35B35 Stability
Refine
Language
- English (3)
Keywords
- alternate oscillations (1)
- analysis (1)
- bistability (1)
- damping (1)
- direct modulation (1)
- eye diagram (1)
- large signal response (1)
- modulation bandwidth (1)
- nonlinear Schrödinger equation (1)
- optical modes (1)
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus
(2013)
It is shown that plane wave solutions to the cubic nonlinear Schrödinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend to arbitrary negative powers of the smallness parameter. The perturbation stays small in the same Sobolev norm over such long times. The proof uses a Hamiltonian reduction and transformation and, alternatively, Birkhoff normal forms or modulated Fourier expansions in time.
We explore the concept of passive-feedback lasers for direct signal
modulation at 40 Gbit/s. Based on numerical simulation and bifurcation
analysis, we explain the main mechanisms in these devices which are
crucial for modulation at high speed. The predicted effects are
demonstrated experimentally by means of correspondingly designed
devices. In particular a significant improvement of the modulation
bandwidth at low injection currents can be demonstrated.
We use the traveling wave model for simulating and analyzing
nonlinear dynamics of complex semiconductor ring laser devices.
This modeling allows to consider temporal-spatial distributions
of the coun\-ter-pro\-pa\-ga\-ting slowly varying optical fields
and the carriers, what can be important when studying
non-homogeneous ring cavities, propagation of short pulses or fast switching.
By performing numerical integration of the model
equations we observe several dynamic regimes as well as transitions
between them. The computation of ring cavity modes explains some
peculiarities of these regimes.