Abstract

Optical bistability of nonlinear guided-mode resonances in photonic crystal slabs (PCSs) are numerically investigated. We perform finite-difference time-domain simulations to determine the linear and nonlinear characteristics of these guided-mode resonances in PCSs. The nonlinear characteristics such as switching intensity and switching time, which are suggested as the performance metric of all-optical switches, are similar to the all-optical switches in slab waveguide gratings. While the slab waveguide gratings are sensitive to the incoming light polarization, the PCSs can offer an advantage of avoiding reduction efficiency and a requirement of careful polarization stabilization of the light source. From the calculations, we introduce a dependency of the normalized switching intensity and the switching time of the all-optical switches on quality factor for our designed guided-mode resonances in PCSs.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2010

2009

2006

2005

2003

2002

S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241–2149 (2002).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

2000

1999

M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

1997

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

1996

1995

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

1994

1990

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum Electron. 20, 856–859 (1990).
[CrossRef]

1985

Agrawal, G. P.

Avrutskii, I. A.

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum Electron. 20, 856–859 (1990).
[CrossRef]

Beheiry, M. E.

Bermel, P.

Bhat, R.

Boroditsky, M.

Burr, G.

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Cada, M.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Coccioli, R.

Dodabalapur, A.

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett. 25, 942–944 (2000).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Erchak, A. A.

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Fan, S.

M. E. Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18, 22702–22714 (2010).
[CrossRef]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Farjadpour, A.

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

George, N.

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Haus, H. A.

H. A. Haus, Waves and Field in Optoelectronics (Prentice-Hall, 1984).

He, J.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Ho, N.

Ibanescu, M.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Imada, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Ippen, E. P.

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Jans, S.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Joannopoulos, J. D.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[CrossRef]

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett. 25, 942–944 (2000).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Johnson, S. G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Johnson, S. R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Kim, S.

Kivshar, Y. S.

Kolodzjeski, L. A.

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Koster, A.

Krauss, T. F.

Laniel, J. M.

Levi, O.

Liu, V.

Luo, C.

MacKenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Magnusson, R.

Meier, M.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Mekis, A.

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett. 25, 942–944 (2000).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Mingaleev, S. F.

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Morris, G. M.

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Neviere, M.

Ngo, Q. M.

Noda, S.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Pacradouni, V.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Paddon, P.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Paraire, N.

Peng, S.

Petrich, G. S.

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Radic, S.

Reinisch, R.

Ripin, D. J.

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

Rodriguez, A.

Roundy, D.

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Slusher, R. E.

A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Opt. Lett. 25, 942–944 (2000).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Soljacic, M.

M. Soljacić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637–639 (2003).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Song, S. H.

Sychugov, V. A.

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum Electron. 20, 856–859 (1990).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech House, 1995).

Tiedje, T.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Timko, A.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

Vallee, R.

Vincent, P.

Vrijen, R.

Wasilewski, Z. R.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Yablonovitch, E.

Young, J. F.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

Appl. Phys. Lett.

S. Jans, J. He, Z. R. Wasilewski, and M. Cada, “Low threshold optical bistable switching in an asymmetric λ/4-shifted distributed-feedback heterostructures,” Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodzjeski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563–565 (2001).
[CrossRef]

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, and J. D. Joannopoulos, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75, 316–318 (1999).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in a air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. B

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Phys. Rev. E

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Sov. J. Quantum Electron.

I. A. Avrutskii and V. A. Sychugov, “Optical bistability in an excited nonlinear corrugated waveguide,” Sov. J. Quantum Electron. 20, 856–859 (1990).
[CrossRef]

Other

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

A. Taflove, Computational Electrodynamics (Artech House, 1995).

H. A. Haus, Waves and Field in Optoelectronics (Prentice-Hall, 1984).

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Figures (6)

Fig. 1.
Fig. 1.

(a) PCS structure with input light of normal incidence plane wave. (b) Reflection spectra for various depths (h). For each depth h, slab thickness t is chosen to get the low-reflection sidebands and symmetric line shape. The insets in (b) show field distributions of side view at resonances. In this example, TM-like polarized light is used; that is, the side view of the magnetic-field is normal to the plane of incidence (in one unit cell).

Fig. 2.
Fig. 2.

Bistability in the nonlinear PCSs depicted in Fig. 1(a). (a) h=20nm, (b) h=30nm, (c) h=50nm, and (d) h=90nm. The working wavelength is at 20% reflection.

Fig. 3.
Fig. 3.

Switching intensity and field strength for optical bistability based on guided-mode resonance in PCS of various quality factors Q. The switching intensity is normalized by (1/n2). The solid lines are fitting curves and their equations are noted. The working wavelength is at 20% reflection.

Fig. 4.
Fig. 4.

Temporal responses of all-optical switches based on guided-mode resonance in PCS of (a) h=20nm and (b) h=90nm. The working wavelength is at 20% reflection.

Fig. 5.
Fig. 5.

Bistability in the nonlinear PCSs depicted in Fig. 1(a). (a) h=20nm and (b) h=90nm. The working wavelength is at 10% reflection.

Fig. 6.
Fig. 6.

(a) Reflection spectra for various depths (h) of the PCS depicted in Fig. 1(a) with input light of TE-like polarized normal incidence plane wave. The overlap of reflection spectra between the TE-like and TM-like polarized normal incident plane wave are observed. (b) Optical incident intensity and field strength for switching of all-optical switches based on guided-mode resonances in PCSs of various quality factors Q of TE-like polarized normal incident plane wave. The optical intensity is normalized by (1/n2). The solid lines are fitting curves, and their equations are noted. The working wavelength is at 20% reflection.

Tables (1)

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Table 1. Linear Characteristics of Guided-Mode Resonances in PCSs

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