Chaos had been a subject of fundamental study for a long time. However, applications of chaos have been opened up after the discoveries of the methods of chaos control and chaos synchronization. Chaos and applications in lasers and laser systems, particularly in semiconductor lasers, are discussed.

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Advances in fabrication technologies have allowed the fabrication of laser cavities with arbitrary 2-D shapes. 2-D cavities have a wide variety of spatial modes, which have different wavefunctions. From the viewpoints of both fundamental physics and practical applications, it is important to selectively excite one desired mode from among many spatial modes. In this paper, we review the methods of selective mode excitation for 2-D microcavity laser diodes based on the control of both cavity shape and electrode contact pattern. We also review two major applications of the selective excitation technique to fundamental research in both quantum and laser chaos. One is the observation of chaos-assisted tunneling, and the other is compact chaotic laser devices that consist of a 2-D microcavity laser and an external feedback cavity. Finally we refer to the potential applications of the selective excitation technique to such functional optical devices as beam-switching devices and polarization-switching devices.

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Natural computing is an unconventional information processing scheme that utilizes various dynamics in nature, including natural substances and nature-inspired computing algorithms. In this article, we introduce maze exploration by natural substances and phenomena and describe our implementation of novel maze exploration by a two-dimensional optical bistable device. In addition, our amoeba-inspired algorithm to solve a combinatorial optimization problem is introduced, and its implementations in a network of nanophotonic quantum dots are described.

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Lyapunov exponent is an indicator which expresses the degree of sensitivity to initial condition of dynamical systems; Lyapunov exponent expresses the level of chaos. Rosenstein et al.1） developed the way to calculate Lyapunov exponents from an experimental non-linear time series which is robust to noise. This method needs the time series to be stationary, but, in many cases, it is difficult to get stationary time series. For example, response of neuron,2） human brain signals3） are said to be chaotic, but chaos levels of these experimental time series are not stationary4）; characteristics of time series changes from time to time depending on conditions. Then, we developed Moving Maximum Lyapunov Exponents (MMLE) based on Rosenstein’s way. MMLE shows the changing Lyapunov exponents of time series, therefore we can know the chaos level at each time and changes of dynamics in time series. We suggest MMLE will be new way of non-linear time series analysis.

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We overview the recent advances of reservoir computing, which is a novel optical computing scheme based on the dynamics of laser systems with time-delayed feedback. Its concept comes from recurrent neural networks, and fast implementation of reservoir computing can be realized using a semiconductor laser with optical feedback over 1 Gbyte/s. Spoken digit recognition and time-series prediction tasks are carried out using reservoir computing.

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In this review, we provide a brief summary of the timing jitter of optical pulse sources. First, we introduce and compare three typical measurement methods of timing jitter: a direct measurement method, a second harmonic cross-correlation method, and a phase noise measurement method. Then the features and the reduction technique of the timing jitter of gain-switched semiconductor lasers are briefly explained. Finally, we propose and demonstrate a simple method for measuring the timing jitter of a distributed feedback (DFB) laser and a Fabry-Perot (FP) laser using a delayed optical feedback system.

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This article addresses a synchronization phenomenon between two uncoupled oscillators subject to a common random external signal. Phase reduction is the most powerful technique for analytically studying the synchronization phenomena of oscillators. After briefly introducing the phase reduction theory, we review the theoretical results of the phase reduction analysis for the synchronization induced by a common random signal and show that it is a universal phenomenon that can occur in a variety of oscillators. Then we review recent experimental observation of common-random-signal induced synchronization in semiconductor lasers.

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The generation of a wide-range THz wave is investigated from a photoconductive antenna excited using a chaotic oscillation multimode semiconductor laser with optical delayed feedback by an external mirror. We compared the properties of the generated THz wave using laser chaos with those using a CW steady state laser which excited photoconductive antenna. Using a laser chaos, a stable THz wave was obtained. For a high sensitive detection, a metal V-grooved waveguide (MVG) is also used. The 1.6 times la

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We numerically estimate the maximum Lyapunov exponent of a semiconductor laser with time-delayed optical feed- back using the transient of generalized synchronization. We used an auxiliary system approach to observe generalized synchronization, where a chaotic input signal from a semiconductor laser is injected into two semiconductor lasers with optical feedback and two injected lasers are identically synchronized. The optical injection signal is removed after synchronization, and the two lasers become desynchronized. The maximum Lyapunov exponent can be evaluated by measuring the exponential growth rate of the differences between the outputs of the two desynchronized lasers. The maximum Lyapunov exponent estimated from this method is consistent with that obtained from linear stability analysis. This method can be applied to estimate the maximum Lyapunov exponent in experimental laser systems.

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We numerically investigated the antiphase dynamics of spatiotemporal chaos in a broad-area semiconductor laser. We resolved the partial intensities from the near-field pattern to observe the phase dynamics. Antiphase periodic oscillation was observed at a low injection current, and spatiotemporal chaos was observed at a high injection current. We calculated the sum of the partial intensities to investigate the phase relationship among partial intensities. Inphase dynamics was observed at the low frequency region including the relaxation oscillation frequency, and antiphase dynamics was observed at a high frequency region. These numerical results qualitatively agree with our experimental results.

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