Physics and applications of laser diode chaos

Abstract

-An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.The emergence of irregular pulsations and dynamical instabilities from a laser were first noted in the very early stages of the laser development. Pulses whose amplitude "vary in an erratic manner" were reported in the output of the ruby solid-state laser 1 [ Fig. 1 a] and then found in numerical simulations 2 . However the lack of knowledge of what would later be termed "chaos" resulted in these initial observations being either left unexplained or wrongly attributed to noise.The situation changed in the late 1960s with the discovery of sensitivity to initial conditions by Lorenz 3 , later popularized as the "butterfly effect". As illustrated in Fig. 1 (b), numerical simulations of a deterministic model of only three nonlinear equations showed an irregular pulsing with a remarkable feature: the state variables evolve along very different trajectories despite starting from approximately the same initial values [ Fig. 1 b]. The distance δ(t) between nearby trajectories diverges exponentially : δ(t) = δ(0) exp(λt) provided that λ, the effective Lyapunov exponent of the dynamical system, is positive. Consequently such systems are unpredictable in the long term. Plotted in the x-y-z phase space of the state variables, the trajectories converge to an "attractor" which has the geometric property of being bounded in space despite the exponential divergence of nearby trajectories [ Fig. 1 c]. Such attractors are found to have a fractional dimension 4 and are thus termed strange. Aperiodicity, sensitive dependency to initial conditions and strangeness are commonly considered as the main properties for "chaos" The fields of laser physics and chaos theory developed independently until 1975 8 when Haken discovered a striking analogy between the Lorenz equations that model fluid convection and the MaxwellBloch equations modelling light-matter interaction in single-mode lasers. The nonlinear interaction between the wave propagation in the laser cavity (represented by the electric field E) and radiative recombination producing macroscopic polarization (encapsulated in the polarization P and carrier inversion N) yield similar dynamical instabilities to those found in the Lorenz equations. More specifically, in addition to the conventional laser threshold, Haken suggested a second threshold would exist above which "spiking occurs ...

PT-Symmetry-Breaking Chaos in Optomechanics

“…Further increasing the strength of the driving laser, chaotic motion emerges both in the optical and mechanical modes requiring no external feedback or modulation [13][14][15][16]. It is useful for generating random numbers [18] and implementing secret information processing [19][20][21]. However, to apply chaos into the secret communication scheme requiring low-power optical interconnects, the chaos threshold should be reduced dramatically [22,23].…”

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“…In order to find the other steady states, we introduce the phase-amplitude decompositions Y = R 1 exp (iϕ 1 ), U = R 2 exp (iϕ 2 ) into Eqs. (A4)-(A6), we obtain…”

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Noise induced stabilization of chaotic free-running laser diode

“…To generate a chaotic output however, since they typically behave as damped oscillators, an external perturbation such as optical feedback or modulation is required 1 .…”