Abstract

We present an effective design of aperiodically stacked layers of nonlinear material and air, sandwiched by two truncated photonic crystals, in terms of the simulation annealing method. The constructed structure can achieve multiple-wavelength second-harmonic generation (SHG) at the preassigned wavelengths. We derive a general solution of SHG in 1D inhomogeneous systems and apply it to evaluate the SHG conversion efficiency. Numerical simulations show that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequencies are assigned to the designed defect states.

© 2006 Optical Society of America

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References

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  1. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
    [CrossRef] [PubMed]
  2. S. Shi, Z. M. Jiang, and Xun Wang, Opt. Lett. 26, 1194 (2001).
    [CrossRef]
  3. D. R. Smith, R. Dalidaouch, N. Kroll, S. Schultz, S. L. McCall, and P. M. Platzman, J. Opt. Soc. Am. B 10, 314 (1993).
    [CrossRef]
  4. J. Martorell and R. Corbalan, Opt. Commun. 108, 319 (1994).
    [CrossRef]
  5. J. Trull, R. Vilaseca, J. Martorell, and R. Corbalan, Opt. Lett. 20, 1746 (1995).
    [CrossRef] [PubMed]
  6. B. Shi, Z. M. Jiang, and X. Wang, Opt. Lett. 26, 1194 (2001).
    [CrossRef]
  7. F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
    [CrossRef]
  8. M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
    [CrossRef] [PubMed]
  9. H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
    [CrossRef]
  10. S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
    [CrossRef] [PubMed]
  11. J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997).
    [CrossRef] [PubMed]
  12. V. G. Dmitriev, G. G. Gurazdyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997), Chap. 3.

2004 (2)

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

J. Martorell and R. Corbalan, Opt. Commun. 108, 319 (1994).
[CrossRef]

1993 (1)

1991 (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

1983 (1)

S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Cao, C.-Q.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

Cao, H.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

Cheng, C.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Corbalan, R.

Dalidaouch, R.

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurazdyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997), Chap. 3.

Fejer, M. M.

Gelatt, C. P.

S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Gurazdyan, G. G.

V. G. Dmitriev, G. G. Gurazdyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997), Chap. 3.

Hall, D. B.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

Hiro, K.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Jiang, Z. M.

Joannopoulos, J. D.

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Kirkpatrick, S.

S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Kroll, N.

Li, R.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Martorell, J.

McCall, S. L.

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Meyn, J.-P.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurazdyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997), Chap. 3.

Platzman, P. M.

Qiu, J.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Ren, F. F.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Schultz, S.

Shi, B.

Shi, S.

Si, J.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Smith, D. R.

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

Torkelson, J. M.

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

Trull, J.

Vecchi, M. P.

S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Vilaseca, R.

Wang, H. T.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Wang, X.

Wang, Xun

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

H. Cao, D. B. Hall, J. M. Torkelson, and C.-Q. Cao, Appl. Phys. Lett. 76, 538 (2000).
[CrossRef]

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

Nat. Mater. (1)

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Martorell and R. Corbalan, Opt. Commun. 108, 319 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (1)

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. Qiu, J. Si, and K. Hiro, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, Phys. Rev. Lett. 67, 3380 (1991).
[CrossRef] [PubMed]

Science (1)

S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef] [PubMed]

Other (1)

V. G. Dmitriev, G. G. Gurazdyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997), Chap. 3.

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Figures (2)

Fig. 1
Fig. 1

Transmission spectrum of the constructed PQW for a normally incident EM wave with the TE polarization.

Fig. 2
Fig. 2

Wavelength dependence of SHG conversion efficiency of the constructed PQW structure (a) for the backward SHG, (b) for the forward SHG.

Equations (10)

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[ d 2 d x 2 + k l ( 1 ) 2 ] E l ( 1 ) ( x ) = 0 ,
[ d 2 d x 2 + k l ( 2 ) 2 ] E l ( 2 ) ( x ) = k 20 2 χ l E l ( 1 ) 2 ( x ) ,
E l ( 1 ) ( x ) = A l ( 1 ) e i k l ( 1 ) ( x x l 1 ) + B l ( 1 ) e i k l ( 1 ) ( x x l 1 ) ,
E l ( 2 ) ( x ) = A l ( 2 ) e i k l ( 2 ) ( x x l 1 ) + B l ( 2 ) e i k l ( 2 ) ( x x l 1 )
+ C l [ A l ( 1 ) 2 e i 2 k l ( 1 ) ( x x l 1 ) + B l ( 1 ) 2 e i 2 k l ( 1 ) ( x x l 1 ) ] 2 k 20 2 χ l k l ( 2 ) 2 A l ( 1 ) B l ( 1 ) ,
C l = k 20 2 χ l k l ( 2 ) 2 4 k l ( 1 ) 2 .
η forth = n N ( 2 ) A N ( 2 ) ( x N 1 ) 2 n 1 ( 1 ) A 1 ( 1 ) 2 , η back = B l ( 2 ) ( x 1 ) 2 A l ( 1 ) 2 .
O = α s [ ω α o ω α ( s ) + β 1 t 0 t α ( s ) ] + β 2 [ max { t α ( s ) } min { t α ( s ) } ] ,
ω α o , ω α ( s ) [ ω α 1 , ω α ] , α = 1 , 2 , 3
ω 0 ( = ω a ) < ω 1 o < ω 1 < ω 2 0 < ω 2 < ω 3 0 < ω 3 ( = ω b ) ,

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