Abstract

We theoretically propose a method to restore weak pulse signals submerged in noise via stochastic resonance, which is based on the optical bistability induced by the molecule reorientation in a Fabry-Perot cavity with an intracavity nematic liquid-crystal film. The bistable properties of this cavity are analyzed with different reflectance of the mirrors, initial phase shift and initial angle between the phase propagation vector and the director. The cross-correlation coefficient between pure input pulses and output is calculated to quantitatively evaluate the influence of noise intensity on output. The simulation results show a cross-correlation gain of 3.2 and that the buried signal can be recovered effectively by this device. It proves the potential of using this structure to recover noise-hidden pulse signals in an all-optical system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
    [Crossref]
  2. R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
    [Crossref]
  3. S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
    [Crossref] [PubMed]
  4. J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
    [Crossref] [PubMed]
  5. H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
    [Crossref] [PubMed]
  6. K. Nishiguchi and A. Fujiwara, “Detecting signals buried in noise via nanowire transistors using stochastic resonance,” Appl. Phys. Lett. 101(19), 193108 (2012).
    [Crossref]
  7. G. Cao, H. Liu, X. Li, N. Huang, and Q. Sun, “Reconstructing signals via stochastic resonance generated by photorefractive two-wave mixing bistability,” Opt. Express 22(4), 4214–4223 (2014).
    [Crossref] [PubMed]
  8. J. Han, H. Liu, Q. Sun, N. Huang, Z. Wang, and S. Li, “Extracting nanosecond pulse signals via stochastic resonance generated by surface plasmon bistability,” Opt. Lett. 40(22), 5367–5370 (2015).
    [Crossref] [PubMed]
  9. P. Jung and P. Hänggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A 44(12), 8032–8042 (1991).
    [Crossref] [PubMed]
  10. R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
    [Crossref]
  11. D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
    [Crossref]
  12. J. Han, H. Liu, Q. Sun, and N. Huang, “Reconstruction of pulse noisy images via stochastic resonance,” Sci. Rep. 5(1), 10616 (2015).
    [Crossref] [PubMed]
  13. C. Horvath, D. Bachman, R. Indoe, and V. Van, “Photothermal nonlinearity and optical bistability in a graphene-silicon waveguide resonator,” Opt. Lett. 38(23), 5036–5039 (2013).
    [Crossref] [PubMed]
  14. Z. Zang and Y. Zhang, “Analysis of optical switching in a Yb3+-doped fiber Bragg grating by using self-phase modulation and cross-phase modulation,” Appl. Opt. 51(16), 3424–3430 (2012).
    [Crossref] [PubMed]
  15. Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285(5), 521–526 (2012).
    [Crossref]
  16. I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
    [Crossref]
  17. M. M. Cheung, S. D. Durbin, and Y. R. Shen, “Optical bistability and self-oscillation of a nonlinear Fabry-Perot interferometer filled with a nematic-liquid-crystal film,” Opt. Lett. 8(1), 39–41 (1983).
    [Crossref] [PubMed]
  18. I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
    [Crossref]

2015 (2)

2014 (2)

G. Cao, H. Liu, X. Li, N. Huang, and Q. Sun, “Reconstructing signals via stochastic resonance generated by photorefractive two-wave mixing bistability,” Opt. Express 22(4), 4214–4223 (2014).
[Crossref] [PubMed]

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

Z. Zang and Y. Zhang, “Analysis of optical switching in a Yb3+-doped fiber Bragg grating by using self-phase modulation and cross-phase modulation,” Appl. Opt. 51(16), 3424–3430 (2012).
[Crossref] [PubMed]

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285(5), 521–526 (2012).
[Crossref]

K. Nishiguchi and A. Fujiwara, “Detecting signals buried in noise via nanowire transistors using stochastic resonance,” Appl. Phys. Lett. 101(19), 193108 (2012).
[Crossref]

2010 (1)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

2007 (1)

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

1998 (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

1997 (1)

S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[Crossref] [PubMed]

1993 (1)

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

1991 (1)

P. Jung and P. Hänggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A 44(12), 8032–8042 (1991).
[Crossref] [PubMed]

1983 (2)

M. M. Cheung, S. D. Durbin, and Y. R. Shen, “Optical bistability and self-oscillation of a nonlinear Fabry-Perot interferometer filled with a nematic-liquid-crystal film,” Opt. Lett. 8(1), 39–41 (1983).
[Crossref] [PubMed]

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

1982 (2)

I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
[Crossref]

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

Abbaspour, H.

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Almog, R.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

Bachman, D.

Benzi, R.

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

Bezrukov, S. M.

S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[Crossref] [PubMed]

Buks, E.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

Cao, G.

Cheung, M. M.

Deveaud, B.

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Douglass, J. K.

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

Durbin, S. D.

Dylov, D. V.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

Fleischer, J. W.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

Fujiwara, A.

K. Nishiguchi and A. Fujiwara, “Detecting signals buried in noise via nanowire transistors using stochastic resonance,” Appl. Phys. Lett. 101(19), 193108 (2012).
[Crossref]

Gammaitoni, L.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Han, J.

Hanggi, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Hänggi, P.

P. Jung and P. Hänggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A 44(12), 8032–8042 (1991).
[Crossref] [PubMed]

Horvath, C.

Hou, J. Y.

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

Huang, N.

Indoe, R.

Jung, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

P. Jung and P. Hänggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A 44(12), 8032–8042 (1991).
[Crossref] [PubMed]

Khoo, I. C.

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
[Crossref]

Li, S.

Li, X.

Liu, H.

Marchesoni, F.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Morier-Genoud, F.

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Moss, F.

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

Nishiguchi, K.

K. Nishiguchi and A. Fujiwara, “Detecting signals buried in noise via nanowire transistors using stochastic resonance,” Appl. Phys. Lett. 101(19), 193108 (2012).
[Crossref]

Normandin, R.

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
[Crossref]

Pantazelou, E.

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

Parisi, G.

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

Portella-Oberli, M. T.

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Shen, Y. R.

Shtempluck, O.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

So, V. C. Y.

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
[Crossref]

Sun, Q.

Sutera, A.

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

Trebaol, S.

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Van, V.

Vodyanoy, I.

S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[Crossref] [PubMed]

Vulpiani, A.

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

Wang, Z.

Wilkens, L.

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

Zaitsev, S.

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

Zang, Z.

Z. Zang and Y. Zhang, “Analysis of optical switching in a Yb3+-doped fiber Bragg grating by using self-phase modulation and cross-phase modulation,” Appl. Opt. 51(16), 3424–3430 (2012).
[Crossref] [PubMed]

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285(5), 521–526 (2012).
[Crossref]

Zhang, Y.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. Nishiguchi and A. Fujiwara, “Detecting signals buried in noise via nanowire transistors using stochastic resonance,” Appl. Phys. Lett. 101(19), 193108 (2012).
[Crossref]

R. Almog, S. Zaitsev, O. Shtempluck, and E. Buks, “Signal amplification in a nanomechanical Duffing resonator via stochastic resonance,” Appl. Phys. Lett. 90(1), 013508 (2007).
[Crossref]

J. Appl. Phys. (1)

I. C. Khoo, R. Normandin, and V. C. Y. So, “Optical bistability using a nematic liquid crystal film in a Fabry-Perot cavity,” J. Appl. Phys. 53(11), 7599–7601 (1982).
[Crossref]

Nat. Photonics (1)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4(5), 323–328 (2010).
[Crossref]

Nature (2)

S. M. Bezrukov and I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997).
[Crossref] [PubMed]

J. K. Douglass, L. Wilkens, E. Pantazelou, and F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993).
[Crossref] [PubMed]

Opt. Commun. (1)

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285(5), 521–526 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (2)

I. C. Khoo, J. Y. Hou, R. Normandin, and V. C. Y. So, “Theory and experiment on optical bistability in a Fabry-Perot interferometer with an intracavity nematic liquid-crystal film,” Phys. Rev. A 27(6), 3251–3257 (1983).
[Crossref]

P. Jung and P. Hänggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A 44(12), 8032–8042 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

H. Abbaspour, S. Trebaol, F. Morier-Genoud, M. T. Portella-Oberli, and B. Deveaud, “Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity,” Phys. Rev. Lett. 113(5), 057401 (2014).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[Crossref]

Sci. Rep. (1)

J. Han, H. Liu, Q. Sun, and N. Huang, “Reconstruction of pulse noisy images via stochastic resonance,” Sci. Rep. 5(1), 10616 (2015).
[Crossref] [PubMed]

Tellus (1)

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–15 (1982).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram to recover noisy signal via stochastic resonance using a Fabry-Perot cavity with an intracavity nematic liquid-crystal film. NLC: nematic liquid crystals. M: mirror. (b) Schematics of the optical field propagation in the nematic liquid crystal. n is the director along z. is the reoriented director. α1 is the angle of incidence, β is the angle between the phase propagation vector and the director axis. θ is the reoriented angle.
Fig. 2
Fig. 2 Bistability transmission characteristics with (a) different reflectance of the mirrors (β = 22°, ϕ0 = −0.36π) and (b) the initial angle between the phase propagation vector and the director (ϕ0 = −0.36π, R = 0.9).
Fig. 3
Fig. 3 (a) Bistability transmission characteristics with different initial round-trip phase shift (β = 22°, R = 0.9). (b) Intersection of the F-P transmission curve and phase shift line with different input intensity. Curve: F-P transmission. Straight line: the round-trip phase shift.
Fig. 4
Fig. 4 Properties of the pulse signal recovery. (a)-(d) Input with noise intensity is 0 W/cm2, 400 W/cm2, 480 W/cm2, 560 W/cm2, respectively. (a′)–(d′) the corresponding output of (a)-(d).
Fig. 5
Fig. 5 (a) Cross-correlation coefficients and (b) the cross-correlation gain versus the noise intensity.

Equations (7)

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

η= η max /[1+F sin 2 (ϕ/2)],
δϕ= π (Δε) 2 d 3 sinαcosαsin2β n (1+GR)η I i 3Kλ ε T G ccosβ( ε Δε cos 2 β) ,
n = n( ε Δε sin 2 α) ε 2 ( ε 2 ε 2 ) sin 2 α ,
I i = I tr (1GR) 2 +4GR sin 2 [ ϕ 0 /2+ I tr π (Δε) 2 d 3 sinαcosαsin2β n (1+GR) 6Kλ ε T G ccosβ( ε Δε cos 2 β) ] T 2 G .
S(t)= S 0 exp(2 (t/ t 0 ) 2 )+N(t),
C S, S 0 = (S S )( S 0 S 0 ) [ (S S ) 2 ( S 0 S 0 ) 2 ] 1/2 .
C g = C S out , S 0 / C S in , S 0 .

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