Nonlinear Wave Propagation
Final rept. 1 Jul 2003-30 Jun 2006
COLORADO UNIV AT BOULDER DEPT OF APPLIED MATHEMATICS
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The dynamics and properties of mode locked lasers, such as Titaniumsapphire lasers, that produce ultrashort pulses were modeled and comparisons with experiments carried out. An important characteristic of short pulse lasers is the carrier-envelope phase CEP slip which is the phase offset between carrier and envelope from pulse to pulse in the pulse train. Control of the phase slip allows researchers to stabilize trains of ultrashort pulses, which are very useful in applications. Accurate models of the slip were obtained. New asymptotic and computational methods describing observed phenomena in photonic lattices were developed. Research in quadratic optical materials has led to novel asymptotic systems of equations. In certain parameter regimes stable localized pulse solutions are found and in other cases the equations have unstable and singular solutions. The possibility of such solutions indicates situations when extreme damage to the optical crystal can occur. New numerical schemes to compute localized states to a broad class of nonlinear systems have been developed. From 1 July 2003 to 30 June 2006, 8 papers were published or accepted in refereed journals, 2 book chapters were published and 19 invited lectures were given.
- Lasers and Masers
- Numerical Mathematics
- Fiber Optics and Integrated Optics