Study Of Novel Dynamics Of Optical Rogue Waves In Nonlinear Resonant Media

The rogue wave concept was first introduced in 1964 to describe the oceanic surface waves by a distinguished oceanographer named L.Draper.These special waves can be identified as doubly localized wave-packets on a finite background occurring in a very short period of time,with their peak amplitude more than twice the significant wave height.One of the remarkable features of rogue waves is that they seem to appear from nowhere and disappear without a trace.Because of their unpredictability and strong destructivity,rogue waves present a considerable danger,particularly to the cruising liners and the oil platforms.As is now known,rogue waves are ubiquitous in nature.In addition to the deep ocean,rogue waves can also be observed in such physical areas as hydrodynamics,plasma physics,acoustics,optics and photonics,and Bose-Einstein condensates.Despite all this,however,a general understanding of the fundamental origin of rogue waves is still in debate.In this thesis,we commit ourselves to explore several more complicated integrable generalized nonlinear Schr?dinger(NLS)equations which govern the propagation of optical waves in nonlinear resonant media.We wish to find their exact rogue wave solutions using the Darboux transformation method,and discuss the novel rogue wave dynamics involved.To be more specific,after briefly introducing the background,mechanism,and recent progress of rogue waves,we present,in a systematical way,significant new results for those rogue wave dynamics occurring in a three-wave resonant interaction(TWRI)system,in a resonant erbium-doped fiber modelled by the Maxwell-Bloch-NLS equations,as well as in a resonant medium modelled by the sine-Gordon equation.These results can be summarized as blow:First,within the framework of TWRI equations,we present explicitly complementary rogue wave solutions up to second order,to describe the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium.Following a detailed analysis of modulation instability(MI),we numerically confirm that such complementary rogue waves are robust,in spite of the onset of MI activated by quantum noise.We also propose several feasible experimental schemes(e.g.,using a dual-mode optical fiber)to realize such types of rogue waves.Second,we consider the resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber and present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves.The existence and stability of these rogue waves is then confirmed by numerical simulations.Lastly,we wish to present a preliminary study on another resonant optical system modelled by the integrable sine-Gordon equation,whose rational rogue wave solutions are not yet known to date.For this end,we establish the connection between the sine-Gordon equation and the well-studied degenerate TWRI equation,and as a comparison,review the current state of research on non-rational rogue wave solutions.We believe our work mentioned above may spark further theoretical and experimental investigation in future among optics community,and help to contribute to maturing the rogue wave science.