We investigate the complexity of the dynamics of two mutually coupled systems with internal delays and vary the coupling delay over 4 orders of magnitude. Karhunen-Loève decomposition of spatiotemporal representations of fiber laser intensity data is performed to examine the eigenvalue spectrum and significant orthogonal modes. We compute the Shannon information from the eigenvalue spectra to quantify the dynamical complexity. A reduction in complexity occurs for short coupling delays while a logarithmic growth is observed as the coupling delay is increased.

The effect of time delay on nonlinear oscillators is an important problem in the study of dynamical systems. The dynamics of an erbium-doped fiber ring laser with an extra loop providing time-delayed feedback is studied experimentally by measuring the intensity of the laser. The delay time for the feedback is varied from approximately 0.3 to approximately 900 times the cavity round-trip time, over four orders of magnitude, by changing the length of fiber in the delay line. Depending on the delay, we observe either regular oscillations or complex dynamics. The size of the fluctuations increases for delays long compared with the round-trip time of the laser cavity. The complexity of the fluctuations is quantified by creating spatiotemporal representations of the time series and performing a Karhunen-Loève decomposition. The complexity increases with increasing delay time. The experiment is extended by mutually coupling two fiber ring lasers together. The delay time for the mutual coupling is varied from approximately 0.2 to approximately 600 times the cavity round-trip time, over four orders of magnitude again. In this case the fluctuations are generally larger than the single laser case. The complexity of the dynamics for the mutually coupled system is less at short delays and larger at long delays when compared to the uncoupled case. The width of the optical spectra of the coupled lasers also narrows.

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Physics students are intrigued by activities in space. To link this natural curiosity with solid problem-solving skills, we developed a spreadsheet simulation for satellites moving through an atmosphere of variable density. The simulation-laboratory has been used in U.S. Air Force Academy (USAFA) introductory physics classes for several semesters. Spreadsheet variants have also been used in a USAFA advanced division space physics class, a high school advanced placement physics class, and in the Center for Integrated Space Weather Modeling graduate summer school course.