**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:**

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

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

**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.