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Leonardo André Ambrosio sel.eescp.br/leonardo Xi’an , China, 2019

AEG. Milli - and micro-structured beams constructed from superpositions of Bessel beams and their potential applications. Leonardo André Ambrosio www.sel.eesc.usp.br/leonardo Xi’an , China, 2019. University of São Paulo. University of São Paulo. World rankings 145th (CWUR) 116th (QS)

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Leonardo André Ambrosio sel.eescp.br/leonardo Xi’an , China, 2019

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  1. AEG Milli- and micro-structured beams constructed from superpositions of Bessel beams and their potential applications Leonardo André Ambrosio www.sel.eesc.usp.br/leonardo Xi’an, China, 2019

  2. University of São Paulo

  3. Universityof São Paulo • World rankings • 145th (CWUR) • 116th (QS) • 251-300th (THE) • 151-200 (ARWU) Center for World University Rankings (CWUR, https://cwur.org/2017.php) QS World University Rankings (https://www.topuniversities.com/university-rankings/world-university-rankings/2020) Times HigherEducation (THE, https://www.timeshighereducation.com/world-university-rankings) Shanghai Ranking 2018 (ARWU, http://www.shanghairanking.com/ARWU2018.html)

  4. Universityof São Paulo – São Carlos Campus Universityof São Paulo • Established: 1934 • Campi: 11 (in 8 cities) • SchoolsandInstitutes: 42 • Annual budget (2018): $1.00b • Undergraduateprograms: 312 • Undergraduatestudents: 58,823 • Graduateprograms: 222 • Graduatestudents: 30,000+ • Academic staff: 5,800+ • Administrative staff: 15,000+ • Established: 1948 • SchoolsandInstitutes: 5 • Undergraduateprograms: 22 • Undergraduatestudents: 4,837 • Graduateprograms: 19 • Graduatestudents: 3,030 • Academic staff: 552 • Administrative staff: 1,052 USP Statistics (CWUR, https://uspdigital.usp.br/anuario/AnuarioControle)

  5. Dept. ofElectricalandComputerEngineering • Established: 1969 • Physicalarea: 5,800+ m² • #1 Graduation in ElectricalEngineering in Brazilaccording to Federal (national) rankings • Undergraduatestudents: 861 • Graduatestudents: 180 • Academic staff: 40 • Administrative staff: 22 • Research Labs: 24

  6. Dept. ofElectricalandComputerEngineering Telecommunications SignalProcessingandInstrumentation Dynamic Systems SEL EESC - USP Electrical Power Systems

  7. AppliedElectromagneticsGroup (AEG)

  8. AppliedElectromagneticsGroup (AEG) www.sel.eesc.usp.br/leonardo

  9. AppliedElectromagneticsGroup (AEG) JournalPapers (2018-2019): • L. A. Ambrosio, “Circularlysymmetricfrozenwaves: Vector approach for light scatteringcalculations,” J. Quant. Spectrosc. Rad. Transfer204, 112-119 (2018). • A. Chefiq, L. A. Ambrosio, G. Gouesbet, and L. Belafhal, “Onthevalidityof integral localizedapproximation for on-axis zeroth-orderMathieubeams,” J. Quant. Spectrosc. Rad. Transfer204, 27-34 (2018). • G. Gouesbet, and L. A. Ambrosio, “On the validity of the use of a localized approximation for helical beams. I. Formal aspects,” J. Quant. Spectrosc. Rad. Transfer 208, 12-18 (2018). • L. A. Ambrosio, and G. Gouesbet, “On the validity of the use of a localized approximation for helical beams. II. Numerical aspects,” J. Quant. Spectrosc. Rad. Transfer 215, 41-50 (2018). • G. Gouesbet, and L. A. Ambrosio, “On localized approximations for Laguerre-Gauss beams focused by a lens,” J. Quant. Spectrosc. Rad. Transfer 218, 100-114 (2018). • L. A. Ambrosio, M. Zamboni-Rached, and G. Gouesbet, “Discrete vector frozen waves in generalized Lorenz-Mie theory: linear, azimuthal and radial polarizations,” Appl. Opt. 57, 3293-3300 (2018). • L. A. Ambrosio, L. F. M. Votto, G. Gouesbet, and J. J. Wang, “Assessing the validity of the localized approximation for discrete superpositions of Bessel beams,” J. Opt. Soc. Am. B 35, 2690-2698 (2018). • L. A. Ambrosio, M. Zamboni-Rached, and G. Gouesbet, “Zeroth-order continuous vector frozen waves for light scattering: exact multipole expansion in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. B 36, 81-89 (2019). • G. Gouesbet, L. A. Ambrosio, and L. F. M. Votto, “Finite series expressions to evaluate the beam shape coefficients of a Laguerre-Gauss beam freely propagating,” J. Quant. Spectrosc. Rad. Transfer227, 12-19 (2019). • L. A. Ambrosio, “Millimeter-Structured Nondiffracting Surface Beams,” J. Opt. Soc. Am. B 36, 638-645 (2019).

  10. AppliedElectromagneticsGroup (AEG) JournalPapers (2018-2019): L. F. M. Votto, L. A. Ambrosio, and G. Gouesbet, “Evaluation of beam shape coefficients of paraxial Laguerre-Gauss beam freely propagating by using three remodelling methods,” In press, J. Quant. Spectrosc. Rad. Transfer (2019). L. A. Ambrosio, L. F. M. Votto, and G. Gouesbet, “Blowing up of beam shape coefficients evaluated by finite series occurs in the case of Maxwellian beams,” Under review, J. Opt. Soc. Am. B (2019). G. Gouesbet, L. A. Ambrosio, and L. F. M. Votto, “Finite series expressions to evaluate the beam shape coefficients of a Laguerre-Gauss beam focused by a lens,” To bepublished, J. Quant. Spectrosc. Rad. Transfer (2019). L. F. M. Votto, L. A. Ambrosio, and G. Gouesbet, “Evaluation of beam shape coefficients of paraxial Laguerre-Gauss beam focused by a lens by using three remodelling methods,” To be published, J. Quant. Spectrosc. Rad. Transfer (2019). R. B. Soarez, A. A. R Neves, M. R. R. Gesualdi, L. A. Ambrosio and M. Zamboni-Rached, “Opticaltrappingof Mie particleswith Frozen waves,” Manuscript in preparation. J. O. de Sarro, e L. A. Ambrosio, “Non-diffractingsurfacebeams in absorbing media,” Manuscript in preparation. N. C. L. Valdivia, L. F. M. Votto, L. A. Ambrosio, and G. Gouesbet, “Finite series expressions to compute beamshapecoefficientsof superpositions of paraxial Bessel-Gauss beams,” Manuscript in preparation. J. A. V. Mendonça, M. Zamboni-Rached, C. H. da Silva-Santos, and L. A. Ambrosio, “Spatialdensificationofcompositionof Bessel beamsbasedongeneticalgorithms,” Manuscript in preparation.

  11. Outline • Non-diffractingwaves: A briefintroduction (PART I) • Milli- andmicro-structuredbeams (PART II) • Applications (PART II) • Conclusions (PART II)

  12. Part I

  13. Outline • Non-diffractingwaves: A briefintroduction • Milli- andmicro-structuredbeams • Applications • Conclusions

  14. Non-diffractingwaves A firstmathematicaldefinition starts fromthescalarwaveequation: andwe search for solutionsoftheform

  15. Non-diffractingwaves SincesolutionswithV < c do existand are ofpractical interest1, let us define a secondbut more general definitionofan IDEAL non-diffractingwave. 1M. Zamboni-Rached, and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A. 77, 033824 (2008).

  16. Non-diffractingwaves Practicalexample #1.Gaussianbeamsand pulses (which are DIFFRACTING WAVES) When (4) is substituted in thewaveequation, onefindsthe usual dispersionrelation .

  17. Non-diffractingwaves Practicalexample #1.Gaussianbeamsand pulses (which are DIFFRACTING WAVES) H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami. Localized Waves. Hoboken, NJ, USA: Wiley & Sons, 2008.

  18. Non-diffractingwaves Practicalexample #1.Gaussianbeamsand pulses (which are DIFFRACTING WAVES)

  19. Non-diffractingwaves Practicalexample #1. Gaussianbeamsand pulses (which are DIFFRACTING WAVES) When (4) is substituted in thewaveequation, onefindsthe usual dispersionrelation .

  20. Non-diffractingwaves Practicalexample #1. Gaussianbeamsand pulses (which are DIFFRACTING WAVES)

  21. Non-diffractingwaves Practicalexample #2. (Ideal) zerothordernon-diffracting Bessel beam When (4) is substituted in thewaveequation, onefindsthe usual dispersionrelation .

  22. Non-diffractingwaves Practicalexample #2. (Ideal) zerothordernon-diffracting Bessel beam Higherorder Bessel beamscanbeconstructedbysetting n > 0 in (4), orintroducingtheoperator

  23. Non-diffractingwaves Practicalexample #2. (Ideal) zerothordernon-diffracting Bessel beam

  24. Non-diffractingwaves Practicalexample #2. (Ideal) zerothordernon-diffracting Bessel beam J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499-1501, 1987.

  25. Non-diffractingwaves Practicalexample #2. (Ideal) zerothordernon-diffracting Bessel beam

  26. Non-diffractingwaves Adaptedfrom X. Yu, M. Zhang, and S. Lei, “MultiphotonPolymerizationUsingFemtosecond Bessel Beam for LayerlessThree-DimensionalPrinting,” J. Micro Nano Manufac. 6, 010901 (2018).

  27. Non-diffractingwaves Practicalexample #3. (Ideal) OrdinaryX-shaped pulse. When (4) is substituted in thewaveequation, onefindsthe usual dispersionrelation .

  28. Non-diffractingwaves Practicalexample #3. (Ideal) OrdinaryX-shaped pulse.

  29. Milli- andmicro-structuredbeams Ordinary Bessel beams present some advantages in comparison with diffracting beams: 1) Resistance to diffraction, self healing (lateral energy) 2) Extended focus and depth of field (cannot be controlled) Can we take any advantage of this type of beam in order to structure more complex light fields? J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499-1501, 1987.

  30. EndofPart I

  31. Part II

  32. Outline • Non-diffractingwaves: A briefintroduction • Milli- andmicro-structuredbeams • Applications • Conclusions

  33. Milli- andmicro-structuredbeams Ordinary Bessel beams present some advantages in comparison with diffracting beams: 1) Resistance to diffraction, self healing (lateral energy) 2) Extended focus and depth of field (cannot be controlled) Can we take any advantage of this type of beam in order to structure more complex light fields? J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499-1501, 1987.

  34. Milli- andmicro-structuredbeams Now, let us considerthefollowingdiscretesuperpositionof Bessel beams: M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves higher-order versions and finite-aperture generation,” Opt. Express 12, 4001-4006, 2004. M. Zamboni-Rached, L. A. Ambrosio, H. E. Hernández-Figueroa, “Diffraction–attenuation resistant beams: their higher-order versions and finite-aperture generation,” Appl. Opt. 49, 5861-5869, 2010.

  35. Milli- andmicro-structuredbeams Adapted from J. Durnin, J. J. Miceli Jr., and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499-1501, 1987.

  36. Milli- andmicro-structuredbeams

  37. Milli- andmicro-structuredbeams • In theliterature, this solution ofthescalarwaveequationhasbeencoined a Frozen Wave(FW), sincetheintensity envelope remainsstatic, i.e., withnullvelocity)

  38. Milli- andmicro-structuredbeams M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves higher-order versions and finite-aperture generation,” Opt. Express 12, 4001-4006, 2004.

  39. Milli- andmicro-structuredbeams M. Zamboni-Rached, L. A. Ambrosio, H. E. Hernández-Figueroa, “Diffraction–attenuation resistant beams: their higher-order versions and finite-aperture generation,” Appl. Opt. 49, 5861-5869, 2010.

  40. Milli- andmicro-structuredbeams Reddye solution T. A. Vieira, M. R. R. Gesualdi, M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37, 2034-2036, 2012.

  41. Milli- andmicro-structuredbeams T. A. Vieira, M. R. R. Gesualdi, M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37, 2034-2036, 2012.

  42. Milli- andmicro-structuredbeams T. A. Vieira, M. R. R. Gesualdi, M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37, 2034-2036, 2012.

  43. T. A. Vieira, M. Zamboni-Rached, M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental Generation of Frozen Waves via holographic method,” Opt. Communications 315, 374-380, 2014.

  44. T. A. Vieira, M. Zamboni-Rached, M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental Generation of Frozen Waves via holographic method,” Opt. Communications 315, 374-380, 2014.

  45. T. A. Vieira, M. Zamboni-Rached, M. R. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental Generation of Frozen Waves via holographic method,” Opt. Communications 315, 374-380, 2014.

  46. Milli- andmicro-structuredbeams Sofarwehaveconsideredonlydiscrete superpositions of (axisymmetric) Bessel beams. Butwehaveseenthatnon-diffractingbeamscanbeconstructedfromcontinuous superpositions of Bessel beams. Therefore, let us considerthelimiting case wherethediscretesum in a Frozen Wave (FW), becomes a continuousone (an integral), thusdefining a continuous FW: In this case, it canbeshownthatbyexpandingthespectrumS(b) in a Fourier series, the solution canbeexpressed in termsofMackinnon-typebeams: M. Zamboni-Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Physical Review A. 77, 033824, 2008.

  47. Milli- andmicro-structuredbeams Sofarwehaveconsideredonlydiscrete superpositions of (axisymmetric) Bessel beams. Butwehaveseenthatnon-diffractingbeamscanbeconstructedfromcontinuous superpositions of Bessel beams. Therefore, let us considerthelimiting case wherethediscretesum in a Frozen Wave (FW), becomes a continuousone (an integral), thusdefining a continuous FW: M. Zamboni-Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Physical Review A. 77, 033824, 2008.

  48. M. Zamboni-Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Physical Review A. 77, 033824, 2008.

  49. Milli- andmicro-structuredbeams L. A. Ambrosio, “Millimeter-structured nondiffracting surface beams,” JOSA B 36, 638-645, 2018.

  50. L. A. Ambrosio, “Millimeter-structured nondiffracting surface beams,” JOSA B 36, 638-645, 2018.

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