Abstract

We identify a family of unusual slow-light modes occurring in lossy multimode grating waveguides, for which either the forward or backward mode components, or both, are degenerate. In the fully degenerate case, the response can be modulated between coherent perfect absorption (zero reflection) and perfect reflection by varying the wave amplitudes in a uniform input waveguide. The perfectly absorbed wave has anomalously short absorption length, scaling as the inverse one-third power of the absorptivity.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Baba, Nat. Photonics 2, 465 (2008).
    [CrossRef]
  2. J. Mork and T. R. Nielsen, Opt. Lett. 35, 2834 (2010).
    [CrossRef]
  3. T. P. White and A. A. Sukhorukov, Phys. Rev. A 85, 043819 (2012).
    [CrossRef]
  4. M. Greenberg and M. Orenstein, Opt. Express 12, 4013 (2004).
    [CrossRef]
  5. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
    [CrossRef]
  6. P. Ginzburg, A. Hayat, V. Vishnyakov, and M. Orenstein, Opt. Express 17, 4251 (2009).
    [CrossRef]
  7. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
    [CrossRef]
  8. M. Spasenovic, T. P. White, S. Ha, A. A. Sukhorukov, T. Kampfrath, Y. S. Kivshar, C. M. de Sterke, T. F. Krauss, and L. Kuipers, Opt. Lett. 36, 1170 (2011).
    [CrossRef]
  9. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
    [CrossRef]
  10. W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
    [CrossRef]
  11. H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
    [CrossRef]
  12. L. Poladian, Phys. Rev. E 54, 2963 (1996).
    [CrossRef]
  13. J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
    [CrossRef]
  14. A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006).
    [CrossRef]
  15. A. A. Sukhorukov, C. J. Handmer, C. M. de Sterke, and M. J. Steel, Opt. Express 15, 17954 (2007).
    [CrossRef]
  16. N. Gutman, C. M. de Sterke, A. A. Sukhorukov, and L. C. Botten, Phys. Rev. A 85, 033804 (2012).
    [CrossRef]
  17. W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
    [CrossRef]

2012 (4)

T. P. White and A. A. Sukhorukov, Phys. Rev. A 85, 043819 (2012).
[CrossRef]

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
[CrossRef]

N. Gutman, C. M. de Sterke, A. A. Sukhorukov, and L. C. Botten, Phys. Rev. A 85, 033804 (2012).
[CrossRef]

2011 (3)

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

M. Spasenovic, T. P. White, S. Ha, A. A. Sukhorukov, T. Kampfrath, Y. S. Kivshar, C. M. de Sterke, T. F. Krauss, and L. Kuipers, Opt. Lett. 36, 1170 (2011).
[CrossRef]

2010 (2)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

J. Mork and T. R. Nielsen, Opt. Lett. 35, 2834 (2010).
[CrossRef]

2009 (1)

2008 (1)

T. Baba, Nat. Photonics 2, 465 (2008).
[CrossRef]

2007 (1)

2006 (1)

A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006).
[CrossRef]

2004 (1)

2002 (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

1998 (1)

W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
[CrossRef]

1996 (1)

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

Baba, T.

T. Baba, Nat. Photonics 2, 465 (2008).
[CrossRef]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Botten, L. C.

N. Gutman, C. M. de Sterke, A. A. Sukhorukov, and L. C. Botten, Phys. Rev. A 85, 033804 (2012).
[CrossRef]

Cao, H.

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

Chong, Y. D.

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

Christodoulides, D. N.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chu, P. L.

W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
[CrossRef]

de Sterke, C. M.

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Figotin, A.

A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006).
[CrossRef]

Ge, L.

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

Ginzburg, P.

Greenberg, M.

Gutman, N.

N. Gutman, C. M. de Sterke, A. A. Sukhorukov, and L. C. Botten, Phys. Rev. A 85, 033804 (2012).
[CrossRef]

Ha, S.

Handmer, C. J.

Hayat, A.

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Kampfrath, T.

Kivshar, Y. S.

Kottos, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Krauss, T. F.

Kuipers, L.

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Lin, Z.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

MacDonald, K. F.

J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
[CrossRef]

Mak, W. C. K.

W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
[CrossRef]

Malomed, B. A.

W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
[CrossRef]

Mork, J.

Nielsen, T. R.

Noh, H.

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Orenstein, M.

Poladian, L.

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

Ramezani, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Spasenovic, M.

Steel, M. J.

Stone, A. D.

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

Sukhorukov, A. A.

Vishnyakov, V.

Vitebskiy, I.

A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006).
[CrossRef]

Wan, W. J.

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

White, T. P.

Zhang, J.

J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
[CrossRef]

Zheludev, N. I.

J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
[CrossRef]

J. Opt. Soc. Am. A (1)

W. C. K. Mak, P. L. Chu, and B. A. Malomed, J. Opt. Soc. Am. A 15, 1685 (1998).
[CrossRef]

Light: Sci. Appl. (1)

J. Zhang, K. F. MacDonald, and N. I. Zheludev, Light: Sci. Appl. 1, e18 (2012).
[CrossRef]

Nat. Photonics (1)

T. Baba, Nat. Photonics 2, 465 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (2)

T. P. White and A. A. Sukhorukov, Phys. Rev. A 85, 043819 (2012).
[CrossRef]

N. Gutman, C. M. de Sterke, A. A. Sukhorukov, and L. C. Botten, Phys. Rev. A 85, 033804 (2012).
[CrossRef]

Phys. Rev. E (3)

A. Figotin and I. Vitebskiy, Phys. Rev. E 74, 066613 (2006).
[CrossRef]

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Lett. 105, 053901 (2010).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

H. Noh, Y. D. Chong, A. D. Stone, and H. Cao, Phys. Rev. Lett. 108, 186805 (2012).
[CrossRef]

Science (1)

W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

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 (4)

Fig. 1.
Fig. 1.

(a) Schematic of a uniform waveguide coupled to a lossy periodic waveguide. (b) Schematic of the perfect absorption mechanism. The arrows represent the mode distribution of the forward and backward components on each side of the interface. The input is normalized to 1, and the periodic waveguide has two excited modes with amplitudes, a1 and a2.

Fig. 2.
Fig. 2.

Complex band structures of absorbing grating waveguides exhibiting coherent perfect absorption. (a) and (b) Partial mode degeneracy, with ρ11=1, ρ22=0.9, ρ12=0.2155, δ=1.8937, and α=102. (c) and (d) Full degeneracy (CDB), with ρ11=ρ22=1, ρ12=0.10016, δ=1.99990, and α=103.

Fig. 3.
Fig. 3.

Decay rate Im(k) versus absorptivity α for (a) partial mode degeneracy and (b) full degeneracy. For each α, the system is retuned by varying ρ12 and δ so as to maintain partial mode degeneracy at some real ωD. (c) Reflection at full degeneracy versus the relative amplitude (β1) and phase (β2) of the inputs, as parameterized in Eq. (9).

Fig. 4.
Fig. 4.

(a) Real band structure and (b) reflection spectrum near a full mode degeneracy point. In (b), the two curves correspond to the input combinations, which would yield perfect absorption (black) and perfect reflection (dashed) at the degeneracy, corresponding to the A and B points in Fig. 3(c). (c) Field intensity in a grating waveguide with partial mode degeneracy (dashed) and full degeneracy (black), with absorptivity of α=103.

Equations (10)

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

(ωωD)=(kkD)2/ξ,
Θ=(ω+iα0ρ11ρ120ωδ+iαρ12ρ22ρ11ρ12ωiα0ρ12ρ220ω+δiα).
E0=(ir)=[i1,i2,r1,r2]T=M[a1,a2,0,0]T,
R=(M31M32M41M42)(M11M12M21M22)1=M/M+.
det(R)=det(M)/det(M+)=0.
J=(kD1kDkD1kD),
Vk1,2+=V0+±ΔkV1++Δk2V2+±Δk3V3+,
Vk1,2=V0±ΔkV1+Δk2V2±Δk3V3,
i1=cos(β1)eiβ2,i2=sin(β1).
E=b1(V1++iV0+ziV0z)eikDz.

Metrics