Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.

On the physical realizability of highly focused electromagnetic field distributions

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.