Abstract

A quasi-zero-average-index photonic crystal structure has been recently demonstrated by using the concept of complementary media. It consists of dielectric photonic crystal superlattices with alternating layers of negative index photonic crystals and positive index dielectric media. This photonic crystal structure has unique optical properties, such as phase-invariant field and self-collimation of light. In particular, the nanofabricated superlattices can be used in chip-scale optical interconnects and interferometers with quasi-zero-average phase difference. However, in potential interconnect applications, crosstalk between neighboring signals needs to be avoided. In this article, we study simulations of the interference of propagating electromagnetic waves in a quasi-zero electric permittivity photonic crystal superlattice. The simulations here are restricted to TM modes, with the main electric field along the vertical direction.

© 2013 Optical Society of America

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    [CrossRef]

2012 (1)

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

2011 (1)

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

2010 (2)

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

L.-G. Wang, G. X. Li, and S. Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81, 1–4 (2010).
[CrossRef]

2009 (3)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

2008 (2)

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

2006 (1)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 1–4 (2006).
[CrossRef]

2005 (4)

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects,” Phys. Rev. B 72, 1–20 (2005).
[CrossRef]

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

2004 (1)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 1–12 (2004).

2003 (3)

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

S. Fonteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 1–4 (2003).

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3610 (2003).
[CrossRef]

2002 (1)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

1998 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Aras, M. S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Asano, T.

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Barbosa, C. L.

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

Biris, C. G.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Cabrini, S.

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

Caprio, G. D.

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

Cazo, R. M.

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

Chang, A. S. P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Chatterjee, R.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Choquette, K. D.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3610 (2003).
[CrossRef]

Coppola, G.

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

Danner, A. J.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3610 (2003).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Dardano, P.

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Dhuey, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

di Cioccio, L.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Dios, Z.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Doan, M. T.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Drouard, E.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

El Melhaoui, L.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Engheta, N.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 1–4 (2006).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Fedeli, J. M.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Fonteinopoulou, S.

S. Fonteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 1–4 (2003).

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects,” Phys. Rev. B 72, 1–20 (2005).
[CrossRef]

Gabitov, I. R.

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

Grillet, C.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

Harteneck, B.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Hattori, H. T.

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

Hsieh, P.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Huh, J.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Hwang, J. K.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Imada, M.

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton2008).

Kaufman, L. J.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Kazmierczak, A.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Kim, J. S.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Kim, S. H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Kocaman, S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

Kwong, D. L.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

Leclercq, J. L.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Lee, Y. H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Letartre, X.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Li, G. X.

L.-G. Wang, G. X. Li, and S. Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81, 1–4 (2010).
[CrossRef]

Li, Z.

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

Litchinitiser, N. M.

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

Liu, D.

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

Liu, K.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Maimistov, A. I.

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

McMillan, J. F.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton2008).

Mocella, V.

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Mochizuki, M.

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Moretti, L.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Noda, S.

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Okano, M.

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Olynick, D.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Osgood, R. M.

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Panoiu, N. C.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Park, H. G.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Premaratne, M.

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

Rendina, I.

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index matematerial,” Phys. Rev. Lett. 102, 1–3 (2009).
[CrossRef]

Rojo-Romeo, P.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Rukhlenko, I. D.

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

Ryu, H. Y.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

Sagdeev, R. Z.

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Schneider, V. M.

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

Seassal, C.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

Shalaev, V. M.

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

Silveirinha, M.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 1–4 (2006).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects,” Phys. Rev. B 72, 1–20 (2005).
[CrossRef]

S. Fonteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 1–4 (2003).

Stein, A.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Viktorovitch, P.

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

Wang, L.-G.

L.-G. Wang, G. X. Li, and S. Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81, 1–4 (2010).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light(Princeton2008).

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Wong, D. L.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic bandgap defect-mode lasers,” Science 284, 1819–1821 (1999).
[CrossRef]

Yokouchi, N.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3610 (2003).
[CrossRef]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

S. Kocaman, R. Chatterjee, N. C. Panoiu, J. F. McMillan, M. B. Yu, R. M. Osgood, D. L. Kwong, and C. W. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 1–4 (2009).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, “Achieving subdiffraction imaging through bound surface states in negative refraction photonic crystals in the near-infrared range,” Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Zhu, S. Y.

L.-G. Wang, G. X. Li, and S. Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81, 1–4 (2010).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 1–12 (2004).

Zussy, M.

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

Appl. Opt. (1)

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069–3076 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Vertical-cavity surface-emitting laser operating with photonic crystal seven-point defect structure,” Appl. Phys. Lett. 82, 3608–3610 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[CrossRef]

J. Lightwave Technol. (1)

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single defect in a 2-D photonic crystal slab: Defect engineering with respect to polarization mode and ratio of emissions from upper and lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

Nat. Photonics (1)

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Wong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5, 499–505 (2011).
[CrossRef]

Opt. Express (5)

E. Drouard, H. T. Hattori, C. Grillet, A. Kazmierczak, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “Directional channel-drop filter based on a slow Bloch mode photonic crystal waveguide section,” Opt. Express 13, 3037–3048 (2005).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998).
[CrossRef]

H. T. Hattori, C. Seassal, X. Letartre, P. Rojo-Romeo, J. L. Leclercq, P. Viktorovitch, M. Zussy, L. di Cioccio, L. El Melhaoui, and J. M. Fedeli, “Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides,” Opt. Express 13, 3310–3322 (2005).
[CrossRef]

V. Mocella, P. Dardano, I. Rendina, and S. Cabrini, “An extraordinary directive radiation based on optical antimatter at near infrared,” Opt. Express 18, 25068–25074 (2010).
[CrossRef]

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

Opt. Lett. (2)

N. M. Litchinitiser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[CrossRef]

G. D. Caprio, P. Dardano, G. Coppola, S. Cabrini, and V. Mocella, “Digital holographic microscopy characterization of superdirective beam by metamaterial,” Opt. Lett. 37, 1142–1144 (2012).
[CrossRef]

Phys. Rev. B (4)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic bandgap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects,” Phys. Rev. B 72, 1–20 (2005).
[CrossRef]

S. Fonteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 1–4 (2003).

L.-G. Wang, G. X. Li, and S. Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81, 1–4 (2010).
[CrossRef]

Phys. Rev. E (1)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 1–12 (2004).

Phys. Rev. Lett. (5)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 1–4 (2006).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

General scheme of the quasi-zero permittivity structures analyzed in this article.

Fig. 2.
Fig. 2.

(a) Band diagram and (b) equifrequency contours for TM modes in a photonic crystal hexagonal lattice of air holes and filling factor of 29%.

Fig. 3.
Fig. 3.

(a) Power distribution in the near-zero permittivity medium (transmission is represented by rhombic markers while reflectivity is represented by square markers). (b) Field distribution (Ey) for the mode propagating in the near-zero permittivity medium.

Fig. 4.
Fig. 4.

Top view of the interferometer in a quasi-zero permittivity photonic crystal structure.

Fig. 5.
Fig. 5.

Phase difference (ΔΦ) as a function of the distance between neighboring waveguides (d3) for monitors positioned at the end of the ith superperiod (i=1, 2, 3, 4).

Fig. 6.
Fig. 6.

Field distribution of two propagating waves with (a) same phase and (b) opposite phase for d3=2μm.

Fig. 7.
Fig. 7.

Field distribution of two propagating waves with (a) same phase and (b) opposite phase for d3=1μm.

Fig. 8.
Fig. 8.

Field distribution of two propagating waves with (a) same phase and (b) opposite phase for d3=0.5μm.

Fig. 9.
Fig. 9.

Power distribution of two propagating waves with (a) same phase and (b) opposite phase for different values of d3.

Fig. 10.
Fig. 10.

Power distribution of two propagating waves with different relative phases for different values of d3: (a) d3=0.5μm, (b) d3=1μm, and (c) d3=3.5μm.

Equations (2)

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neff=(n1d1+n2d2)/(d1+d2)=0,
Et=A1cos(ωt+ϕ1)+A2cos(ωt+ϕ2)=A12+2A1A2cos(ϕ1ϕ2)+A22cos(ωt+ϕt)=Atcos(ωt+ϕt),

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