Time-delay signature concealment of chaos and ultrafast decision making in mutually coupled semiconductor lasers with a phase-modulated Sagnac loop

Yuanting Ma; Shuiying Xiang; Shuiying Xiang; Xingxing Guo; Ziwei Song; Aijun Wen; Yue Hao

doi:10.1364/OE.384378

Optics Express
Vol. 28,
Issue 2,
pp. 1665-1678
(2020)
•https://doi.org/10.1364/OE.384378

Time-delay signature concealment of chaos and ultrafast decision making in mutually coupled semiconductor lasers with a phase-modulated Sagnac loop

Yuanting Ma, Shuiying Xiang, Xingxing Guo, Ziwei Song, Aijun Wen, and Yue Hao

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Yuanting Ma, Shuiying Xiang, Xingxing Guo, Ziwei Song, Aijun Wen, and Yue Hao, "Time-delay signature concealment of chaos and ultrafast decision making in mutually coupled semiconductor lasers with a phase-modulated Sagnac loop," Opt. Express 28, 1665-1678 (2020)

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Table of Contents Category
- Lasers, Optical Amplifiers, and Laser Optics
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About this Article
History
- Original Manuscript: November 26, 2019
- Revised Manuscript: December 25, 2019
- Manuscript Accepted: December 26, 2019
- Published: January 10, 2020

Abstract

We propose and experimentally demonstrate the generation of dual-channels chaos with time delay signature (TDS) concealment by introducing a phase-modulated Sagnac loop in mutually coupled semiconductor lasers (MCSL). Furthermore, we demonstrate the utilization of the dual-channels chaos to solve multi-armed bandit (MAB) problem in reinforcement learning. The experimental results agree well with the numerical simulations. For the purpose of comparison, the MCSL with a conventional Sagnac loop is also considered. It is found that the TDS of dual-channels chaotic signals can be better concealed in our proposed system. Besides, the proposed system allows for a better decision making performance in MAB problem. Moreover, compared with the one-channel chaotic system, the proposed dual-channels chaotic system achieves ultrafast decision making in parallel, and thus, is highly valuable for further improving the security of communication systems and the performance of photonic intelligence.

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Fig. 1. Experimental setup of a dual-channels chaotic system with a phase-modulated Sagnac loop. DFB1, DFB2: distributed feedback semiconductor lasers; FC: fiber coupler; VOA: variable optical attenuator;

${t_1},{t_2}$

: fiber jumper with different length; PM: electro-optic phase modulator; PRBS generator: pseudo-random binary sequence generator; PC: polarization controller, LDC: laser diode controller, OI: optical isolator, OPM: optical power meter, OSA: optical spectrum analyzer; PD: photodiode; OSC: oscilloscope. Optical spectra are presented in the insets.

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Fig. 2. The chaotic time series (column a), the corresponding ACFs (column b) and the power spectra (column c) for two lasers. The row 1 and row 2 are the results of DFB1 and DFB2 in the CSL-MC system respectively. The row 3 and row 4 are the results of DFB1 and DFB2 in the PMSL-MC system respectively.

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Fig. 3. (a)

${\rho _1}$

, (b)

${\rho _2}$

in the CSL-MC system (

${\rho _{\textrm{CSL - MC1}}}$

${\rho _{\textrm{CSL - MC2}}}$

) and the PMSL-MC system (

${\rho _{\textrm{PMSL - MC1}}}$

${\rho _{\textrm{PMSL - MC2}}}$

), as a function of

${k_r}$

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Fig. 4. Two dimensional maps of

${\rho _m}$

in the parameter space of

${k_r}$

and

$\Delta {f_{ 1 2}}$

for DFB1 (left column) and DFB2 (right column). The row 1 is for the CSL-MC system and the row 2 is for the PMSL-MC system.

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Fig. 5. Two dimensional maps of

${\rho _m}$

in the parameter space of

${k_r}$

and

${k_{PM}}$

for (a) DFB1 and (b) DFB2.

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Fig. 6. Two dimensional maps of

${\rho _m}$

in the parameter space of

${\tau _1}$

and

${\tau _2}$

for (a) DFB1 and (b) DFB2.

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Fig. 7. Architecture for reinforcement learning based on dual-channels laser chaos.

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Fig. 8. (a) The CDR as a function of cycle for the CSL-MC system and for the PMSL-MC system. (b) The CC as a function of

${k_r}$

for the CSL-MC system and the PMSL-MC system.

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Fig. 9. Threshold value as a function of cycle for the 1-st, 2500-th, and 5000-th decision making process for (a)

$T{V_1}$

(b)

$T{V_{2,0}}$

(c)

$T{V_{2,1}}$

in the PMSL-MC system.

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Fig. 10. (a) The CDR as a function of the number of cycles for dual-channels and one-channel in the PMSL-MC system. (b) The CC as a function of

${k_r}$

for dual-channels and one-channel in the PMSL-MC system.

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Fig. 11. The CDR as a function of the number of cycles for the CSL-MC system and the PMSL-MC system in a changing environment.

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Fig. 12. Experimental (a)

${\rho _1}$

, (b)

${\rho _2}$

in the CSL-MC system (

${\rho _{\textrm{CSL - MC1}}}$

${\rho _{\textrm{CSL - MC2}}}$

) and the PMSL-MC system (

${\rho _{\textrm{PMSL - MC1}}}$

${\rho _{\textrm{PMSL - MC2}}}$

), as a function of

${P_{inj}}$

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Fig. 13. Experimental (a) The CDR as a function of cycle for the CSL-MC system and for the PMSL-MC system with

${P_{inj}} = 98.15\mu \textrm{W}$

. Experimental (b) The CC as a function of

${P_{inj}}$

for the CSL-MC system and the PMSL-MC system.

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Equations (8)

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\begin{aligned} \frac{d E_{1} (t)}{d t} = & \frac{1 + i a}{2} [\frac{g [N_{t} - N_{0}]}{1 + ε | E_{1} (t) |^{2}} - \frac{1}{τ_{p}}] E_{1} (t) \\ + k_{1} [\frac{1}{2} E_{1} (t - τ_{1}) \exp (- i ω_{1} τ_{1} + i ϕ_{P M}) + \frac{1}{2} E_{1} (t - τ_{1}) \exp (- i ω_{1} τ_{1})] \\ + k_{2} [\frac{1}{2} E_{2} (t - τ_{21}) \exp (- i ω_{1} τ_{21} + i ϕ_{P M}) + \frac{1}{2} E_{2} (t - τ_{21}) \exp (- i ω_{1} τ_{21})] \end{aligned}

\begin{aligned} \frac{d E_{2} (t)}{d t} = & \frac{1 + i a}{2} [\frac{g [N_{t} - N_{0}]}{1 + ε | E_{2} (t) |^{2}} - \frac{1}{τ_{p}}] E_{2} (t) \\ + k_{2} [\frac{1}{2} E_{2} (t - τ_{2}) \exp (- i ω_{2} τ_{2} + i ϕ_{P M}) + \frac{1}{2} E_{2} (t - τ_{2}) \exp (- i ω_{2} τ_{2})] \\ + k_{1} [\frac{1}{2} E_{1} (t - τ_{12}) \exp (- i ω_{2} τ_{12} + i ϕ_{P M}) + \frac{1}{2} E_{1} (t - τ_{12}) \exp (- i ω_{2} τ_{12})] \end{aligned}

\frac{d N_{1, 2} (t)}{d t} = \frac{I_{1, 2}}{q} - \frac{N_{1, 2} (t)}{τ_{n}} - \frac{g [N_{t} - N_{0}]}{1 + ε | E_{1, 2} (t) |^{2}} | E_{1, 2} (t) |^{2}

C_{m} (Δ t) = \frac{< [I_{m} (t + Δ t) - < I_{m} (t + Δ t) >] [I_{m} (t) - < I_{m} (t) >] >}{\sqrt{< {[I_{m} (t + Δ t) - < I_{m} (t + Δ t) >]}^{2} >< {[I_{m} (t) - < I_{m} (t) >]}^{2} >}}

T (t) = {\begin{cases} k L & (⌊ T V (t) ⌋ > L) \\ k \times ⌊ T V (t) ⌋ & (| ⌊ T V (t) ⌋ | \leq L) \\ - k L & (⌊ T V (t) ⌋ < L) \end{cases}

\begin{aligned} T V_{1} (t + 1) & = + Δ_{1} - Ω_{1} + a T V_{1} (t) ( if D_{1} = 0) \\ T V_{1} (t + 1) & = - Δ_{1} + Ω_{1} + a T V_{1} (t) ( if D_{1} = 1) \\ T V_{2, 0} (t + 1) & = + Δ_{2, 0} - Ω_{2, 0} + a T V_{2, 0} (t) (if D_{1} = 0, D_{2} = 0) \\ T V_{2, 0} (t + 1) & = - Δ_{2, 0} + Ω_{2, 0} + a T V_{2, 0} (t) (if D_{1} = 0, D_{2} = 1) \\ T V_{2, 1} (t + 1) & = + Δ_{2, 1} - Ω_{2, 1} + a T V_{2, 1} (t) (if D_{1} = 1, D_{2} = 0) \\ T V_{2, 1} (t + 1) & = - Δ_{2, 1} + Ω_{2, 1} + a T V_{2, 1} (t) (if D_{1} = 1, D_{2} = 1) \end{aligned}

\begin{array}{cc} Ω_{1} = {\hat{P}}_{D_{1} = 0} + {\hat{P}}_{D_{1} = 1} & Δ_{1} = 2 - ({\hat{P}}_{D_{1} = 0} + {\hat{P}}_{D_{1} = 1}) \\ Ω_{2, 0} = {\hat{P}}_{D_{1} = 0, D_{2} = 0} + {\hat{P}}_{D_{1} = 0, D_{2} = 1} & Δ_{2, 0} = 2 - ({\hat{P}}_{D_{1} = 0, D_{2} = 0} + {\hat{P}}_{D_{1} = 0, D_{2} = 1}) \\ Ω_{2, 1} = {\hat{P}}_{D_{1} = 1, D_{2} = 0} + {\hat{P}}_{D_{1} = 1, D_{2} = 1} & Δ_{2, 1} = 2 - ({\hat{P}}_{D_{1} = 1, D_{2} = 0} + {\hat{P}}_{D_{1} = 1, D_{2} = 1}) \end{array}

{\hat{P}}_{D_{1} = k} = \frac{N_{D_{1} = k, h i t}}{N_{D_{1} = k, t o t a l}} {\hat{P}}_{D_{1} = k, D_{2} = k} = \frac{N_{D_{1} = k, D_{2} = k, h i t}}{N_{D_{1} = k, D_{2} = k, t o t a l}} (k = 0,1)

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Equations (8)

Optics Express