
Fig. 1. a. A 3D-schematic drawing of the single tooth GNR structure supported on its substrate. b. Top view of the proposed single-tooth GNR structure
Fig. 2.
Fig. 2. a. The side view of the proposed filter with a monolayer graphene ribbon deposited on the $SiO_2/Si$ substrate. A gating voltage $V_{bias}$ is applied between a layer of metal $Au$ and the $Si$ substrate to produce the desired chemical potential of graphene. b. Relationship curve between the gating voltage and the chemical potential with the thickness of t = 50 nm.
Fig. 3.
Fig. 3. The $E_z$ field distributions of the SPPs of GNR in the y-z axis section at a wavelength of 5000 nm. It can be observed that the edge mode was excited and hence confined the energy of SPP along the edge of the GNR
Fig. 4.
Fig. 4. a. Transmission characteristics versus lateral GNR length $d$ varied from 30 nm to 40 nm b. Transmission characteristics versus width $w$ changed from 12.5 nm to 17.5 nm.
Fig. 5.
Fig. 5. Transmission characteristics of a single-tooth filter for different chemical potential values
Fig. 6.
Fig. 6. a. A 3D-schematic drawing of the multiple-tooth GNR structure on its substrate. b. Top view sketch of the proposed multiple-tooth bandpass filter structure.
Fig. 7.
Fig. 7. Transmission characteristics of the multiple-tooth structure filter with a width $w$ of 15 nm, length $d$ of 30 nm and a chemical potential of 0.3 eV
Fig. 8.
Fig. 8. The contour profiles of the field $E_z$ of the bandpass filter with wavelength of a. 7000 nm and b. 8200 nm.
Fig. 9.
Fig. 9. Transmission spectrum dependence on different parameters:a. widths of GNR, $w$; b. length of lateral GNRs, $d$; c. period, $\Lambda$; and d. chemical potential of GNR.

Tables (3)

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Table 1. Geometry Parameters of the Proposed Single-tooth GNRs Structure

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Table 2. Summarized Values of the Proposed Multiple-Teeth GNRs Structure

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Table 3. Comparison between the proposed filter and some reported filters

Equations (6)

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σ g = i e 2 k B T π 2 ( ω i 2 Γ ) ( μ c k B T + 2 ln ( e μ c k B T + 1 ) )
μ c = v f π ε S i O 2 ε 0 V bias e t
n eff = 1 ( 2 η 0 σ g ) 2
ε | | = 1 + i σ g ω ε 0 Δ
T = | E 2 o u t E 1 i n | 2 = | t 1 + s 1 s 3 1 r 3 exp ( i ϕ ( λ ) ) exp ( i ϕ ( λ ) ) | 2
λ m = 4 n eff d ( 2 m + 1 ) Δ ϕ ( λ ) π

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