Echelon Film Gratings

Analog tunable gratings driven by thin-film piezoelectric microelectromechanical actuators.

We present a microfabricated grating whose period can be tuned in analog fashion to within a fraction of a nanometer. The tunable angular range is more than 400 microrad in the first diffracted order. The design concept consists of a diffractive grating defined onto a 400-nm membrane, with the membrane subsequently strained in the direction perpendicular to the grating grooves by thin-film piez...

Echelon analysis

Echelon Form

In this work we present the formalization of an algorithm to compute the Echelon Form of a matrix. We have proved its existence over Bezout domains and we have made it executable over Euclidean domains, such as Z and K[x]. This allows us to compute determinants, inverses and characteristic polynomials of matrices. The work is based on the HOL-Multivariate Analysis library, and on both the Gauss...

Echelon Spaces of Order »

The notion of Echelon spaces was introduced by Köthe [2] as a means of constructing sequence spaces by taking the intersection of multiples of I1 (see below for definitions). The definition was extended by Dieudonné and Gomes [l] to include lp for \^p< °o. It is the purpose of this note to consider the case, p = co. AH of the terminology defined below is due to Köthe. A sequence of complex numb...

Analysis of optical response of long period fiber gratings to nm-thick thin-film coating.

We theoretically and experimentally demonstrated that the resonant wavelength of long period fiber gratings (LPG) could be shifted in a large magnitude by coating only nm-thick thin-film whose refractive index is higher than that of the glass cladding. The resonant wavelength shift results from either the variation of the thickness of the film and/or the variation of the refractive index of the...