Síntesi de camps vectorials de llum amb polarització tridimensional no uniforme mitjançant holografia digital

[cat] La introducció dels feixos amb polaritzacions no uniformes ha aportat grans avenços en multitud d'àrees. En un nivell més fonamental, ha permès entendre la naturalesa de la llum d'una manera més amplia, estenent les teories òptiques conegudes, com ('escalar, a d'altres més precises com la vectorial. La síntesi de feixos amb una distribució no uniforme de la polarització segueix sent una tasca desafiant. Mentre que algunes tècniques utilitzen sistemes totalment òptics, en aquesta tesi, s'ha optat per incorporar dispositius optoelectrònics per modular la llum, obtenint així una major flexibilitat a la hora de dissenyar el feix. Per altra banda, el muntatge òptic utilitzat està basat en un interferòmetre de Mach-Zehnder per tal de manipular les dues components del feix, d'una manera independent, en cada braç de l'interferòmetre. D'aquesta manera, utilitzant en cada braç de l'interferòmetre un modulador de cristall líquid, tenim la capacitat de modular ambdues components del feix incident. Aquests moduladors són els proporcionats per Holoeye, concretament el model HEO 0017, els quals treballen en transmissió. Compten amb una configuració pixelada, dotant-nos d'una capacitat de modulació espacial amb una resolució de 32gm. Complementant aquesta modulació amb una tècnica d'holografia digital, som capaços de modular tant l'amplitud com la fase d'ambdues components del camp i, per tant, d'esculpir qualsevol forma amb qualsevol distribució de la polarització. Per tal de mostrar aquesta flexibilitat, s'ha sintetitzat un conjunt de feixos amb diversos perfils i diverses distribucions de la polarització. Els feixos generats s’han avaluat mitjançant un analitzador, compost d’una làmina retardadora λ/4 i un polaritzador lineal, enfront d’una càmera CCD de 14 bits de rang dinàmic del model Stingray F080B A5G. D’aquesta manera, s’han obtingut les distribucions dels paràmetres d’Stokes en el pla de la càmera. Aprofitant aquesta capacitat de modulació, s’ha dissenyat una tècnica d’encriptació hologràfica utilitzant el mateix sistema òptic amb lleugeres modificacions. Les claus secretes, que garanteixen la seguretat en la codificació, són màscares de polarització. Per incrementar el nivell de seguretat del sistema, s’han afegit dos paràmetres físics necessaris per poder desencriptar la informació. A més, s’ha simulat, sobre els resultats experimentals obtinguts, la resposta del sistema sota condicions de molt baixa il·luminació. Aquestes condicions, sovint utilitzades en treballs previs, augmenten significativament la robustesa del mètode d’encriptació. Un cop garantida la correcta manipulació d’ambdues components d’un feix paraxial, s’ha procedit a desenvolupar un marc teòric per sintetitzar feixos altament focalitzats amb una polarització tridimensional arbitrària. Per tal d’obtenir aquests feixos, s’ha utilitzat un objectiu de microscopi amb una obertura numèrica de NA=0.85, on s’ha modulat el camp en la pupil·la d’entrada mitjançant el mètode hologràfic anterior. El disseny del camp en la zona focal, en funció de la distribució de la polarització en la pupil·la d’entrada, s’ha realitzat en el marc de la teoria vectorial desenvolupada per B. Richards i E. Wolf. Per avaluar el funcionament del sistema, s’ha sintetitzat un feix altament focalitzat amb polarització circular en qualsevol pla, i s’ha comparat els resultats obtinguts experimentalment amb els extrets numèricament. La definició del grau de polarització en feixos altament focalitzats, encara ara, genera certs debats degut a que no es pot expandir d’una manera inequívoca com una suma directa del camp totalment polaritzat i del camp totalment despolaritzat. En aquesta tesi, hem fet l’estudi en el marc dels paràmetres d’Stokes generalitzats, obtenint una correspondència entre la distribució del paràmetres d’Stokes en la pupil·la d’entrada i la distribució del paràmetres d’Stokes de la contribució transversal del camp focalitzat. S’ha proposat un feix paraxial, que, un cop focalitzat, genera un camp amb les components transversals despolaritzades i que compta amb una component longitudinal no nul·la. Aquests tipus de feixos són de gran utilitat, entre d’altres camps, en la confecció de capes de invisibilitat.[eng] Non uniformly polarized beams have provided great strides in many areas. The synthesis of arbitrary polarized beams remains a challenging task. While some techniques use full optics systems, in this dissertation we introduce a system where optoelectronic devices modulate the light, providing more flexibility in the beam design. Complementing this modulation with a digital holography method, we modulate both amplitude and phase of the field. Moreover, the optical assembly is based on a Mach-Zehnder interferometer where the two components of the field can be independently manipulated in each arm of the interferometer. Applying an arbitrary modulation in both compontents, we can sculpt any profile with any distribution of polarization. To show this flexibility, a set of beams with multiple profiles and polarization distribution have been presented. In addition, taking this modulation capability, we introduce an holographic encryption technique where the secret keys are polarization masks. Two physical parameters are necessary to decrypt the information, increasing the security of the system. We have simulated the system response under very low illumination. Once guaranteed the flexibility in the design of paraxial beams with arbitrary polarization distribution, a theoretical framework to synthesize highly focused beams with an arbitrary three-dimensional polarization has been developed. The B. Richards y E. Wolf theory relates the polarization distribution on the entrance pupil of a microscope objective with the vectorial structure of the field in the focal region. To evaluate the performance of the system we have implemented a highly focused beam (NA=0.85) with circular polarization in any plane. The definition of the degree of polarization in highly focused beams even now generates some discussion because it can not be expanded unequivocally as a direct sum of completely polarized fields and completely depolarized fields. In this thesis, we have made the study within the frame of generalized Stokes parameters. We have obtained a correspondence between the distribution of the Stokes parameters in the entrance pupil and the distribution of the transverse Stokes parameters in the focused field. We have proposed a paraxial beam, which once focused, it generates a field with the transverse components depolarized and a non-zero longitudinal component

Experimental implementation of tightly focused beams with unpolarized transversal component at any plane

The aim of this paper is to provide a formal framework for designing highly focused fields with specific transversal features when the incoming beam is partially polarized. More specifically, we develop a field with a transversal component that remains unpolarized in the focal area. Moreover, its longitudinal component exhibits non-zero values on axis. Special attention is paid to the design of the input beam and the development of the experiment. The implementation of such fields is possible by using an interferometric setup combined with the use of digital holography techniques. Experimental results are compared with those obtained numerically

On the behavior of vector light needles using modulation functions with topological charge

In the present communication, we describe how to produce long light distributions in the focal area of a high numerical aperture optical system using a custom modulation function with spiral charge. This analysis expands our previous developments in the field. We analyze the effect of this new element on the behavior of light along the optical axis

Synthesis of light needles with tunable length and nearly constant irradiance

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques. In this way, a polarized input beam is shaped and subsequently focused using a high numerical aperture (NA) objective lens. As a result, needles with variable length and nearly constant irradiance are produced using conventional optics components. This procedure is experimentally demonstrated obtaining a 53λ-long and 0.8λ-wide needle

Effect of linear polarizers on the behavior of partially coherent and partially polarized highly focused fields

In this Letter, we describe the behavior of partially coherent, partially polarized focused vector beams after passing a linear polarizer placed at the focal plane of a high numerical aperture microscope lens. In particular, we develop a mathematical framework for such beams that helps the understanding of the performance of polarizers when interact with non-paraxial beams. The features of the focused field after the polarizer are numerically evaluated for some illustrative examples

Optical Encryption using Photon-Counting Polarimetric Imaging

We present a polarimetric-based optical encoder for image encryption and verification. A system for generating random polarized vector keys based on a Mach-Zehnder configuration combined with translucent liquid crystal displays in each path of the interferometer is developed. Polarization information of the encrypted signal is retrieved by taking advantage of the information provided by the Stokes parameters. Moreover, photon-counting model is used in the encryption process which provides data sparseness and nonlinear transformation to enhance security. An authorized user with access to the polarization keys and the optical design variables can retrieve and validate the photon-counting plain-text. Optical experimental results demonstrate the feasibility of the encryption method

Experimental Estimation of the Longitudinal Component of a Highly Focused Electromagnetic Field

The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss's theorem. Experimental results show an excellent agreement with theoretical predictions

Modeling axial irradiance distortion in holographic optical needles produced with high numerical aperture lenses

Optical needles produced by means of diffractive technology might display limited quality and uniformity. It has been suggested that the bulky optical elements present on these setups can be responsible of such behavior. In particular, issues such as the lack of flatness of the optical components, modulation errors in the holographic displays, and optical aberrations might degrade the quality of the needle. In this paper, we model how these variables affect the uniformity of the irradiance of the needle on the propagation axis. A comparison between experimental and computationally estimated results is provided

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation

Effect of linear polarizers on highly focused spirally polarized fields

Linear polarizers are commonly used for projecting the direction of the electric field of a transverse paraxial beam on the direction of the polarizer axis. However, the use of these devices with highly convergent field poses a practical problem because the non transversal character of electric field. In this article, we discuss the behavior of highly focused beams with spiral polarization when they pass through a polarizer. Interestingly, beams with azimuthal polarization display a non negligible irradiance in the direction of propagation after passing through a polarizer. On top of that, we found that the irradiance of a highly focused radially polarized beam after a polarizer is notably different from the projection of the field on the direction of the polarizer axis