Enhancement of ``logical'' responses by noise in a bistable optical system

Enhancement of “logical” responses by noise in a bistable optical system

Kamal P. Singh and Sudeshna Sinha

Phys. Rev. E 83, 046219 – Published 25 April 2011

Abstract

We verify numerically the phenomenon of logical stochastic resonance in a polarization bistable laser. Namely, we show that when one presents two weak binary inputs to the laser system, the response mirrors a logical or(nor) output. The reliability of the logic operation is dependent on the noise intensity. As one increases the noise, the probability of the output reflecting the desired or(nor) operation increases to nearly unity and then decreases. We also demonstrate that changing the bias morphs the output into another logic operation, and(nand), whose probability displays analogous behavior. Furthermore, we highlight the possibility of processing two logic gates in parallel in our laser system by exploiting two coupled orthogonal polarizations that can be detected simultaneously. This suggests that the computational power of the optical system may be enhanced by this additional potential for parallel processing.

Received 29 September 2010

DOI:https://doi.org/10.1103/PhysRevE.83.046219

Authors & Affiliations

Kamal P. Singh^* and Sudeshna Sinha^†,‡

Indian Institute of Science Education and Research (IISER) Mohali, Transit Campus: MGSIPAP Complex, Sector 26, Chandigarh 160019, India

^*kpsingh@iisermohali.ac.in
^†sudeshna@imsc.res.in
^‡On leave from Institute of Mathematical Sciences, Chennai 600113, India.

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Vol. 83, Iss. 4 — April 2011

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Images

Figure 1
(a) Schematic of LSR: The logic gate is comprised of a noisy nonlinear system driven by an input signal $I_{input} = I_{1} + I_{2}$ . (b) Optical potential $V (θ)$ for the polarization vector. The minima along $θ = 0, π$ ( $x$ axis) and $θ = π / 2, 3 π / 2$ ( $y$ axis) are the stable polarization states. The laser polarization can hop by external optical or magnetic perturbations (see the text for details). (c) Two-parameter potential $V (E_{x}, E_{y})$ for the laser in the inhibition regime. Two minima along the $x$ and $y$ axes are visible. The two potentials in (b) and (c) correspond to two different regimes of polarization bistability.Reuse & Permissions
Figure 2
Intensity $I_{x} (t)$ [see Eq. (4)] for different multiplicative noise intensities (from top to bottom): $0$ , $5 \times 10^{- 7}$ , and $5 \times 10^{- 6}$ . The dashed line shows the desired or (or nor) logic output. The parameters in Eq. (1) are $B = 0.5$ , $V_{0} = 10^{5}, M_{0} = 10^{5}$ , $θ_{polarizer} = - π / 2$ , and $I_{\max} = 1.0$ and the additive noise amplitude is $0$ . Specifically we take the input level to be $0.5$ for logic input 1 and $- 0.5$ for logic input 0.Reuse & Permissions
Figure 3
From top to bottom the panels show logic inputs $I_{1} + I_{2}$ , intensity mirroring the or(nor) logic response, and intensity mirroring the and(nand) logic response. The bias $B$ is $0.5$ for the middle panel and $- 0.5$ for the bottom panel. The additive noise amplitude is $5 \times 10^{- 7}$ and the multiplicative noise amplitude is $5 \times 10^{- 7}$ . The parameters in Eq. (1) are $V_{0} = 10^{5}, M_{0} = 10^{5}$ , $θ_{polarizer} = - π / 2$ , and $I_{\max} = 1.0$ and we take the input level to be $0.5$ for logic input 1 and $- 0.5$ for logic input 0.Reuse & Permissions
Figure 4
Probability of obtaining the correct logic response $P (logic)$ for logic functionsor(nor) (top panel) and(nand) (bottom panel). The $x$ axis displays the multiplicative noise levels (in units of $10^{- 6}$ ) and the $y$ axis displays the bias $B$ . Specifically we take the input level to be $0.5$ for logic input 1 and $- 0.5$ for logic input 0. The logic output is $1$ if $x > 0.5;$ otherwise it is $0$ (or vice versa for the complementary logic operation). Here the additive noise amplitude is $0$ . Note that very similar results are obtained for small (nonzero) additive noise amplitudes as well.Reuse & Permissions
Figure 5
Time series showing two parallel complementary gates for (a) a three-level input signal $I_{1} + I_{2}$ ; (b)or gates detected on $I_{x}$ and (c) nor gates detected on $I_{y}$ , both for bias $B = 0.5$ and optical noise amplitude $4.1 \times 10^{- 5}$ ; and (d)and gates on $I_{x}$ and (e) nand gates on $I_{y}$ , both in response to input signals in (a) for $B = - 0.5$ and the same noise amplitude. The panels display intensity vs time. The noise intensity is taken at the optimum point.Reuse & Permissions
Figure 6
Probability of obtaining a successful gate operation (see the text for definition) vs optical noise amplitude. nor gate, solid circles; nand gate, open circle. Inset: Two complementary bistability cycles when the laser outputs $I_{x}$ and $I_{y}$ are detected simultaneously.Reuse & Permissions

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