Abstract

We propose a method for controlling the local spin and orbital angular momentum (SAM and OAM) of a focused light beam in a uniaxial crystal by means of Pockels effect. For an input circularly polarized Bessel-Gaussian (BG) beam, both the local SAM and OAM of the output beam are circularly symmetric, their patterns and peak values vary with the applied electric field E0. Let the output beam pass through a quarter-wave plate, the OAM keeps while the SAM varies. The local SAM density is nearly directly proportional to ± sin(2φ), where φ is the azimuthal angle and the signs are dependent on the radius and E0.

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    [CrossRef] [PubMed]
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2012

2011

2010

2009

2008

2007

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE6609, 660907, 660907-8 (2007).
[CrossRef]

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express15(23), 15214–15227 (2007).
[CrossRef] [PubMed]

2006

2005

2004

2003

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

A. Ciattoni, G. Cincotti, and C. Palma, “Circularly polarized beams and vortex generation in uniaxial media,” J. Opt. Soc. Am. A20(1), 163–171 (2003).
[CrossRef] [PubMed]

A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(3), 036618 (2003).
[CrossRef] [PubMed]

2001

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A18(7), 1618–1626 (2001).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel light beams in uniaxial crystals,” Quantum Electron.31(1), 85–89 (2001).
[CrossRef]

1995

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

1992

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1987

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Ahlawat, S.

Allen, L.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Barnett, S. M.

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express15(23), 15214–15227 (2007).
[CrossRef] [PubMed]

R. Zambrini and S. M. Barnett, “Local transfer of angular momentum to matter,” J. Mod. Opt.52, 1045–1052 (2005).
[CrossRef]

Beijersbergen, M. W.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Borghi, R.

Bouchal, Z.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE6609, 660907, 660907-8 (2007).
[CrossRef]

Brasselet, E.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Burge, R. E.

Chávez-Cerda, S.

Chen, L.

Ciattoni, A.

A. Ciattoni, G. Cincotti, and C. Palma, “Circularly polarized beams and vortex generation in uniaxial media,” J. Opt. Soc. Am. A20(1), 163–171 (2003).
[CrossRef] [PubMed]

A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(3), 036618 (2003).
[CrossRef] [PubMed]

Cincotti, G.

A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(3), 036618 (2003).
[CrossRef] [PubMed]

A. Ciattoni, G. Cincotti, and C. Palma, “Circularly polarized beams and vortex generation in uniaxial media,” J. Opt. Soc. Am. A20(1), 163–171 (2003).
[CrossRef] [PubMed]

Cizmar, T.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE6609, 660907, 660907-8 (2007).
[CrossRef]

Curtis, J. E.

Dasgupta, R.

Desyatnikov, A. S.

Dholakia, K.

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Dudley, A.

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

Egorov, Y. A.

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “The fine structure of singular beams in crystals: colours and polarization,” J. Opt. Soc. Am. A6(5), S217–S228 (2004).
[CrossRef]

Fadeyeva, T. A.

T. A. Fadeyeva and A. V. Volyar, “Extreme spin-orbit coupling in crystal-travelling paraxial beams,” J. Opt. Soc. Am. A27(3), 381–389 (2010).
[CrossRef]

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “The fine structure of singular beams in crystals: colours and polarization,” J. Opt. Soc. Am. A6(5), S217–S228 (2004).
[CrossRef]

Forbes, A.

Friese, M. E.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Garcés-Chávez, V.

K. Volke-Sepulveda, S. Chávez-Cerda, V. Garcés-Chávez, and K. Dholakia, “Three-dimensional optical forces and transfer of orbital angular momentum from multiringed light beams to spherical microparticles,” J. Opt. Soc. Am. B21, 1749–1757 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Gupta, P. K.

He, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Izdebskaya, Y.

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Khilo, N. A.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel light beams in uniaxial crystals,” Quantum Electron.31(1), 85–89 (2001).
[CrossRef]

Kivshar, Y. S.

Kollarova, V.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE6609, 660907, 660907-8 (2007).
[CrossRef]

Krolikowski, W.

Lin, J.

Litvin, I. A.

Loussert, C.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96(16), 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96(16), 163905 (2006).
[CrossRef] [PubMed]

McGloin, D.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

Niu, H. B.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3(2), 161–204 (2011) (and references therein).
[CrossRef]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Palma, C.

A. Ciattoni, G. Cincotti, and C. Palma, “Circularly polarized beams and vortex generation in uniaxial media,” J. Opt. Soc. Am. A20(1), 163–171 (2003).
[CrossRef] [PubMed]

A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(3), 036618 (2003).
[CrossRef] [PubMed]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96(16), 163905 (2006).
[CrossRef] [PubMed]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Peng, X.

Petrova, E. S.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel light beams in uniaxial crystals,” Quantum Electron.31(1), 85–89 (2001).
[CrossRef]

Porras, M. A.

Rubinsztein-Dunlop, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Ryzhevich, A. A.

N. A. Khilo, E. S. Petrova, and A. A. Ryzhevich, “Transformation of the order of Bessel light beams in uniaxial crystals,” Quantum Electron.31(1), 85–89 (2001).
[CrossRef]

Santarsiero, M.

Schmitz, C. H. J.

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

She, W.

Shvedov, V.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science292(5518), 912–914 (2001).
[CrossRef] [PubMed]

Spatz, J. P.

Spreeuw, R. J. C.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Tao, S. H.

Uhrig, K.

Vaziri, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Verma, R. S.

Volke-Sepulveda, K.

Volyar, A. V.

T. A. Fadeyeva and A. V. Volyar, “Extreme spin-orbit coupling in crystal-travelling paraxial beams,” J. Opt. Soc. Am. A27(3), 381–389 (2010).
[CrossRef]

Y. A. Egorov, T. A. Fadeyeva, and A. V. Volyar, “The fine structure of singular beams in crystals: colours and polarization,” J. Opt. Soc. Am. A6(5), S217–S228 (2004).
[CrossRef]

Weihs, G.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Woerdman, J. P.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Yao, A. M.

Yuan, X. C.

Yuan, X.-C.

Zambrini, R.

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express15(23), 15214–15227 (2007).
[CrossRef] [PubMed]

R. Zambrini and S. M. Barnett, “Local transfer of angular momentum to matter,” J. Mod. Opt.52, 1045–1052 (2005).
[CrossRef]

Zeilinger, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

Zemanek, P.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE6609, 660907, 660907-8 (2007).
[CrossRef]

Zhu, W.

Adv. Opt. Photon.

J. Mod. Opt.

R. Zambrini and S. M. Barnett, “Local transfer of angular momentum to matter,” J. Mod. Opt.52, 1045–1052 (2005).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(3), 036618 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum,” Phys. Rev. Lett.91(22), 227902 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multi-ringed light beam to an optically trapped particle,” Phys. Rev. Lett.91(9), 093602 (2003).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett.96(16), 163905 (2006).
[CrossRef] [PubMed]

Proc. SPIE

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[CrossRef]

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[CrossRef]

Science

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[CrossRef] [PubMed]

Other

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Figures (4)

Fig. 1
Fig. 1

The intensity distributions of the input beam |Ein|2 (a) and the output beam |Eout|2 (b) for a RHP BG0 incident beam with β = 1 μm−1 and w0 = 10 μm when E0 = 0. (c) The dependences of the normalized SAM (blue line) and OAM (red line) densities on the radius for different applied electric fields E0 (in kV/mm).

Fig. 2
Fig. 2

The dependences of the global SAM and OAM on E0 for a RHP BG0 incident beam with β = 1 μm−1 and w0 = 10 μm.

Fig. 3
Fig. 3

The conversion efficiency from SAM to OAM as a function of the applied electric field E0 and the beam waist w0 for L = 8 mm and β = 1 μm−1. The dashed line shows the maximum conversion efficiency.

Fig. 4
Fig. 4

The patterns of the normalized SAM density for different E0 with a RHP BG0 beam of β = 1 μm−1 and w0 = 10 μm incident. E0 is in kV/mm.

Equations (8)

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2 E(r)[E(r)]+ k 0 2 ε eff E(r)=0.
E + (r,φ,z)= 1 2 exp( β 2 w 0 2 4 imφ ) [ 1 σ o J m ( βr σ o )exp( r 2 w 0 2 σ o + β 2 w 0 2 4 σ o ) + 1 σ e J m ( βr σ e )exp( r 2 w 0 2 σ e + β 2 w 0 2 4 σ e ) ],
E (r,φ,z)= 1 2 ( β w 0 2 ) m ( r w 0 ) m2 exp[ β 2 w 0 2 4 i(m2)φ ]× n=0 n+1 (n+m)! ( β 2 w 0 2 4 ) n [ 1 σ o n+m2 exp( r 2 w 0 2 σ o ) L n+1 m2 ( r 2 w 0 2 σ o ) 1 σ e n+m2 exp( r 2 w 0 2 σ e ) L n+1 m2 ( r 2 w 0 2 σ e ) ],
l z = ε 0 2ω Im( E x * φ E x + E y * φ E y ),
s z = ε 0 ω Im( E x * E y )= ε 0 ω S 3 ,
S z =Re{ 2 σ o + σ e * I m [ β 2 w 0 2 2( σ o + σ e * ) ]exp[ β 2 w 0 2 2 ( 1 σ o + σ e * 1 2 ) ] }/ I m ( β 2 w 0 2 4 ),
L z =1m S z .
E= A 1 (r,z)exp(imφ)x+ A 2 (r,z)exp[i(m2)φiπ/2]y = | A 1 (r,z) | 2 + | A 2 (r,z) | 2 exp[imφ+iarg( A 1 (r,z))][ cosΨ(r,z) sinΨ(r,z) e iδ(r,φ,z) ],

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