Application software for teaching the polarization ellipse

Aplicación para la enseñanza de la elipse de polarización

By: C. Cano, S. Echeverri-Chacón, C. Cuartas-Vélez, L. ángel, R. Restrepo

Main Information

Volume:
Vol.51-N3 / 2018 - Ordinario
Section:
Image Processing and Imaging Techniques
Pages:
50307:1-9
DOI:
http://doi.org/10.7149/OPA.51.3.50307
Type:
Education Paper
Language:
English
Attachments:
Keywords:
Polarization ellipse; Jones calculus; Minimization.

Elipse de polarización; Cálculo de Jones; Minimización.
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Abstract

This paper describes the development of a computational application that calculates the configuration of a polarization state generator, according to the parameters of a desired polarization ellipse. The most general way to describe the polarization state of light is an ellipse, however, it is rarely used in practical courses in which applications are limited to the case of linear or circular polarization. To generate a desired polarization ellipse, a polarizer and a pair of retarders of λ/2 and λ/4 can be used, the problem is to determine the angle of rotation of the retarders. We present an open source algorithm to calculate these angles by using a minimization method applied to the Jones calculus description of polarizing elements. This development aims to help research and education activities to promote a more practical understanding of the polarimetric properties of light.


En este trabajo se presenta el desarrollo de una aplicación computacional que permite determinar la configuración de un generador de estados de polarización en función de los parámetros de una elipse de polarización deseada. La manera más general de describir la polarización de la luz es una elipse, sin embargo, este estado rara vez se aborda en un curso práctico en los cuales las aplicaciones se limitan al caso de la polarización lineal o circular. Para generar una elipse de polarización deseada se puede utilizar un polarizador y un par de retardadores de λ/2 y λ/4, el problema está en determinar a qué ángulo deben estar ubicados los retardadores. Se presenta un algoritmo de acceso libre que calcula estos ángulos mediante un método de minimización aplicado al cálculo de Jones. Este desarrollo va dirigido a actividades de investigación y educación, para promover una comprensión práctica de las propiedades polarimétricas de la luz.

References

[1] G. Duree, Optics for Dummies. Indianapolis, John Wiley & Sons (2011).

[2] E. Hecht, Óptica. Madrid, Pearson Educación (2000).

[3] E. Wolf, Progress in Optics. New York, Elsevier (2000).

[4] G. Brooker, Modern Classical Optics. New York, OUP Oxford (2003).

[5] G. Gurin, K. Titov, Y Ilyin, A. Tarasov, "Induced polarization of disseminated electronically conductive minerals: a semi-empirical model", Geophys. J. Int. 200, 1555-1565 (2015).

[6] C. Bérubé, M. Chouteau, P. Shamsipour, R. Enkin, G. Olivo, "Bayesian inference of spectral induced polarization parameters for laboratory complex resistivity measurements of rocks and soils", Comput. Geosci. 105, 51-64 (2017).

[7] F. Fontaine, G. Barruol, B. Kennett, G. Bokelmann, D. Reymond, "Upper mantle anisotropy beneath Australia and Tahiti from P wave polarization: Implications for real-time earthquake location", J. Geophys. Res. 114, B3 (2009).

[8] H. Sarkissian, S. Serak, N. Tabiryan, L. Glebov, V. Rotar, B. Zeldovich, "Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals", Opt. Lett. 31, 2248-2250 (2006).

[9] A. Golaraei, L. Kontenis, R. Cisek, D. Tokarz, S. Done, B. Wilson, V. Barzda, "Changes of collagen ultrastructure in breast cancer tissue determined by second-harmonic generation double Stokes-Mueller polarimetric microscopy," Biomed. Opt. Express 7, 4054-4068 (2016).

[10] T. Novikova, A. Pierangelo, A. De Martino, A. Benali, P. Validire, "Polarimetric Imaging for Cancer Diagnosis and Staging," Opt. Photonics News 23(10), 26-33 (2012).

[11] A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Radiation, New Jersey (2002).

[12] A. Pitilakis, D. Zografopoulos, E. Kriezis, "In-Line Polarization Controller Based on Liquid-Crystal Photonic Crystal Fibers," J. Lightwave Technol. 29, 2560-2569 (2011).

[13] W. Sparks, J. Hough, L. Kolokolova, T. Germer, F. Chen, S. DasSarma, P. DasSarma, F. Robb, N. Manset, I. Reid, F. Macchetto, W. Martin, "Circular polarization in scattered light as a possible biomarker", J. Quant. Spectrosc. Ra. 110, 1771-1779 (2009).

[14] B. Wen, R. Petschek, C. Rosenblatt, "Nematic liquid-crystal polarization gratings by modification of surface alignment," Appl. Opt. 41, 1246-1250 (2002).

[15] E. Collet, Field Guide to Polarization. Bellingham, SPIE Press (2005).

[16] D. Goldstein, Polarized Light, New York. Taylor & Francis Group (2011).

[17] W. McMaster, "Matrix Representation of Polarization", Rev. Mod. Phys. 33, 8-28 (1961).

[18] L. Rios, "Derivative-free optimization: a review of algorithms and comparison of software implementations", J. Global Optim. 56, 1247-1293 (2013).