A 12.5 GHz-Spaced Optical Frequency Comb Spanning >400 nm for near-Infrared Astronomical Spectrograph Calibration

A 12.5 GHz-spaced optical frequency comb locked to a Global Positioning disciplined oscillator for near-IR spectrograph calibration is presented. The comb is generated via filtering a 250 MHz-spaced comb. Subsequency nonlinear broadening of the 12.5 GHz comb extends the wavelength range to cover 1380 nm to 1820 nm, providing complete coverage over the H-band transmission widow of Earth's atmosphere. Finite suppression of spurious sidemodes, optical linewidth and instability of the comb have been examined to estmiate potential wavelength biases in spectrograph calibration. Sidemode suppression varies between 20 db and 45 dB, and the optical linewidth is ~350 kHz at 1550 nm. The comb frequency uncertainty is bounded by +/- 30 kHz (corresponding to a radial velocity of +/- 5 cm/s), limited by the Global Positioning System disciplined oscillator reference. These results indicate this comb can readily support radial velocity measurements below 1 m/s in the near-IR.Comment: 16 pages, 12 figures, new file fixes some readability problems on Mac

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad