Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30302
Modeling Bessel Beams and Their Discrete Superpositions from the Generalized Lorenz-Mie Theory to Calculate Optical Forces over Spherical Dielectric Particles

Authors: Leonardo A. Ambrosio, Carlos. H. Silva Santos, Ivan E. L. Rodrigues, Ayumi K. de Campos, Leandro A. Machado

Abstract:

In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.

Keywords: Numerical Methods, Bessel Beams and Frozen Waves, Generalized Lorenz-Mie Theory, optical forces

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1339039

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1646

References:


[1] H. L. Guo and Z. Y. Li, “Optical tweezers technique and its applications,” Science China Phys. Mech. Astron., vol. 56, pp. 2351–2360, December 1993.
[2] P. H. Jones, O. M. Maragò, and G. Volpe, Optical Tweezers: Principles and Applications. Cambridge: Cambridge University Press, 2015, Part III.
[3] M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape, by superposing equal frequency Bessel beams: frozen waves,” Opt. Express, vol. 12, pp. 4001–4006, August 2004.
[4] M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of ‘frozen waves’: modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A, vol. 22, pp. 2465–2475, November 2005.
[5] M. Zamboni-Rached, L. A. Ambrosio, and H. E. Hernández-Figueroa, “Diffraction-attenuation resistant beams: their higher-order versions and finite-aperture generations,” Appl. Opt., vol. 49, pp. 5861–5869, October2010.
[6] T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett., vol. 37, pp. 2034–2036, June 2012.
[7] G. Gouesbet, and G. Gréhan, Generalized Lorenz-Mie Theories. Berlin: Springer-Verlag, 2011.
[8] J. Durnin, J. J. Miceli, and J. H. Eberli, “Diffraction-free beams,” Phys. Rev. Lett., vol. 58, pp. 1499−1501, April 1987.
[9] J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A, vol. 4, pp. 651−654, April 1987.
[10] V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam”, Nature, vol. 419, pp. 145−147, September 2002.
[11] D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett., vol. 28, pp. 657−659, April 2003.
[12] A. N. Rubinov, A. A. Afanas’ev, I. E. Ermolaev, Y. A. Kurochkin, and S. Y. Mikhnevich, “Localization of spherical particles under the action of gradient forces in the field of a zero-order Bessel beam. Rayleigh-Gans approximation”, J. Appl. Spectr., vol. 70, pp. 565−572, July 2003.
[13] V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, “Optical levitation in a Bessel light beam”, Appl. Phys. Lett., vol. 85, pp. 4001−4003, November 2004.
[14] G. Milne, K. Dholakia, D. McGloin, K. Volke-Sepulveda, and P. Zemánek, “Transverse particle dynamics in a Bessel beam”, Opt. Express, vol. 15, pp. 13972−13987, October 2007.
[15] L. A. Ambrosio, and M. Zamboni-Rached, “Analytical approach of ordinary frozen waves for optical trapping and micromanipulation,” Appl. Opt., vol. 54, pp. 2584−2593, April 2015.
[16] L. A. Ambrosio, and M. de M. Ferreira, “Time-average forces over Rayleigh particles by superposition of equal-frequency arbitrary-order Bessel beams,” J. Opt. Soc. Am. B, vol. 32, pp. 67−74, May 2015.
[17] L. A. Ambrosio, and M. Zamboni-Rached, “Optical forces experienced by arbitrary-sized spherical scatterers from superpositions of equal-frequency Bessel beams,” J. Opt. Soc. Am. B, vol. 32, pp. 37−46, May 2015.
[18] L. A. Ambrosio, and H. E. Hernández-Figueroa, “Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces,” Biomed. Opt. Express, vol. 2, pp. 1893−1906, July 2011.
[19] W. L. Moreira, A. A. R. Neves, M. K. Garbos, T. G. Euser, P. St. J. Russell, and C. L. Cesar, “Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions,” http://arxiv.org/abs/1003.2392v3, May 2012.
[20] P. T. Hacken, “Computer-assisted language learning and the revolution in computational linguistics,” Linguistik online, vol. 17, pp. 23–39, 2003.
[21] S. van der Walt, S. C. Colbert, and G. Varoquaux. “The NumPy array: a structure for efficient numerical computation,” Comp. Sci. & Eng., vol. 13, pp. 22–30, March-April 2011.
[22] A. Bultheel, “Book Review: 'Numerical Methods in Engineering with Python 3 (J. Kiusalaas)',” Euro. Math. Soc., October 2013.
[23] E. Ayars, “Finally, a Python-Based Computational Physics Text," Comp. Sci. & Eng., vol. 16, pp. 6–7, January-February 2014.
[24] F. Perez, B. E. Granger, and J. D. Hunter. “Python: an ecosystem for scientific computing,” Comp. Sci. & Eng., vol. 13, pp. 13–21, March-April 2010.
[25] G. Rashed, and R. Ahsan, “Python in computational science: applications and possibilities,” Intl. J. Comp. Appl., vol. 46, pp. 26–30, May 2012.
[26] Python Software Foundation, available on: https://www.python.org/psf/, accessed on: 12/15/2015.
[27] Python Source Page, available on: https://www.python.org/, accessed on 12/15/2015.
[28] K. Han, P. C. Shih, V. Bellotti, and J. M. Carroll, “It's Time There Was an App for That Too: A Usability Study of Mobile Timebanking,” Intl. J. Mob. Human Computer Interactions, vol. 7, pp. 1–22, April-June 2015.
[29] J. T. Pintas, D. de Oliveira, K. A. C. S. Ocaña, E. Ogasawara, and M. Mattoso, “SciLightning: A Cloud Provenance-Based Event Notification for Parallel Workflows,” Service-Oriented Computing–ICSOC 2013 Workshops, Lecture Notes in Computer Science, vol. 8377, pp. 352-365, 2014.
[30] T. Page, “Touchscreen mobile devices and older adults: a usability study,” Intl. J. Human Factors and Ergonomics, vol. 3, pp. 65–85.
[31] Available on http://docs.scipy.org/doc/scipy/reference/special.html, accessed on 12/29/2015.
[32] J. D. Hunter, “Matplotlib: A 2D graphics environment,” Comp. Sci. & Eng., vol. 9, 90–95, May-June 2007.