Abstract

In this paper, a straightforward approach is presented to generate Bessel beam sources in three-dimensional finite-difference time-domain (FDTD) method. Based on the angular spectrum representation (ASR), the incident Bessel beam is described as a superposition of plane waves whose wavevectors covering a conical surface. This decomposition of Bessel beam is then approximated by a finite collection of plane waves, which are injected into FDTD simulation domain using the total-field/scattered-field (TF/ST) method. The present method’s correctness and accuracy are verified by comparing the reconstructed field in FDTD with the original field. Far-field scattered diagrams of a dielectric sphere and a spheroid particle illuminated by a zero-order or a higher-order Bessel beam are calculated using FDTD. The results are compared with those calculated using the generalized Lorenz-Mie theory (GLMT) and surface integral equation method (SIEM). Very good agreements have been achieved, which partially indicate the correctness of our method. Internal and near-surface field distributions for a two-layer hemisphere particle, which are illuminated by Bessel beams, are also displayed to show the potentials of this approach in solving scattering problems of complex particles. This approach can also be applied to generate other structured beam sources in FDTD, which provides an access to solve structured beam scattering by complex particles using FDTD.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

N. Mphuthi, R. Botha, and A. Forbes, “Are Bessel beams resilient to aberrations and turbulence?” J. Opt. Soc. Am. A 35(6), 1021–1027 (2018).
[Crossref] [PubMed]

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

L. Han, “Scattering of a high-order Bessel beam by a spheroidal particle,” J. Quant. Spectrosc. Radiat. Transf. 211, 129–137 (2018).
[Crossref]

A. Chen, J. Wang, Y. Han, Z. Cui, and M. Yu, “Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles,” Opt. Express 26(20), 26766–26775 (2018).
[Crossref]

2017 (7)

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

R. Li, C. Ding, and F. G. Mitri, “Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size,” J. Quant. Spectrosc. Radiat. Transf. 196, 53–68 (2017).
[Crossref]

F. G. Mitri, “Reverse orbiting and spinning of a Rayleigh dielectric spheroid in a J0 Bessel optical beam,” J. Opt. Soc. Am. B 34(10), 2169–2178 (2017).
[Crossref]

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

B. S. Luk’yanchuk, R. Paniagua-Domínguez, I. Minin, O. Minin, and Z. Wang, “Refractive index less than two: photonic nanojets yesterday, today and tomorrow [Invited],” Opt. Mater. Express 7(6), 1820–1847 (2017).
[Crossref]

2016 (5)

F. Courvoisier, R. Stoian, and A. Couairon, "[INVITED] Ultrafast laser micro- and nano-processing with nondiffracting and curved beams,” Opt. Laser Technol. 80, 125–137 (2016).
[Crossref]

D. Fan, L. Wang, and Y. Ekinci, “Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength,” Sci. Rep. 6(1), 31301 (2016).
[Crossref] [PubMed]

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

2015 (3)

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

X. Wei, C. Liu, L. Niu, Z. Zhang, K. Wang, Z. Yang, and J. Liu, “Generation of arbitrary order Bessel beams via 3D printed axicons at the terahertz frequency range,” Appl. Opt. 54(36), 10641–10649 (2015).
[Crossref] [PubMed]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

2014 (1)

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

2013 (3)

J. A. Lock, “Angular spectrum and localized model of Davis-type beam,” J. Opt. Soc. Am. A 30(3), 489–500 (2013).
[Crossref] [PubMed]

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

İ. R. Çapoğlu, A. Taflove, and V. Backman, “Computation of tightly-focused laser beams in the FDTD method,” Opt. Express 21(1), 87–101 (2013).
[Crossref] [PubMed]

2012 (1)

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of Propagating Bessel Beams Using Leaky-Wave Modes: Experimental Validation,” IEEE Trans. Antenn. Propag. 60(6), 2645–2653 (2012).
[Crossref]

2011 (2)

F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36(5), 766–768 (2011).
[Crossref] [PubMed]

F. G. Mitri, “Electromagnetic Wave Scattering of a High-Order Bessel Vortex Beam by a Dielectric Sphere,” IEEE Trans. Antenn. Propag. 59(11), 4375–4379 (2011).
[Crossref]

2010 (1)

2008 (3)

2007 (1)

J. Xi, Q. Li, and J. Wang, “Numerical simulation of Bessel beams by FDTD employing the superposition principle,” Optik (Stuttg.) 118(7), 315–318 (2007).
[Crossref]

2006 (1)

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

2005 (2)

D. Li and K. Imasaki, “Vacuum laser-driven acceleration by a slits-truncated Bessel beam,” Appl. Phys. Lett. 86(3), 031110 (2005).
[Crossref]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

1991 (1)

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85(2-3), 159–161 (1991).
[Crossref]

1987 (1)

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Ayers, K.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Backman, V.

Baize, R. R.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Botha, R.

Bouchal, Z.

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

Brandes, A.

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

Çapoglu, I. R.

Chai, Y.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Chang, J. Y.

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

Chen, A.

Chen, J.

Chen, Z.

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

Chen, Z. Y.

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

Cižmár, T.

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

Couairon, A.

F. Courvoisier, R. Stoian, and A. Couairon, "[INVITED] Ultrafast laser micro- and nano-processing with nondiffracting and curved beams,” Opt. Laser Technol. 80, 125–137 (2016).
[Crossref]

Courvoisier, F.

F. Courvoisier, R. Stoian, and A. Couairon, "[INVITED] Ultrafast laser micro- and nano-processing with nondiffracting and curved beams,” Opt. Laser Technol. 80, 125–137 (2016).
[Crossref]

Cui, Z.

A. Chen, J. Wang, Y. Han, Z. Cui, and M. Yu, “Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles,” Opt. Express 26(20), 26766–26775 (2018).
[Crossref]

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Ding, C.

R. Li, C. Ding, and F. G. Mitri, “Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size,” J. Quant. Spectrosc. Radiat. Transf. 196, 53–68 (2017).
[Crossref]

Ding, C. Y.

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

Dong, D.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Durnin, J.

Ekinci, Y.

D. Fan, L. Wang, and Y. Ekinci, “Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength,” Sci. Rep. 6(1), 31301 (2016).
[Crossref] [PubMed]

Elmaklizi, A.

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

Ettorre, M.

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of Propagating Bessel Beams Using Leaky-Wave Modes: Experimental Validation,” IEEE Trans. Antenn. Propag. 60(6), 2645–2653 (2012).
[Crossref]

Fan, D.

D. Fan, L. Wang, and Y. Ekinci, “Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength,” Sci. Rep. 6(1), 31301 (2016).
[Crossref] [PubMed]

Forbes, A.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Gong, Q.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Gong, S.

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Gong, Z.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Grbic, A.

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of Propagating Bessel Beams Using Leaky-Wave Modes: Experimental Validation,” IEEE Trans. Antenn. Propag. 60(6), 2645–2653 (2012).
[Crossref]

Guo, L.

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Guo, L. X.

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

Han, L.

L. Han, “Scattering of a high-order Bessel beam by a spheroidal particle,” J. Quant. Spectrosc. Radiat. Transf. 211, 129–137 (2018).
[Crossref]

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

Han, X. e.

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Han, Y.

A. Chen, J. Wang, Y. Han, Z. Cui, and M. Yu, “Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles,” Opt. Express 26(20), 26766–26775 (2018).
[Crossref]

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

Han, Y. P.

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

Hu, Y.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Imasaki, K.

D. Li and K. Imasaki, “Vacuum laser-driven acceleration by a slits-truncated Bessel beam,” Appl. Phys. Lett. 86(3), 031110 (2005).
[Crossref]

Ji, Z.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Kienle, A.

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

Kollárová, V.

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

Kriezis, E. E.

Lee, T.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Lee, Y.-G.

Li, D.

D. Li and K. Imasaki, “Vacuum laser-driven acceleration by a slits-truncated Bessel beam,” Appl. Phys. Lett. 86(3), 031110 (2005).
[Crossref]

Li, Q.

J. Xi, Q. Li, and J. Wang, “Numerical simulation of Bessel beams by FDTD employing the superposition principle,” Optik (Stuttg.) 118(7), 315–318 (2007).
[Crossref]

Li, R.

R. Li, C. Ding, and F. G. Mitri, “Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size,” J. Quant. Spectrosc. Radiat. Transf. 196, 53–68 (2017).
[Crossref]

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Li, R. X.

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

Li, W.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Lin, Z.

Liu, C.

Liu, J.

Lock, J. A.

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

J. A. Lock, “Angular spectrum and localized model of Davis-type beam,” J. Opt. Soc. Am. A 30(3), 489–500 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B. S.

Mädler, L.

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Minin, I.

Minin, O.

Mishra, S. R.

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85(2-3), 159–161 (1991).
[Crossref]

Mitri, F. G.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

R. Li, C. Ding, and F. G. Mitri, “Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size,” J. Quant. Spectrosc. Radiat. Transf. 196, 53–68 (2017).
[Crossref]

F. G. Mitri, “Reverse orbiting and spinning of a Rayleigh dielectric spheroid in a J0 Bessel optical beam,” J. Opt. Soc. Am. B 34(10), 2169–2178 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

F. G. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36(5), 766–768 (2011).
[Crossref] [PubMed]

F. G. Mitri, “Electromagnetic Wave Scattering of a High-Order Bessel Vortex Beam by a Dielectric Sphere,” IEEE Trans. Antenn. Propag. 59(11), 4375–4379 (2011).
[Crossref]

Mphuthi, N.

Munro, P. R. T.

Ng, J.

Niu, L.

Paniagua-Domínguez, R.

Reitzle, D.

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

Ren, K. F.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Rudolph, S. M.

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of Propagating Bessel Beams Using Leaky-Wave Modes: Experimental Validation,” IEEE Trans. Antenn. Propag. 60(6), 2645–2653 (2012).
[Crossref]

Sheng, X.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

Shi, K.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Stoian, R.

F. Courvoisier, R. Stoian, and A. Couairon, "[INVITED] Ultrafast laser micro- and nano-processing with nondiffracting and curved beams,” Opt. Laser Technol. 80, 125–137 (2016).
[Crossref]

Sun, W.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Sung, S.-Y.

Taflove, A.

Török, P.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

Wang, J.

A. Chen, J. Wang, Y. Han, Z. Cui, and M. Yu, “Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles,” Opt. Express 26(20), 26766–26775 (2018).
[Crossref]

J. Xi, Q. Li, and J. Wang, “Numerical simulation of Bessel beams by FDTD employing the superposition principle,” Optik (Stuttg.) 118(7), 315–318 (2007).
[Crossref]

Wang, J. J.

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

Wang, K.

Wang, L.

D. Fan, L. Wang, and Y. Ekinci, “Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength,” Sci. Rep. 6(1), 31301 (2016).
[Crossref] [PubMed]

Wang, P.

Wang, Z.

Wei, X.

Weimer, C.

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

Wriedt, T.

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

Wu, Y.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

Wu, Z.

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

Xi, J.

J. Xi, Q. Li, and J. Wang, “Numerical simulation of Bessel beams by FDTD employing the superposition principle,” Optik (Stuttg.) 118(7), 315–318 (2007).
[Crossref]

Xi, P.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Xiao, Y.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Yang, M.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

Yang, X.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Yang, Z.

Yu, M.

Yu, W.

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Zemánek, P.

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

Zhang, Z.

Zhao, Y.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Ann. Phys. (1)

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations,” Ann. Phys. 361, 120–147 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. Li and K. Imasaki, “Vacuum laser-driven acceleration by a slits-truncated Bessel beam,” Appl. Phys. Lett. 86(3), 031110 (2005).
[Crossref]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of Propagating Bessel Beams Using Leaky-Wave Modes: Experimental Validation,” IEEE Trans. Antenn. Propag. 60(6), 2645–2653 (2012).
[Crossref]

F. G. Mitri, “Electromagnetic Wave Scattering of a High-Order Bessel Vortex Beam by a Dielectric Sphere,” IEEE Trans. Antenn. Propag. 59(11), 4375–4379 (2011).
[Crossref]

J. Biomed. Opt. (1)

A. Elmaklizi, D. Reitzle, A. Brandes, and A. Kienle, “Penetration depth of focused beams in highly scattering media investigated with a numerical solution of Maxwell’s equations in two dimensions,” J. Biomed. Opt. 20(6), 065007 (2015).
[Crossref] [PubMed]

J. Opt. (1)

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Computational study of scattering of a zero-order Bessel beam by large nonspherical homogeneous particles with the multilevel fast multipole algorithm,” J. Opt. 19(12), 125606 (2017).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transf. (8)

L. Han, “Scattering of a high-order Bessel beam by a spheroidal particle,” J. Quant. Spectrosc. Radiat. Transf. 211, 129–137 (2018).
[Crossref]

R. Li, K. F. Ren, X. e. Han, Z. Wu, L. Guo, and S. Gong, “Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series,” J. Quant. Spectrosc. Radiat. Transf. 126, 69–77 (2013).
[Crossref]

J. J. Wang, Y. P. Han, J. Y. Chang, and Z. Y. Chen, “Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model,” J. Quant. Spectrosc. Radiat. Transf. 206, 22–30 (2018).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

R. Li, C. Ding, and F. G. Mitri, “Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size,” J. Quant. Spectrosc. Radiat. Transf. 196, 53–68 (2017).
[Crossref]

Z. Cui, Y. Han, Z. Chen, and L. Han, “Scattering of Bessel beam by arbitrarily shaped composite particles with core–shell structure,” J. Quant. Spectrosc. Radiat. Transf. 144, 108–116 (2014).
[Crossref]

J. J. Wang, T. Wriedt, J. A. Lock, and L. Mädler, “General description of circularly symmetric Bessel beams of arbitrary order,” J. Quant. Spectrosc. Radiat. Transf. 184, 218–232 (2016).
[Crossref]

W. Sun, Y. Hu, C. Weimer, K. Ayers, R. R. Baize, and T. Lee, “A FDTD solution of scattering of laser beam with orbital angular momentum by dielectric particles: Far-field characteristics,” J. Quant. Spectrosc. Radiat. Transf. 188, 200–213 (2017).
[Crossref]

J. Sound Vibrat. (1)

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Laser Photonics Rev. (1)

W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016).
[Crossref]

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

New J. Phys. (1)

areT. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8(3), 43 (2006).
[Crossref]

Ocean Eng. (1)

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Opt. Commun. (3)

S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85(2-3), 159–161 (1991).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151(4–6), 207–211 (1998).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

F. Courvoisier, R. Stoian, and A. Couairon, "[INVITED] Ultrafast laser micro- and nano-processing with nondiffracting and curved beams,” Opt. Laser Technol. 80, 125–137 (2016).
[Crossref]

Opt. Lett. (2)

Opt. Mater. Express (1)

Optik (Stuttg.) (1)

J. Xi, Q. Li, and J. Wang, “Numerical simulation of Bessel beams by FDTD employing the superposition principle,” Optik (Stuttg.) 118(7), 315–318 (2007).
[Crossref]

Sci. Rep. (1)

D. Fan, L. Wang, and Y. Ekinci, “Nanolithography using Bessel Beams of Extreme Ultraviolet Wavelength,” Sci. Rep. 6(1), 31301 (2016).
[Crossref] [PubMed]

Other (4)

G. Gouesbet and G. Gréhan, Generalized lorenz-mie theories (Springer, 2011).

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd ed. (Artech house, 2005).

J. Stoer and R. Bulirsch, Introduction to numerical analysis (Springer Science & Business Media, 2013).

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge university, 2006).

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Figures (7)

Fig. 1
Fig. 1 Amplitude distributions of the x-component electric field of reconstructed Bessel beams with θ0 = 30° on yoz plane in FDTD simulations. (a) L = 0, (b) L = 1, (c) L = 2. The beams are traveling along the + z direction. The first three columns show the time domain results at different time instants: 500Δt, 700Δt, 900Δt from left to right. The rightmost column shows the results in the frequency domain at λ = 600nm after Fourier transform.
Fig. 2
Fig. 2 Comparisons between Bessel beams with θ0 = 30°, λ = 600nm in FDTD and analytical results along the y-axis. (a) Amplitude of the x-component electric field. (b) Relative deviation |EFDTD xEana x|/max(|Eana x|).
Fig. 3
Fig. 3 Comparisons of the x-component electric field amplitude on xoy plane for zero-order Bessel beams between FDTD and original field. Different numbers of plane waves are chosen N = 15,30,60 to represent Bessel beams. Parameters of Bessel beams are: (a) θ0 = 30°, λ = 600nm, (b) θ0 = 80°, λ = 600nm and (c) θ0 = 80°, λ = 800nm.
Fig. 4
Fig. 4 Comparisons of the x-component electric field amplitude on xoy plane for first-order Bessel beams between FDTD and original field. Different numbers of plane waves are chosen N = 15,30,60 to represent Bessel beams. Parameters of Bessel beams are: (a) θ0 = 30°, λ = 600nm, (b) θ0 = 80°, λ = 600nm.
Fig. 5
Fig. 5 Comparisons of scattering intensity for a dielectric sphere (r = 2.0μm, m = 2) illuminated by a zero-order Bessel beam (half cone angle is θ0 = 30°) obtained from FDTD(2,2), FDTD(2,4) and GLMT. (a) ϕsc = 0°, (b) ϕsc = 90° at λ = 532nm and (c) ϕsc = 0°, (d) ϕsc = 90° at λ = 633nm.
Fig. 6
Fig. 6 Scattering results for higher-order Bessel beams. (a) Spherical particle (r = 2μm, m = 1.33) under a first-order Bessel beam (θ0 = 20°, λ = 628.3nm) illumination, results are obtained from FDTD(2,4) and GLMT. (b) Spheroid particle (semi-major axes a = λ, semi-minor axes b = 0.5λ) under a second-order Bessel beam (θ0 = 15°, λ = 633nm) illumination, results are obtained from FDTD(2,4) and SIEM.
Fig. 7
Fig. 7 Intensity distributions of electric field on yoz plane when a two-layer hemisphere is illuminated by Bessel beams (θ0 = 20°, λ = 633nm) with different beam order: (a) L = 0, (b) L = 1, (c) L = 2. Radius and the refractive index of the particle are rs = 2μm and ms = 1.6 for shell region, rc = 1μm and mc = 1.33 for core region.

Equations (9)

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E(r)= ik f 0 e ik f 0 2π θ θ max ϕ=0 2π E pw e ikr sinθdθdϕ , B(r)= 1 iω ×E(r)
E pw =Q( θ 0 ,ϕ) E pw0 ( θ 0 ,ϕ) e iLϕ δ(θ θ 0 ) sinθ ,
Q(θ,ϕ)=[ p x (cosθ cos 2 ϕ+ sin 2 ϕ) p y (1cosθ)sinϕcosϕ p x (1-cosθ)sinϕcosϕ+ p y (cosθ sin 2 ϕ+ cos 2 ϕ) p x sinθcosϕ p y sinθsinϕ ],
E(r)= ϕ=0 2π E pw0 Q( θ 0 ,ϕ) e iLϕ e ikr dϕ
E(r,t)= n C n E pw0 Q( θ 0 , ϕ n ) e iL ϕ n e i(ωtkr) , n=0,1...N,
ϕ n =2πn/N, n=0,1...N, C n ={ π/N, n=0,N 2π/N, others
E(r,t)= n C n E i ( θ 0 , ϕ n ,tt ' n kr/ω)Q( θ 0 , ϕ n ) , n=0,1...N.,
E i (t)=cos(2π f 0 t)exp[4π (t t 0 ) 2 / τ 2 ],
E x | i+1/2,j,k n+1 = E x | i+1/2,j,k n + Δt ε(m) ( 27 24 H z | i+1/2,j+1/2,k n+1/2 H z | i+1/2,j1/2,k n+1/2 Δy 1 24 H z | i+1/2,j+3/2,k n+1/2 H z | i+1/2,j3/2,k n+1/2 Δy , 27 24 H y | i+1/2,j,k+1/2 n+1/2 H y | i+1/2,j,k1/2 n+1/2 Δz + 1 24 H y | i+1/2,j,k+3/2 n+1/2 H y | i+1/2,j,k3/2 n+1/2 Δz )