This paper describes the overview of special issues for the research and development on new developments of optical complex systems. The topics of this issue covers methods of analysis to chaos, terahertz waves, simultaneity of laser modes, modulation method and reservoir computing.

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We examined the influence of noise on the pulse oscillations from a gain-switched multimode semiconductor laser using multimode semiconductor laser rate equations that include Langevin noise. We found that in the multimode oscillation, the Langevin noise suppressed the timing jitter and disturbed the temporal synchronization of the pulse oscillations. By numerically estimating the output energy in the THz time-domain spectroscopy, the degree of the temporal synchronization was estimated to be 95.5%.

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We investigated the simultaneity of laser longitudinal modes by measuring the optical beats between modes. This simultaneity usually can’t be observed by an optical spectrum analyzer, since a scan time over several tens of seconds is necessary. Through the photomixer, these optical beats are down-converted to the radio frequency region around 1 GHz. For laser chaos, optical beats are more stable than using a conventional continuous wave laser.

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Reservoir computing (RC), which is a computational paradigm that uses dynamical systems, is a powerful tool for solving highly complex and abstract computational tasks. RC has recently been implemented in a variety of physical systems, including photonic systems. This article introduces its fundamental concepts and recent advances in its optical implementation. As relevant topics, optical implementations of extreme learning machine and deep learning are also discussed.

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Based on the expansion in the capacity of communication networks to connect not only persons but also machine-to-machine systems, we propose an almost periodic frequency arrangement (APFA) constructed with disjoint sets of irrational number groups created using the power root of a prime number. In this paper, we explain the research process of spreading codes using chaotic codes, and the chaotic features of APFA that are derived from the approximate periodic frequency function using a new frame Lyapunov exponent, which estimates the phase difference sensitivity depending on the frame number. The findings of this study indicate that it is possible to connect more than one million channels at a base station using the super-multicarrier APFA systems with the same communication quality characteristics as current systems.

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Entropic chaos degree is a criterion for quantifying chaos by applying information dynamics. Entropic chaos degree of a time series can be directly computed without any dynamical systems. Some authors have recently demonstrated that an improved (extended) entropic chaos degree of a difference equation has nearly the same value as its Lyapunov exponent under typical chaotic conditions. In this paper, chaos associated with the time series obtained from experiments based on semiconductor laser chaos is quantified by incorporating the improved entropic chaos degree.

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Chaos Degree (CD)，proposed by Ohya, behaves like the Lyapunov exponent (LE). CD has a significant advantage because it can be calculated from data without knowing the dynamical systems or equations that produced the data. However, a non-negligible quantitative difference exists between CD and LE. Recently our research has shown that the quantitative differences between CD and LE can be explained by information theory under the assumption that the data are uniformly distributed. We defined a Modified CD that eliminates the difference. This paper explains the estimation of the Lyapunov exponent using Modified CD and its properties.

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Terahertz quantum cascade lasers (THz QCLs) are semiconductor-based promising high output power THz sources with narrow bandwidth and wide operation frequency. Here we report the progress on high-power THz QCLs based on optimization of the active region simulated using the non-equilibrium Green’s function (NEGF) method. The simulations reveal a horizontal parasitic carrier leakage channel via high energy states in the neighboring period. Through tuning these levels by modifying the Al1-xGaxAs barriers and wells, the carrier population at these parasitic high energy levels is reduced and the leakage current significantly is suppressed, resulting in higher output power. Peak power of > 400 mW and average power > 0.4 mW with 3.8 THz emission at 20 K are routinely obtained. Moreover, we developed a compact THz source unit with the QCL device installed inside a 77 K Dewar condenser.

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We estimated the Lyapunov exponent, which indicates chaoticity from a time series. In generalized Boole transformations, an analytic form of the Lyapunov exponent is obtained as a function of one parameter. We showed that if we add Gaussian noise, we cannot estimate the Lyapunov exponent using Rosenstein’s method, which we also apply to a time series of laser chaos.

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Recently, an information- processing method was proposed based on a semiconductor laser with time-delayed optical feedback and optical injection. This method is called reservoir computing, which is a machine learning paradigm based on information processing in the human brain. In this scheme, consistency is a critical characteristic and represents the reproducibility of the responses of a dynamical system when repeatedly driven by similar inputs. The convergence of consistent laser outputs is also important for reservoir computing performance. In this study, we investigate the dependence of the convergence of laser outputs on the initial optical frequency detuning between the two lasers. The convergence is quantitatively evaluated using a conditional Lyapunov exponent. We also demonstrate reservoir computing based on a semi-conductor laser and investigate the relationship between the performances of reservoir computing and convergence of consistent laser output.

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