Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View

Abstract

International audienceA critical issue in optical chaos-based communications is the possibility to identify the parameters of the chaotic emitter and, hence, to break the security. In this paper, we study theoretically the identification of a chaotic emitter that consists of a semiconductor laser with an optical feedback. The identification of a critical security parameter, the external-cavity round-trip time (the time delay in the laser dynamics), is performed using both the auto-correlation function and delayed mutual information methods applied to the chaotic time-series. The influence on the time-delay identification of the experimentally tunable parameters, i.e., the feedback rate, the pumping current, and the time-delay value, is carefully studied. We show that difficult time-delay-identification scenarios strongly depend on the time-scales of the system dynamics as it undergoes a route to chaos, in particular on how close the relaxation oscillation period is from the external-cavity round-trip time

Optical Heterodyne Generation of High-Dimensional and Broadband White Chaos

“…These intrinsic oscillations impose restrictions on random number generation from physical chaos [10] and raise arguments that the extracted numbers are not truly random [14]. Worse yet, the intrinsic oscillations are easily intercepted from time series [9,13] and then pose a risk of cracking to chaos systems [15].A reliable physical chaos should have a wide and flat power spectrum containing various frequency components with homogeneous amplitudes so that system's intrinsic frequencies cannot be determined. Such a chaos having a white spectrum is referred to as white chaos, which has only been founded in some mathematical maps such as the piecewise-linear Markov map [16] and the Logistic map [17].…”

“…Taking the paradigm of a delay system, i.e., an ECL, as an example, the relaxation oscillation of the semiconductor laser dominates the laser intensity chaos and leads to a strong peak projecting from the power spectrum [8]. Additionally, the resonance of the external feedback cavity excites many external-cavity modes (ECMs) in the laser field and leads to a periodically modulated spectrum similar to that of a frequency comb with a spacing equal to the reciprocal of the feedback delay [9,10]. Considerable effort has recently been devoted to expand the power spectrum [8,11] or to depress the external-cavity resonances [12], but it is difficult to completely eliminate the effects of the intrinsic oscillations [3,13].…”

“…These intrinsic oscillations impose restrictions on random number generation from physical chaos [10] and raise arguments that the extracted numbers are not truly random [14]. Worse yet, the intrinsic oscillations are easily intercepted from time series [9,13] and then pose a risk of cracking to chaos systems [15].…”

“…The periodic spectral pattern means that the chaos has correlation at the delay value and its integer multiples [9,10,13]. Because the two chaotic lasers are independent, the autocorrelation function (ACF) of I bt is …”

Method to identify time delay of chaotic semiconductor laser with optical feedback

“…Recently, Wu et al experimentally showed that the TD signatures can be suppressed in two limits when double external cavities are used; one is that the two external cavities have roughly equal lengths, and the other is that one cavity length is approximately half of the other [11] . Rontani et al proposed that TD signature identification would be impossible when the TD is close to the relaxation period of the laser operating with weak feedback [12] . Their theory was demonstrated experimentally in 2010 [13] .…”