In this contribution we study the relation between the second order intensity moments and the Goos-Hänchen shift for partially coherent totally polarized beams. The results are applied to a type of partially coherent beams, the Cosine-Gaussian Schell-model beams with rectangular symmetry.
In this work a new type of partially polarized and partially coherent sources is proposed. The coherence characteristics of these sources are dependent on the difference of the radial distances from the source center of the two points to be compared. The coherence is perfect for points located on the same circle centered on the source center and decreases for points that belongs to different concentric circles. The maximum attainable coherence is related to the degree of polarization of the source. Coherence and polarization characteristics of this kind of fields at the source plane and upon free space propagation are analyzed in detail for a simple case. For the particular presented example, a partially polarized and partially coherent field is obtained, whose polarization properties are invariant in propagation.
In this communication we analyze the light field distribution of a highly focused radially polarized beam when passes through a linear polarizer. The polarizer is modeled as a plane-parallel uniaxial absorbing medium with the optical axis parallel to the plate surfaces of the polarizer. Analytical results and numerical calculations are provided.
Analytical expressions are provided for describing the overall free-space evolution of the polarization structure of paraxial vortex beams whose electric-field vector at some transverse plane exhibits a radially polarized behaviour. At each transverse plane, the polarization distribution across the beam profile is characterized by means the percentage of the irradiance associated with the radial or azimuthal components. The propagation laws for these percentages are also shown. As an illustrative example, a radially polarized partially coherent vortex beam is analized.
The target of this communication is to present a method for tailoring the complex amplitude and the polarization at the entrance pupil of a high numerical aperture objective lens in order to obtain focused fields with transverse circular polarization at any plane. Analytical expressions within the framework of the Richards-Wolf vectorial model are derived and some numerical results are presented.
On the basis of the second order irradiance-moments formalism some relations between the normalized weighted average of the Gouy phase shift and the spatial structure of partially coherent beams have been investigated.
A method for generating beams with arbitrary polarization and shape is proposed. Our design requires the use of
a Mach-Zehnder set-up combined with translucent liquid crystal displays in each arm of the interferometer; in this
way, independent manipulation of each transverse beam components is possible. The target of this communication
is to develop a numerical procedure for calculating the holograms required for dynamically encode any amplitude
value and polarization state in each point of the wavefront. Several examples demonstrating the capabilities of
the method are provided.
Recently, the development of optical setups capable of generating beams with arbitrary polarization have attracted
broad interest. One possible way to implement such devices is by taking advantage of the properties
of liquid crystal spatial light modulators, which act as optical phase retarders controlled by computer. In this
communication we present the design of an alternative experimental setup for the generation of light beams
with arbitrary spatially-variant polarization distribution. The objective is to develop a flexible optical device
capable of dynamically encode any elliptical polarization state in each point of the wavefront. Our approach is
based on a Mach-Zehnder setup combined with a translucent modulator in each path of the interferometer. The
transverse beam components of the incident light beam are processed independently, and modified by means of
their respective modulator displaying a specifically tailored computer generated phase hologram.
We investigate the contributions of the propagating and the evanescent waves associated to freely-propagating
nonparaxial light beams whose transverse component at some plane is azimuthally polarized. In terms of the plane-wave
angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above
components and their relative weight integrated over the whole transverse plane. The results are applied to a kind of
doughnut-like beams with transverse azimuthal polarization.
Within the paraxial framework, use of spiral phase elements is proposed for the shaping of light beams. More
specifically, we analytically investigate some anisotropic optical devices for inducing controlled changes in several
spatial and vectorial characteristics of light. As an illustrative example, depleted-center beams are considered.
Analytical definitions are proposed for the width of both the transverse and the longitudinal component of a nonparaxial
radially-polarized light field at the focal plane of a highly focusing system. By means of an illustrative example, it is also
shown that the irradiance is significant within a circle whose radius is given by the proposed beam width. Moreover, the
power contained within such circular region around the focal point is shown to concentrate the main part of the total
Several overall parameters are introduced to characterize the linear or circular polarization content of a non-uniformly totally polarized beam over the region of its wavefront where the irradiance is significant. These parameters are determined from the values of the Stokes parameters. Experimental examples are also given to check both, the physical meaning of the proposed parameters and the validity of the measurement procedure.
On the basis of the irradiance-moments formalism, four matrices are proposed whose elements, defined for any partially coherent field, are closely related with the second-order measurable parameters handled in the ISO standard 11146. These matrices are shown to exhibit a number of properties concerning the orientation of the transverse beam profile. This behavior is described by the rotation of the principal axes of the field around its propagation axis. In addition, a new parameter is introduced in terms of the above matrices, which is invariant through rotationally-symmetric first-order optical systems.
More than 60 demonstrations and basic experiments in Optics have been compiled. They can be carried out by secondary and university students in the classroom or at home, and have been conceived considering low cost and easy-to-get materials. The goal is to offer didactic resources, showing that Optics can be taught in an attractive and amusing way. The experiments try to stimulate scientific curiosity, and generate interest in the observation of our physical world. The work could be collected as a book, where each demonstration would be contained in one or two pages, including a title, a list of the required materials and a concise explanation about what to do and observe. Associated with the experimental content, we propose a web page, namely, http://www.ucm.es/info/expoptic, that accepts experiments sent by anyone interested in Optics, which can be used as a forum to interchange information on this educational topic.
Use of anisotropic pure phase plates to improve the quality parameter of certain partially coherent and partially polarized beams is investigated. Analytical expressions for the beam quality after propagation through these anisotropic transmittances are obtained. Conditions to get the best quality are also derived.
On the basis of a representation of the general solution of the Maxwell equations in terms of the angular spectrum of the electromagnetic field, the concept of the so-called closest solution to a given field is analyzed. In particular, we investigate the spatial profile and the polarization structure of the closest field to a polarized Gaussian beam.
The behavior of the so-called generalized degree of polarization of partially coherent partially polarized beams upon free propagation is investigated. On the basis of this parameter a general classification scheme of partially polarized beams is proposed. The results are applied to certain classes of fields of special interest.
In the present work we extend the intensity-moment spatial characterization to partially polarized beams by means of a generalization of the Stokes-Mueller formalism. A simple classification scheme of partially polarized beams is proposed and propagation laws through non-polarizing and polarizing optical systems are provided. Some invariant parameters are investigated and a general measuring procedure is pointed out.
We investigate from both a theoretical and an experimental point of view the dependence of the spatial parameters (integrated along the pulse length) of TEA carbon dioxide laser pulses on the presence of nitrogen in the gas mixture and also on the size of an intracavity diaphragm used to attenuate higher-order modes.
As is well-known, pure-phase transmittances are not, in general, first-order optical systems. It thus seems that a simple ABCD-propagation law cannot be applied to this kind of transmittance. In other words, such optical elements could not be characterized by an overall ABCD matrix. The aim of the present contribution is to overcome this trouble. In fact, the propagation laws of the intensity moments of a laser beam through ABCD optical systems are generalized to include pure phase transmittances. This is done by representing the behavior of such transmittances by means of a 4 by 4 matrix, M, which can be handled, to some extent, as the ABCD-matrices associated with ordinary first-order optical systems. This formalism enables the application of ABCD propagation formulae to cascaded optical systems containing pure phase transmittances. Matrix M is applied, in particular, to determine the intensity moments and the beam quality parameter at the output of special quartic phase transmittances, namely, thin and thick spherically aberrated lenses.
Several key parameters of use to characterize the spatial behaviour of arbitrary partially coherent beams are reviewed. A number of the existing open problems and physical aspects, in which the up-to-date formalism is not completely satisfactory, are briefly discussed.
The spatial behavior of a certain class of depleted-center intensity beams is analyzed by introducing a number of characteristic parameters, including the concept of lateral mean position, lateral beam width, and lateral far-field divergence.
New parameters are proposed which characterize arbitrary multimode tridimensional laser beams propagating through ABCD optical systems. Such definitions are shown to be related with the bidimensional concept of beam quality. Dependence on the propagation distance and coherence properties of the input field is illustrated by means of some examples.
A general analytical-numerical procedure has been established to calculate the amplitude of a laser beam propagating through an active amplifying medium, valid for arbitrary spatial inhomogeneities. The characteristic parameters representing the medium are small-signal gain, refractive index and saturation intensity.
Using the thin-sheet bidimensional model, propagation of the beam quality of arbitrary multimode beams through laser amplifiers is analysed. An stochastic formalism based on the Wigner distribution function of the field is employed, and some general properties of the spatial characteristics of the beams are pointed out.
For general multimode laser beams, a number of parameters is derived which are invariant under propagation through ABCD optical systems. Wigner formalism is used and the bidimensional case is considered, The relationship between these parameters and quasihomogeneous fields is also discussed.