Input-output relations for a 3-port grating coupled Fabry-Perot cavity

We analyze an optical 3-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3 orders of diffraction are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input output relations of a 3-port grating coupled cavity and find distinct properties not present in 2-port coupled cavities. The cavity relations further reveal that the 3-port coupler can be designed such that the additional cavity port interferes destructively. In this case the all-reflective, low-loss, single-ended Fabry-Perot cavity becomes equivalent to a standard transmissive, 2-port coupled cavity

Three-port beam splitters-combiners for interferometer applications

We derive generic phase and amplitude coupling relations for beam splitters-combiners that couple a single port with three output ports or input ports, respectively. We apply the coupling relations to a reflection grating that serves as a coupler to a single-ended Fabry-Perot ring cavity. In the impedance-matched case such an interferometer can act as an all-reflective ring mode cleaner. It is further shown that in the highly undercoupled case almost complete separation of carrier power and phase signal from a cavity strain can be achieved

Sustained coevolution of phage Lambda and Escherichia coli involves inner- as well as outer- membrane defences and counter- defences

Bacteria often evolve resistance to phage through the loss or modification of cell surface receptors. In Escherichia coli and phage λ, such resistance can catalyze a coevolutionary arms race focused on host and phage structures that interact at the outer membrane. Here, we analyse another facet of this arms race involving interactions at the inner membrane, whereby E. coli evolves mutations in mannose permease- encoding genes manY and manZ that impair λ’s ability to eject its DNA into the cytoplasm. We show that these man mutants arose concurrently with the arms race at the outer membrane. We tested the hypothesis that λ evolved an additional counter- defence that allowed them to infect bacteria with deleted man genes. The deletions severely impaired the ancestral λ, but some evolved phage grew well on the deletion mutants, indicating that they regained infectivity by evolving the ability to infect hosts independently of the mannose permease. This coevolutionary arms race fulfils the model of an inverse gene- for- gene infection network. Taken together, the interactions at both the outer and inner membranes reveal that coevolutionary arms races can be richer and more complex than is often appreciated

Diffractive Optics for Gravitational Wave Detectors

All-reflective interferometry based on nano-structured diffraction gratings offers new possibilities for gravitational wave detection. We investigate an all-reflective Fabry-Perot interferometer concept in 2nd order Littrow mount. The input-output relations for such a resonator are derived treating the grating coupler by means of a scattering matrix formalism. A low loss dielectric reflection grating has been designed and manufactured to test the properties of such a grating cavity

High reflectivity grating waveguide coatings for 1064nm

We propose thin single-layer grating waveguide structures to be used as high-reflectivity, but low thermal noise, alternative to conventional coatings for gravitational wave detector test mass mirrors. Grating waveguide (GWG) coatings can show a reflectivity of up to 100% with an overall thickness of less than a wavelength. We theoretically investigate GWG coatings for 1064nm based on tantala (Ta2O5) on a Silica substrate focussing on broad spectral response and low thickness

Demonstration of 3-port grating phase relations

We experimentally demonstrate the phase relations of 3-port gratings by investigating 3-port coupled Fabry-Perot cavities. Two different gratings which have the same 1st order diffraction efficiency but differ substantially in their 2nd order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities we could validate the results of an earlier theoretical description of the phases at a three port grating

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Impulsiveness Mediates the Association between \u3ci\u3eGABRA2\u3c/i\u3e SNPs and Lifetime Alcohol Problems

Genetic variants in GABRA2 have previously been shown to be associated with alcohol measures, electroencephalography (EEG) β waves and impulsiveness-related traits. Impulsiveness is a behavioral risk factor for alcohol and other substance abuse. Here, we tested association between 11 variants in GABRA2 with NEO-impulsiveness and problem drinking. Our sample of 295 unrelated adult subjects was from a community of families with at least one male with DSM-IV alcohol use diagnosis, and from a socioeconomically comparable control group. Ten GABRA2 SNPs (single-nucleotide polymorphisms) were associated with the NEO-impulsiveness (P \u3c 0.03). The alleles associated with higher impulsiveness correspond to the minor alleles identified in previous alcohol dependence studies. All ten SNPs are in linkage disequilibrium (LD) with each other and represent one effect on impulsiveness. Four SNPs and the corresponding haplotype from intron 3 to intron 4 were also associated with Lifetime Alcohol Problems Score (LAPS, P \u3c 0.03) (not corrected for multiple testing). Impulsiveness partially mediates (22.6% average) this relation between GABRA2 and LAPS. Our results suggest that GABRA2 variation in the region between introns 3 and 4 is associated with impulsiveness and this effect partially influences the development of alcohol problems, but a direct effect of GABRA2 on problem drinking remains. A potential functional SNP rs279827, located next to a splice site, is located in the most significant region for both impulsiveness and LAPS. The high degree of LD among nine of these SNPs and the conditional analyses we have performed suggest that all variants represent one signal

Experimental demonstration of a suspended diffractively coupled optical cavity

All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry–Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound–Drever–Hall length sensing and control techniques to maintain the required operating condition