Abstract

We numerically investigate counter-propagating beams in a one-dimensionally, periodic structure with non-instantaneous Kerr nonlinearity for the design of efficient optical limiters. The performance of the Photonic Band Gap optical limiter with different response times is compared with the instantaneous case. Dynamic range and the cutoff intensity can be improved over a range of relaxation times.

© 2009 Optical Society of America

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  1. T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, "Optimization of optical limiting devices based on excited-state absorption," Appl. Opt. 36, 4110-4122 (1997).
    [CrossRef] [PubMed]
  2. J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
    [CrossRef]
  3. J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
    [CrossRef]
  4. P. Tran, "All-optical switching with a nonlinear chiral photonic bandgap structure," J. Opt. Soc. Am. B 16, 70-73 (1999).
    [CrossRef]
  5. 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, 1896-1899 (1994).
    [CrossRef]
  6. M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
    [CrossRef]
  7. M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
    [CrossRef] [PubMed]
  8. M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).
  9. B. Y. Soon and J. W. Haus, "One-dimensional photonic crystal optical limiter," Opt. Express 11, 2007-2018 (2003).
    [CrossRef] [PubMed]
  10. B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
    [CrossRef]
  11. J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, I. Mel’nikov, "Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients," J. Opt. Soc. Am. B 19, 2282-2291 (2002).
    [CrossRef]
  12. J. W. Haus, B. Y. Soon, M. Scalora, M. Bloemer, C. Bowden, C. Sibilia, and A. Zheltikov, "Spatiotemporal instabilities for counter-propagating waves in periodic media," Opt. Express 10, 114-121 (2002).
    [PubMed]
  13. M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
    [CrossRef] [PubMed]
  14. X. Liu, J. W. Haus and S. M. Shahriar, "Modulation instability for a relaxational Kerr medium," Opt. Commun. 281, 2907-2912 (2008).
    [CrossRef]
  15. M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
    [CrossRef] [PubMed]

2008 (1)

X. Liu, J. W. Haus and S. M. Shahriar, "Modulation instability for a relaxational Kerr medium," Opt. Commun. 281, 2907-2912 (2008).
[CrossRef]

2006 (1)

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

2003 (1)

2002 (3)

1999 (1)

1997 (1)

1996 (3)

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[CrossRef]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

1994 (3)

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, 1896-1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

1993 (1)

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Bartoli, F.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Bartoli, F. J.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Bloemer, M.

Bloemer, M. J.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

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, 1896-1899 (1994).
[CrossRef]

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Bowden, C.

Bowden, C. M.

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

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, 1896-1899 (1994).
[CrossRef]

Bowden, C.M.

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Boyle, M.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Chen, Z.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

D'Aguanno, G.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

deSterke, C. M.

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[CrossRef]

Dogariu, A.

Dowling, J. P.

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

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, 1896-1899 (1994).
[CrossRef]

Dowling, J.P.

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Eggleton, B. J.

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[CrossRef]

Flom, S.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Hagan, D. J.

Haus, J. W.

Jeng, C.-C.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Larciprete, M. C.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

Lin, C.-Y.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Liu, X.

X. Liu, J. W. Haus and S. M. Shahriar, "Modulation instability for a relaxational Kerr medium," Opt. Commun. 281, 2907-2912 (2008).
[CrossRef]

Mattiucci, N.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

Mel’nikov, I.

Mitchell, M.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Pong, R.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Pong, R. G. S.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Said, A. A.

Scalora, M.

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

J. W. Haus, B. Y. Soon, M. Scalora, M. Bloemer, C. Bowden, C. Sibilia, and A. Zheltikov, "Spatiotemporal instabilities for counter-propagating waves in periodic media," Opt. Express 10, 114-121 (2002).
[PubMed]

J. W. Haus, B. Y. Soon, M. Scalora, C. Sibilia, I. Mel’nikov, "Coupled-mode equations for Kerr media with periodically modulated linear and nonlinear coefficients," J. Opt. Soc. Am. B 19, 2282-2291 (2002).
[CrossRef]

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, 1896-1899 (1994).
[CrossRef]

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

Segev, M.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Shahriar, S. M.

X. Liu, J. W. Haus and S. M. Shahriar, "Modulation instability for a relaxational Kerr medium," Opt. Commun. 281, 2907-2912 (2008).
[CrossRef]

Sheu, F.-W.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Shih, M. F.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

Shih, M.-F.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Shirk, J.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Shirk, J. S.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Sibilia, C.

Sipe, J. E.

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[CrossRef]

Snow, A.

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

Snow, A. W.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Soon, B. Y.

Tran, P.

Van Stryland, E. W.

Xia, T.

Zheltikov, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, and A. W. Snow, "Optical limiter using a lead phthalocyanine," Appl. Phys. Lett. 63, 1880-1882 (1993).
[CrossRef]

Electron. Lett. (1)

B. J. Eggleton, C. M. deSterke, R. E. Slusher and J. E. Sipe, "Distributed feedback pulse generator based on nonlinear fiber grating," Electron. Lett. 32, 2341-2342 (1996).
[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, 1896-1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, M. J. Bloemer and C. M. Bowden, "The photonic band edge optical diode," J. Appl. Phys. 76, 2023-2026 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

X. Liu, J. W. Haus and S. M. Shahriar, "Modulation instability for a relaxational Kerr medium," Opt. Commun. 281, 2907-2912 (2008).
[CrossRef]

Opt. Express (2)

Phys. Rev. E (1)

M. Scalora, N. Mattiucci, G. D'Aguanno, M. C. Larciprete, and M. J. Bloemer, "Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: Ultrawide bandwidth optical limiting," Phys. Rev. E 73, 016603 (2006).

Phys. Rev. Lett. (3)

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, "Self-trapping of partially spatially incoherent light," Phys. Rev. Lett. 77, 490-493 (1996).
[CrossRef] [PubMed]

M. Scalora, J.P. Dowling, C.M. Bowden and M. J. Bloemer," Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

J. Shirk, R. Pong, S. Flom, F. Bartoli, M. Boyle, and A. Snow, "Lead phthalocyanine reverse saturable absorption optical limiters," Pure Appl. Opt. 5, 701-707 (1996).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Transmission curve of the PBG structure and the spectrum of the input pulse.

Fig. 2(a).
Fig. 2(a).

A snapshot of the pulse evolution through an instantaneous nonlinear medium placed in a PBG. Top frame is the initial pulse, which is launched outside the medium. The central frame and bottom frame are the forward propagating and backward propagating pulse, respectively. The initial amplitude of the wave is A = 0.75.

Fig. 2(b).
Fig. 2(b).

A snapshot of the forward- and backward waves with a non-instantaneous nonlinear medium embedded in the PBG. The relaxation time is τ 1 = 0.1 and the amplitude is the same as in Fig. 2(a).

Fig. 2(c).
Fig. 2(c).

A snapshot of the forward- and backward waves with a non-instantaneous nonlinear medium embedded in the PBG. The relaxation time is τ 2 = 1 and the amplitude is the same as in Fig. (2a).

Fig. 2(d).
Fig. 2(d).

A snapshot of the forward- and backward waves with a non-instantaneous nonlinear medium embedded in the PBG. The relaxation time is τ 3 = 4 and the amplitude is the same as in Fig. 2(a).

Fig. 3.
Fig. 3.

3-D plot of the forward propagating pulse.

Fig. 4.
Fig. 4.

Aperture placed in the Fraunhofer regime to block out energy flow (A = 0.75,τ = 1). The Fresnel number is F =107.

Fig. 5.
Fig. 5.

Transmission curves for PBG structures with different response time.

Tables (1)

Tables Icon

Table 1, The figures of merit for instantaneous and non-instantaneous nonlinear media embedded in a PBG optical limiter.

Equations (19)

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

1 v E f t = E f z + i F Δ 2 E f + E f + E b + N f E f ,
1 v E b t = E b z + i F Δ 2 E b + E b + E f + N b E b ,
N f t = 1 τ ( N f + E f 2 + 2 E b 2 ) ,
N b t = 1 τ ( N b + E b 2 + 2 E f 2 ) ,
E f ( x , 0 , t ) = E f ( x , t )
E b ( x , L , t ) = 0
dU dt = ( L ˜ + N ˜ ) U ,
U = ( E f , E b ) T ,
L ˜ = z + i F Δ 2 + 0 0 z + i F Δ 2 + + ( 0 0 ) = V ˜ + K ˜ ,
N ˜ = N f 0 0 N b .
U L ( t + dt 2 ) = exp ( V dt 2 ) exp ( K dt 2 ) U ( t )
N f ( x , z , t ) = 1 τ t e ( t t ' ) τ ( 2 E b ( x , z , t ' ) 2 + E f ( x , z , t ' ) 2 ) dt '
N b ( x , z , t ) = 1 τ t e ( t t ' ) τ ( 2 E f ( x , z , t ' ) 2 + E b ( x , z , t ' ) 2 ) dt '
U N ( t + dt 2 ) = exp ( Ndt ) U ( t ) .
U ( t + dt ) = exp ( V dt 2 ) exp ( K dt 2 ) exp ( Ndt ) exp ( V dt 2 ) exp ( K dt 2 ) U ( t )
E f ( x , z , 0 ) = A exp ( ( z z 0 ) 2 / σ z 2 ) exp ( x 2 / σ x 2 )
E b ( x , z , 0 ) = 0
TDR = ψ = T max T min
TCO = T 80 % T 20 % T 80 % + T 20 %

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