Ikeda-like chaos on a dynamically filtered supercontinuum light source

We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

Figure 1

Schematic representation of the visible-wavelength nonlinear delayed-feedback loop oscillator. SC: collimated supercontinuum light source; IR: infrared blocking filter; AOTF: acousto-optic tunable filter; BWP: birefringent quartz wave plate; PBS: polarization beam splitter; MP: mirror prism extracting the zero-order AOTF output, for further display of rainbows through mirrors and diffraction gratings; OEC: optoelectronic circuit performing photodetection, filtering, delaying, amplification, and offset setting; VCO: voltage-controlled oscillator; RF: radio-frequency driver.

Figure 2

Part of a chaotic signal. The two right plots are calculated from a long chaotic time series [top: autocorrelation function revealing the echo in the chaotic time series at approximately $(\tau +{\tau }_D)$; bottom: amplitude of the Fourier spectrum, showing the nearly flat filling of the Fourier components within the oscillator bandwidth].

Figure 3

Plot of the filling factor $\rho$ as a function of the time lag ${\tau }_s$, following the definition of Eq. (2). Note that the filling factor sharply drops to a value very close to zero when the lag time fulfills the condition ${\tau }_s={\tau }_D=0.513$ s. In that case, the dynamics of the system is projected onto the nonlinear transfer function in the plane $x_{{\tau }_s}-x$. On the other hand, when ${\tau }_s$ is significantly different from the time delay ${\tau }_D$, the dynamics of the system in the plane $x_{{\tau }_s}-x$ is chaotically distributed. This plot provides evidence about the fact that the dynamics displayed in Fig. 2 is a chaotic behavior resulting from the nonlinear Ikeda feedback loop.