Abstract

We demonstrate simultaneous control of both the phase and amplitude of light using a conjugate gradient minimisation-based hologram calculation technique and a single phase-only spatial light modulator (SLM). A cost function, which incorporates the inner product of the light field with a chosen target field within a defined measure region, is efficiently minimised to create high fidelity patterns in the Fourier plane of the SLM. A fidelity of F = 0.999997 is achieved for a pattern resembling an LG10 mode with a calculated light-usage efficiency of 41.5%. Possible applications of our method in optical trapping and ultracold atoms are presented and we show uncorrected experimental realisation of our patterns with F = 0.97 and 7.8% light efficiency.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

16 May 2017: A correction was made to Table 2.


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References

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2016 (3)

2015 (6)

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photon. 7, 66–106 (2015).
[Crossref]

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23, 1052–1062 (2015).
[Crossref] [PubMed]

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

2014 (4)

T. Harte, G. D. Bruce, J. Keeling, and D. Cassettari, “Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms,” Opt. Express 22, 26548–26558 (2014).
[Crossref] [PubMed]

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22, 17999–18009 (2014).
[Crossref] [PubMed]

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4, 7441 (2014).
[Crossref] [PubMed]

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

2013 (1)

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

2012 (1)

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

2011 (4)

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

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

2010 (1)

T. Cižár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

2008 (3)

2006 (1)

2005 (1)

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

1996 (1)

1982 (1)

Ahmed, N.

Aldossary, O. M.

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Alpmann, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Anderson, M.

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Arnold, A. S.

Ashrafi, N.

Ashrafi, S.

Babiker, M.

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Babujian, H.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Bao, C.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
[Crossref] [PubMed]

Bertolotti, J.

Bowman, D.

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Bruce, G. D.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

T. Harte, G. D. Bruce, J. Keeling, and D. Cassettari, “Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms,” Opt. Express 22, 26548–26558 (2014).
[Crossref] [PubMed]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Buccheri, F.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Butera, S.

S. Butera, N. Westerberg, D. Faccio, and P. Öhberg, “Nonlinear synthetic gauge potentials and sonic horizons in Bose-Einstein condensates,” arXiv:1605.05556 (2016).

Campbell, G. K.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Cao, Y.

Cassettari, D.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

T. Harte, G. D. Bruce, J. Keeling, and D. Cassettari, “Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms,” Opt. Express 22, 26548–26558 (2014).
[Crossref] [PubMed]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Chardonnet, V.

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Cheng, S.

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Cižár, T.

T. Cižár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Clark, T. W.

Cormack, E.

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

Courtial, J.

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

DeMarco, B.

Denny, S. J.

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Denz, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

Dholakia, K.

T. Cižár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Esseling, M.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

Faccio, D.

S. Butera, N. Westerberg, D. Faccio, and P. Öhberg, “Nonlinear synthetic gauge potentials and sonic horizons in Bose-Einstein condensates,” arXiv:1605.05556 (2016).

Franke-Arnold, S.

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24, 6249–6264 (2016).
[Crossref] [PubMed]

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Gaunt, A. L.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Goorden, S. A.

Greiner, M.

Grier, D. G.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Y. Roichman and D. G. Grier, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31, 1675–1677 (2006).
[Crossref] [PubMed]

Groot, C. De

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Hadzibabic, Z.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

Harte, T.

Harte, T. L.

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Helmerson, K.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Hill, W. T.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Huang, H.

Huo, M.-X.

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

Hutchinson, D. A. W.

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

Ina, H.

Ireland, P.

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Islam, R.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
[Crossref] [PubMed]

Johnson, M. Y. H.

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

Keeling, J.

Kobayashi, S.

Korepin, V. E.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Kwek, L. C.

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

Lavery, M. P. J.

Le Goc, G.

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

Lembessis, V. E.

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Li, L.

Lobb, C. J.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Lukin, A.

Ma, R.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
[Crossref] [PubMed]

Mayoh, J.

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

Mazilu, M.

T. Cižár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Molisch, A. F.

Mosk, A. P.

Muniz, S. R.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Neto, L. G.

Nie, W.

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

Offer, R. F.

Öhberg, P.

S. Butera, N. Westerberg, D. Faccio, and P. Öhberg, “Nonlinear synthetic gauge potentials and sonic horizons in Bose-Einstein condensates,” arXiv:1605.05556 (2016).

Padgett, M. J.

Pasienski, M.

Phillips, W. D.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Preiss, P. M.

Radwell, N.

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24, 6249–6264 (2016).
[Crossref] [PubMed]

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Ramachandran, S.

Ramanathan, A.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Ren, Y.

Richards, D. A. W.

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

Rispoli, M.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
[Crossref] [PubMed]

Roberge, D.

Roichman, Y.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Y. Roichman and D. G. Grier, “Projecting extended optical traps with shape-phase holography,” Opt. Lett. 31, 1675–1677 (2006).
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Schimmel, H.

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

Schwaighofer, A.

Selyem, A.

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Senthilkumaran, P.

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

Sheng, Y.

Shewchuk, J. R.

J. R. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain(Carnegie Mellon University, 1994).

Smirne, G.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

Sodano, P.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Sun, B.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Tai, M. E.

Takeda, M.

Tao, S.

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23, 1052–1062 (2015).
[Crossref] [PubMed]

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Torralbo-Campo, L.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

Trombettoni, A.

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Tur, M.

Wang, J.

Westerberg, N.

S. Butera, N. Westerberg, D. Faccio, and P. Öhberg, “Nonlinear synthetic gauge potentials and sonic horizons in Bose-Einstein condensates,” arXiv:1605.05556 (2016).

Willner, A. E.

Woerdemann, M.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

Wright, K. C.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Wu, L.

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

Wyrowski, F.

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

Xie, G.

Yan, Y.

Yao, A. M.

Yu, W.

Zelan, M.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Zhao, Z.

Zhu, L.

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4, 7441 (2014).
[Crossref] [PubMed]

Zupancic, P.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Phys. B: At. Mol. Opt. Phys. (1)

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. A. W. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” J. Phys. B: At. Mol. Opt. Phys. 48, 115303 (2015).
[Crossref]

Laser Photonics Rev. (2)

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7, 839–854 (2013).
[Crossref]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
[Crossref]

Nat. Photonics (1)

T. Cižár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

New J. Phys. (1)

F. Buccheri, G. D. Bruce, A. Trombettoni, D. Cassettari, H. Babujian, V. E. Korepin, and P. Sodano, “Holographic optical traps for atom-based topological Kondo devices,” New J. Phys. 18, 075012 (2016).
[Crossref]

Opt. Express (8)

P. Zupancic, P. M. Preiss, R. Ma, A. Lukin, M. E. Tai, M. Rispoli, R. Islam, and M. Greiner, “Ultra-precise holographic beam shaping for microscopic quantum control,” Opt. Express 24, 13881–13893 (2016).
[Crossref] [PubMed]

D. Bowman, P. Ireland, G. D. Bruce, and D. Cassettari, “Multi-wavelength holography with a single spatial light modulator for ultracold atom experiments,” Opt. Express 23, 8365–8372 (2015).
[Crossref] [PubMed]

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24, 6249–6264 (2016).
[Crossref] [PubMed]

S. A. Goorden, J. Bertolotti, and A. P. Mosk, “Superpixel-based spatial amplitude and phase modulation using a digital micromirror device,” Opt. Express 22, 17999–18009 (2014).
[Crossref] [PubMed]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
[Crossref] [PubMed]

S. Tao and W. Yu, “Beam shaping of complex amplitude with separate constraints on the output beam,” Opt. Express 23, 1052–1062 (2015).
[Crossref] [PubMed]

T. Harte, G. D. Bruce, J. Keeling, and D. Cassettari, “Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms,” Opt. Express 22, 26548–26558 (2014).
[Crossref] [PubMed]

M. Pasienski and B. DeMarco, “A high-accuracy algorithm for designing arbitrary holographic atom traps,” Opt. Express 16, 2176–2190 (2008).
[Crossref] [PubMed]

Opt. Laser Eng. (1)

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

Opt. Lett. (1)

Phys. Rev. A (1)

V. E. Lembessis, J. Courtial, N. Radwell, A. Selyem, S. Franke-Arnold, O. M. Aldossary, and M. Babiker, “Graphene-like optical light field and its interaction with two-level atoms,” Phys. Rev. A 92, 063833 (2015).
[Crossref]

Phys. Rev. Lett. (2)

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable-weak link,” Phys. Rev. Lett. 106, 130401 (2011).
[Crossref]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref] [PubMed]

Phys. Scr. (1)

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. T143, 014008 (2011).
[Crossref]

Sci. Rep. (4)

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

M.-X. Huo, W. Nie, D. A. W. Hutchinson, and L. C. Kwek, “A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms,” Sci. Rep. 4, 5992 (2014).
[Crossref] [PubMed]

L. Wu, S. Cheng, and S. Tao, “Simultaneous shaping of amplitude and phase of light in the entire output plane with a phase-only hologram,” Sci. Rep. 5, 15426 (2015).
[Crossref] [PubMed]

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4, 7441 (2014).
[Crossref] [PubMed]

Other (6)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. R. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain(Carnegie Mellon University, 1994).

Theano Development Team, “Theano: A Python framework for fast computation of mathematical expressions,” arXiv:1605.02688 (2016).

University of St. Andrews Research Data D. Bowman, T. L. Harte, V. Chardonnet, C. De Groot, S. J. Denny, G. Le Goc, M. Anderson, P. Ireland, D. Cassettari, and G. D. Bruce, (2017),
[Crossref]

S. Butera, N. Westerberg, D. Faccio, and P. Öhberg, “Nonlinear synthetic gauge potentials and sonic horizons in Bose-Einstein condensates,” arXiv:1605.05556 (2016).

Images downloaded from Wikimedia Commons, 11/11/16

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Figures (4)

Fig. 1
Fig. 1

Block diagram of the phase distribution calculation process using conjugate gradient minimisation.

Fig. 2
Fig. 2

The far-field results from the conjugate gradient optimisation showing normalised intensity Ĩ (colour) and phase φ (grey) in the region of interest. (a) Laguerre-Gaussian mode, (b) ring lattice with azimuthally-varying phase, (c) square lattice with azimuthally-varying phase, (d) graphene lattice with alternating phase, (e) flat-top intensity with inverse-square power-law phase, (f) Gaussian line with linear phase gradient, (g) chicken intensity with egg phase. The flat top pattern (e) has the light outside the measure region removed for clarity. The error metrics for each pattern are shown in Table 1.

Fig. 3
Fig. 3

(a) Evolution of fidelity F for the Gaussian Line pattern shown in Fig. 2(f) with σ = 1.5 mm and R = 3.5 mrad px−2. At low values of the steepness d of the cost function, the algorithm stagnates earlier and returns a lower fidelity hologram. (b) The final fidelity and the time per iteration t both improve as d is increased. (c) Fidelity and (d) efficiency η as a function of incident laser beam size σ and quadratic guess phase curvature R. Small beam sizes and reduced guess phase curvature give highest efficiency but lowest fidelity.

Fig. 4
Fig. 4

(a) Experimental Setup. The laser light is separated into two beams with a polarising beam splitter (PBS), using a half-waveplate (λ/2) to control the relative power in each beam. One beam is phase-modulated by the SLM, and focussed onto a CCD camera with an achromatic doublet lens. The second beam is co-polarized and overlapped with the first using a non-polarizing beam splitter (BS). To image only intensity, we block the second beam. The interference pattern produced on the CCD camera when both beams are unblocked is used to detect the phase. (b) - (d) Measured intensity (left) and phase (right) for (b) Gaussian line, (c) Laguerre-Gaussian and (d) graphene lattice. The white scalebar in (b) denotes 300 µm, and is common to all images. Color scaling as in Fig. 2.

Tables (2)

Tables Icon

Table 1 Error metrics for the calculated patterns in Fig. 2, with optimal values of σ, R and region of interest diameter ROI.

Tables Icon

Table 2 Error metrics for the measured patterns in Fig. 4.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E n , m out = S p , q N T p , q exp ( i ϕ p , q ) exp [ ( 2 π i N T ) ( p n + q m ) ] ,
= I n , m exp ( i φ n , m ) ,
α i = g i + ( g i g i ( g i 1 g i 1 ) ) α i 1 .
C = 10 d ( 1 n , m Re { | τ ˜ n , m * E ˜ n , m out | } ) 2 ,
= 10 d ( 1 n , m I ˜ n , m T ˜ n , m cos ( Φ n , m φ n , m ) ) 2 ,
ϵ Φ =   n , m | ( Φ n , m φ n , m + P ) | 2   n , m | Φ n , m | 2 ,
ϵ nu =   n , m | M n , m ( I ˜ n , m I a ) | 2   n , m | M n , m T ˜ n , m | 2 ,

Metrics