Measuring the translational and rotational velocity of particles in helical motion using structured light

We measure the rotational and translational velocity components of particles moving in helical motion using the frequency shift they induced to the structured light beam illuminating them. Under Laguerre-Gaussian mode illumination, a particle with a helical motion reflects light that acquires an additional frequency shift proportional to the angular velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.Comment: 5 pages,5 figure

Direction-sensitive transverse velocity measurement by phase-modulated structured light beams

The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a challenge since detection is usually done by means of an interferometric setup which only provides an absolute value of the frequency shift. Here, we put forward a novel method that addresses this issue. It uses dynamic control of the phase in the transverse plane of the structured light beam so that the direction of the particles' movement can be deduced. This is done by noting the change in the magnitude of the frequency shift as the transverse phase of the structured light is moved appropriately. We demonstrate our method with rotating micro-particles that are illuminated by a Laguerre-Gaussian beam with a rotating phase about its propagation axis. Our method, which only requires a dynamically configurable optical beam generator, can easily be used with other types of motion by appropriate engineering and dynamic modulation of the phase of the light beam.Comment: 5 pages, 4 figure

Photonic applications based on the use of structured light

Structured light beams, this is, beams whose phase changes from point to point in the transverse plane, provides with an alternative tool to search for new applications, or simply to expand the capabilities of current applications where commonly used light beams have encountered physical limitations. Applications can be found not only in the field of optics but also in areas as diverse as astrophysics, telecommunications and quantum computing, to mention some. In this thesis we put forward three new applications in which the use of structured light beams plays a crucial role. In the field of optical remote sensing, the Doppler effect is widely used to measure the component of the velocity along the line of sight, \textit{i.e.}, the longitudinal component. The Doppler effect alone, does not allow to measure the transverse component. In this context, structured light beams provides with a tool that makes this possible: its structured phase. The main idea resides in the fact that this beams, reflected from transversally moving targets, are frequency shifted proportional to the velocity of the target. The information of the velocity can be extracted using interferometric methods, in a similar way to the longitudinal Doppler shift. In a first experiment we validated this theoretical concept for two particular cases: rotation and longitudinal motions along the transverse plane of illumination. Some current existing techniques to measure small layer thicknesses are based on the use of common-pant interferometers. In particular the self-referencing type, in which both the reference and the signal beams are generated locally. A reflective surface is engineered in the form of a ridge or cliff, in such a way when illuminated with a Gaussian beam half of it is reflected from the top and the other half from the base. This two "new beams" acquire a phase difference that depends on the height of the ridge and the wavelength of the illuminating source. This phase variations are detected on-axis in the far filed as intensity changes. Hence, if we place a thick layer on top of the ridge, the change in intensity will immediately yield the height of the layer. This scheme becomes highly sensitive to small phase variations when the height of the ridge is $1/8$ of the wavelength, known as the quadrature condition. This restriction might unfortunately limit the use of this technique to specific cases, since it highly depends on the construction of the ridge. To overcome this drawback we proposed and demonstrated experimentally a technique in which the quadrature condition is not needed a priori. Our approach is based on the use of spatial mode projection. For its implementation, we project the light reflected from the sample onto appropriately tailored spatial modes. Finally, we investigated theoretically the role that light endowed with Orbital Angular Momentum (OAM) might play for the discrimination of chiral molecules. Traditionally, this discrimination has been always related to Circularly Polarized Light (CPL), this is, to the Spin angular momentum of light. In this approach, the chiral response of molecules only depends on the properties of the same, and in many cases is very small. An approach to enhance this response was proposed very recently, in which the electromagnetic field that illuminates the molecule is properly tailored, in such a way the chiral response depends on both the molecular properties and the electromagnetic field. These types of electromagnetic fields have been termed "chiral fields'' and are characterised through a quantity known as optical chirality (denoted as C). This quantity measures how contorted is the field at each point in space, the higher the value of C, the higher the chiral response. In our approach, we started from exact solutions to the Helmholtz equation. We found that a proper superposition of this two beams produces an on-axis, enhanced chiral response that can be several times larger.Los haces estructurados, es decir, haces cuya fase difiere de un punto a otro en el plano transversal, representan una herramienta alternativa para buscar nuevas aplicaciones, o simplemente para expandir las capacidades de las aplicaciones existentes en donde los haces comúnmente utilizados han encontrado limitaciones físicas. En la actualidad podemos encontrar aplicaciones no solo en el campo de la óptica sino ambién en áreas tan diversa como astrofísica, telecomunicaciones y computación cuántica por mencionar algunas. En esta tesis, introducimos tres nuevas aplicaciones, en las cuales el uso the haces estructurados juega un papel crucial. En el campo de sensado remoto, el efecto Doppler es utilizado ampliamente para medir la componente de la velocidad a lo largo de la linea de visión, es decir, la componente longitudinal. El efecto Doppler por si solo, no permite medir la componente transversal. En este contexto, los haces estructurados proveen con una herramienta, su fase estructurada, mediante la cual se puede medir esta componente. La idea principal reside en el hecho de que la frecuencia de estos haces, cuando son reflejados de un objeto que se mueve trasversalmente, cambia de forma proporcional a la velocidad del objeto. La informacón de la velocidad puedes ser extraída utilizando métodos interferométricos, de forma similar al efecto Doppler longitudinal. En un primer experimento validamos este concepto teórico para dos casos particulares: rotación y translación longitudinal en el plano transversal al de iluminación. Por otro lado, algunas de las téecnicas que existen actualmente para medir grosores están basadas en el uso de interferómetros de camino óptico común. En particular los autoreferenciados, en los cuales tanto el haz de referencia como el que lleva la información son generados localmente. Una superficie reflectante con forma de acantilado es diseñada, de tal forma que cuando es iluminada con un haz Gaussiano, una mitad es reflejada en la base y la otra en la cima. Estos dos "nuevos haces'' adquieren una diferencia de fase que depende de la altura de del acantilado y de la longitud de onda del haz. Estas variaciones son detectadas en campo lejano a lo largo del eje de propagación como cambios de intensidad. De esta forma, si colocamos una capa delgada sobre del acantilado, el cambio en la intensidad nos dará inmediatamente el grosor de la capa. Este esquema es muy sensible a cambios pequeñoos de fase cuando la altura del acantilado es 1/8 de la longitud de onda, conocida como condición de cuadratura. Desafortunadamente, esta restricción puede limitar el uso de esta técnica a casos específicos, ya que depende en gran medida de la construcción apropiada del acantilado. Para solventar esta desventaja propusimos y demostramos experimentalmente una técnica en la cual la condición de cuadratura no es necesaria a priori. Nuestro metodo esta basado en la proyección espacial en modos. Para su implementación, proyectamos la luz reflejada por la muestra sobre modos espaciales diseñados apropiadamente. Finalmente, investigamos teóricamante el papel que los haces provistos con momento angular pueden desempeñar en la discriminación de moléculas quirales. Tradicionalmente, esta discriminación ha estado asociada a la luz circularmente polarizada, es decir, al momento angular espinorial. En esta aproximación, la respuesta chiral de las moléculas depende únicamente de las propiedades de la misma, que en muchos casos es muy pequeña. Una aproximación para incrementar esta respuesta conciste en el diseño apropiado del campo electromagnético que ilumina las moléculas, de esta forma la respuesta quiral depende no solo de las propiedades de la molécula sino también del campo electromagnético. Este tipo de campos electromagnèticos han sido denominados "campos quirales''. Nosotros abordamos el problema utilizando soluciones exactas a la ecuación de Helmholtz, los haces Bessel de orden superior

Basis independent tomography of complex vectorial light fields by Stokes projections

Complex vectorial light fields, non-separable in their polarization and spatial degree of freedom, are of relevance in a wide variety of fields encompassing microscopy, metrology, communication and topological studies. Controversially, they have been suggested as analogues to quantum entanglement, raising fundamental questions on the relation between non-separability in classical systems, and entanglement in quantum systems. Here we propose and demonstrate basis-independent tomography of arbitrary vectorial light fields by relating their concurrence to spatially resolved Stokes projections. We generate vector fields with controllable non-separability using a novel compact interferometer that incorporates a digital micro-mirror device (DMD), thus offering a holistic toolbox for the generation and quantitative analysis of arbitrary vectorial light fields

Generation of tunable optical skyrmions on Skyrme-Poincar\'e sphere

In recent time, the optical-analogous skyrmions, topological quasiparticles with sophisticated vectorial structures, have received an increasing amount of interest. Here we propose theortically and experimentally a generalized family of these, the tunable optical skyrmion, unveiling a new mechanism to transform between various skyrmionic topologies, including N\'eel-, Bloch-, and antiskyrmion types, via simple parametric tuning. In addition, Poincar\'e-like geometric representation is proposed to visualize the topological evolution of tunable skyrmions, which we termed Skyrme-Poincar\'e sphere, akin to the spin-orbit representation of complex vector modes. To generate experimentally the tunable optical skyrmions we implemented a digital hologram system based on a spatial light modulator, showing great agreement with our theoretical prediction