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

Abstract

We propose a power spectrum analysis method to directly identify the time delay of a chaotic semiconductor laser with optical feedback. By measuring the radio frequency (RF) power spectrum of the chaotic laser and performing an inverse Fourier transform, we can easily unveil all the time delay signatures, regardless of whether the chaotic output is induced by single or multiple feedback. This method successfully retrieves the two time delay signatures from the power spectrum of a semiconductor laser with double-cavity feedback.OCIS codes: 190.3100, 140.5960. doi: 10.3788/COL201210.061901. Optical chaos has attracted considerable attention in recent years due to its great applications in various fields, such as chaos-based communication encryption systems [1] , chaotic lidars [2] , fast random bit sequences generators (RNGs) [3] , and chaotic optical time-domain reflectometry [4] . Through perturbing a semiconductor laser (SL) with optical injection, optical feedback, or optoelectronic feedback, the laser can be driven into broadband chaotic output [5] . Among the mentioned methods, the semiconductor laser with optical feedback (SL-OFB) may be the most common applied chaotic sources due to its unique virtues, such as simple configuration, small size, feasible controllability, and rich chaotic dynamics.Nevertheless, the output of SL-OFB usually has periodic intensity fluctuations. These fluctuations are nearly identically repeated at the photon round-trip time in the external cavity, and are widely called the time delay (TD) signature. The TD signature seriously affects the performance of chaotic system in some applications. For example, the TD signature provides the clue to break the chaos-based secure communication and can deteriorate the randomness of RNGs based on SL-OFB. Some scenarios have been proposed to conceal the TD signature of SL-OFB. Typical scenarios are to generate high-dimensional chaos [6] , to modulate the delay time [7,8] , and to use multiple feedback [9,10] . 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] . In contrast, several techniques for extracting the TD signature also exist; however, usually, their observables are the recorded chaotic time series. Two widely applied techniques are the autocorrelation function (ACF) and the delay mutual information (DMI) [14] . Other techniques include the phase information [15] , the minimal forecast error [16] , the filling factor analysis [17] , the permutation-information theory [18] , and the extrema interval analysis [19] . In 2010, we found that the TD signature could be identified t...