P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

J. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281, 923–934 (2008).

[CrossRef]

A. Y. Bekshaev and A. I. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281, 5687–5696 (2008).

[CrossRef]

S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of coma on the focusing of an apertured singular beam,” Opt. Lasers Eng. 45, 488–494 (2007).

[CrossRef]

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Influence of astigmatism and defocusing on the focusing of a singular beam,” Opt. Commun. 270, 128–138 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of astigmatism on the diffraction of a vortex-carrying beam with Gaussian background,” J. Opt. A Pure Appl. Opt. 9, 543–554 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

L. E. Helsenth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).

[CrossRef]

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

A. M. Stewart, “Angular momentum of light,” J. Mod. Opt. 52, 1145–1154 (2005).

[CrossRef]

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).

[CrossRef]

F. M. Denaro, “On the application of the Helmholtz–Hodge decomposition in projection methods for incompressible flows with general boundary conditions,” Int. J. Numer. Methods Fluids 43, 43–69 (2003).

[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).

[CrossRef]

P. Senthilkumaran and F. Wyrowski, “Phase synthesis in wave-optical engineering: mapping and diffuser-type approaches,” J. Mod. Opt. 49, 1831–1850 (2002).

[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).

[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).

[CrossRef]

S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).

[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

[CrossRef]

H. Weber and G. Arfken, Essential Mathematical Methods for Physicists (Academic, 2003).

S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).

[CrossRef]

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).

[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).

[CrossRef]

A. Y. Bekshaev and A. I. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281, 5687–5696 (2008).

[CrossRef]

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007).

[CrossRef]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

F. M. Denaro, “On the application of the Helmholtz–Hodge decomposition in projection methods for incompressible flows with general boundary conditions,” Int. J. Numer. Methods Fluids 43, 43–69 (2003).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).

[CrossRef]

D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, 1999).

L. E. Helsenth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).

[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

A. Y. Bekshaev and A. I. Karamoch, “Astigmatic telescopic transformation of a high-order optical vortex,” Opt. Commun. 281, 5687–5696 (2008).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

K. Polthier and E. Preuss, “Identifying vector field singularities using a discrete Hodge decomposition,” in Visualization and Mathematics III, H. C. Hege and K. Polthier, eds. (Springer-Verlag, 2002), pp. 113–134.

K. Polthier and E. Preuss, “Identifying vector field singularities using a discrete Hodge decomposition,” in Visualization and Mathematics III, H. C. Hege and K. Polthier, eds. (Springer-Verlag, 2002), pp. 113–134.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).

[CrossRef]

M. Bahl and P. Senthilkumaran, “Helmholtz Hodge decomposition of scalar optical fields,” J. Opt. Soc. Am. A 29, 2421–2427 (2012).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281, 923–934 (2008).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Influence of astigmatism and defocusing on the focusing of a singular beam,” Opt. Commun. 270, 128–138 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of coma on the focusing of an apertured singular beam,” Opt. Lasers Eng. 45, 488–494 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of astigmatism on the diffraction of a vortex-carrying beam with Gaussian background,” J. Opt. A Pure Appl. Opt. 9, 543–554 (2007).

[CrossRef]

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).

[CrossRef]

P. Senthilkumaran and F. Wyrowski, “Phase synthesis in wave-optical engineering: mapping and diffuser-type approaches,” J. Mod. Opt. 49, 1831–1850 (2002).

[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281, 923–934 (2008).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of astigmatism on the diffraction of a vortex-carrying beam with Gaussian background,” J. Opt. A Pure Appl. Opt. 9, 543–554 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Influence of astigmatism and defocusing on the focusing of a singular beam,” Opt. Commun. 270, 128–138 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of coma on the focusing of an apertured singular beam,” Opt. Lasers Eng. 45, 488–494 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma,” Opt. Commun. 281, 923–934 (2008).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of coma on the focusing of an apertured singular beam,” Opt. Lasers Eng. 45, 488–494 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Influence of astigmatism and defocusing on the focusing of a singular beam,” Opt. Commun. 270, 128–138 (2007).

[CrossRef]

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of astigmatism on the diffraction of a vortex-carrying beam with Gaussian background,” J. Opt. A Pure Appl. Opt. 9, 543–554 (2007).

[CrossRef]

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).

[CrossRef]

A. Y. Bekshaev and M. S. Soskin, “Transverse energy flows in vectorial fields of paraxial beams with singularities,” Opt. Commun. 271, 332–348 (2007).

[CrossRef]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

[CrossRef]

A. M. Stewart, “Angular momentum of light,” J. Mod. Opt. 52, 1145–1154 (2005).

[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377, 1154–1156 (2013).

[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).

[CrossRef]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).

[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).

[CrossRef]

H. Weber and G. Arfken, Essential Mathematical Methods for Physicists (Academic, 2003).

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).

[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

[CrossRef]

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).

[CrossRef]

P. Senthilkumaran and F. Wyrowski, “Phase synthesis in wave-optical engineering: mapping and diffuser-type approaches,” J. Mod. Opt. 49, 1831–1850 (2002).

[CrossRef]

H. Bhatia, G. Norgard, V. Pascucci, and P. T. Bremer, “The Helmholtz–Hodge decomposition: a survey,” IEEE Trans. Vis. Comput. Graph. 19, 1386–1404 (2013).

F. M. Denaro, “On the application of the Helmholtz–Hodge decomposition in projection methods for incompressible flows with general boundary conditions,” Int. J. Numer. Methods Fluids 43, 43–69 (2003).

[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Paakkonen, and J. Turunen, “Astigmatic Bessel laser beams,” J. Mod. Opt. 51, 677–686 (2004).

[CrossRef]

A. M. Stewart, “Angular momentum of light,” J. Mod. Opt. 52, 1145–1154 (2005).

[CrossRef]

P. Senthilkumaran and F. Wyrowski, “Phase synthesis in wave-optical engineering: mapping and diffuser-type approaches,” J. Mod. Opt. 49, 1831–1850 (2002).

[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, S. N. Khonina, R. V. Skidanov, V. A. Soifer, H. Elfstrom, N. Tossavainen, and J. Turunen, “Diffraction of conic and Gaussian beams by a spiral phase plate,” J. Opt. A Pure Appl. Opt. 45, 2656–2665 (2006).

R. K. Singh, P. Senthilkumaran, and K. Singh, “Effect of astigmatism on the diffraction of a vortex-carrying beam with Gaussian background,” J. Opt. A Pure Appl. Opt. 9, 543–554 (2007).

[CrossRef]

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).

[CrossRef]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955–1964 (2007).

[CrossRef]

M. Bahl and P. Senthilkumaran, “Helmholtz Hodge decomposition of scalar optical fields,” J. Opt. Soc. Am. A 29, 2421–2427 (2012).

[CrossRef]

S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).

[CrossRef]

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