Biomedical subjects

Johannes Skaar

Publications and source records attributed to Johannes Skaar.

5 recordsLinked to original sources

PubMed2006

On resolving the refractive index and the wave vector.

The identification of the refractive index and the wave vector for general (possibly active) linear, isotropic, homogeneous, and nonspatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions epsilon=epsilon(omega) and mu=mu(omega). On the other hand, a necessary and sufficient condition for left handedness can be identified at a single frequency (Re epsilon/|epsilon|+Re mu/|mu|<0). At oblique incidence to semi-infinite, active media, it is explained that the wave vector generally loses its usual interpretation for real frequencies.

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PubMed2006

Fresnel equations and the refractive index of active media.

A class of realizable active media exists for which the refractive index cannot be defined as an analytic function in the upper half-plane of complex frequency. The conventional definition of the refractive index based on analyticity is modified such that it is valid for active media in general, and associated Fresnel equations are proved. In certain active media, the presence of a "backward" wave, for which both phase velocity and Poynting's vector point towards the excitation source, is demonstrated.

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PubMed2004

Design of short fiber Bragg gratings by use of optimization.

We demonstrate an optimization approach for designing fiber Bragg gratings. A layer-peeling inverse-scattering algorithm is used to produce an initial solution, which is optimized numerically with an iterative optimization method. To avoid problems with local minima, we use merit functions that are zero for wavelengths for which the predefined demands (acceptance limits) are fulfilled, making it possible to alter the local minima under the optimization process without disturbing the global minimum. Because short gratings are difficult to design with inverse scattering, and because the time consume of the optimization increases rapidly with the grating length, the method is particularly useful for designing short gratings. The method is also useful when the demands are complex and difficult to handle with inverse-scattering methods. Design examples are given, including a dispersionless bandpass filter suitable for dense wavelength-division multiplexing and a filter with linear reflectivity.

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PubMed2004

Synthesis of birefringent reflective gratings.

The layer-peeling method for reconstruction of fiber and waveguide gratings is extended to the case of birefringent reflective gratings with polarization-dependent background index and polarization-dependent effective index contrast. Using a discrete grating model, we characterize the set of possible reflection and transmission Jones matrices and show that for a given wavelength, the total structure can be represented by a discrete reflector sandwiched between two retardation sections. In reflection the discrete reflector acts as a partial polarizer. A method for designing birefringent gratings is developed and tested numerically.

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PubMed2002

Reconstruction of gratings from noisy reflection data.

The worst-case error amplification factor in reconstructing a grating from its complex reflection spectrum is shown to be of the order 1/T(min), where T(min) is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient-length product kappaL, the error amplification is exp(2kappaL). The exponential dependence on the grating strength shows that spatial characterization of gratings from a measured reflection spectrum is impossible if the grating is sufficiently strong. For moderately strong gratings, a simple regularization technique is proposed to stabilize the solution of the inverse-scattering problem of computing the grating structure from the reflection spectrum.

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