Germanium-on-silicon mid-infrared waveguides and Mach-Zehnder interferometers

In this paper we describe Ge-on-Si waveguides and Mach-Zehnder interferometers operating in the 5.2 - 5.4 mu m wavelength range. 3dB/cm waveguide losses and Mach-Zehnder interferometers with 20dB extinction ratio are presented

CeCu_2Ge_2: Challenging our Understanding of Quantum Criticality

Here, we unveil evidence for a quantum phase-transition in CeCu_2Ge_2 which displays both an incommensurate spin-density wave (SDW) ground-state, and a strong renormalization of the quasiparticle effective masses (mu) due to the Kondo-effect. For all angles theta between an external magnetic field (H) and the crystallographic c-axis, the application of H leads to the suppression of the SDW-state through a 2^nd-order phase-transition at a theta-dependent critical-field H_p(theta) leading to the observation of small Fermi surfaces (FSs) in the paramagnetic (PM) state. For H || c-axis, these FSs are characterized by light mu's pointing also to the suppression of the Kondo-effect at H_p with surprisingly, no experimental evidence for quantum-criticality (QC). But as $H$ is rotated towards the a-axis, these mu's increase considerably becoming undetectable for \theta > 56^0 between H and the c-axis. Around H_p^a~ 30 T the resistivity becomes proportional T which, coupled to the divergence of mu, indicates the existence of a field-induced QC-point at H_p^a(T=0 K). This observation, suggesting FS hot-spots associated with the SDW nesting-vector, is at odds with current QC scenarios for which the continuous suppression of all relevant energy scales at H_p(theta,T) should lead to a line of quantum-critical points in the H-theta plane. Finally, we show that the complexity of its magnetic phase-diagram(s) makes CeCu_2Ge_2 an ideal system to explore field-induced quantum tricritical and QC end-points.Comment: 10 pages, 5 figures, Phys. Rev. B (in press

Germanium-on-silicon planar concave grating wavelength (de)multiplexers in the mid-infrared

Mid-infrared wavelength (de)multiplexers based on planar concave gratings (PCGs) fabricated on a germanium-on-silicon waveguide platform are presented. PCGs with two different types of gratings (flat facet and distributed bragg reflectors) are analyzed for both transverse electric (TE) and transverse magnetic (TM) polarizations. The insertion loss and cross talk for flat facet PCGs are found to be -7.6/-6.4¿dB and 27/21¿dB for TE/TM polarization. For distributed bragg reflector PCGs the insertion loss and cross talk are found to be -4.9/-4.2¿dB and 22/23¿dB for TE/TM polarization

On the interpretation of the multicolour disc model for black hole candidates

We present a critical analysis of the usual interpretation of the multicolour disc model parameters for black hole candidates in terms of the inner radius and temperature of the accretion disc. Using a self-consistent model for the radiative transfer and the vertical temperature structure in a Shakura-Sunyaev disc, we simulate the observed disc spectra, taking into account doppler blurring and gravitational redshift, and fit them with multicolour models. We show not only that such a model systematically underestimates the value of the inner disc radius, but that when the accretion rate and/or the energy dissipated in the corona are allowed to change the inner edge of the disc, as inferred from the multicolour model, appears to move even when it is in fact fixed at the innermost stable orbit.Comment: 4 pages including 2 figures, accepted for publication in MNRA

Arithmetic Spacetime Geometry from String Theory

An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.Comment: 36 page

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for

A systematic look at the Very High and Low/Hard state of GX 339-4: Constraining the black hole spin with a new reflection model

We present a systematic study of GX 339-4 in both its very high and low hard states from simultaneous observations made with XMM-Newton and RXTE in 2002 and 2004. The X-ray spectra of both these extreme states exhibit strong reflection signatures, with a broad, skewed Fe-Kalpha line clearly visible above the continuum. Using a newly developed, self-consistent reflection model which implicitly includes the blackbody radiation of the disc as well as the effect of Comptonisation, blurred with a relativistic line function, we were able to infer the spin parameter of GX 339-4 to be 0.935 +/- 0.01 (statistical) +/- 0.01 (systematic) at 90 per cent confidence. We find that both states are consistent with an ionised thin accretion disc extending to the innermost stable circular orbit around the rapidly spinning black hole.Comment: 10 pages, 10 figures, accepted for publication in MNRAS 17/04/0