Abstract

We report here the generation of a chain of three-dimensional (3-D) optical bottle beams by focusing a π-phase shifted multi-ring hollow Gaussian beam (HGB) using a lens with spherical aberration. The rings of the HGB of suitable radial (kr) and axial (kz) wave vectors are generated using a double-negative axicon chemically etched in the optical fiber tips. Moving the lens position with respect to the fiber tip results in variation of the semi-angle of the cones of wave vectors of the HGBs and their diameter, using which we demonstrate tunability in the size and the periodicity of the 3-D optical bottle beams over a wide range, from micrometers to millimeters. The propagation characteristics of the beams resulting from focusing of single- and multi-ring HGBs and resulting in a quasi-non-diffracting beam and a chain of 3-D optical bottle beams, respectively, are simulated using only the input beam parameters and are found to agree well with experimental results.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2010

T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

N. K. Viswanathan, G. M. Philip, and Y. V. Jayasurya, “Generic dark hollow beams using negative cones chemically etched in fiber tips,” Proc. SPIE 7613, 761307-1 (2010).
[CrossRef]

2009

A. A. Ryzhevich, S. V. Solonevich, and A. G. Smirnov, “Method for creating hollow light beams with local intensity minima and possibilities for their application,” J. Appl. Spectrosc. 76, 570–576 (2009).
[CrossRef]

2008

X. Zeng and F. Wu, “The analytical description and experiments of the optical bottle generated by an axicon and a lens,” J. Mod. Opt. 55, 3071–3081 (2008).
[CrossRef]

Z. Jaroszewicz, A. Burvall, A. V. Goncharov, and K. Kolacz, “Spheric long focal depth lens: A comment,” Opt. Commun. 281, 4849–4850 (2008).
[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Focal shift of hollow Gaussian beams through a thin lens,” Opt. Laser Technol. 40, 58–63 (2008).
[CrossRef]

2007

B.E. A.Saleh and M.C.Teich, eds., Fundamentals of Photonics, 2nd ed. (Wiley Interscience, 2007).

2006

2005

Y. Zhao, Q. Zhan, Y. Zhang, and Y.-P. Li, “Creation of a three dimensional optical chain for controllable particle delivery,” Opt. Lett. 30, 848–850 (2005).
[CrossRef] [PubMed]

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

M.-D. Wei, W.-L. Shiao, and Y.-T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

2004

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

B. P. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, “Generation of self-imaged optical bottle beams,” Opt. Commun. 238, 177–184 (2004).
[CrossRef]

J. Garcia-Sucerquia, F. F. Medina, and G. Matteucci, “Optical tubular structures produced by diffraction of circular apertures,” Opt. Lasers Eng. 42, 61–70 (2004).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, “Simple lens axicon,” Appl. Opt. 43, 4838–4844 (2004).
[CrossRef] [PubMed]

2003

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef] [PubMed]

T. Watanabe, Y. Iketaki, T. Omatsu, K. Yamamoto, M. Sakai, and M. Fuji, “Two point separation in super-resolution fluorescence microscope based on up-conversion fluorescence depletion technique,” Opt. Express 11, 3271–3276 (2003).
[CrossRef] [PubMed]

J. Yin, W. Gao, and Y. Zhan, “Generation of dark hollow beams and their applications,” in Progress in Optics, E.Wolf, ed., Vol. 45 (Elsevier, 2003), pp.119–204.
[CrossRef]

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

2002

N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” Adv. At., Mol., Opt. Phys. 48, 99–151 (2002).
[CrossRef]

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

2001

J. Kyvalsky and Z. Bouchal, “Realistic description of the self-reconstruction effect,” Optik (Stuttgart) 112, 225–231 (2001).
[CrossRef]

D. J. Han, M. T. DePue, and D. S. Weiss, “Loading and compressing Cs atoms in a very far-off-resonant light trap,” Phys. Rev. A 63, 023405 (2001).
[CrossRef]

2000

1998

1991

1990

K. Patorsky, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed., Vol. 26 (Elsevier, 1990), pp. 3–108.

1983

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

1937

R. Kingslake, “The knife-edge test for spherical aberration,” Proc. Phys. Soc. 49, 376–380 (1937).
[CrossRef]

Ahluwalia, B. P. S.

Andrews, D. L.

T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Arlt, J.

Bokor, N.

Bouchal, Z.

J. Kyvalsky and Z. Bouchal, “Realistic description of the self-reconstruction effect,” Optik (Stuttgart) 112, 225–231 (2001).
[CrossRef]

Bu, J.

Burvall, A.

Z. Jaroszewicz, A. Burvall, A. V. Goncharov, and K. Kolacz, “Spheric long focal depth lens: A comment,” Opt. Commun. 281, 4849–4850 (2008).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, “Simple lens axicon,” Appl. Opt. 43, 4838–4844 (2004).
[CrossRef] [PubMed]

Cacciapuoti, L.

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Cai, Y.

Chavez-Cerda, S.

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265, 411–417 (2006).
[CrossRef]

Cheong, W. C.

Cizmar, T.

T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Cooper, J.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

Davidson, N.

de Angelis, M.

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

DePue, M. T.

D. J. Han, M. T. DePue, and D. S. Weiss, “Loading and compressing Cs atoms in a very far-off-resonant light trap,” Phys. Rev. A 63, 023405 (2001).
[CrossRef]

Dholakia, K.

T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

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

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Friberg, A. T.

Friedman, N.

N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” Adv. At., Mol., Opt. Phys. 48, 99–151 (2002).
[CrossRef]

Fuji, M.

Gao, W.

J. Yin, W. Gao, and Y. Zhan, “Generation of dark hollow beams and their applications,” in Progress in Optics, E.Wolf, ed., Vol. 45 (Elsevier, 2003), pp.119–204.
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Garcia-Sucerquia, J.

J. Garcia-Sucerquia, F. F. Medina, and G. Matteucci, “Optical tubular structures produced by diffraction of circular apertures,” Opt. Lasers Eng. 42, 61–70 (2004).
[CrossRef]

Goncharov, A. V.

Z. Jaroszewicz, A. Burvall, A. V. Goncharov, and K. Kolacz, “Spheric long focal depth lens: A comment,” Opt. Commun. 281, 4849–4850 (2008).
[CrossRef]

Han, D. J.

D. J. Han, M. T. DePue, and D. S. Weiss, “Loading and compressing Cs atoms in a very far-off-resonant light trap,” Phys. Rev. A 63, 023405 (2001).
[CrossRef]

Herman, R. M.

Iketaki, Y.

Jaroszewicz, Z.

Z. Jaroszewicz, A. Burvall, A. V. Goncharov, and K. Kolacz, “Spheric long focal depth lens: A comment,” Opt. Commun. 281, 4849–4850 (2008).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, “Simple lens axicon,” Appl. Opt. 43, 4838–4844 (2004).
[CrossRef] [PubMed]

Jayasurya, Y. V.

N. K. Viswanathan, G. M. Philip, and Y. V. Jayasurya, “Generic dark hollow beams using negative cones chemically etched in fiber tips,” Proc. SPIE 7613, 761307-1 (2010).
[CrossRef]

Jordan, P.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

Kaplan, A.

N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” Adv. At., Mol., Opt. Phys. 48, 99–151 (2002).
[CrossRef]

Kingslake, R.

R. Kingslake, “The knife-edge test for spherical aberration,” Proc. Phys. Soc. 49, 376–380 (1937).
[CrossRef]

Kolacz, K.

Z. Jaroszewicz, A. Burvall, A. V. Goncharov, and K. Kolacz, “Spheric long focal depth lens: A comment,” Opt. Commun. 281, 4849–4850 (2008).
[CrossRef]

A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. T. Friberg, “Simple lens axicon,” Appl. Opt. 43, 4838–4844 (2004).
[CrossRef] [PubMed]

Kyvalsky, J.

J. Kyvalsky and Z. Bouchal, “Realistic description of the self-reconstruction effect,” Optik (Stuttgart) 112, 225–231 (2001).
[CrossRef]

Leach, J.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

Li, Y.-P.

Lin, Q.

Lin, Y.-T.

M.-D. Wei, W.-L. Shiao, and Y.-T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Lu, X.

C. Zhao, L. Wang, and X. Lu, “Focal shift of hollow Gaussian beams through a thin lens,” Opt. Laser Technol. 40, 58–63 (2008).
[CrossRef]

Y. Cai, X. Lu, and Q. Lin, “Hollow Gaussian beams and their propagation properties,” Opt. Lett. 28, 1084–1086 (2003).
[CrossRef] [PubMed]

Matteucci, G.

J. Garcia-Sucerquia, F. F. Medina, and G. Matteucci, “Optical tubular structures produced by diffraction of circular apertures,” Opt. Lasers Eng. 42, 61–70 (2004).
[CrossRef]

McGloin, D.

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

McGloin, M.

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Medina, F. F.

J. Garcia-Sucerquia, F. F. Medina, and G. Matteucci, “Optical tubular structures produced by diffraction of circular apertures,” Opt. Lasers Eng. 42, 61–70 (2004).
[CrossRef]

Melville, H.

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Meneses-Nava, M. A.

Miguel Hickmann, J.

Omatsu, T.

Padgett, M. J.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
[CrossRef]

Patorsky, K.

K. Patorsky, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed., Vol. 26 (Elsevier, 1990), pp. 3–108.

Philip, G. M.

N. K. Viswanathan, G. M. Philip, and Y. V. Jayasurya, “Generic dark hollow beams using negative cones chemically etched in fiber tips,” Proc. SPIE 7613, 761307-1 (2010).
[CrossRef]

Pierattini, G.

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Ramirez, G.

Romero, L. C. D.

T. Cizmar, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Ryzhevich, A. A.

A. A. Ryzhevich, S. V. Solonevich, and A. G. Smirnov, “Method for creating hollow light beams with local intensity minima and possibilities for their application,” J. Appl. Spectrosc. 76, 570–576 (2009).
[CrossRef]

Sakai, M.

Shiao, W.-L.

M.-D. Wei, W.-L. Shiao, and Y.-T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Sibbett, W.

V. Garces-Chavez, M. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Sinclair, G.

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

Smirnov, A. G.

A. A. Ryzhevich, S. V. Solonevich, and A. G. Smirnov, “Method for creating hollow light beams with local intensity minima and possibilities for their application,” J. Appl. Spectrosc. 76, 570–576 (2009).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Solonevich, S. V.

A. A. Ryzhevich, S. V. Solonevich, and A. G. Smirnov, “Method for creating hollow light beams with local intensity minima and possibilities for their application,” J. Appl. Spectrosc. 76, 570–576 (2009).
[CrossRef]

Tao, S. H.

B. P. S. Ahluwalia, X.-C. Yuan, and S. H. Tao, “Generation of self-imaged optical bottle beams,” Opt. Commun. 238, 177–184 (2004).
[CrossRef]

Tao, S.-H.

Tepichin, E.

Tino, G. M.

M. de Angelis, L. Cacciapuoti, G. Pierattini, and G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Viswanathan, N. K.

N. K. Viswanathan, G. M. Philip, and Y. V. Jayasurya, “Generic dark hollow beams using negative cones chemically etched in fiber tips,” Proc. SPIE 7613, 761307-1 (2010).
[CrossRef]

Wang, H.

Wang, L.

C. Zhao, L. Wang, and X. Lu, “Focal shift of hollow Gaussian beams through a thin lens,” Opt. Laser Technol. 40, 58–63 (2008).
[CrossRef]

Watanabe, T.

Wei, M.-D.

M.-D. Wei, W.-L. Shiao, and Y.-T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Weiss, D. S.

D. J. Han, M. T. DePue, and D. S. Weiss, “Loading and compressing Cs atoms in a very far-off-resonant light trap,” Phys. Rev. A 63, 023405 (2001).
[CrossRef]

Wiggins, T. A.

Wu, F.

X. Zeng and F. Wu, “The analytical description and experiments of the optical bottle generated by an axicon and a lens,” J. Mod. Opt. 55, 3071–3081 (2008).
[CrossRef]

Yamamoto, K.

Yin, J.

J. Yin, W. Gao, and Y. Zhan, “Generation of dark hollow beams and their applications,” in Progress in Optics, E.Wolf, ed., Vol. 45 (Elsevier, 2003), pp.119–204.
[CrossRef]

Yuan, X.-C.

Zeng, X.

X. Zeng and F. Wu, “The analytical description and experiments of the optical bottle generated by an axicon and a lens,” J. Mod. Opt. 55, 3071–3081 (2008).
[CrossRef]

Zhan, Q.

Zhan, Y.

J. Yin, W. Gao, and Y. Zhan, “Generation of dark hollow beams and their applications,” in Progress in Optics, E.Wolf, ed., Vol. 45 (Elsevier, 2003), pp.119–204.
[CrossRef]

Zhang, L.-S.

Zhang, Y.

Zhao, C.

C. Zhao, L. Wang, and X. Lu, “Focal shift of hollow Gaussian beams through a thin lens,” Opt. Laser Technol. 40, 58–63 (2008).
[CrossRef]

Zhao, Y.

Adv. At., Mol., Opt. Phys.

N. Friedman, A. Kaplan, and N. Davidson, “Dark optical traps for cold atoms,” Adv. At., Mol., Opt. Phys. 48, 99–151 (2002).
[CrossRef]

Appl. Opt.

Contemp. Phys.

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

J. Appl. Spectrosc.

A. A. Ryzhevich, S. V. Solonevich, and A. G. Smirnov, “Method for creating hollow light beams with local intensity minima and possibilities for their application,” J. Appl. Spectrosc. 76, 570–576 (2009).
[CrossRef]

J. Mod. Opt.

X. Zeng and F. Wu, “The analytical description and experiments of the optical bottle generated by an axicon and a lens,” J. Mod. Opt. 55, 3071–3081 (2008).
[CrossRef]

G. Sinclair, P. Jordan, J. Leach, M. J. Padgett, and J. Cooper, “Defining the trapping limits of holographic optical tweezers,” J. Mod. Opt. 51, 409–414 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. B

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup used to generate tunable 3-D optical bottle beam; (b) optical microscope image of the chemically etched fiber tip showing double-negative axicon; (c) CCD image of the output beam from the fiber with the device for a fixed input launch condition measured at a distance of 50 μ m from the fiber tip; (d) line profile of the CCD image taken along the white line shown in (c) (open circles) and the corresponding double hollow Gaussian fit (continuous curve).

Fig. 2
Fig. 2

Geometry of the output end of the experimental setup showing the generation of quasi-non-diffracting beam by focusing two π-phase shifted annular rings using a lens with spherical aberration.

Fig. 3
Fig. 3

(a) Free-space propagation of the experimentally generated non-diffracting Bessel beam formed by focusing the third annular ring using lens L 2 kept at Z = 12 mm ; (b) Bessel beam propagation simulated using the input beam parameters in Eq. (1).

Fig. 4
Fig. 4

(a) Transverse intensity image (in log scale) corresponding to Fig. 3a taken at Z = 50 mm ; (b) the corresponding line profile (open circles) with Bessel fit (continuous curve); (c) and (d) line profiles of the images taken at Z = 25 mm and 90 mm , respectively, and the corresponding theoretical fit; (e) peak intensity and FWHM of the quasi-non-diffracting beam generated experimentally as a function of the propagation distance.

Fig. 5
Fig. 5

3-D optical bottle beams generated for different positions of the lens L 2 . (a), (c), (e) One period of the experimentally generated beams; (b), (d), (f) corresponding simulation results obtained using Eq. (2). See text for details.

Fig. 6
Fig. 6

Transverse intensity image corresponding to Fig. 5a taken (a) outside and (c) inside the 3-D bottle beam corresponding to Z 0 = 0.5 mm and 2.5 mm , respectively; (b), (d) corresponding line profiles; (e)–(h) images and line profiles corresponding to Figs. 5c for Z 0 = 1.3 mm and 7.5 mm . (i)–(l) are the images and line profiles corresponding to Fig. 5e for Z 0 = 6 mm and 22 mm .

Fig. 7
Fig. 7

Axial intensity and FWHM of quasi-non-diffracting chain of 3-D bottle beams as a function of propagation distance ( Z ) for Z = 12 mm .

Equations (2)

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E ( r l Φ l z ) = 2 π k r ω 0 ( Z Z max ) 1 2 exp ( z z z max z ) exp [ i ( π 4 ) ] J 0 ( k r r )
I ( r , z ) = a 2 J 0 2 ( k r 1 ) + b 2 J 0 2 ( k r 2 ) + 2 a b J 0 ( k r 1 ) J 0 ( k r 2 ) cos [ ( k z 1 k z 2 ) z + ϕ ] .

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