As a type of nonlinear system with complexity, mode-locked fiber lasers are known for their complex behaviour. It is a challenging task to understand the fundamental physics behind such complex behaviour, and a unified description for the nonlinear behaviour and the systematic and quantitative analysis of the underlying mechanisms of these lasers have not been developed. Here, we present a complexity science-based theoretical framework for understanding the behaviour of mode-locked fiber lasers by going beyond reductionism. This hierarchically structured framework provides a model with variable dimensionality, resulting in a simple view that can be used to systematically describe complex states. Moreover, research into the attractors' basins reveals the origin of stochasticity, hysteresis and multistability in these systems and presents a new method for quantitative analysis of these nonlinear phenomena. These findings pave the way for dynamics analysis and system designs of mode-locked fiber lasers. We expect that this paradigm will also enable potential applications in diverse research fields related to complex nonlinear phenomena.

Laser high-order harmonic generation in the presence of relatively weak interfering light is investigated. The interfering pulses intersect the primary harmonic-generating laser pulse at the laser focus. The interfering light creates a standing intensity and phase modulation on the field, which disrupts microscopic phase matching and shuts down local high harmonic production. Suppression of the 23rd harmonic (by two orders of magnitude) is observed when a counter-propagating interfering pulse of light is introduced. A sequence of counter-propagating pulses can be used to shut down harmonic production in out-of-phase zones of the generating volume to achieve quasi phase matching. Harmonic emission is enhanced in this case. A new high-power laser system with higher pulse energy has been constructed to further investigate quasi phase matching of high-order harmonics generated in difficult-to-ionize atomic gases (e.g., neon as opposed to argon). The new system can also be used to study harmonic generation in ions. A new counter-propagating beam produces a train of 5 pulses with regulated timing. In preliminary tests, the new system has produced high harmonics up to the 65th order in neon. This should increase with additional adjustments to the laser system. The high-order harmonics have also demonstrated to be useful for polarized reflectometry measurements of optical surfaces in the extreme ultraviolet (EUV) wavelength range.