Apparatus for precision focussing and positioning of a beam waist on a target

The invention relates to optical focussing apparatus and, more particularly, to optical apparatus for focussing a highly collimated Gaussian beam which provides independent and fine control over the focus waist diameter, the focus position both along the beam axis and transverse to the beam, and the focus angle. A beam focussing and positioning apparatus provides focussing and positioning for the waist of a waisted beam at a desired location on a target such as an optical fiber. The apparatus includes a first lens, having a focal plane f sub 1, disposed in the path of an incoming beam and a second lens, having a focal plane f sub 2 and being spaced downstream from the first lens by a distance at least equal to f sub 1 + 10 f sub 2, which cooperates with the first lens to focus the waist of the beam on the target. A rotatable optical device, disposed upstream of the first lens, adjusts the angular orientation of the beam waist. The transverse position of the first lens relative to the axis of the beam is varied to control the transverse position of the beam waist relative to the target (a fiber optic as shown) while the relative axial positions of the lenses are varied to control the diameter of the beam waist and to control the axial position of the beam waist. Mechanical controllers C sub 1, C sub 2, C sub 3, C sub 4, and C sub 5 control the elements of the optical system. How seven adjustments can be made to correctly couple a laser beam into an optical fiber is illustrated. Prior art systems employing optical techniques to couple a laser beam into an optical fiber or other target simply do not provide the seven necessary adjustments. The closest known prior art, a Newport coupler, provides only two of the seven required adjustments

Photoionization cross sections of rovibrational levels of the B^1Σ^+_u state of H_2

We report theoretical cross sections for direct photoionization of specific rovibrational levels of the B ^1Σ^+_u electronic state of H_2. The calculated cross sections differ considerably from values recently determined by resonant enhanced multiphoton ionization (REMPI) studies. In an attempt to understand the disagreement, we analyze in detail the REMPI dynamics and find that the multiphoton ionization probability is extremely sensitive to the spatial and temporal profiles of the laser pulses. Accurate characterization of laser profiles and their jitter is therefore necessary for a comparison between theory and experiment

Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets

We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and thereby the allowed traversals. We study such gadgets in the 0-, 1-, and 2-player settings, in particular extending past motion-planning-through-gadgets work to 0-player games for the first time, by considering "branchless" connections between gadgets that route every gadget's exit to a unique gadget's entrance. Our complexity results include containment in L, NL, P, NP, and PSPACE; as well as hardness for NL, P, NP, and PSPACE. We apply these results to show PSPACE-completeness for certain mechanics in Factorio, [the Sequence], and a restricted version of Trainyard, improving prior results. This work strengthens prior results on switching graphs and reachability switching games.Comment: 37 pages, 36 figure

Compression of Martian atmosphere for production of oxygen

The compression of CO2 from the Martian atmosphere for production of O2 via an electrochemical cell is addressed. Design specifications call for an oxygen production rate of 10 kg per day and for compression of 50 times that mass of CO2. Those specifications require a compression rate of over 770 cfm at standard Martian temperature and pressure (SMTP). Much of the CO2 being compressed represents waste, unless it can be recycled. Recycling can reduce the volume of gas that must be compressed to 40 cfm at SMTP. That volume reduction represents significant mass savings in the compressor, heating equipment, filters, and energy source. Successful recycle of the gas requires separation of CO (produced in the electrochemical cell) from CO2, N2, and Ar found in the Martian atmosphere. That aspect was the focus of this work

Improving green manure quality with phosphate rocks in Ontario Canada

Phosphate rock (PR) was applied to one conventional and two organic dairy fields and planted with buckwheat (Fagopyrum esculentum) as a green manure crop. In total, five types of PR were applied at three application rates in order to determine the yield, concentration of P in the aboveground tissue and the P uptake of buckwheat. It was found that PR of relatively high carbonate substitution and small particle diameter could increase buckwheat tissue concentrations to a quality such that mineralization of the buckwheat mulch could occur. Buckwheat mulch and residual PR increased soil P flux as determined by anion exchange membranes in situ in the following spring. This provides evidence that buckwheat of high P quality has the potential to supply P to a subsequent crop

(2+1) resonant enhanced multiphoton ionization of H_2 via the E, F^(1)Σ^+_g state

In this paper, we report the results of ab initio calculations of photoelectron angular distributions and vibrational branching ratios for the (2+1) REMPI of H_2 via the E, F^(1)Σ^+_g state, and compare these with the experimental data of Anderson et al. [Chem. Phys. Lett. 105, 22 (1984)]. These results show that the observed non‐Franck–Condon behavior is predominantly due to the R dependence of the transition matrix elements, and to a lesser degree to the energy dependence. This work presents the first molecular REMPI study employing a correlated wave function to describe the Rydberg–valence mixing in the resonant intermediate state

Light transmission assisted by Brewster-Zennek modes in chromium films carrying a subwavelength hole array

This work confirms that not only surface plasmons but many other kinds of electromagnetic eigenmodes should be considered in explaining the values of the transmittivity through a slab bearing a two-dimensional periodic corrugation. Specifically, the role of Brewster-Zennek modes appearing in metallic films exhibiting regions of weak positive dielectric constant. It is proposed that these modes play a significant role in the light transmission in a thin chromium film perforated with normal cylindrical holes, for appropriate lattice parameters.Comment: 5 pages, 4 figures. Published versio

Adaptive evolution of molecular phenotypes

Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dependent trait optimum in a given population. We derive analytical expressions for the distribution of the time-dependent trait divergence between populations and of the trait diversity within populations. Based on this solution, we develop a method to infer adaptive evolution of quantitative traits. Specifically, we show that the ratio of the average trait divergence and the diversity is a universal function of evolutionary time, which predicts the stabilizing strength and the driving rate of the fitness seascape. From an information-theoretic point of view, this function measures the macro-evolutionary entropy in a population ensemble, which determines the predictability of the evolutionary process. Our solution also quantifies two key characteristics of adapting populations: the cumulative fitness flux, which measures the total amount of adaptation, and the adaptive load, which is the fitness cost due to a population's lag behind the fitness peak.Comment: Figures are not optimally displayed in Firefo

Bulk photonic metamaterial with hyperbolic dispersion

In this work, we demonstrate a self-standing bulk three-dimensional metamaterial based on the network of silver nanowires in an alumina membrane. This constitutes an anisotropic effective medium with hyperbolic dispersion, which can be used in sub-diffraction imaging or optical cloaks. Highly anisotropic dielectric constants of the material range from positive to negative, and the transmitted laser beam shifts both toward the normal to the surface, as in regular dielectrics, and off the normal, as in anisotropic dielectrics with the refraction index smaller than one. The designed photonic metamaterial is the thickest reported in the literature, both in terms of its physical size 1cm x 1cm x 51 mm, and the number of vacuum wavelengths, N=61 at l=0.84 mm.Comment: 6 pages, 4 figur