Abstract

The studies of photonic crystals had focused on the band structures and complete photonic bandgaps in past decades. However, properties of photonic bands in finite systems are more important for practical applications. Here we report the study of the reflection phase of photonic bands in finite bi-directional 1D dielectric photonic crystal modeled as a dielectric slab using an effective medium with a Fano-like dispersion. The reflection peaks/troughs of the finite photonic crystal slab are analyzed using an interference model to obtain the reflection phase for the photonic bands of the PC. We show that our model works very well in the photonic bands except very close to the band edges. Our work could shed light on practical applications in phase measurements and manipulations using photonic crystals.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  19. W. S. Gao, M. Xiao, C. T. Chan, and W. Y. Tam, “Determination of Zak phase by reflection phase in 1D photonic crystals,” Opt. Lett. 40(22), 5259–5262 (2015).
    [Crossref] [PubMed]
  20. W. S. Gao, M. Xiao, B. Chen, E. Y. B. Pun, C. T. Chan, and W. Y. Tam, “Controlling interface states in 1D photonic crystals by tuning bulk geometric phases,” Opt. Lett. 42(8), 1500–1503 (2017).
    [Crossref]
  21. S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
    [Crossref]
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    [Crossref] [PubMed]
  23. D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
    [Crossref]
  24. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
    [Crossref]

2017 (1)

2016 (1)

2015 (1)

2014 (1)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

2012 (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

2011 (1)

S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
[Crossref]

2010 (1)

2006 (2)

T. Komikado, S. Yoshida, and S. Umegaki, “Surface-emitting distributed-feedback dye laser of a polymeric multilayer fabricated by spin coating,” Appl. Phys. Lett. 89(6), 061123 (2006).
[Crossref]

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

2005 (2)

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[Crossref]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

2003 (1)

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

2002 (1)

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
[Crossref]

2001 (1)

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

1998 (1)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

1996 (1)

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

1990 (3)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65(21), 2650–2653 (1990).
[Crossref] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

1989 (1)

E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case,” Phys. Rev. Lett. 63(18), 1950–1953 (1989).
[Crossref] [PubMed]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Bawendi, M.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Bertolotti, M.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Bloemer, M. J.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

Bowden, C. M.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Caruge, J. M.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Centini, M.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

Chan, C. T.

W. S. Gao, M. Xiao, B. Chen, E. Y. B. Pun, C. T. Chan, and W. Y. Tam, “Controlling interface states in 1D photonic crystals by tuning bulk geometric phases,” Opt. Lett. 42(8), 1500–1503 (2017).
[Crossref]

W. S. Gao, M. Xiao, C. T. Chan, and W. Y. Tam, “Determination of Zak phase by reflection phase in 1D photonic crystals,” Opt. Lett. 40(22), 5259–5262 (2015).
[Crossref] [PubMed]

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Chen, B.

Chiao, R. Y.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

Corcoran, B.

D’Aguanno, G.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

Dowling, J. P.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

Ebnali-Heidari, M.

Eggleton, B. J.

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Gao, W.

Gao, W. S.

Gmitter, T. J.

E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case,” Phys. Rev. Lett. 63(18), 1950–1953 (1989).
[Crossref] [PubMed]

Grillet, C.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Hickmann, J. M.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Istrate, E.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[Crossref]

Jeong, D. Y.

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
[Crossref]

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Komikado, T.

T. Komikado, S. Yoshida, and S. Umegaki, “Surface-emitting distributed-feedback dye laser of a polymeric multilayer fabricated by spin coating,” Appl. Phys. Lett. 89(6), 061123 (2006).
[Crossref]

Kooi, S.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Krauss, T. F.

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Lee, W.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Leung, H. M.

Leung, K. M.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Li, J.

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Lu, L.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

McCormick, C. F.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Monat, C.

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

O’Faolain, L.

Prasad, P. N.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Prasad, S.

S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
[Crossref]

Pun, E. Y. B.

Sargent, E. H.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[Crossref]

Satpathy, S.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65(21), 2650–2653 (1990).
[Crossref] [PubMed]

Scalora, M.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

Sibilia, C.

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Singh, A. K.

S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
[Crossref]

Singh, V.

S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
[Crossref]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

Solli, D. R.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Tam, W. Y.

Thomas, E. L.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Tocci, M. D.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

Umegaki, S.

T. Komikado, S. Yoshida, and S. Umegaki, “Surface-emitting distributed-feedback dye laser of a polymeric multilayer fabricated by spin coating,” Appl. Phys. Lett. 89(6), 061123 (2006).
[Crossref]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Wang, X.

White, T. P.

Xiao, M.

Yablonovitch, E.

E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case,” Phys. Rev. Lett. 63(18), 1950–1953 (1989).
[Crossref] [PubMed]

Ye, Y. H.

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
[Crossref]

Yoon, J.

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

Yoshida, S.

T. Komikado, S. Yoshida, and S. Umegaki, “Surface-emitting distributed-feedback dye laser of a polymeric multilayer fabricated by spin coating,” Appl. Phys. Lett. 89(6), 061123 (2006).
[Crossref]

Yung, T. K.

Zhang, Q. M.

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
[Crossref]

Zhang, Z.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65(21), 2650–2653 (1990).
[Crossref] [PubMed]

Zhang, Z. Q.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Zhao, Q.

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[Crossref]

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[Crossref]

T. Komikado, S. Yoshida, and S. Umegaki, “Surface-emitting distributed-feedback dye laser of a polymeric multilayer fabricated by spin coating,” Appl. Phys. Lett. 89(6), 061123 (2006).
[Crossref]

J. Yoon, W. Lee, J. M. Caruge, M. Bawendi, E. L. Thomas, S. Kooi, and P. N. Prasad, “Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal,” Appl. Phys. Lett. 88(9), 091102 (2006).
[Crossref]

J. Appl. Phys. (2)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896–1899 (1994).
[Crossref]

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, “Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,” J. Appl. Phys. 92(8), 4194–4200 (2002).
[Crossref]

J. Electromagn. Anal. Appl. (1)

S. Prasad, V. Singh, and A. K. Singh, “Enhancement of phase matching ability in one-dimensional photonic crystal through plasma materials,” J. Electromagn. Anal. Appl. 3(7), 255–260 (2011).
[Crossref]

Nature (2)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998).
[Crossref]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. 64(4), 046606 (2001).
[Crossref] [PubMed]

Phys. Rev. A (1)

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53(4), 2799–2803 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered-cubic case,” Phys. Rev. Lett. 63(18), 1950–1953 (1989).
[Crossref] [PubMed]

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65(21), 2650–2653 (1990).
[Crossref] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Other (2)

R. R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

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Figures (5)

Fig. 1
Fig. 1 (a) Band diagram of 1D PC: bands (blue) and bandgaps (red) curves. (b) Effective refractive index (green circles). The blue circles and red curve are fits to the effective refractive index with and without the PC terms. The inset shows residuals of the fits with (blue circles) and without (red circles) the bandgap contributions. (PC parameters: nA, B = nA0, B0 (1 + n12), for nA0 = 1.4659, nB0 = 1.2741, n1 = 0.0054, dA = 166 nm and dB = 34 nm and Λ = 200 nm.)
Fig. 2
Fig. 2 Reflectance of 1D photonic crystal of 165 unit cells obtained by TMM calculations using the same parameters as in Fig. 1 for Type I (a) (green curves) and Type II (b) (red curves) PCs. The pink and blue curves are the corresponding envelopes. The insets are reflectance in expanded scales showing the FP troughs and the envelope zeros as indicated by the black arrows.
Fig. 3
Fig. 3 Reflectance (in green) and reflection phase normalized by 2π, (in red) from 165 unit cells TMM calculations with no_PC slab (a) and with Type II PC (b). For the no_PC simulation, we use nA, = nB = 1.433294 (1 + 0.00542). (c) and (d) Interference order m of the FP troughs vs wave number 1/λm (green circles). The blue curve in (c) and the red curve and blue circles in (d) are fits to the m vs 1/λm. The insets are residuals of the corresponding fits.
Fig. 4
Fig. 4 Results of reflection phase from fits (blue dashed curves) and from TMM calculations (red curves) for no_PC (a)-(b), Type I (c)-(d), and Type II (e)-(f) PCs. The green curves are the reflectance. The black arrows indicate the envelope zeros and the bandgaps are labelled in black.
Fig. 5
Fig. 5 Results of reflection phase from fits (blue dashed curves) and from TMM calculations (red curves) for Type I (a)-(b) and Type II (c)-(d). The green curves are the reflectance in expanded scales. The black arrows indicate the envelope zeros. (e) and (f) are the phase difference Δφ of the fitting results and the TMM calculations for the no_PC slab in Figs. 4(a) and 4(b) and Type II PC in (c) to (d).

Tables (1)

Tables Icon

Table 1 Fitting results for the neff and m vs 1/λm. The mid-gap wave numbers (in 1/μm) for the first three bandgaps are: 1.71691, 3.29525, and 4.6794 [24].

Equations (5)

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cos[ ΚΛ ]=cos( n A ω d A c )cos( n B ω d B c )Δsin( n A ω d A c )sin( n B ω d B c ),
n eff = n 0 { 1+ n 1 λ 2 + i C i ( 1 λ 1 λ i ) D i + ( 1 λ 1 λ i ) 2 },
  E r =| E r | e iφ = r 12 1 e i2δ 1 r 12 2 e i2δ , 
R= 4 | r 12 | 2 si n 2 ( 2π n eff L λ ) ( 1 | r 12 | 2 ) 2 +4 | r 12 | 2 si n 2 ( 2π n eff L λ +π ) , 
φ=ta n 1 [ ( 1 | r 12 | 2 )sin( 2π 2 n eff L λ ) ( 1+ | r 12 | 2 )( 1cos( 2π 2 n eff L λ ) ) ]+ π.