Publications: Electromagnetic beams in the focal domain
Analysis of the behavior of highly focused, radially coherent Dirichlet sources
Rosario Martínez-Herrero, Marcos Aviñoá, Artur Carnicer
Optics & Laser Technology Vol. 174, 110720 (2024)
We introduce a novel class of electromagnetic light sources that exhibit radial coherence, a degree of coherence characterized by a Dirichlet kernel, and with radial or azimuthal polarization. We provide a mathematical description of the spectral irradiance, 3D degree of polarization, and electromagnetic degree of coherence for such sources when they are focused using a high numerical aperture microscope lens. Since the incident beam can be described as a modal expansion, we also consider how the number of terms affects the behavior of the field in the focal area. The formal analysis is complemented with numerical simulations. The study reveals interesting properties in the focal area, despite the focused beam is no longer radially coherent.
https://doi.org/10.1016/j.optlastec.2024.110720
Local characterization of the polarization state of 3D electromagnetic fields: an alternative approach
Rosario Martínez-Herrero, David Maluenda, Marcos Aviñoá, Artur Carnicer, Ignasi Juvells, and Ángel S. Sanz
Photonics Research Vol. 11, Issue 7, pp. 1326-1338 (2023)
A precise knowledge of the polarization state of light is crucial in technologies that involve the generation and application of structured light fields. The implementation of efficient methods to determine and characterize polarization states is mandatory; more importantly, these structured light fields must be at any spatial location at a low expense. Here, we introduce a new characterization method that relies on a rather convenient description of electric fields without neglecting their 3D nature. This method is particularly suitable for highly focused fields, which exhibit important polarization contributions along their propagation direction in the neighborhood of the focal region; i.e., the contributions out of the planes transverse to the optical axis, conventionally used to specify the polarization state of these fields. As shown, the method allows the extraction of information about the three field components at relatively low computational and experimental costs. Furthermore, it also allows characterization of the polarization state of a field in a rather simple manner. To check the feasibility and reliability of the method, we determined both analytically and experimentally the local polarization states for a series of benchmark input fields with it, finding excellent agreement between the theory and experiment.
https://doi.org/10.1364/PRJ.488703
Experimental estimation of the longitudinal component of a highly focused electromagnetic field
David Maluenda, Marcos Aviñoá, Kavan Ahmadi, Rosario Martínez-herrero, and Artur Carnicer
Scientific Reports Vol. 11, 17992 (2021).
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.
https://doi.org/10.1038/s41598-021-97164-z
Efficient calculation of highly focused electromagnetic Schell-model beams
Marcos Aviñoá, Rosario Martínez-Herrero, and Artur Carnicer
Optics Express Vol. 29(16), 26220-26232 (2021)
The calculation of the propagation of partially coherent and partially polarized optical beams involves using 4D Fourier Transforms. This poses a major drawback, taking into account memory and computational capabilities of nowadays computers. In this paper we propose an efficient calculation procedure for retrieving the irradiance of electromagnetic Schell-model highly focused beams. We take advantage of the separability of such beams to compute the cross-spectral density matrix by using only 2D Fourier Transforms. In particular, the number of operations depends only on the number of pixels of the input beam, independently on the coherence properties. To provide more insight, we analyze the behavior of a beam without a known analytical solution. Finally, the numerical complexity and computation time is analyzed and compared with some other algorithms.
https://doi.org/10.1364/OE.432677
Code: M. Aviñoá, Mode-less convolution algorithm, https://github.com/kramos966/moleca.
Uncertainty principle for axial power content of highly focused fields
Rosario Martínez-Herrero, Artur Carnicer, Ignasi Juvells, Ángel S. Sanz
Optics Express 28(20), 29676-29690 (2020)
In the analysis of the on-axis intensity for a highly focused optical field, it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of the region where the axial power content mainly concentrates is proposed on the basis of an uncertainty principle. Accordingly, a meaningful relationship is provided for both the spread of the incident beam at the entrance of the highly focused optical system and the size of the region where the on-axis power mainly concentrates.
https://doi.org/10.1364/OE.401073
Modeling axial irradiance distortion in holographic optical needles produced with high numerical aperture lenses
David Maluenda, Ignasi Juvells, Rosario Martínez-Herrero, Artur Carnicer
OSA Continuum 2(5), 1539-1547 (2019)
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.
https://doi.org/10.1364/OSAC.2.001539
Code: M. Maluenda, A numerical tool to evaluate highly focused holographic optical needles, https://figshare.com/s/d91bac6b21e43939cbcb
Effect of linear polarizers on the behavior of partially coherent and partially polarized highly focused fields
R. Martínez-Herrero, D. Maluenda, I. Juvells, A. Carnicer
Optics Letters 43(14), 3445-3448 (2019)
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.
https://doi.org/10.1364/OL.43.003445
Partially-coherent spirally-polarized gradual-edge imaging
M. Pérez-Aviñoa, R. Martínez-Herrero, S. Vallmitjana, P. Latorre-Carmona, I. Juvells, A. Carnicer
Optics and Lasers in Engineering 112, 53-58 (2019)
In this work we develop a partially-coherent spirally-polarized imaging system for generating gradual edge detection images. A rotating diffuser is used for producing illumination sources with tunable degree of coherence. Using a 4f configuration, the frequency content of the image is modified by means of a vortex half-wave retarder as a spatial filter. Accordingly, we analytically describe a spirally-polarized imaging system illuminated with a Gauss–Schell source using paraxial coherence-polarization theory. Numerical simulations and experimental results demonstrate the validity of our approach. We use a referenceless spatial content descriptor to assess the quality of the recorded images as a function of the coherence state of the source.
https://doi.org/10.1016/j.optlaseng.2018.09.003
Effect of linear polarizers on the behavior of partially coherent and partially polarized highly focused fields
R. Martínez-Herrero, D. Maluenda, I. Juvells, A. Carnicer
Optics Letters 43(14) 3445-3448 (2018)
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.
https://doi.org/10.1364/OL.43.003445
Synthesis of light needles with tunable length and nearly constant irradiance
Rosario Martínez-Herrero, David Maluenda, Ignasi Juvells, Artur Carnicer
Scientific Reports 8(1), 1-10 (2018)
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.
https://doi.org/10.1038/s41598-018-21007-7
Effect of linear polarizers on highly focused spirally polarized fields
Rosario Martínez-Herrero, David Maluenda, Ignasi Juvells, Artur Carnicer
Optics and Lasers in Engineering (98), 176-180 (2017)
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.
https://doi.org/10.1016/j.optlaseng.2017.06.027
Polarisers in the focal domain: Theoretical model and experimental validation
Rosario Martínez-Herrero, David Maluenda, Ignasi Juvells, Artur Carnicer
Scientific Reports 8, 42122 (2017)
Polarisers are one of the most widely used devices in optical set-ups. They are commonly used with paraxial beams that propagate in the normal direction of the polariser plane. Nevertheless, the conventional projection character of these devices may change when the beam impinges a polariser with a certain angle of incidence. This effect is more noticeable if polarisers are used in optical systems with a high numerical aperture, because multiple angles of incidence have to be taken into account. Moreover, the non-transverse character of highly focused beams makes the problem more complex and strictly speaking, the Malus’ law does not apply. In this paper we develop a theoretical framework to explain how ideal polarisers affect the behavior of highly focused fields. In this model, the polarisers are considered as birefringent plates, and the vector behaviour of focused fields is described using the plane-wave angular spectrum approach. Experiments involving focused fields were conducted to verify the theoretical model and a satisfactory agreement between theoretical and experimental results was found.
https://doi.org/10.1038/srep42122
Experimental implementation of tightly focused beams with unpolarized transversal component at any plane
Rosario Martínez-Herrero, David Maluenda, Ignasi Juvells, Artur Carnicer
Optics Express 22(26), 32419-32428 (2014)
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. 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.
https://doi.org/10.1364/OE.22.032419
Design of highly focused fields that remain unpolarized on axis
Rosario Martínez-Herrero, Ignasi Juvells, Artur Carnicer
Optics Letters 39(20) 6025-6028 (2014)
Research on the properties of highly focused fields mainly involved fully polarized light, whereas partially polarized waves received less attention. The aim of this Letter is to provide an appropriate framework, for designing some features of the focused field, when dealing with incoming partially polarized beams. In particular, in this Letter, we describe how to get an unpolarized field on the axis of a high numerical aperture objective lens. Some numerical results that corroborate theoretical predictions are provided.
https://doi.org/10.1364/OL.39.006025
Synthesis of highly focused fields with circular polarization at any transverse plane
David Maluenda, Rosario Martínez-Herrero, Ignasi Juvells, Artur Carnicer
Optics Express 22(6) 6859-6867 (2014)
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.
https://doi.org/10.1364/OE.22.006859
Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields
Rosario Martínez-Herrero, Pedro M Mejías, Ignasi Juvells, Artur Carnicer
Applied Physics B 112(1), 123-131 (2013)
The contribution of the propagating and the evanescent waves associated with freely propagating non-paraxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysis is carried out within the framework of the plane-wave angular spectrum approach. These results are used to illustrate the behavior of a kind of donut-like beams with transverse azimuthal polarization at some plane.
https://doi.org/10.1007/s00340-013-5408-3
On the physical realizability of highly focused electromagnetic field distributions
Rosario Martínez-Herrero, Ignasi Juvells, Artur Carnicer
Optics Letters 39(12), 2065-2067 (2013)
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.
https://doi.org/10.1364/OL.38.002065
Reconfigurable beams with arbitrary polarization and shape distributions at a given plane
David Maluenda, Ignasi Juvells, Rosario Martínez-Herrero, Artur Carnicer
Optics Express 21(5) 5432-5439 (2013)
Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.
https://doi.org/10.1364/OE.21.005432
On the longitudinal component of paraxial fields
Artur Carnicer, Ignasi Juvells, David Maluenda, Rosario Martínez-Herrero, Pedro M Mejías
European Journal of Physics 33(5), 1235 (2012)
The analysis of paraxial Gaussian beams features in most undergraduate courses in laser physics, advanced optics and photonics. These beams provide a simple model of the field generated in the resonant cavities of lasers, thus constituting a basic element for understanding laser theory. Usually, uniformly polarized beams are considered in the analytical calculations, with the electric field vibrating at normal planes to the propagation direction. However, such paraxial fields do not verify the Maxwell equations. In this paper we discuss how to overcome this apparent contradiction and evaluate the longitudinal component that any paraxial Gaussian beam should exhibit. Despite the fact that the assumption of a purely transverse paraxial field is useful and accurate, the inclusion of the above issue in the program helps students to clarify the importance of the electromagnetic nature of light, thus providing a more complete understanding of the paraxial approach.
https://doi.org/10.1088/0143-0807/33/5/1235
Transverse and longitudinal components of the propagating and evanescent waves associated to radially polarized nonparaxial fields
Rosario Martínez-Herrero, Pedro M Mejías, Ignasi Juvells, Artur Carnicer
Applied Physics B 106(1), 151-159 (2012)
A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. 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 two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.
https://doi.org/10.1007/s00340-011-4720-z
Evanescent field of vectorial highly non-paraxial beams
R Martinez-Herrero, PM Mejias, A Carnicer
Optics Express 16(5), 2845-2858 (2008)
In terms of the Fourier spectrum, a simple but general analytical expression is given for the evanescent field associated to a certain kind of non-paraxial exact solutions of the Maxwell equations. This expression enables one to compare the relative weight of the evanescent wave with regard to the propagating field. In addition, in those cases in which the evanescent term is significant, the magnitude of the field components across the transverse profile (including the evanescent features) can be determined. These results are applied to some illustrative examples.
https://doi.org/10.1364/OE.16.002845
Structure of the transverse profile of Gaussian-model non-paraxial electromagnetic beams
R Martínez-Herrero, PM Mejías, S Bosch, A Carnicer
Journal of Optics A: Pure and Applied Optics 8(6), 524 (2006)
Starting from the (inexact) Gaussian beam model, and on the basis of a plane-wave spectrum representation of non-paraxial electromagnetic fields, three free-propagating exact solutions of the Maxwell equations are investigated. The transverse part of one of these solutions is shown to closely resemble both the beam profile irradiance and the polarization distribution of a typical Gaussian beam. A limit has also been established for the validity of the paraxial regime, particularly for focused beams whose size at the waist approaches the light wavelength.
https://doi.org/10.1088/1464-4258/8/6/006
Spatial width and power-content ratio of hard-edge diffracted beams
Rosario Martı́nez-Herrero, Pedro M Mejı́as, Salvador Bosch, Artur Carnicer
Journal of the Optical Society of America A 20(2), 388-391 (2003)
On the basis of the intensity-moment formalism, certain analytical relationships are obtained for both the angular domain and the size of a transverse region of the beam that ensure a power content of at least 75% of the total power. As an illustrative application, the analytical results are compared with the exact values (numerically computed) of the amplitude of a lowest-order Gaussian beam diffracted by slits.
https://doi.org/10.1364/JOSAA.20.000388
Vectorial structure of nonparaxial electromagnetic beams
Rosario Martnez-Herrero, Pedro M Mejas, Salvador Bosch, Artur Carnicer
Journal of the Optical Society of America A 18(7), 1678-1680 (2001)
A representation of the general solution of the Maxwell equations is proposed in terms of the plane-wave spectrum of the electromagnetic field. In this representation the electric field solution is written as a sum of two terms that are orthogonal to each other at the far field: One is transverse to the propagation axis, and the magnetic field associated with the other is also transverse. The concept of the so-called closest field to a given beam is introduced and applied to the well-known linearly polarized Gaussian beam.
https://doi.org/10.1364/JOSAA.18.001678
Research funded by Ministerio de Ciencia e Innovación, Spain MCIN/AEI / 10.13039/501100011033
- Grant PID2022-136796OB-I00
- Grant PID2019-104268GB-C22
