We present the first integrated multimode photonic spectrograph, a device we call PIMMS #1. The device comprises a set of multimode fibres that convert to single-mode propagation using a matching set of photonic lanterns. These feed to a stack of cyclic array waveguides (AWGs) that illuminate a common detector. Such a device greatly reduces the size of an astronomical instrument at a fixed spectroscopic resolution. Remarkably, the PIMMS concept is largely independent of the telescope diameter, input focal ratio and entrance aperture -i.e. one size fits all! The instrument architecture can also exploit recent advances in astrophotonics (e.g. OH suppression fibres). We present a movie of the instrument's operation and discuss the advantages and disadvantages of this approach.

,TC describe the differential mulfipole method, an extended multipole method used to calculate the modes of mlcroetructured optical fibers with uoncircular inclusions. Vole use a multipole expansion centered on each inclusion and a differential method to calculate the scattering properties of the individual inclusions. Reprosentative results for a flber with one ring of elliptical inclusions are presented. and a direct comparison is made with an existing method. The new method is also applied to a microstructured optical fiber with seven rings of elliptical inclusions, which is found. in effect, to support a single polarization of the fundamental mode.

We consider lamellar gratings made of dielectric or lossy materials used in classical diffraction mounts. We show how the modal diffraction formulation may be generalized to deal with slanted lamellar gratings and illustrate the accuracy and versatility of the new method through study of highly slanted gratings in a homogenization limit. We also comment on the completeness of the eigenmode basis and present tests enabling this completeness to be verified numerically.

A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.