Abstract

The resonant transmission of self-collimated beams through zigzag-box resonators is demonstrated experimentally and numerically. Numerical simulations show that the flat-wavefront and the width of the beam are well maintained after passing through zigzag-box resonators because the up and the down zigzag-sides prevent the beam from spreading out and the wavefront is perfectly reconstructed by the output zigzag-side of the resonator. Measured split resonant frequencies of two- and three-coupled zigzag-box resonators are well agreed with those predicted by a tight binding model to consider optical coupling between the nearest resonators. Slowing down the speed of self-collimated beams is also demonstrated by using a twelve-coupled zigzag-box resonator in simulations. Our work could be useful in implementing devices to manipulate self-collimated beams in time domain.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2011

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

2010

2009

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett.95, 011119 (2009).
[CrossRef]

2008

T. F. krauss, “Why do we need slow light?” Nat. Photon.2, 448–450 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photon.2, 465–473 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2, 741–747 (2008).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express16, 4270–4277 (2008).
[CrossRef] [PubMed]

2006

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

2005

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett.87, 181106 (2005).
[CrossRef]

2004

Z. Li, H. Chen, Z. Song, F. Yang, and S. Feng, “Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals,” Appl. Phys. Lett.85, 4834–4386 (2004).
[CrossRef]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett.29, 50–52 (2004).
[CrossRef] [PubMed]

2003

D. Chigrin, S. Enoch, C. Sotomayor Torres, and G. Tayeb, “Self-guiding in two-dimensional photonic crystals,” Opt. Express11, 1203–1211 (2003).
[CrossRef] [PubMed]

C.-S. Kee and H. Lim, “Coupling characteristics of localized photons in two-dimensional photonic crystals,” Phys. Rev. B67, 073103 (2003).
[CrossRef]

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett.83, 3251–3253 (2003).
[CrossRef]

2000

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84, 2140–2143 (2000).
[CrossRef] [PubMed]

1999

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

A. Yariv, Y Xu, R. K. Lee, and A. Scherer, “Coupled- resonator optical waveguide: a proposal and analysis,” Opt. Lett.24, 711–713 (1999).
[CrossRef]

1994

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Abeyta, A.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photon.2, 465–473 (2008).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84, 2140–2143 (2000).
[CrossRef] [PubMed]

Biswas, R.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Chan, C. T.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Chen, C.

Chen, H.

Z. Li, H. Chen, Z. Song, F. Yang, and S. Feng, “Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals,” Appl. Phys. Lett.85, 4834–4386 (2004).
[CrossRef]

Chigrin, D.

Choi, J.-S.

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Enoch, S.

Fan, S.

X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystals,” Appl. Phys. Lett.83, 3251–3253 (2003).
[CrossRef]

Feng, S.

Z. Li, H. Chen, Z. Song, F. Yang, and S. Feng, “Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals,” Appl. Phys. Lett.85, 4834–4386 (2004).
[CrossRef]

Ho, K. M.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

Kee, C.-S

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

Kee, C.-S.

Khurgin, J. B.

Kim, J.-E

Kim, J.-E.

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett.95, 011119 (2009).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express16, 4270–4277 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett.87, 181106 (2005).
[CrossRef]

Kim, M.-W.

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett.95, 011119 (2009).
[CrossRef]

Kim, S.-H.

Kim, T.-T.

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E Kim, H. Y. Park, and C.-S. Kee, “Asymmetric Mach-Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express18, 5384–5389 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E Kim, H. Y. Park, and C.-S. Kee, “Ring-type Fabry-Perot filter based on the self-collimation effect in a 2D photonic crystal,” Opt. Express18, 17106–17113 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett.95, 011119 (2009).
[CrossRef]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

krauss, T. F.

T. F. krauss, “Why do we need slow light?” Nat. Photon.2, 448–450 (2008).
[CrossRef]

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2, 741–747 (2008).
[CrossRef]

Lee, R. K.

Lee, S.-G.

Li, Z.

Z. Li, H. Chen, Z. Song, F. Yang, and S. Feng, “Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals,” Appl. Phys. Lett.85, 4834–4386 (2004).
[CrossRef]

Lim, H.

C.-S. Kee and H. Lim, “Coupling characteristics of localized photons in two-dimensional photonic crystals,” Phys. Rev. B67, 073103 (2003).
[CrossRef]

Lu, Z.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

Murakowski, J.

Murakowski, J. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics2, 741–747 (2008).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

Oh, S. S.

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett.87, 181106 (2005).
[CrossRef]

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett.84, 2140–2143 (2000).
[CrossRef] [PubMed]

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B50, 1945–1948 (1994).
[CrossRef]

Park, H. Y.

S.-H. Kim, T.-T. Kim, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S Kee, “Experimental demonstration of self-collimation of spoof surface plasmons,” Phys. Rev. B83, 165109 (2011).
[CrossRef]

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E Kim, H. Y. Park, and C.-S. Kee, “Asymmetric Mach-Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express18, 5384–5389 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, S.-H. Kim, J.-E Kim, H. Y. Park, and C.-S. Kee, “Ring-type Fabry-Perot filter based on the self-collimation effect in a 2D photonic crystal,” Opt. Express18, 17106–17113 (2010).
[CrossRef] [PubMed]

T.-T. Kim, S.-G. Lee, M.-W. Kim, H. Y. Park, and J.-E. Kim, “Experimental demonstration of reflection minimization at two-dimensional photonic crystal interfaces via antireflection structures,” Appl. Phys. Lett.95, 011119 (2009).
[CrossRef]

S.-G. Lee, J.-S. Choi, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express16, 4270–4277 (2008).
[CrossRef] [PubMed]

S.-G. Lee, S. S. Oh, J.-E. Kim, H. Y. Park, and C.-S. Kee, “Line-defect-induced bending and splitting of selfcollimated beams in two-dimensional photonic crystals,” Appl. Phys. Lett.87, 181106 (2005).
[CrossRef]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Prather, D. W.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett.29, 50–52 (2004).
[CrossRef] [PubMed]

Pustai, D. M.

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett.74, 1212–1214 (1999).
[CrossRef]

Scherer, A.

Schneider, G. J.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett.29, 50–52 (2004).
[CrossRef] [PubMed]

Schuetz, C. A.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

Sharkawy, A.

Shi, S.

Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, “Experimental Demonstration of Self-Collimation inside a Three-Dimensional Photonic Crystal,” Phys. Rev. Lett.96, 173902 (2006).
[CrossRef] [PubMed]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett.29, 50–52 (2004).
[CrossRef] [PubMed]

Soljaciv´, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačiv́, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5, 93–96 (2006).
[CrossRef] [PubMed]

Song, Z.

Z. Li, H. Chen, Z. Song, F. Yang, and S. Feng, “Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals,” Appl. Phys. Lett.85, 4834–4386 (2004).
[CrossRef]

Sotomayor Torres, C.

Soukoulis, C. M.

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Other

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http://ab-initio.mit.edu/wiki/index.php/Meep .

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Figures (4)

Fig. 1
Fig. 1

Experimental and FDTD simulated transmittances of self-collimated beams through the zigzag-shape mirror in a range of frequency from 12.1 to 12.9 GHz. An inset depicts a zigzag-shape mirror to reflect strongly an incident self-collimated beam with a frequency of 12.5 GHz.

Fig. 2
Fig. 2

(a) Top view of a two-dimensional zigzag-box resonator. Gray circles denote alumina rods. (b) Transmission spectra of self-collimated beams through the resonator. Black-thick and red-thin lines indicate experimental and FDTD simulated results, respectively. (c) Simulated spatial distribution of the electric-field of a resonant self-collimated beam at f0 = 12.559 GHz. Arrows denote a propagation direction of the beam.

Fig. 3
Fig. 3

Transmission spectra of self-collimated beams through a two-coupled zigzag-box resonator with two resonant frequencies of Ω1 and Ω2 (a). Black-thick and red-thin lines indicate experimental and FDTD simulated results, respectively. The simulated electric-field distributions of the resonant modes with resonant frequencies of Ω1 (b) and Ω2 (c).

Fig. 4
Fig. 4

(a) Transmission spectrum of self-collimated beams through a twelve-coupled zigzag-box resonator. (b) Dispersion relations of the transmission band obtained from the phase calculations (black-thick line) and the TB model (red-thin line). (c) Group velocities obtained from the FDTD simulations (black-solid rectangle) and the TB model (red-thin line). Dashed vertical lines represent the resonant frequencies of a twelve-coupled zigzag-box resonator.

Tables (1)

Tables Icon

Table 1 Three resonant frequencies of a three-coupled resonator obtained from measured (simulated) transmission spectra. TBmea. (TBsim.) frequencies were calculated by the measured (simulated) TB parameters obtained from the measured (simulated) two resonant frequencies of a two-coupled resonator. The unit of frequency is GHz.

Equations (1)

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k ( f ) = ϕ res ϕ pc L res + ϕ p c ϕ air L p c + 2 π f c .

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