OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 4 — Feb. 24, 2014
  • pp: 4214–4223
« Show journal navigation

Reconstructing signals via stochastic resonance generated by photorefractive two-wave mixing bistability

Guangzhan Cao, Hongjun Liu, Xuefeng Li, Nan Huang, and Qibing Sun  »View Author Affiliations


Optics Express, Vol. 22, Issue 4, pp. 4214-4223 (2014)
http://dx.doi.org/10.1364/OE.22.004214


View Full Text Article

Acrobat PDF (1543 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Stochastic resonance is theoretically investigated in an optical bistable system, which consists of a unidirectional ring cavity and a photorefractive two-wave mixer. It is found that the output properties of stochastic resonance are mainly determined by the applied noise, the crystal length and the applied electric field. The influences of these parameters on the stochastic resonance are also numerically analyzed via cross-correlation, which offers general guidelines for the optimization of recovering noise-hidden signals. A cross-correlation gain of 4 is obtained by optimizing these parameters. This provides a general method for reconstructing signals in nonlinear communications systems.

© 2014 Optical Society of America

1. Introduction

Stochastic resonance was described as a phenomenon that a weak periodic signal is optimized by the presence of an appropriate level of noise [1

1. H. Chen, P. K. Varshney, S. M. Kay, and J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007). [CrossRef]

]. With the development of stochastic resonance, it has far been found to account for many natural phenomena and shown a large number of applications in different areas of technology including climatic patterns [2

2. R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982). [CrossRef]

, 3

3. C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982). [CrossRef]

], electrical systems [4

4. S. Fauve and F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983). [CrossRef]

, 5

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

] and biology [6

6. 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]

, 7

7. A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, and K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996). [CrossRef] [PubMed]

]. Nowadays, signal processing via stochastic resonance becomes a research focus. Generally, low level optical signals are overwhelmed by the noise, which lead to an extremely low signal-to-noise ratio (SNR). The stochastic resonance systems have been used for amplifying [8

8. R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005). [CrossRef] [PubMed]

, 9

9. H. B. Chan and C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006). [CrossRef]

] and self-filtering signal [10

10. D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

] to improve the detection sensitivity and output SNR. As we know, the well known conditions for a system to exhibit stochastic resonance are the energy threshold, applied subthreshold modulation and source of noise. One of the classic examples of a system that undergoes stochastic resonance is that of a particle in a double-well potential. With a subthreshold modulation but no noise, the particle will undergo a periodic motion in a small local area of one of the two wells. However, when the external noise is considered, there will be an interaction between the modulation and the nonlinear system. Then the particle will undergo a periodic transition between the two wells, and resulting in an enhancement in the SNR.

For the domain of optics, stochastic resonance has been reported in the context of periodically driven bistable dynamic systems [11

11. F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, and F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15(11), 2674–2680 (1998). [CrossRef]

]. Several implementations have been proposed to realize a bistable optical system that is switched between its two stable states by a modulation signals aided by noise. Early theoretical and experimental investigations have indicated that any bistable system can exhibit the stochastic resonance effect [12

12. B. M. Jost and B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996). [CrossRef] [PubMed]

]. Weiss and Fischer proposed that photorefractive two-wave mixing in a ring cavity exhibits the bistability [13

13. S. Weiss and B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989). [CrossRef]

]. The configurations permit bistable operation when the photorefractive crystal is oriented such that optical power is transferred from the signal beam to the pump beam during two-wave mixing. Optical bistability, indubitably, has potential applications in optical logic, optical switching, and optical memory elements, and can play a major role in the development of optical communication systems. Extensive work has been done in the area of photorefractive two-wave mixing bistability (PTWMB) [12

12. B. M. Jost and B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996). [CrossRef] [PubMed]

14

14. R. Daisy and B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992). [CrossRef] [PubMed]

], however, there are still few reports about the application of reconstructing signals via stochastic resonance in the PTWMB system.

In this paper, we theoretically investigate the nonlinear enhancement of noisy signals via all-optical stochastic resonance in a ring cavity firstly. The stochastic resonance effect is generated by the bistable system which is based on a photorefractive two-wave mixer. The optical power is transferred from the pump beam to the signal beam that is different from the works demonstrated in [12

12. B. M. Jost and B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996). [CrossRef] [PubMed]

, 13

13. S. Weiss and B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989). [CrossRef]

]. The influences of the bistable parameters on the stochastic resonance signals are analyzed in detail, and the cross-correlation gain of noisy signals can be improved by using the bistability system which can be optimized by tuning the bistable parameters.

2. Theory model of stochastic resonance in optical bistability

The nonlinear dynamics equation of the stochastic resonance is usually described by the Langevin equation, which is different at various bistability systems [15

15. R. Bartussek, P. Hänggi, and P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994). [CrossRef] [PubMed]

17

17. M. Misono, T. Kohmoto, Y. Fukuda, and M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998). [CrossRef]

]. Here, we investigate the optical bistability occurs in the ring cavity with a photorefractive two-wave mixer. The ring cavity provides a signal feedback as evident from Fig. 1
Fig. 1 Principle diagram of the unidirectional photorefractive ring cavity with an injected signal. C, crystal; BS, beam splitters; M1,2, mirrors.
. The photorefractive crystal is a cerium-doped Sr0.6Ba0.4Nb2O6 (SBN:60) [18

18. J. E. Ford, J. Ma, Y. Fainman, and S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

]. To describe the process of nonlinear intensity exchange between the pump and the signal light, we consider near-degenerate two-wave mixing in a unidirectional photorefractive ring cavity. The two waves interact in the photorefractive crystal via the photoinduced reversible refractive-index grating. The coupled wave equations for this case can be expressed as [19

19. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

]
dA1dz=γA1A2A2I0α2A1,dA2dz=γA1A1A2I0α2A2,
(1)
where α is the absorption coefficient, Aj (j = 1,2) are the complex amplitudes of the pump and signal, Ij = |Aj|2, and I0(z) = I1(z) + I2(z) is the total light intensity at z, respectively. The two beams symmetrically incident upon the photorefractive crystal with the incident angles of θ1 = θ2 = θ. The complex coupling coefficient γ is given by [20

20. S. K. Kwong, M. C. Golomb, and A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986). [CrossRef]

]
γ=ωreffn034cEq(E0+iED)[E0Ωτ0(ED+Eμ)]+i[ED+Eq+Ωτ0E0],
(2)
where reff is the relevant electrooptic coefficient, n0 is the ordinary refractive index of the crystal, τ0 is the characteristic time, Ω = ω2-ω1, E0 is the externally applied electric field parallel to the grating wave vector in the crystal, Eμ, ED, and Eq are internal electric fields characteristic of drift, diffusion, and maximum space charge, respectively. With Aj = Ij1/2 exp(j), ψj = kjz + φj, Γ = 2Re(γ) and Γ′ = Im(γ), the Eq. (1) can be rewritten as
dI1dz=ΓI1I2I0αI1,dI2dz=ΓI1I2I0αI2dφ1dz=ΓI2I1+I2,dφ2dz=ΓI1I1+I2.
(3)
The solutions of Eq. (3) are
I1(z)=I1(0)1+m1+mexp(Γz)exp(αz)I2(z)=I2(0)1+mm+exp(Γz)exp(αz)Δφ1(z)=ΓΓln(1+mm+exp(Γz)),Δφ2(z)=ΓΓln(1+mm+exp(Γz))
(4)
where m is the input intensity ratio m = I2(0)/I1(0).

The photorefractive two-wave mixing with a signal feedback from the ring cavity is used to produce the optical bistability. The boundary condition for the ring configuration is
A2(0)=T1/2Ain+R1/2A2(l)exp(iδ0),
(5)
and the output signal amplitude is given by
Aout=T1/2A2(l),
(6)
where T and R are the transmissivity and reflectivity of the beam splitter (T = 1-R), respectively. The cavity detuning δ0 is defined by δ0 = (ω2-ωc)/(c/L), L is the effective cavity length, ωc = q(2πc/L) is the cavity mode nearest to the frequency of the incident field ω2 and q is an integer.

The complex amplitude in Eqs. (5) and (6) can be expressed in intensity
Iin=AinAin=T1[I2(0)+RI2(l)2RI2(0)I2(l)cos(δ0+Δφ2)],
(7)
and
Iout=TI2(l),
(8)
where Δφ2 = φ2(l)-φ2(0) is the additional phase due to the nonlinear process and can be obtained from Eq. (4). For convenience, the normalized input intensity and output intensity are simplified as Y = Iin/[TI1(0)] and X = Iout/[TI1(0)], respectively. According to Eq. (7), the steady-state equation of optical bistability in the ring cavity can be rewritten as
Y=[m(X)+RX2m(X)RXcos(δ0+Δφ2)].
(9)
The ratio m(X) is acquired from the second equation of Eq. (4)
m(X)=12[aX1+(aX1)2+4aX/b],
(10)
where a and b are defined as a = exp(αl) and b = exp(Γl), respectively.

Figure 2
Fig. 2 Schematic diagram of the stochastic resonance system.
details the physical mechanism of the stochastic resonance. The nonlinear dynamics of the stochastic resonance is excited by an additive white Gaussian noise [15

15. R. Bartussek, P. Hänggi, and P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994). [CrossRef] [PubMed]

] and a subthreshold signal. The subthreshold signals will undergo a nonlinear enhancement when an appropriate noise is injected to the stochastic resonance generator. In order to better understand the nonlinear dynamic process of the stochastic resonance, a model for the stochastic resonance in photorefractive unidirectional ring cavity is deduced from the classical stochastic resonance [1

1. H. Chen, P. K. Varshney, S. M. Kay, and J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007). [CrossRef]

, 15

15. R. Bartussek, P. Hänggi, and P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994). [CrossRef] [PubMed]

17

17. M. Misono, T. Kohmoto, Y. Fukuda, and M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998). [CrossRef]

, 21

21. R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978). [CrossRef]

]. The nonlinear Langevin equation for the normalized transmitted intensity X and input intensity Y is given by
dXdt=B(Y,X)=dV(X)dX,
(11)
B(Y,X)=Y[m(X)+RX2m(X)RXcos(δ0+Δφ2)],
(12)
where the potential function V(X) reads
V(X)=0XB(X)dX.
(13)
Having chosen a value for the input pulse sequence intensity Y(t) = Y0(t) within the region of bistability, we then modulate the value with the additive noise. Both the input and output signals are normalized by the pump intensity, so D is considered to be a normalized intensity. The normalized input intensity Y in Eq. (11) should be substituted by
Y(t)=Y0(t)+DN(t),
(14)
where D denotes the noise intensity, N(t) is the additive white Gaussian noise and the noise correlation N(t)N(t)=2δ(tt), respectively. According to Eqs. (11) and (12), the time dependence of the transmitted light intensity X can be described by the nonlinear Langevin equation.

3. Results and discussion

3.1. Properties of the optical bistability

In simulations, a laser with output power of a few hundred milliwatts at 514.5 nm is used as the coherent light source. The intensity of the pump beam keeps constant and is assumed much lager than the periodic signal pulses. That is, the normalized value of Y0(t) is less than 1. The transmissivity of the beam splitter is T = 0.5. M1 and M2 are total reflection mirrors as presented in Fig. 1. The electric field was applied antiparallel to the optic axis. The material parameters for the calculation of the complex coupling coefficient γ are according to reference [18

18. J. E. Ford, J. Ma, Y. Fainman, and S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

]. Moreover, the ring cavity without an injected signal can oscillate over a large range of cavity detuning [13

13. S. Weiss and B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989). [CrossRef]

, 22

22. P. Yeh, “Theory of unidirectional photorefractive ring oscillators,” J. Opt. Soc. Am. B 2(12), 1924–1928 (1985). [CrossRef]

], but here we assume the cavity detuning to be a constant (δ0 = 0.01) and the boundary conditions are not satisfied to allow the oscillation to occur. To determine the optimum operating parameters for the optical bistability in the unidirectional ring cavity, the output property of the optical bistability with different interaction lengths and electric field intensities are numerically simulated and analyzed as illustrated in Fig. 3
Fig. 3 Photorefractive optical bistability. Normalized output intensity X versus normalized input intensity Y for (a): E0 = 0 kV/cm, leff = 1 mm (red), 3 mm (green) and 5 mm (blue) ; (b) leff = 2 mm, E0 = 0 kV/cm (red), 2 kV/cm (green) and 4 kV/cm (blue), respectively.
. Figure 3(a) shows the relationship between X and Y for various interaction lengths with E0 = 0 kV/cm. It is found that there is only one stationary X for a fixed Y when the interaction length is 1 mm. The bistability appears with the increase of the interaction length, and three stationary X appear in the bistable region, which are the stable lower branch, the stable upper branch, and the unstable intermediate branch. As seen from Fig. 3(b), the bistability region moves toward to the larger Y direction when the electric field is applied. The bistability region is enlarged by tuning the interaction length and applied electric field. Starting with a weak signal beam, the photorefractive grating transfers a moderate percentage of the pump energy to the signal beam, and the output signal intensity increases slowly with the increase of the input signal intensity at the beginning. As the signal intensity increases further, the photorefractive grating reaches its saturation, the output signal jump to the upper branch. At present, if the signal intensity begins to reduce, the balance in the cavity would not be broken immediately. However, the output signal will jump to the low branch again when the incident light is faint.

In terms of the potential function V(X), we get two minima of V(X) from Eq. (13) when the system exhibits optical bistability as illustrated in Fig. 4
Fig. 4 Potential V is plotted versus the input and output light intensity Y and X.
. The dynamic stochastic resonance system has two stable stationary states corresponding to the two minima of the potential, which generally is a double-well potential.

3.2. Numerical analysis of the stochastic resonance

The term stochastic resonance has been adopted to describe an interesting statistical property of periodically modulated and noise-driven bistable dynamical systems. Under proper conditions, an increase in the input noise level results in a raise in the output signal-to-noise ratio. A continuous wave (CW) pump beam with a constant intensity and a train of periodic signal pulses with an additive white Gaussian noise are incident into the bistable system. The signal is a Gaussian pulse with a normalized peak intensity, which can be expressed as
Y0(t)=y0exp[2(t/tg)2],
(15)
where y0 = 0.05 is located in the bistable region illustrated by the green curve in Fig. 3(b), tg = tp /1.777 and tp is the pulse width, respectively. The observation time is about 20 s, and the sampling period is 0.001 s in the calculations.

Figure 5
Fig. 5 Transmission property of the optical stochastic resonance system. (a)-(d) Input signals Y with the white Gaussian noise intensity D = 0, D = 0.4, D = 1.2 and D = 2.0, respectively; (a′)-(d′) are the output signals X corresponding to the input signals. Insets: detail showing the signals at t = 5 s. In simulations, E0 = 2 kV/cm, leff = 2 mm.
depicts the ability to reconstruct signals of the optical stochastic resonance system with different levels of the applied noise. The signals are effectively extracted from the noise background via the stochastic resonance system and the trailing edge appears simultaneously. Nevertheless, as the noise intensity is raised further, the output signals gradually become indistinguishable and distorted compared with to the pure input signals. This is because the output signals become increasingly dominated by the noise.

To describe the energy transfer of the nonlinear dynamical process, we use the cross-correlation as a quantitative measure of the similarity between input signals Y(t) and output signals X(t). The normalized cross-correlation coefficients are defined as [23

23. J. Ma, D. Zeng, and H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006). [CrossRef]

]
CY0X=Y0|X=(Y0Y0)(XX)[(Y0Y0)2(XX)2]1/2,
(16)
and
CY0Y=Y0|Y=(Y0Y0)(YY)[(Y0Y0)2(YY)2]1/2.
(17)
The cross-correlation gain of the bistable system is then given by
Cg=CY0X/CY0Y=Y0|X/Y0|Y.
(18)
CY 0X is close to 0 when the output signal is severely distorted, while it is close to 1 under the condition that the output signal X are very similar with the pure input signal Y0. CY 0Y has the same variation trend as CY 0X.

According to Eqs. (16)(18), the cross-correlation coefficients and cross-correlation gain as a function of the noise intensity D are numerically calculated and analyzed. The normalized intensity of the input signal is set at Y0 = 0.05, and the noise intensity D is gradually increased from zero in our simulations. Figure 6(a)
Fig. 6 Cross-correlation coefficients (a) and the cross-correlation gain (b) as a function of the noise intensity D. The black curves are under the particular conditions of fixed noise distribution. In simulations, E0 = 2 kV/cm, leff = 2 mm.
clearly shows that CY 0Y and CY 0X decrease as the noise intensity increases, and CY 0Y decays much faster than CY 0X when D is small. As seen from Fig. 6(b), the cross-correlation gain increases to a maximum value of 4 firstly, and then begins to drop dramatically. The reason is that the stochastic resonance system becomes increasingly dominated by the noise, which leads to the distortion of extracted signals. Too little noise disables the reversal of the potential well, but too much noise leads to excessive distortion. Therefore, there exists an optimal noise level for acquiring the maximum cross-correlation gain that can be realized by adjusting the input noise intensity. This is the signature of the stochastic resonance effect, which is caused by the interaction between the random noise and weak signal in the potential well.

In addition, the impacts of the interaction length and applied electric field on the stochastic resonance are also numerically calculated and shown in Fig. 7
Fig. 7 The cross-correlation coefficients versus (a) the interaction length leff with E0 = 2 kV/cm and (b) the applied electric field E0 with leff = 2 mm,(Y0 = 0.05, D = 1.2), respectively. Insets: cross-correlation gain. and fixed noise intensity.
. It is found that the cross-correlation varies with the interaction length and there exist an optimal interaction length of 2 mm for obtaining the maximum cross-correlation gain. Moreover, the cross-correlation can be maximized by tuning of the applied electric field with an optimal interaction length of 2 mm. According to Eq. (2), the complex coupling coefficients γ at different applied electric fields E0 are acquired as shown in Fig. 8 (a)
Fig. 8 The complex coupling coefficient (a) and the value of﹣Γ′/ Γ (b) versus the applied electric field E0, respectively.
. Figure 8(b) presents the curve of -Γ′/ Γ versus E0 calculated from Eq. (4)(d). The dependence of stochastic resonance on the parameter of E0 can be clearly seen from Figs. 7(b) and 8(b). It is found that the maximum of the cross-correlation gain and the value of -Γ′/ Γ can be achieved at nearly the same E0. As a result, the stochastic resonance effect performed by tuning the parameter of E0 is mainly depending on -Γ′/Γ.

4. Conclusion

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61078029, 61178023 and 61275134.

References and links

1.

H. Chen, P. K. Varshney, S. M. Kay, and J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007). [CrossRef]

2.

R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982). [CrossRef]

3.

C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982). [CrossRef]

4.

S. Fauve and F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983). [CrossRef]

5.

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

6.

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]

7.

A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, and K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996). [CrossRef] [PubMed]

8.

R. L. Badzey and P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005). [CrossRef] [PubMed]

9.

H. B. Chan and C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006). [CrossRef]

10.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).

11.

F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, and F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15(11), 2674–2680 (1998). [CrossRef]

12.

B. M. Jost and B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996). [CrossRef] [PubMed]

13.

S. Weiss and B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989). [CrossRef]

14.

R. Daisy and B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992). [CrossRef] [PubMed]

15.

R. Bartussek, P. Hänggi, and P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994). [CrossRef] [PubMed]

16.

L. Zhang, L. Cao, and D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008). [CrossRef]

17.

M. Misono, T. Kohmoto, Y. Fukuda, and M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998). [CrossRef]

18.

J. E. Ford, J. Ma, Y. Fainman, and S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).

19.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).

20.

S. K. Kwong, M. C. Golomb, and A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986). [CrossRef]

21.

R. Bonifacio and L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978). [CrossRef]

22.

P. Yeh, “Theory of unidirectional photorefractive ring oscillators,” J. Opt. Soc. Am. B 2(12), 1924–1928 (1985). [CrossRef]

23.

J. Ma, D. Zeng, and H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006). [CrossRef]

24.

V. S. Anishchenko, M. A. Safonova, and L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993). [CrossRef]

25.

B. Xu, Z. P. Jiang, X. Wu, and D. W. Repperger, “Theoretical analysis of image processing using parameter-tuning stochastic resonance technique,” in IEEE American Control Conference ACC'07 (2007), pp. 1747–1752. [CrossRef]

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(190.0190) Nonlinear optics : Nonlinear optics
(190.1450) Nonlinear optics : Bistability
(190.7070) Nonlinear optics : Two-wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 29, 2013
Revised Manuscript: December 26, 2013
Manuscript Accepted: December 31, 2013
Published: February 18, 2014

Citation
Guangzhan Cao, Hongjun Liu, Xuefeng Li, Nan Huang, and Qibing Sun, "Reconstructing signals via stochastic resonance generated by photorefractive two-wave mixing bistability," Opt. Express 22, 4214-4223 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4214


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Chen, P. K. Varshney, S. M. Kay, J. H. Michels, “Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors,” IEEE Trans. Signal Processing 55(7), 3172–3184 (2007). [CrossRef]
  2. R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, “Stochastic resonance in climatic change,” Tellus 34(1), 10–16 (1982). [CrossRef]
  3. C. Nicolis, “Stochastic aspects of climatic transitions—response to a periodic forcing,” Tellus 34(1), 1–9 (1982). [CrossRef]
  4. S. Fauve, F. Heslot, “Stochastic resonance in a bistable system,” Phys. Lett. A 97(1–2), 5–7 (1983). [CrossRef]
  5. S. M. Bezrukov, I. Vodyanoy, “Stochastic resonance in non-dynamical systems without response thresholds,” Nature 385(6614), 319–321 (1997). [CrossRef] [PubMed]
  6. J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, “Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance,” Nature 365(6444), 337–340 (1993). [CrossRef] [PubMed]
  7. A. R. Bulsara, T. C. Elston, C. R. Doering, S. B. Lowen, K. Lindenberg, “Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 3958–3969 (1996). [CrossRef] [PubMed]
  8. R. L. Badzey, P. Mohanty, “Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance,” Nature 437(7061), 995–998 (2005). [CrossRef] [PubMed]
  9. H. B. Chan, C. Stambaugh, “Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator,” Phys. Rev. B 73(22), 224301 (2006). [CrossRef]
  10. D. V. Dylov, J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nature 4, 323–328 (1993).
  11. F. Vaudelle, J. Gazengel, G. Rivoire, X. Godivier, F. Chapeau-Blondeau, “Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering,” J. Opt. Soc. Am. B 15(11), 2674–2680 (1998). [CrossRef]
  12. B. M. Jost, B. E. A. Saleh, “Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator,” Opt. Lett. 21(4), 287–289 (1996). [CrossRef] [PubMed]
  13. S. Weiss, B. Fischer, “Photorefractive saturable absorptive and dispersive optical bistability,” Opt. Commun. 70(6), 515–521 (1989). [CrossRef]
  14. R. Daisy, B. Fischer, “Optical bistability in a nonlinear - linear interface with two-wave mixing,” Opt. Lett. 17(12), 847–849 (1992). [CrossRef] [PubMed]
  15. R. Bartussek, P. Hänggi, P. Jung, “Stochastic resonance in optical bistable systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(5), 3930–3939 (1994). [CrossRef] [PubMed]
  16. L. Zhang, L. Cao, D. J. Wu, “Effect of correlated noises in an optical bistable system,” Phys. Rev. A 77(1), 015801 (2008). [CrossRef]
  17. M. Misono, T. Kohmoto, Y. Fukuda, M. Kunitomo, “Stochastic resonance in an optical bistable system driven by colored noise,” Opt. Commun. 152(4), 255–258 (1998). [CrossRef]
  18. J. E. Ford, J. Ma, Y. Fainman, S. H. Lee, “Multiplex holography in strontium barium niobate with applied field,” J. Opt. Soc. Am. B 9(7), 1183–1192 (1992).
  19. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
  20. S. K. Kwong, M. C. Golomb, A. Yariv, “Oscillation with photorefractive gain,” IEEE J. Quantum Electron. 22(8), 1508–1523 (1986). [CrossRef]
  21. R. Bonifacio, L. A. Lugiato, “Optical bistability and cooperative effects in resonance fluorescence,” Phys. Rev. A 18(3), 1129–1144 (1978). [CrossRef]
  22. P. Yeh, “Theory of unidirectional photorefractive ring oscillators,” J. Opt. Soc. Am. B 2(12), 1924–1928 (1985). [CrossRef]
  23. J. Ma, D. Zeng, H. Chen, “Spatial-temporal cross-correlation analysis: a new measure and a case study in infectious disease informatics,” in IEEE International Conference on Intelligence and Security Informatics (2006). [CrossRef]
  24. V. S. Anishchenko, M. A. Safonova, L. O. Chua, “Stochastic resonance in the nonautonomous Chua's circuit,” J. Circuits Syst. Comput. 3(2), 553–578 (1993). [CrossRef]
  25. B. Xu, Z. P. Jiang, X. Wu, and D. W. Repperger, “Theoretical analysis of image processing using parameter-tuning stochastic resonance technique,” in IEEE American Control Conference ACC'07 (2007), pp. 1747–1752. [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited