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Taking the broadband chaotic output from a weak-resonant-cavity Fabry-Perot laser diode (WRC-FPLD) under filtered feedback as a chaotic entropy source, we propose and experimentally demonstrate a scheme for generating fast physical random bits (PRBs) at a rate up to 240 Gbits/s. First, we investigate the dependence of the dynamical properties of the filtered feedback WRC-FPLD on the system parameters, and determine the optimized parameter region for generating wavelength-tunable and broadband chaotic signals. Second, a broadband chaotic signal with a bandwidth beyond 20 GHz output from the WRC-FPLD is sampled and transferred to a digital bit sequence by an 8-bit analog-to-digital converter at a rate of 40 GS/s. Finally, by utilizing multi-bit post-processing method, PRBs is generated at a rate up to 240 Gbits/s, which can pass all the 15 NIST statistics tests and meet the strict criteria of the statistical bias and the serial correlation coefficient.

We investigate the solution structure and stability of a semiconductor laser receiving time-delayed and frequency-filtered optical feedback from two external filters. This system is referred to as the 2FOF laser, and it has been used as pump laser in optical telecommunication and as light source in sensor applications. The underlying idea is that the two filter loops provide a means of stabilizing and controling the laser output. The mathematical model takes the form of delay differential equations for the (real-valued) population inversion of the laser active medium and for the (complex-valued) electric fields of the laser cavity and of the two filters. There are two time delays, which are the travel times of the light from the laser to each of the filters and back. Our analysis of the 2FOF laser focuses on the basic solutions, known as continuous waves or external filtered modes (EFMs), which correspond to laser output with steady amplitude and frequency. Specifically, we consider the EFM-surface in the $(\omega_s,\,N_s,\,dC_p)$-space of steady frequency $\omega_s$, the corresponding steady population inversion $N_s$, and the feedback phase difference $dC_p$. This surface emerges as the natural object for the study of the 2FOF laser because it conveniently catalogues information about available frequency ranges of the EFMs. We identify five transitions, through four different singularities and a cubic tangency, which change the type of the EFM-surface locally and determine the EFM-surface bifurcation diagram in the $(\Delta_1,\,\Delta_2)$-plane. In this way, we classify the possible types of the EFM-surface, which consist of a combination of bands (covering the entire $dC_p$-range) and islands (covering only a finite range of $dC_p$). We also investigate the stability of the EFMs, where we focus on saddle-node and Hopf bifurcation curves that bound regions of stable EFMs on the EFM-surface. It is shown how these stability regions evolve when parameters are changed along a chosen path in the $(\Delta_1,\,\Delta_2)$-plane. From a viewpoint of practical interests, we find various bands and islands of stability on the EFM-surface that may be accessible experimentally. Beyond their relevance for the 2FOF laser system, the results presented here also showcase how advanced tools from bifurcation theory and singularity theory can be employed to uncover and represent the complex solution structure of a delay differential equation model that depends on a considerable number of input parameters, including two time delays.

We present an analysis of a semiconductor laser subject to filtered optical feedback from two filtering elements (2FOF). The motivation for this study comes from applications where two filters are used to control and stabilise the laser output. Compared to a laser with a single filtered optical feedback loop, the introduction of the second filter significantly influences the structure of the basic continuous-wave solutions, which are also known as external filtered modes (EFMs). We compute and represent the EFMs of the underlying delay differential equation model as surfaces in the space of frequency ω s and inversion level N s of the laser, and feedback phase difference dC p . The quantity dC p is a key parameter since it is associated with interference between the two filter fields and, hence, controls the effective feedback strength. We further show how the EFM surface in ( ω s , dC p , N s )-space changes upon variation of other filter parameters, in particular, the two delay times. Overall, the investigation of the EFM-surface provides a geometric approach to the multi-parameter analysis of the 2FOF laser, which allows for comprehensive insight into the solution structure and dynamics of the system.