Chirped optical pulses are used in time stretch analog-to-digital converters to stretch high speed electric signals so that they can be measured with conventional detectors. Here an extension of the time domain beam propagation method is presented, which is applicable to strongly linearly chirped signals propagating along a specified direction.
By examining the propagation of chirped pulses in homogeneous waveguides, using Fourier transforms and the method of stationary phase, we derive a phase factor which captures the rapidly oscillating part of the chirped pulse. We then solve for the slowly varying envelope with respect to this phase factor in a time window moving with the pulse. The new method is implemented using finite elements in the time direction and transverse space directions, and a time-stepping scheme in the longitudinal direction. Stability of the method is shown, and numerical results are presented for the cases of a z-invariant metallic waveguide with good accuracy, and simulation of a dielectric Mach-Zehnder geometry with promising results.
Authors and Affiliations
- S. Jakobsson, Fraunhofer-Chalmers Centre
- E. Solberg, Fraunhofer-Chalmers Centre
- F. Edelvik, Fraunhofer-Chalmers Centre