Abstract

Based on the wavefront modulation of photonic crystal (PhC), zero phase delay of propagating electromagnetic wave (EMW) can be realized with a relaxed incident condition in the PhC. The phase velocity is modulated perpendicular to the group velocity with wavefronts extending along the direction of energy flow, which lead to the phenomenon of zero phase delay with a finite spatial period. This effect can be realized simultaneously in both positive and negative refracted waves. The phase difference between the incident and transmitted waves are measured within a wide incident angle region to demonstrate zero phase delay can be realized easily instead of zero–n or zero–averaged–n materials. Further investigations prove that the phenomena of zero phase delay induced by this way can also be realized easily in various PhC configurations and can be accurately manipulated by changing the incident angle or the flexible design of PhC configuration.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
    [CrossRef]
  2. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
    [CrossRef] [PubMed]
  3. J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
    [CrossRef]
  4. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
    [CrossRef]
  5. N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
    [CrossRef]
  6. C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
    [CrossRef]
  7. A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
    [CrossRef]
  8. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
    [CrossRef]
  9. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
    [CrossRef] [PubMed]
  10. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  11. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  12. J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
    [CrossRef] [PubMed]
  13. S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
    [CrossRef]
  14. G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
    [CrossRef]
  15. S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects,” Phys. Rev. B72(16), 165112 (2005).
    [CrossRef]

2013

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[CrossRef]

G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
[CrossRef]

2011

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
[CrossRef]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

2010

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
[CrossRef]

2008

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

2007

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

2005

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects,” Phys. Rev. B72(16), 165112 (2005).
[CrossRef]

2003

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

2002

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
[CrossRef]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

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

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[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. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[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. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Cai, L.

G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
[CrossRef]

Chan, C. T.

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

Ciattoni, A.

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[CrossRef]

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
[CrossRef]

Di Falco, A.

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
[CrossRef]

Dong, G. Y.

G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
[CrossRef]

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects,” Phys. Rev. B72(16), 165112 (2005).
[CrossRef]

Garcia, N.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Hao, J.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
[CrossRef]

Hsieh, P.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

John, S.

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

Kocaman, S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

Kwong, D. L.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Li, J. S.

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

Marinelli, R.

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[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. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Palange, E.

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[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. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Ponizovskaya, E. V.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
[CrossRef]

Qiu, M.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
[CrossRef]

Rizza, C.

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[CrossRef]

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Sheng, P.

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

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. B72(16), 165112 (2005).
[CrossRef]

Stein, A.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Xiao, J. Q.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yan, W.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
[CrossRef]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Zhou, J.

G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
[CrossRef]

Zhou, L.

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

Appl. Phys. B.

A. Ciattoni, R. Marinelli, C. Rizza, and E. Palange, “|ε|-near-zero materials in the near-infrared,” Appl. Phys. B.110(1), 23–26 (2013).
[CrossRef]

Appl. Phys. Lett.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96(10), 101109 (2010).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80(7), 1120–1122 (2002).
[CrossRef]

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett.99(22), 221107 (2011).
[CrossRef]

Nat. Mater.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

Nat. Photonics

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5(8), 499–505 (2011).
[CrossRef]

Phys. Rev. B

G. Y. Dong, J. Zhou, and L. Cai, “Zero phase delay induced by wavefront modulation in photonic crystals,” Phys. Rev. B87(12), 125107 (2013).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects,” Phys. Rev. B72(16), 165112 (2005).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B75(7), 075119 (2007).
[CrossRef]

Phys. Rev. Lett.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

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

J. S. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett.90(8), 083901 (2003).
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: MOV (735 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Diagram of the fourth band of the triangular PhC with hexagonal Si rods in air for TM polarization.

Fig. 2
Fig. 2

(a) EFCs plot of the fourth band with the wave vector diagram at ω = 0.36 with θinc = 30°; (b) the corresponding equal frequency surface; (c) schematic diagram of EMW propagating through the PhC slab with two refracted waves.

Fig. 3
Fig. 3

(a) The included angle between k and vgr for the refracted waves A and B with different incident angles.

Fig. 4
Fig. 4

(a) Electric field distribution (Media 1) and (b) transmissivity of two refracted waves in the holographic triangular PhC slab at the frequency of 0.36 with θinc = 30°.

Fig. 5
Fig. 5

Electric field distributions with zero phase delay in various PhC configurations. (a) The triangular PhC composed of hexagonal Si rods at ω = 0.36 with θinc = 13.3°, (b) the honeycomb PhC composed of air rods with r = 0.1a in dielectric background at ω = 0.345 and θinc = 20°, (c) the triangular PhC composed of round rods with r = 0.5a at ω = 0.35 and θinc = 30°, (d) the square PhC composed of dielectric rods with r = 0.4a at ω = 0.365 and θinc = 40°.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

E( x,r )=Acos( krωt+ φ 0 ),

Metrics