Approximation method for fast calculation of transmission in multi-mode waveguides.

Freeform dielectric waveguides connect optical chips made of different materials in fully integrated photonic devices. With a spatial extent in the order of 100 µm, they constitute a computational challenge and make Maxwell full-wave solvers unhandy for the accelerated design. Therefore, it is of utmost importance to have tools that permit the fast prediction of waveguide loss to enable the rapid optimization of waveguide trajectories. Previously developed methods relied on the assumption that only a single mode propagates in the waveguide. However, the propagation of higher-order modes is not just unavoidable due to the geometry of the waveguides, but also, sometimes, beneficial as it increases the number of channels to transmit information. In this contribution, we present an approximate method for the fast calculation of transmission that accommodates the presence of higher-order waveguide modes, and assess its liability by describing light propagation through selected devices.

Transformation-optics modeling of 3D-printed freeform waveguides.

Multi-photon lithography allows us to complement planar photonic integrated circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However, design and optimization of such freeform waveguides using time-domain Maxwell's equations solvers often requires comparatively large computational volumes, within which the structure of interest only occupies a small fraction, thus leading to poor computational efficiency. In this paper, we present a solver-independent transformation-optics-(TO-) based technique that allows to greatly reduce the computational effort related to modeling of 3D freeform waveguides. The concept relies on transforming freeform waveguides with curved trajectories into equivalent waveguide structures with modified material properties but geometrically straight trajectories, that can be efficiently fit into rather small cuboid-shaped computational volumes. We demonstrate the viability of the technique and benchmark its performance using a series of different freeform waveguides, achieving a reduction of the simulation time by a factor of 3-6 with a significant potential for further improvement. We also fabricate and experimentally test the simulated waveguides by 3D-printing on a silicon photonic chip, and we find good agreement between the simulated and the measured transmission at λ = 1550 nm.

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence.

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor-Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Diffusion driven optofluidic dye lasers encapsulated into polymer chips.

Lab-on-a-chip systems made of polymers are promising for the integration of active optical elements, enabling e.g. on-chip excitation of fluorescent markers or spectroscopy. In this work we present diffusion operation of tunable optofluidic dye lasers in a polymer foil. We demonstrate that these first order distributed feedback lasers can be operated for more than 90 min at a pulse repetition rate of 2 Hz without fluidic pumping. Ultra-high output pulse energies of more than 10 µJ and laser thresholds of 2 µJ are achieved for resonator lengths of 3 mm. By introducing comparatively large on-chip dye solution reservoirs, the required exchange of dye molecules is accomplished solely by diffusion. Polymer chips the size of a microscope cover slip (18 × 18 mm(2)) were fabricated in batches on a wafer using a commercially available polymer (TOPAS(®) Cyclic Olefin Copolymer). Thermal imprinting of micro- and nanoscale structures into 100 µm foils simultaneously defines photonic resonators, liquid-core waveguides, and fluidic reservoirs. Subsequently, the fluidic structures are sealed with another 220 µm foil by thermal bonding. Tunability of laser output wavelengths over a spectral range of 24 nm on a single chip is accomplished by varying the laser grating period in steps of 2 nm. Low-cost manufacturing suitable for mass production, wide laser tunability, ultra-high output pulse energies, and long operation times without external fluidic pumping make these on-chip lasers suitable for a wide range of lab-on-a-chip applications, e.g. on-chip spectroscopy, biosensing, excitation of fluorescent markers, or surface enhanced Raman spectroscopy (SERS).

Primary charge effects on prolate spheroids with moderate aspect ratios.

In this article, we investigate the behavior of charged spheroidal colloids with moderate aspect ratios in linear flow fields. We use direct numerical simulation with body-fitted grids for the solution of the Stokes-Poisson-Nernst-Planck system to include all non-linear effects. Therefore, we propose an efficient semi-implicit time discretization based on a splitting of the Stokes equation. We will study the effects of the electric double layer on the forces, torques and on the motion of spheroidal particles. For low Reynolds numbers, we find approximating linear expressions between the ambient fluid flow and the force and torque on the particle. The description of this linear behavior is based on the resistance functions, whose dependencies on the Debye length and the zeta potential are investigated. It is recovered that the resistance functions obey a quadratic dependence on the zeta potential in the small zeta potential regime. For low values of the zeta potential, approximate formulas for the resistance functions are given. The approximation properties are carefully studied by comparing the approximate results with direct numerical simulations. For the case of a shear flow, the approximate formulas can be used to avoid time-consuming direct numerical simulations.

Investigation of the nonlinear effects during the sedimentation process of a charged colloidal particle by direct numerical simulation.

In this article we study the settling process of a colloidal particle under the influence of a gravitational or centrifugal field in an unbounded electrolyte solution. Since particles in aqueous solutions normally carry a non-zero surface charge, a microscopic electric field develops which alters the sedimentation process compared to an uncharged particle. This process can be mathematically modelled via the Stokes-Poisson-Nernst-Planck system, a system of coupled partial differential equations that have to be solved in an exterior domain. After a dimensional analysis we investigate the influence of the various characteristic dimensionless numbers on the sedimentation velocity. Thereby the linear-response (weak-field) approximation that underpins almost all existing theoretical work on classical electrokinetic phenomena is relaxed, such that no additional assumption on the thickness of the double layer as well as on its displacement is needed. We show that there exists a strong influence of the fluid Reynolds number and the ionic strength on the sedimentation velocity. Further we have developed an asymptotic expansion to describe the limit of small values of the surface potential of a single particle. This expansion incorporates all nonlinear effects and extends the well-known results of Booth (1954) [1] and Ohshima et al. (1984) [2] to higher fluid Reynolds numbers.