Biomedical subjects

Niels Asger Mortensen

Publications and source records attributed to Niels Asger Mortensen.

12 recordsLinked to original sources

PubMed2006

Calculation of optical-waveguide grating characteristics using Green's functions and Dyson's equation.

We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation profile of the grating. Numerically, the method scales as O(N) where N is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast gratings and 1D photonic crystals.

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PubMed2006

Universal dynamics in the onset of a Hagen-Poiseuille flow.

The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of an arbitrary cross section. We find that the steady state is reached after a characteristic time scale tau=(A/P)2(1/nu), where A and P are the cross-sectional area and perimeter, respectively, and nu is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate Q for t<<tau we find a universal linear dependence, Q(t)=Q(infinity) (alpha/C)(t/tau), where Q(infinity) is the asymptotic steady-state flow rate, alpha is the geometrical correction factor, and C=P2/A is the compactness parameter. For the long-time dynamics Q(t) approaches Q(infinity) exponentially on the time scale , but with a weakly geometry-dependent prefactor of order unity, determined by the lowest eigenvalue of the Helmholz equation.

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PubMed2006

Universality in edge-source diffusion dynamics.

We show that in edge-source diffusion dynamics the integrated concentration N(t) has a universal dependence with a characteristic time scale tau=(A/P)2pi/(4D), where D is the diffusion constant while A and P are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence N(t)=N0(sqrt)t/tau while in the long-time dynamics N(t) saturates exponentially at N0. The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.

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PubMed2005

Semianalytical approach to short-wavelength dispersion and modal properties of photonic crystal fibers.

Photonic crystal fibers made from arbitrary base materials are considered, and a unified semianalytical approach for the dispersion and modal properties is derived that applies to the short-wavelength regime. In particular, the dispersion and the effective index are calculated and compared with fully vectorial plane-wave simulations, and excellent agreement is found. Asymptotic results for the mode-field diameter and the V parameter are also calculated, and from the latter it is predicted that the fibers are endlessly single mode for a normalized airhole diameter smaller than 0.42, independently of the base material.

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PubMed2005

Electrohydrodynamics of binary electrolytes driven by modulated surface potentials.

We study the electrohydrodynamics of the Debye screening layer that arises in an aqueous binary solution near a planar insulating wall when applying a spatially modulated ac voltage. Combining this with first order perturbation theory we establish the governing equations for the full nonequilibrium problem and obtain analytic solutions in the bulk for the pressure and velocity fields of the electrolyte and for the electric potential. We find good agreement between the numerics of the full problem and the analytics of the linear theory. Our work provides the theoretical foundations of circuit models discussed in the literature. The nonequilibrium approach also reveals unexpected high-frequency dynamics not predicted by circuit models.

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PubMed2005

Reexamination of Hagen-Poiseuille flow: shape dependence of the hydraulic resistance in microchannels.

We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.

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PubMed2005

Quantum computing via defect states in two-dimensional antidot lattices.

We propose a new structure suitable for quantum computing in a solid-state environment: designed defect states in antidot lattices superimposed on a two-dimensional electron gas at a semiconductor heterostructure. State manipulation can be obtained with gate control. Model calculations indicate that it is feasible to fabricate structures whose energy level structure is robust against thermal dephasing.

Computer Simulation↗

PubMed2004

Modeling of realistic cladding structures for air-core photonic bandgap fibers.

Cladding structures of photonic bandgap fibers often have airholes of noncircular shape, and, typically, close-to-hexagonal airholes with curved corners are observed. We study photonic bandgaps in such structures by aid of a two-parameter representation of the size and curvature. For the fundamental bandgap we find that the bandgap edges (the intersections with the air line) shift toward shorter wavelengths when the air-filling fraction f is increased. The bandgap also broadens, and the relative bandwidth increases exponentially with f2. Compared with recent experiments [Nature 424, 657 (2003)] we find very good agreement.

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PubMed2003

Mode-field radius of photonic crystal fibers expressed by the V parameter.

We numerically calculate the equivalent mode-field radius of the fundamental mode in a photonic crystal fiber (PCF) and show that this is a function of the V parameter only and not the relative hole size. This dependence is similar to what is found for graded-index standard fibers, and we furthermore show that the relation for the PCF can be excellently approximated with the same general mathematical expression. This is to our knowledge the first semianalytical description of the mode-field radius of a PCF.

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PubMed2003

Modal cutoff and the V parameter in photonic crystal fibers.

We address the long-standing unresolved problem concerning the V parameter in a photonic crystal fiber. In formulating the parameter appropriate for a core defect in a periodic structure, we argue that the multimode cutoff occurs at a wavelength lambda* that satisfies VPCF(lambda*) = pi. By comparing this approach with numerics and recent cutoff calculations we confirm this result.

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PubMed2003

Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers.

Modal cutoff is investigated experimentally in a series of high-quality nonlinear photonic crystal fibers. We demonstrate a suitable measurement technique with which to determine the cutoff wavelength and verify the technique by inspecting the near field of the modes that may be excited below and above the cutoff. We observe a double-peak structure in the cutoff spectra, which is attributed to splitting of the higher-order modes. The cutoff is measured for seven different fiber geometries with different pitches and relative hole sizes, and very good agreement with recent theoretical work is found.

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PubMed2003

Reduced microdeformation attenuation in large-mode-area photonic crystal fibers for visible applications.

We consider large-mode-area photonic crystal fibers for visible applications in which microdeformation-induced attenuation becomes a potential problem when the effective area A(eff) is sufficiently large compared to lambda2. We argue that a slight increase in fiber diameter D can be used in screening the high-frequency components of the microdeformation spectrum mechanically, and we confirm this experimentally for both 15- and 20-microm core fibers. For typical bending radii (R approximately 16 cm) the operating bandwidth increases by approximately 3-400 nm to the low-wavelength side.

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