Per Jakobsen

Generalized coupled-mode model for the multistripe index-guided laser arrays

We develop a generalized coupled-mode model for multistripe index-guided laser arrays that includes explicitly the influence of carrier-induced antiguiding, gain guiding, and carrier diffusion in the gain stripe. As an illustration of an application of the model, stability criteria for two-element laser arrays are derived that show that the phase-locked solution is intrinsically unstable. We find that the phase-locked solution can be stabilized at a low external injection-locking power at the suitably chosen injection-locking frequency. We have tested our model in the large carrier-diffusion case and still find good qualitative agreement between the coupled-mode model and a full coupled partial differential equation model.

Metastable electronic states and nonlinear response for high-intensity optical pulses

In this paper we propose and demonstrate that the ultrafast nonlinear optical response of atoms may be accurately calculated in terms of metastable states obtained as solutions of the stationary Schrodinger equation including the quasi-static applied electric field. We first develop the approach in the context of an exactly soluble one-dimensional atomic model with delta-function potential, as this allows comparison between the exact ultrafast nonlinear optical response and our approximate approach, both in adiabatic approximation and beyond. These ideas are then applied to a three-dimensional hydrogen-like atom and yield similar excellent agreement between the metastable state approach and simulations of the Schrodinger equation for off-resonant excitation. Finally, our approach yields a model for the ultrafast nonlinear optical response with no free parameters. It can potentially replace the light–matter interaction treatment currently used in optical filamentation, and we present a numerical example of application to femtosecond pulse propagation.

Diode-laser array modes: Discrete and continuous models and their stability

A new class of mode profiles appropriate to large one-dimensional evanescently coupled laser diode arrays can be conveniently approximated by solutions to a Riccatti equation derived from a continuous model of the discrete array. Solutions of the latter model are shown to agree with the continuous solutions in the large-N limit. The continuous model has the advantage that new types of discrete array modes can readily be identified. Stability analyses of the discrete array modes as a function of increasing N confirm that these laser systems are intrinsically unstable in the free-running mode.

Stem cell regulation: Implications when differentiated cells regulate symmetric stem cell division

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells.

Invariant measures and entropy production in wave turbulence

We define, for wave turbulence, probability density functions ρ (pdfs) on a suitably chosen phase space. We derive the Liouville equation for their evolution and identify their long time behaviours corresponding to equipartition and finite flux Kolmogorov–Zakharov (KZ) spectra. We demonstrate that, even in nonisolated systems, entropy production is well defined and plays an important role in the systems evolution and we find its representation in the wave turbulence approximation.

On the convergence of quantum resonant-state expansion

Completeness of the system of Stark resonant states is investigated for a one-dimensional quantum particle with the Dirac-delta potential exposed to an external homogeneous field. It is shown that the resonant series representation of a given wavefunction converges on the negative real axis while the series diverges on the positive axis. Despite the divergent nature of the resonantexpansion, good approximations can be obtained in a compact spatial domain.

Reflectionless Beam Propagation on a Piecewise Linear Complex Domain

We describe a new class of transparent boundary conditions for beam-propagation simulation. The method is based on a transformation that breaks the original real-axis computational domain into a piecewise linear complex-plane contour, with higher-order analogues of Riemann-Cauchy conditions imposed at sharp corners of the contour. The resulting boundary conditions are extremely effective in terminating outgoing waves, and are easy to implement in an arbitrary beam-propagation method.

Localized states in fluid convection and multi-photon lasers

Abstract The Weiss, Tabor, Carnevale (WTC) formalism for expanding a solution about a complex pole is used to determine various finite and infinite localized solutions to the Complex Ginzburg-Landau equation in parameter regimes corresponding to binary convection. The stability of the WTC soliton is analyzed, and the dimension of the null space of the stability operator is connected to a Painleve extension of the WTC soliton. It is argued that this makes the WTC soliton very robust, which we proceed to demonstrate numerically. Numerical spike solutions are found which may be related to the infinite, but localized, WTC solutions. The relationship between the analytic solutions and physical experiments in fluids and lasers is discussed.

Leaky modes of solid dielectric spheres

In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and a solid glass cylinder, by examining those solutions of Maxwells equations (for dispersive as well as non-dispersive media) which admit of a complex-valued oscillation frequency. Under certain circumstances, these leaky modes constitute a complete set into which an arbitrary distribution of the electromagnetic field residing inside a dielectric body can be expanded. We provide completeness proofs, and also present results of numerical calculations that illustrate the relationship between the leaky modes and the resonances of dielectric cavities formed by a simple parallel-plate slab, a glass sphere, and a glass cylinder.In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions of Maxwells equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a completeness proof, and also present results of numerical calculations that illustrate the close relationship between the leaky modes and the resonances of solid dielectric spherical cavities.

Space-time complexity in nonlinear optics

Abstract Traveling wave solutions are found to be the natural nonlinear modes of wide aperture two-level and Raman lasers for frequency detunings to the positive side of the gain peak.