Abstract

The complex band structures of a 1D anisotropic graphene photonic crystal are investigated, and the dispersion relations are confirmed using the transfer matrix method and simulation of commercial software. It is found that the result of using effective medium theory can fit the derived dispersion curves in the low wave vector. Transmission, absorption, and reflection at oblique incident angles are studied for the structure, respectively. Omni-gaps exist for angles as high as 80° for two polarizations. Physical mechanisms of the tunable dispersion and transmission are explained by the permittivity of graphene and the effective permittivity of the multilayer structure.

© 2017 Chinese Laser Press

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2017 (6)

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene-dielectric metamaterials,” J. Appl. Phys. 121, 033101 (2017).
[Crossref]

P. Cao, X. Yang, S. Wang, Y. Huang, N. Wang, D. Deng, and C. Liu, “Ultrastrong graphene absorption induced by one-dimensional parity-time symmetric photonic crystal,” IEEE Photon. J. 9, 1–9 (2017).

J. P. Pandey, “Enlargement of omnidirectional reflection range using cascaded photonic crystals,” Int. J. Pure Appl. Phys. 13, 167–173 (2017).

Z. Saleki, S. R. Entezar, and A. Madani, “Optical properties of a one-dimensional photonic crystal containing a graphene-based hyperbolic metamaterial defect layer,” Appl. Opt. 56, 317–323 (2017).
[Crossref]

F. Wang, Z. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Asymmetric plasmonic supermodes in nonlinear graphene multilayers,” Opt. Express 25, 1234–1241 (2017).
[Crossref]

Y. Li, L. Qi, J. Yu, Z. Chen, Y. Yao, and X. Liu, “One-dimensional multiband terahertz graphene photonic crystal filters,” Opt. Mater. Express 7, 1228–1239 (2017).
[Crossref]

2016 (9)

Y. Wu, M. Qu, L. Jiao, Y. Liu, and Z. Ghassemlooy, “Graphene-based Yagi-Uda antenna with reconfigurable radiation patterns,” AIP Adv. 6, 065308 (2016).
[Crossref]

G. Yao, F. Ling, J. Yue, C. Luo, Q. Luo, and J. Yao, “Dynamically electrically tunable broadband absorber based on graphene analog of electromagnetically induced transparency,” IEEE Photon. J. 8, 7800808 (2016).
[Crossref]

A. Marini and F. J. García de, “Graphene-based active random metamaterials for cavity-free lasing,” Phys. Rev. Lett. 116, 217401 (2016).
[Crossref]

A. Khaleque and H. T. Hattori, “Absorption enhancement in graphene photonic crystal structures,” Appl. Opt. 55, 2936–2942 (2016).
[Crossref]

Y. V. Bludov, N. M. R. Peres, G. Smirnov, and M. I. Vasilevskiy, “Scattering of surface plasmon polaritons in a graphene multilayer photonic crystal with inhomogeneous doping,” Phys. Rev. B 93, 245425 (2016).
[Crossref]

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380, 1793–1798 (2016).
[Crossref]

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene-hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2016).
[Crossref]

L. Bian, P. Liu, G. Li, Z. Lu, and C. Liu, “Characterization for one-dimensional graphene-embedded photonic crystals at terahertz frequencies,” Opt. Quantum Electron. 48, 436–450 (2016).
[Crossref]

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik 127, 3945–3948 (2016).
[Crossref]

2015 (8)

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

F. U. Y. Al-sheqefi and W. Belhadj, “Photonic band gap characteristics of one-dimensional graphene-dielectric periodic structures,” Superlattices Microstruct. 88, 127–138 (2015).
[Crossref]

S. A. El-Naggar, “Tunable terahertz omnidirectional photonic gap in one dimensional graphene-based photonic crystals,” Opt. Quantum Electron. 47, 1627–1636 (2015).
[Crossref]

Y. Tang, Z. Zhu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “A transmission-type electrically tunable polarizer based on graphene ribbons at terahertz wave band,” Chin. Phys. Lett. 32, 025202 (2015).
[Crossref]

I. Nefedov and L. Melnikov, “Plasmonic terahertz amplification in graphene-based asymmetric hyperbolic metamaterial,” Photonics 2, 594–603 (2015).
[Crossref]

X. He, “Tunable terahertz graphene metamaterials,” Carbon 82, 229–237 (2015).
[Crossref]

Y. Zhang, T. Li, Q. Chen, H. Zhang, J. F. O’Hara, E. Abele, A. J. Taylor, H. Chen, and A. K. Azad, “Independently tunable dual band perfect absorber based on graphene at mid-infrared frequencies,” Sci. Rep. 5, 18463 (2015).
[Crossref]

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24, 118103 (2015).
[Crossref]

2014 (4)

C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multilayers,” Opt. Express 22, 25324–25332 (2014).
[Crossref]

Y. O. Averkov, V. M. Yakovenko, V. A. Yampol’skii, and F. Nori, “Terahertz transverse-electric-and transverse-magne-tic-polarized waves localized on graphene in photonic crystals,” Phys. Rev. B 90, 045415 (2014).
[Crossref]

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: general existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90, 155429 (2014).
[Crossref]

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014).
[Crossref]

2013 (11)

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophoton. 7, 073089 (2013).
[Crossref]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87, 075416 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

A. Madan and S. R. Entezar, “Optical properties of one-dimensional photonic crystals containing graphene sheets,” Phys. B 431, 1–5 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114, 033102 (2013).
[Crossref]

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88, 241403 (2013).
[Crossref]

Y. V. Bludov, N. M. R. Peres, and M. I. Vasilevskiy, “Unusual reflection of electromagnetic radiation from a stack of graphene layers at oblique incidence,” J. Opt. 15, 114004 (2013).
[Crossref]

K. V. Sreekanth, S. Zeng, K. T. Yong, and T. Yu, “Sensitivity enhanced biosensor using graphene-based one-dimensional photonic crystal,” Sens. Actuators B 182, 424–428 (2013).
[Crossref]

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21, 17089–17096 (2013).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Nonlinear control of absorption in one-dimensional photonic crystal with graphene-based defect,” Opt. Lett. 38, 3550–3553 (2013).
[Crossref]

2012 (5)

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref]

C. Wu, T. Yang, C. Li, and P. Wu, “Investigation of effective plasma frequencies in one-dimensional plasma photonic crystals,” Prog. Electromagn. Res. 126, 521–538 (2012).
[Crossref]

J. Liu, N. Liu, J. Li, X. Li, and J. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101, 052104 (2012).
[Crossref]

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85, 245407 (2012).
[Crossref]

O. L. Berman and R. Y. Kezerashvili, “Graphene-based one-dimensional photonic crystal,” J. Phys. 24, 015305 (2012).
[Crossref]

2011 (1)

V. Kumar, A. Kumara, K. H. S. Singh, and P. Kumar, “Broadening of omni-directional reflection range by cascade 1D photonic crystal,” Optoelectron. Adv. Mater. 5, 488–490 (2011).

2010 (1)

2008 (1)

D. Li, M. B. Mueller, S. Gilje, R. B. Kaner, and G. G. Wallace, “Processable aqueous dispersions of graphene nanosheets,” Nat. Nanotechnol. 3, 101–105 (2008).
[Crossref]

2006 (1)

S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442, 282–286 (2006).
[Crossref]

2005 (1)

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

2004 (1)

D. Soto-Puebla, M. Xiaoc, and F. Ramos-Mendieta, “Optical properties of a dielectric-metallic superlattice: the complex photonic bands,” Phys. Lett. A 326, 273–280 (2004).
[Crossref]

1997 (2)

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one-and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55, 7427–7444 (1997).
[Crossref]

A. Sentenac, J. J. Greffet, and F. Pincemin, “Structure of the electromagnetic field in a slab of photonic crystal,” J. Opt. Soc. Am. B 14, 339–347 (1997).
[Crossref]

1993 (1)

Abele, E.

Y. Zhang, T. Li, Q. Chen, H. Zhang, J. F. O’Hara, E. Abele, A. J. Taylor, H. Chen, and A. K. Azad, “Independently tunable dual band perfect absorber based on graphene at mid-infrared frequencies,” Sci. Rep. 5, 18463 (2015).
[Crossref]

Al-sheqefi, F. U. Y.

F. U. Y. Al-sheqefi and W. Belhadj, “Photonic band gap characteristics of one-dimensional graphene-dielectric periodic structures,” Superlattices Microstruct. 88, 127–138 (2015).
[Crossref]

Andryieuski, A.

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: general existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90, 155429 (2014).
[Crossref]

Arefinia, Z.

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

Asgari, A.

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

Averkov, Y. O.

Y. O. Averkov, V. M. Yakovenko, V. A. Yampol’skii, and F. Nori, “Terahertz transverse-electric-and transverse-magne-tic-polarized waves localized on graphene in photonic crystals,” Phys. Rev. B 90, 045415 (2014).
[Crossref]

Azad, A. K.

Y. Zhang, T. Li, Q. Chen, H. Zhang, J. F. O’Hara, E. Abele, A. J. Taylor, H. Chen, and A. K. Azad, “Independently tunable dual band perfect absorber based on graphene at mid-infrared frequencies,” Sci. Rep. 5, 18463 (2015).
[Crossref]

Belhadj, W.

F. U. Y. Al-sheqefi and W. Belhadj, “Photonic band gap characteristics of one-dimensional graphene-dielectric periodic structures,” Superlattices Microstruct. 88, 127–138 (2015).
[Crossref]

Belov, P. A.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Novel hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87, 075416 (2013).
[Crossref]

Berman, O. L.

O. L. Berman and R. Y. Kezerashvili, “Graphene-based one-dimensional photonic crystal,” J. Phys. 24, 015305 (2012).
[Crossref]

Bian, L.

L. Bian, P. Liu, G. Li, Z. Lu, and C. Liu, “Characterization for one-dimensional graphene-embedded photonic crystals at terahertz frequencies,” Opt. Quantum Electron. 48, 436–450 (2016).
[Crossref]

Bludov, Y. V.

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Yu, T.

K. V. Sreekanth, S. Zeng, K. T. Yong, and T. Yu, “Sensitivity enhanced biosensor using graphene-based one-dimensional photonic crystal,” Sens. Actuators B 182, 424–428 (2013).
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Y. Tang, Z. Zhu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “A transmission-type electrically tunable polarizer based on graphene ribbons at terahertz wave band,” Chin. Phys. Lett. 32, 025202 (2015).
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X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
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AIP Adv. (1)

Y. Wu, M. Qu, L. Jiao, Y. Liu, and Z. Ghassemlooy, “Graphene-based Yagi-Uda antenna with reconfigurable radiation patterns,” AIP Adv. 6, 065308 (2016).
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Appl. Opt. (2)

Appl. Phys. Lett. (2)

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Chin. Phys. B (1)

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Chin. Phys. Lett. (1)

Y. Tang, Z. Zhu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “A transmission-type electrically tunable polarizer based on graphene ribbons at terahertz wave band,” Chin. Phys. Lett. 32, 025202 (2015).
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IEEE Photon. J. (2)

P. Cao, X. Yang, S. Wang, Y. Huang, N. Wang, D. Deng, and C. Liu, “Ultrastrong graphene absorption induced by one-dimensional parity-time symmetric photonic crystal,” IEEE Photon. J. 9, 1–9 (2017).

G. Yao, F. Ling, J. Yue, C. Luo, Q. Luo, and J. Yao, “Dynamically electrically tunable broadband absorber based on graphene analog of electromagnetically induced transparency,” IEEE Photon. J. 8, 7800808 (2016).
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Nature (1)

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Opt. Commun. (2)

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
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Opt. Express (4)

Opt. Lett. (1)

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Optik (1)

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Optoelectron. Adv. Mater. (1)

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Y. O. Averkov, V. M. Yakovenko, V. A. Yampol’skii, and F. Nori, “Terahertz transverse-electric-and transverse-magne-tic-polarized waves localized on graphene in photonic crystals,” Phys. Rev. B 90, 045415 (2014).
[Crossref]

Phys. Rev. Lett. (1)

A. Marini and F. J. García de, “Graphene-based active random metamaterials for cavity-free lasing,” Phys. Rev. Lett. 116, 217401 (2016).
[Crossref]

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Sci. Rep. (3)

Y. Zhang, T. Li, Q. Chen, H. Zhang, J. F. O’Hara, E. Abele, A. J. Taylor, H. Chen, and A. K. Azad, “Independently tunable dual band perfect absorber based on graphene at mid-infrared frequencies,” Sci. Rep. 5, 18463 (2015).
[Crossref]

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative refraction with superior transmission in graphene-hexagonal boron nitride (hBN) multilayer hyper crystal,” Sci. Rep. 6, 25442 (2016).
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K. V. Sreekanth, S. Zeng, K. T. Yong, and T. Yu, “Sensitivity enhanced biosensor using graphene-based one-dimensional photonic crystal,” Sens. Actuators B 182, 424–428 (2013).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. (a) Schematic view of oblique wave in 1D GPC. (b) Field distribution of TE polarization in the graphene layer.
Fig. 2.
Fig. 2. Dispersion relation of the 1D GPC at normal incidence. (a) Real part. (b) Imaginary part.
Fig. 3.
Fig. 3. Transmission, reflection, and absorption curves using the TMM (solid line) and CST simulation (dotted line). Insert shows the simulation model with N=20 periods.
Fig. 4.
Fig. 4. Dispersion curves of TM and TE polarization using EMT method (solid line) and dispersion equation. (a) Real part. (b) Imaginary part.
Fig. 5.
Fig. 5. Color map of (a) transmission, (b) absorption, and (c) the difference of reflection and absorption versus frequencies and incident angles for TM and TE polarizations.
Fig. 6.
Fig. 6. Dispersion relation for chemical potential μc=0.1, 0.5, and 0.9 eV. (a) Real part. (b) Imaginary part.
Fig. 7.
Fig. 7. Transmission and absorption curves for chemical potential μc=0.1, 0.5, and 0.9 eV.
Fig. 8.
Fig. 8. Color map of (a) transmission and (b) absorption for different μc=0.11.0  eV.
Fig. 9.
Fig. 9. Influence of the chemical potential on real and imaginary part of (a) graphene tangential permittivity and (b) effective dielectric constant of the multilayer for normal incidence.

Equations (26)

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ϵg=[ϵg,t000ϵg,t000ϵg,].
ϵg,t=1+jσ(ω)ϵ0ωa.
σintra=je2kBTπ2(ωjΓ)[μckBT+2ln(eμckBT+1)],
σinter=je24πln[2μc(ωjΓ)2μc+(ωjΓ)],
(ExIHyI)=M1(ExIIHyII),
M1=(cos(k1za)jη1sin(k1za)jη1sin(k1za)cos(k1za)),
M2=(cos(k2zb)jη2sin(k2zb)jη2sin(k2zb)cos(k2zb)),
HzxHxz=jωϵ0ϵg,tEy,
Eyz=jωμ0Hx,
Eyx=jωμ0Hz.
2Eyz2+2Eyx2+k02ϵg,tEy=0.
k1z2+k1x2=k02ϵg,t.
M1=(cos(k1za)jη1sin(k1za)jη1sin(k1za)cos(k1za)),
M2=(cos(k2zb)jη2sin(k2zb)jη2sin(k2zb)cos(k2zb)),
M=M1M2=(cos(k1za)cos(k2zb)η2η1sin(k1za)sin(k2zb)jη2cos(k1za)sin(k2zb)jη1sin(k1za)cos(k2zb)jη2cos(k1za)sin(k2zb)jη1sin(k1za)cos(k2zb)cos(k1za)cos(k2zb)η1η2sin(k1za)sin(k2zb)).
(ExIHyI)=MN(ExN+1HyN+1)=(m11m12m21m22)(ExN+1HyN+1),
r=HyrIHyiI=m11η0+m12η0ηN+1m21m22ηN+1m11η0+m12η0ηN+1+m21+m22ηN+1,t=HytN+1HyiI=2η0m11η0+m12η0ηN+1+m21+m22ηN+1,
η0={ϵ0/μ0cosθ0ForTEϵ0/μ0/cosθ0ForTM,ηN+1={ϵ0/μ0cosθN+1ForTEϵ0/μ0/cosθN+1ForTM,
R=|r|2,T=|t|2,A=1RT.
cos(kzd)=12Tr(M)=cos(k1za)cos(k2zb)12(η1η2+η2η1)sin(k1za)sin(k2zb),
f12(ω)cos2(kRd)f22(ω)sin2(kRd)=1real,
f12(ω)cosh2(kId)+f22(ω)sinh2(kId)=1imaginary,
f1(ω)=cos(k2zb)cos(kR1za)cosh(kI1za)12sin(k2zb)[ξRsin(kR1za)cosh(kI1za)ξIcos(kR1za)sinh(kI1za)],f2(ω)=cos(k2zb)sin(kR1za)sinh(kI1za)12sin(k2zb)[ξRcos(kR1za)sinh(kI1za)+ξIsin(kR1za)cosh(kI1za)],k1z=kR1z+jkI1z,ξR+jξI=η1η2+η2η1={k2zϵg,tk1zϵb+k1zϵbk2zϵg,t(TM)k1zk2z+k2zk1z(TE),k1z={k02ϵg,tk1x2(ϵg,t/ϵg,)(TM)k02ϵg,tk1x2(TE),k2z=k02ϵbk2x2(TE,TM).
kz2ϵxeff+kx2ϵzeff=k02(TM),
kz2+kx2=ϵxeffk02(TE),
ω2c2=kz2ϵxeff.

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