Abstract: A method for providing fast and efficient solution of partial differential equations to calculate the permittivity modes of an arbitrarily complex scatterer geometry using a modal approach, comprising the steps of defining the background geometry and the scatterer's geometry; embedding each scatterer in a simpler geometry; calculating the base transverse modes for each embedding geometry; for each scatterer, calculating the longitudinal modes; calculating the overlap matrix; solving and the resulting eigenvalue equation, using the base transverse modes that have been calculated for each embedding geometry and the longitudinal modes that have been calculated for the each scatterer; if there is more than one scatterer, hybridizing the modes of each pair of scatterers, otherwise, solving the resulting eigenvalue equation for the complete structure; projecting the source is on target modes; substituting the result is in the final equation.

Abstract: A method for obtaining transient Bragg gratings in optical waveguides and several different applications of the transient Bragg gratings obtained using this method are presented. The basic mechanisms for obtaining the transient gratings in the waveguides are refractive index change due to Kerr nonlinearity, free carrier generation, and gratings formed by linear or non-linear absorption of thermal energy. The exemplary applications include an ultra-fast fiber laser source at any central wavelength, a fast spectral switch/modulator, transient pulse stretchers based on transient chirped gratings, Q-switching based on transient gratings, and time reversal of ultra-short pulses and low power sub-nanosecond pulse generations.

Abstract: A method for obtaining transient Bragg gratings in optical waveguides and several different applications of the transient Bragg gratings obtained using this method are presented. The basic mechanisms for obtaining the transient gratings in the waveguides are refractive index change due to Kerr nonlinearity, free carrier generation, and gratings formed by linear or non-linear absorption of thermal energy. The exemplary applications include an ultra-fast fiber laser source at any central wavelength, a fast spectral switch/modulator, transient pulse stretchers based on transient chirped gratings, Q-switching based on transient gratings, and time reversal of ultra-short pulses and low power sub-nanosecond pulse generations.