The region of transition between solitons and fronts in dissipative systems governed by the complex Ginzburg-
Landau equation is rich with bifurcations. We found that the number of transitions between various types of
localized structures is enormous. For the first time, we have found a sequence of period-doubling bifurcations of
creeping solitons and also a symmetry-breaking instability of creeping solitons. Creeping solitons may involve
many frequencies in their dynamics resulting, in particular, in a variety of zig-zag motions.
By using a reduced model for dissipative optical soliton beams, we show that there are two disjoint
sets of fixed points. These correspond to stationary solitons of the radial complex cubic-quintic Ginzburg -
Landau equation with concave and convex phase profiles, respectively. We confirm these results by numerical
simulations which reveal soliton solutions of two different types: continuously self-focussing and continuously
self-defocusing.
The majority of optical processing devices that are employed in optical transmission systems are based on optical fibres or planar optical waveguides that rely on basic physical phenomena such as coupling, interference or Bragg grating reflection for their functionality. These devices include, for example, a wide variety of single- and multi-mode couplers and splitters, Mach-Zehnder interferometers, wavelength filters, dispersion compensators, arrayed waveguide gratings (AWGs), resonators, etc.
In addition to these devices, there is a further range of devices that rely solely on their geometrical design for their functionality and involve none of the above physical phenomena. Simple examples of these devices include velocity couplers, null couplers, Y-junctions and tapers. Each of these devices relies on the approximately adiabatic propagation of each of its modes along the length of the device. A key feature of such propagation is that each mode essentially conserves both its power and field symmetry.
Recent work has demonstrated that it is possible to switch modes passively with wavelength using the approximately adiabatic transformation of one mode into a mode with dissimilar field symmetry. This transformation is achieved through appropriate geometrical design of the device. For example, it is possible to transform the symmetric fundamental mode into the first odd mode of a planar waveguide by employing a two-mode asymmetric Y-junction. Using this and other mode transformations, it is possible to design compact planar devices that will combine or separate 2 or 3 channels in a coarse wavelength division multiplexing (CWDM) system.
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