Abstract

We study second-harmonic generation in a negative-index material cavity. The transmission spectrum shows a bandgap between the electric and magnetic plasma frequencies. The nonlinear process is made efficient by local phase-matching conditions between a forward-propagating pump and a backward-propagating second-harmonic signal. By simultaneously exciting the cavity with counterpropagating pulses, and by varying their relative phase difference, one is able to enhance or inhibit linear absorption and the second-harmonic conversion efficiency.

© 2007 Optical Society of America

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  1. Focus issue on Metamaterials, J. Opt. Soc. Am. B 23, 386 (2006), and references therein.
  2. M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
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  3. A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
    [CrossRef] [PubMed]
  4. I. V. Shadrivov, S. K. Morrison, and Yu. S. Kivshar, Opt. Express 14, 9344 (2006).
    [CrossRef] [PubMed]
  5. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
    [CrossRef]
  6. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, J. Opt. Soc. Am. B 23, 529 (2006).
    [CrossRef]
  7. M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
    [CrossRef] [PubMed]
  8. G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).
  9. G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
    [CrossRef] [PubMed]
  10. M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
    [CrossRef]
  11. R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  12. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

2006

2005

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

2004

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

2003

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

2001

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Bertolotti, M.

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Bloemer, M. J.

M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Bowden, C. M.

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Centini, M.

M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

D'Aguanno, G.

M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

de Ceglia, D.

Gorkunov, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Heyman, E.

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Kivshar, Y. S.

Kivshar, Yu. S.

Lapine, M.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Mattiucci, N.

M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Morrison, S. K.

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Scalora, M.

M. Scalora, G. D'Aguanno, M. J. Bloemer, M. Centini, D. de Ceglia, N. Mattiucci, and Y. S. Kivshar, Opt. Express 14, 4746 (2006).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Shadrivov, I. V.

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Sibilia, C.

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, J. Opt. Soc. Am. B 23, 529 (2006).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys.

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Laser Phys. 15, 590 (2005).

Opt. Express

Phys. Rev. B

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Phys. Rev. B 69, 165112 (2004).
[CrossRef]

Phys. Rev. E

M. Centini, G. D'Aguanno, M. Scalora, M. J. Bloemer, C. M. Bowden, C. Sibilia, N. Mattiucci, and M. Bertolotti, Phys. Rev. E 67, 036617 (2003).
[CrossRef]

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 056625 (2001).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, Phys. Rev. E 67, 065601 (2003).
[CrossRef]

Phys. Rev. Lett.

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, Phys. Rev. Lett. 91, 037401 (2003).
[CrossRef] [PubMed]

G. D'Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef] [PubMed]

Other

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

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Figures (3)

Fig. 1
Fig. 1

(a) Transmission spectrum of a 3.85 μ m thick NIM slab. Dashed curve, Re ( n ) . Dotted curve, Im ( n ) . At the midgap frequency the transmittance is 10 10 , and Re ( n ) 10 6 . In the tuning configuration indicated by the arrows, the phase-matching condition Re [ n ( ω ̃ F ) ] = Re [ n ( ω ̃ S H ) ] is satisfied, as shown by the two circles. (b) Overall SHG conversion efficiency versus pulse duration of a pump input having a peak intensity I in = 500 MW cm 2 . We assume χ e ( 2 ) = 25 pm V and χ m ( 2 ) = 0 .

Fig. 2
Fig. 2

Delay accumulated for reflected (backward) and transmitted (forward) pulses as a function of the relative phase difference between the two coherent, CP incident pulses. Pulse duration is 3.5 ps in all cases.

Fig. 3
Fig. 3

SHG efficiency (squares) and energy at the FF (triangles) as functions of Δ φ . The conversion efficiency for the single, incident pulse ( I in = 500 MW cm 2 ) is 5 % (dashed line). The CP pulses have a peak intensity of I in 2 , and a duration of 3.5 ps . The absorption reaches 20 % for Δ φ = 0 , and it is suppressed along with the SHG process, for Δ φ = 180 ° .

Equations (2)

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( E x , H y ) t = 1 ( ϵ 0 , μ 0 ) [ ( H y , E x ) z + ( J x , K y ) ] χ e , m ( 2 ) ( E x 2 , H y 2 ) t ,
( J x , K y ) t + γ e , m ( J x , K y ) = ( ϵ 0 , μ 0 ) ω e , m 2 ( J x , H y ) ,

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