- Matthew O. Williams and J. Nathan Kutz, “Spatial Mode-Locking of Light Bullets in Planar Waveguide Arrays.” Optics Express, Vol. 17, Issue 20, pp. 18320-18329
- Matthew O. Williams, Colin W. McGrath, and J. Nathan Kutz, “Control of Light Bullets in Planar Waveguide Arrays.” (In Preparation)
Light Bullet Formation
Waveguide arrays are systems of waveguides able to exchange energy through evanescent coupling. In this project, we use a model based of off the Nonlinear Schrodinger Equation (NLS) with the inclusion of gain, loss, and coupling. This model, given in a paper by Kutz and Sandstede, has been successfully used to model mode-locking in a one-dimensional waveguide array. Using this model with planar waveguides, show that light bullets can be produced.
Using a combination of Bragg solitons in the vertical direction and the NLS governing equations in the plane, mode-locked bullets form naturally from noise. In addition to a single bullet, increasing gain causes the single bullet to split into multiple pulses.
Pulse Evolution and Pulse Control
For use in various applications, a method for light-bullet control is necessary. In this project, we use sloped gain profiles to move the bullet along the plane. By pumping the system from multiple electrodes rather than a single electrode, these ramped gain profiles can be generated. The mode-locked pulse naturally seeks out the area of largest gain it has access to.
This allows a great deal of freedom in the routing of pulses. For instance, a paraboloid shaped gain profile may be used to route and collect pulses at a specific point along the waveguide array. A linearly ramped slope, on the other hand, may be used as a photonic wire guiding already formed pulses from point to point. This basic structure may be used to route pulses around kinks or other sharp bends. Lastly, time-dependent gain profiles may be used to control the location of a pulse as a function of time. A cone-shaped profile is used to control the location of the pulse simply by moving the cone. The combination of these different method for pulse control gives a great deal of freedom when it comes to designing systems to control and route the pulse.