Comparison of Calculation Methods for Chaotic Laser in Semiconductor Laser System

Xiangshuai Guo; Shangqi Kuang; Yuling Feng

doi:10.3788/LOP212600

Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 1 >Page 0119001 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 1, 0119001 (2023)

Comparison of Calculation Methods for Chaotic Laser in Semiconductor Laser System

Xiangshuai Guo, Shangqi Kuang^*, and Yuling Feng^**

Author Affiliations

School of Physics, Changchun University of Science and Technology, Changchun 130022, Jilin , China

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DOI: 10.3788/LOP212600 Cite this Article Set citation alerts

Xiangshuai Guo, Shangqi Kuang, Yuling Feng. Comparison of Calculation Methods for Chaotic Laser in Semiconductor Laser System[J]. Laser & Optoelectronics Progress, 2023, 60(1): 0119001 Copy Citation Text

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Abstract

The dynamic equation of the semiconductor laser system is a critical theoretical basis for investigating chaotic lasers, whose calculation accuracy directly determines the simulation reliability of the chaotic laser generated by the system. In this study, different semiconductor laser systems are evaluated and compared based on the two widely used methods of photoelectric field decomposition: amplitude-phase decomposition and real-imaginary part solution. The comparison shows that the computational results of both methods have a minimal difference in the case of low complexity of output light, but a significant difference exists in the case of high complexity. Furthermore, the numerical simulation of the photoelectric field using the real-imaginary part solution has higher precision and is more suitable than the amplitude-phase decomposition for analyzing semiconductor laser systems that generate chaotic lasers with higher complexity.

Keywords

chaos complexity maximum Lyapunov index nonlinear optics semiconductor laser

\frac{d E (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} - \frac{1}{τ_{P}}\} E (t) + κ E (t - τ) c o s θ (t)

，（1）

\frac{d Φ (t)}{d t} = \frac{α}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} - \frac{1}{τ_{P}}\} + κ \frac{E (t - τ)}{E (t)} s i n θ (t)

，（2）

\frac{d N (t)}{d t} = J - \frac{N (t)}{τ_{s}} - \frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} E^{2} (t)

，（3）

θ (t) = ω τ + Φ (t) - Φ (t - τ)

。（4）

\begin{array}{l} \frac{d E_{R} (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε [{E^{2}}_{R} (t) + E_{I}^{2} (t)]} - \frac{1}{τ_{P}}\} \cdot \\ [E_{R} (t) - α E_{I} (t)] + κ E_{R} (t - τ) c o s (ω τ) + \\ κ E_{I} (t - τ) s i n (ω τ) \end{array}

，（5）

\begin{array}{l} \frac{d E_{I} (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε (E_{R}^{2} + E_{I}^{2})} - \frac{1}{τ_{P}}\} \cdot \\ [E_{R} (t) - α E_{I} (t)] + κ E_{R} (t - τ) c o s (ω τ) - \\ κ E_{R} (t - τ) s i n (ω τ) \end{array}

，（6）

\begin{array}{l} \frac{d N (t)}{d t} = J - \frac{N (t)}{τ_{s}} - \\ \frac{G_{N} [N (t) - N_{0}]}{1 + ε [E_{R}^{2} (t) + E_{I}^{2} (t)]} [E_{R}^{2} (t) + E_{I}^{2} (t)] \end{array}

。（7）

\begin{array}{l} \frac{d E (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} - \frac{1}{τ_{P}}\} E (t) + \\ κ E (t - τ) c o s φ (t) + κ_{i n j} A_{s} c o s ϕ (t) \end{array}

，（8）

\begin{array}{l} \frac{d Φ (t)}{d t} = \frac{α}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} - \frac{1}{τ_{P}}\} + \\ κ \frac{E (t - τ)}{E (t)} s i n φ (t) - κ_{i n j} \frac{A_{s}}{E (t)} s i n ϕ (t) \end{array}

，（9）

\frac{d N (t)}{d t} = J - \frac{N (t)}{τ_{s}} - \frac{G_{N} [N (t) - N_{0}]}{1 + ε E^{2} (t)} E^{2} (t)

，（10）

φ (t) = ω τ + Φ (t) - Φ (t - τ)

，（11）

ϕ (t) = ω_{d} τ_{i n j} - Δ ω t + Φ (t) - Φ_{i n j} (t - τ_{i n j})

，（12）

\begin{array}{l} \frac{d E_{R} (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε [E_{R}^{2} (t) + E_{I}^{2} (t)]} - \frac{1}{τ_{P}}\} \cdot \\ [E_{R} (t) - α E_{I} (t)] + κ [E_{R} (t - τ) c o s (ω τ) + E_{I} (t - τ) s i n (ω τ)] + κ_{i n j} A_{s} c o s (Δ ω t - ω_{d} τ_{i n j}) \end{array}

，（13）

\begin{array}{l} \frac{d E_{I} (t)}{d t} = \frac{1}{2} \{\frac{G_{N} [N (t) - N_{0}]}{1 + ε [E_{R}^{2} (t) + E_{I}^{2} (t)]} - \frac{1}{τ_{P}}\} \cdot \\ [E_{I} (t) + α E_{R} (t)] + κ [E_{I} (t - τ) c o s (ω τ) - E_{R} (t - τ) s i n (ω τ)] + κ_{i n j} Α_{S} s i n (Δ ω t - ω_{d} τ_{i n j}) \end{array}

，（14）

\begin{array}{l} \frac{d N (t)}{d t} = J - \frac{N (t)}{τ_{s}} - \\ \frac{G_{N} [N (t) - N_{0}]}{1 + ε [E_{R}^{2} (t) + E_{I}^{2} (t)]} [E_{R}^{2} (t) + E_{I}^{2} (t)] \end{array}

。（15）

λ_{m a x} = \frac{1}{M τ} l n d_{j}

，（16）

d_{j} = \frac{D (t + τ)}{D (t)}

，（17）

D (t) = \sqrt[]{\sum_{k = 0}^{O - 1} [δ_{E}^{2} (t + k h) + δ_{Φ}^{2} (t + k h) + δ_{N}^{2} (t + k h)]}

，（18）

\begin{matrix} D (t + τ) = \\ \sqrt[]{\sum_{k = 0}^{O - 1} [δ_{E}^{2} (t + τ + k h) + δ_{Φ}^{2} (t + τ + k h) + δ_{N}^{2} (t + τ + k h)]} \end{matrix}

，（19）

Xiangshuai Guo, Shangqi Kuang, Yuling Feng. Comparison of Calculation Methods for Chaotic Laser in Semiconductor Laser System[J]. Laser & Optoelectronics Progress, 2023, 60(1): 0119001

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