Chaotic Time-Delay Signature Suppression and Entropy Growth Enhancement Using Frequency-Band Extractor

Abstract

By frequency-band extracting, we experimentally and theoretically investigate time-delay signature (TDS) suppression and entropy growth enhancement of a chaotic optical-feedback semiconductor laser under different injection currents and feedback strengths. The TDS and entropy growth are quantified by the peak value of autocorrelation function and the difference of permutation entropy at the feedback delay time. At the optimal extracting bandwidth, the measured TDS is suppressed up to 96% compared to the original chaos, and the entropy growth is higher than the noise-dominated threshold, indicating that the dynamical process is noisy. The effects of extracting bandwidth and radio frequencies on the TDS and entropy growth are also clarified experimentally and theoretically. The experimental results are in good agreements with the theoretical results. The skewness of the laser intensity distribution is effectively improved to 0.001 with the optimal extracting bandwidth. This technique provides a promising tool to extract randomness and prepare desired entropy sources for chaotic secure communication and random number generation.

Keywords: chaos; entropy growth; frequency-band extractor; semiconductor lasers; time delay signature.

Figure 1

Experimental setup: TC, temperature controller; CS, current source; DFB-LD, distributed feedback laser diode; PC, polarization controller; OC, optical coupler; VOA, variable optical attenuator; FC, 50:50 fiber coupler; ISO, isolator; PD, photodetector; M, mixer; SG, signal generator; Filter, low-pass filter; SA, spectrum analyzer; OSC, oscilloscope.

Figure 2

(a) Measured-origin chaotic laser when $J=1.6J_{th}$, $\eta =18\%$ power spectrum; (b) extracted power spectrum of chaotic laser with 3 GHz effective bandwidth.

Figure 3

(a) ACF of origin chaotic laser and extracted chaotic laser. (b) Entropy growth $G_d$ of origin chaotic laser and extracted chaotic laser with embedding dimension $d=4$.

Figure 4

(a1–c1) Theoretical and (a2–c2) experimental results for $G_d$ and $C_p$ of extracted chaotic laser as a function of the injection current for 44 ns${}^{-1}$ ($35\%$), 22 ns${}^{-1}$ ($18\%$), 16 $n{s}^{-1}$ ($5.6\%$). The embedding dimension d is chosen as 4.

Figure 5

(a1–c1) Theoretical and (a2–c2) experimental results for $G_d$ and $C_p$ of extracted chaotic laser as a function of the feedback strength for $1.6J_{th}$, $1.9J_{th}$, $2.2J_{th}$. The embedding dimension d is chosen as 4.

Figure 6

Theoretical and experimental TDS results of the extracted chaotic laser versus RF frequency for (a) 580 MHz, (b) 1 GHz, and (c) 3 GHz extracting bandwidth.

Figure 7

(a) Theoretical and (b) experimental results of the minima $C_p^{min}$ in the TDS suppression and the entropy growth $G_d$ of extracted chaotic laser as a function of LPF bandwidth.

Figure 8

Experimental results of the time series, intensity distribution and its skewness of the chaotic laser (a) before and (b) after 3 GHz frequency-band extraction. (c) Measured skewness of intensity distribution versus feedback strength at the injection current $J=1.6J_{th}$.