Abstract

Spatial light modulators are ubiquitous tools for wavefront control and laser beam shaping but have traditionally been used with monochromatic sources due to the inherent wavelength dependence of the calibration process and subsequent phase manipulation. In this work we show that such devices can also be used to shape broadband sources without any wavelength dependence on the output beam’s phase. We outline the principle mathematically and then demonstrate it experimentally using a supercontinuum source to shape rotating white-light Bessel beams carrying orbital angular momentum.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2013

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

2012

A. Forbes, F. Dickey, M. DeGama, A. du Plessis, “Wavelength tunable laser beam shaping,” Opt. Lett. 37, 49–51 (2012).
[CrossRef] [PubMed]

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

2011

X. Zhu, A. Schulzgen, H. Wei, K. Kieu, N. Peyghambarian, “White light Bessel-like beams generated by miniature all-fiber device,” Opt. Express 19, 11365–11374 (2011).
[CrossRef] [PubMed]

M. Padgett, R. Bowman, “Tweezers with a twist,” Nat. Photon. 5, 343–348 (2011).
[CrossRef]

K. Dholakia, T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[CrossRef]

2009

2008

2007

2006

2005

2003

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

V. Arrizon, “Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,” Opt. Lett. 28, 2521–2523 (2003).
[CrossRef] [PubMed]

J. Leach, M. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
[CrossRef]

2002

Alfano, R.

Arrizon, V.

Baumgartl, J.

Bernet, S.

Bowman, R.

M. Padgett, R. Bowman, “Tweezers with a twist,” Nat. Photon. 5, 343–348 (2011).
[CrossRef]

Brown, C.T.A.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

Chen, G.

Cizmar, T.

DeGama, M.

Dholakia, K.

K. Dholakia, T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[CrossRef]

J. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, K. Dholakia, “Propagation characteristics of Airy beams: dependence upon spatial coherence and wavelength,” Opt. Express 17, 13236–13245 (2009).
[CrossRef] [PubMed]

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

Dickey, F.

du Plessis, A.

Dudley, A.

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

R. Vasilyeu, A. Dudley, N. Khilo, A. Forbes, “Generating superpositions of higher-order bessel beams,” Opt. Express 17, 23389–23395 (2009).
[CrossRef]

Duparre, M.

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

Esposito, E.

Feurer, T.

Fischer, P.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

Flamm, D.

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

Forbes, A.

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

A. Forbes, F. Dickey, M. DeGama, A. du Plessis, “Wavelength tunable laser beam shaping,” Opt. Lett. 37, 49–51 (2012).
[CrossRef] [PubMed]

R. Vasilyeu, A. Dudley, N. Khilo, A. Forbes, “Generating superpositions of higher-order bessel beams,” Opt. Express 17, 23389–23395 (2009).
[CrossRef]

Frumker, E.

Furhapter, S.

Gibson, G.

Girkin, J.

Grier, D.

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

Hornung, T.

Jesacher, A.

Kartazayev, V.

Khilo, N.

Kieu, K.

Koehl, Richard M.

Leach, J.

Little, H.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

Lopez-Mariscal, C.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

López-Mariscal, C.

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

Maurer, C.

Mazilu, M.

McConnell, G.

Morris, J.

Morris, J.E.

Naidoo, D.

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

Nelson., K. A.

Nelson., Keith A.

Ngcobo, S.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

Padgett, M.

Peyghambarian, N.

Ritsch-Marte, M.

Rop, R.

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

Schroter, S.

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

Schulze, C.

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

Schulzgen, A.

Schwaighofer, A.

Sibbett, W.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

Silberberg, Y.

Smith, R.L.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

Sztul, H.

Vasilyeu, R.

Vaughan, J. C.

Vaughan, Joshua C.

Wei, H.

Wong, D.W.K.

Wright, A.

Wright, E.M.

Zhu, X.

Appl. Opt.

J. Lightwave Tech.

D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Lightwave Tech. 31, 1023–1032 (2013).
[CrossRef]

J. Mod. Opt

R. Rop, A. Dudley, C. López-Mariscal, A. Forbes, “Measuring the rotation rates of superpositions of higher-order bessel beams,” J. Mod. Opt., 59, 259–267 (2012).
[CrossRef]

J. Opt.

P. Fischer, H. Little, R.L. Smith, C. Lopez-Mariscal, C.T.A. Brown, W. Sibbett, K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. 8, 477–482 (2006).

J. Opt. Soc. Am. B

Nat. Commun.

S. Ngcobo, I. Litvin, L. Burger, A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[CrossRef] [PubMed]

Nat. Photon.

M. Padgett, R. Bowman, “Tweezers with a twist,” Nat. Photon. 5, 343–348 (2011).
[CrossRef]

K. Dholakia, T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[CrossRef]

Nature

D. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

New J. of Physics

C. Schulze, A. Dudley, D. Flamm, M. Duparre, A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. of Physics 15, 073025 (2013).
[CrossRef]

New J. Phys.

J. Leach, M. Padgett, “Observation of chromatic effects near a white-light vortex,” New J. Phys. 5, 154 (2003).
[CrossRef]

Opt. Express

S. Furhapter, A. Jesacher, S. Bernet, M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
[CrossRef] [PubMed]

P. Fischer, C.T.A. Brown, J.E. Morris, C. Lopez-Mariscal, E.M. Wright, W. Sibbett, K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005).
[CrossRef] [PubMed]

J. Leach, G. Gibson, M. Padgett, E. Esposito, G. McConnell, A. Wright, J. Girkin, “Generation of achromatic Bessel beams using a compensated spatial light modulator,” Opt. Express 14, 5581–5587 (2006).
[CrossRef] [PubMed]

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

A. Wright, J. Girkin, G. Gibson, J. Leach, M. Padgett, “Transfer of orbital angular momentum from a super-continuum, white-light beam,” Opt. Express 16, 9495–9500 (2008).
[CrossRef] [PubMed]

J. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, K. Dholakia, “Propagation characteristics of Airy beams: dependence upon spatial coherence and wavelength,” Opt. Express 17, 13236–13245 (2009).
[CrossRef] [PubMed]

R. Vasilyeu, A. Dudley, N. Khilo, A. Forbes, “Generating superpositions of higher-order bessel beams,” Opt. Express 17, 23389–23395 (2009).
[CrossRef]

X. Zhu, A. Schulzgen, H. Wei, K. Kieu, N. Peyghambarian, “White light Bessel-like beams generated by miniature all-fiber device,” Opt. Express 19, 11365–11374 (2011).
[CrossRef] [PubMed]

Opt. Lett.

Supplementary Material (4)

» Media 1: MOV (1182 KB)     
» Media 2: MOV (1247 KB)     
» Media 3: MOV (900 KB)     
» Media 4: MOV (497 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental set-up [division 1 in red: imaging system for a single wavelength measurement; division 2 in blue: imaging system for a broadband wavelength measurement]. L: lens (f1 = 50 mm, f2 = 150 mm, f3 and f4 = 500 mm, f5 = 300 mm); SLM: spatial light modulator; P: pinhole; M: mirror; CM: curved mirror; KM: knife edge mirror; O: objective; CCD: camera. (a) The physical mask used to perform the two spot interference experiment without the blazed grating. The hologram encoded on the SLM for (b) the digital two spot interference experiment and (c) the annular ring interference experiment. (d) The holograms shown with the blazed grating encoded on the SLM to assist division 2 with the compensation of the lateral spatial dispersion for the broadband source.

Fig. 2
Fig. 2

(a) The measured phase shift plotted against the gray-level for different wavelengths (blue: 475 nm; green: 550 nm; red: 650 nm and black: 775 nm). (b) The ratio between the measured and ideal phase (kd) plotted against the gray-level. (c) The ratio between the measured and ideal phase (kd) for various wavelengths for the physical mask and (d) the two spot hologram in the first diffraction order.

Fig. 3
Fig. 3

The measured interference fringe shift plotted against the encoded phase difference for (a) a single wavelength (λ = 532 nm) and (b) the broadband source. Corresponding videos illustrating the shift in the interference pattern can be viewed as ( Media 1) and ( Media 2), respectively.

Fig. 4
Fig. 4

The measured petal rotation rate plotted against the encoded phase difference for (a) a single wavelength (λ = 532 nm) and (b) the broadband source. Corresponding videos illustrating the rotation in the interference pattern can be viewed as ( Media 3) and ( Media 4), respectively.

Fig. 5
Fig. 5

Cross-section view of a linear phase gradient wrapped around a phase of θ with sections spaced with a pitch p.

Equations (18)

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

f ( x ) = | f ( x ) | exp ( i ϕ ( x ) ) ,
u ( x ) = f ( x ) × g ( x ) = | f ( x ) | exp ( i [ ϕ ( x ) + 2 π p x ] ) .
u wr ( x ) = n = sinc ( π [ n k d ] ) | f ( x ) | exp ( in [ ϕ ( x ) + 2 π p x ] ) ,
u wr ( x ) = n = sinc ( π [ n k d ] ) | f ( x ) | exp ( in ϕ ( x ) ) exp ( i 2 π n p x ) ,
U wr ( X ) = 2 π n = sinc ( π [ n k d ] ) × { | f ( x ) | exp ( in ϕ ( x ) ) } δ ( X 2 π n p ) .
U wr ( X ) | n = 1 = 2 π A 1 { | f ( x ) | exp ( i ϕ ( x ) ) } δ ( X 2 π p ) = 2 π A 1 F ( X 2 π p ) .
t ( r , ϕ ) = { exp ( i l ϕ ) if R r R Δ exp ( i l ϕ ) exp ( i φ ) if R r R + Δ ,
u ( r , ϕ ) = J l ( r ) exp ( i l ϕ ) + J l ( r ) exp ( i l ϕ ) exp ( i φ ) ,
f ( x ) = | f ( x 1 ) | e i k d Φ 1 δ ( x x 1 ) + | f ( x 2 ) | e i k d Φ 2 δ ( x x 2 ) + | f ( x 3 ) | e i k d Φ 3 δ ( x x 3 ) + ,
| f ( x m ) | e i k d Φ m δ ( x x m ) = | f ( x m ) | e i k d Φ m x m x δ ( x x m ) , where m .
p = 2 π l x m Φ m .
g ( x , 2 π l k d , 2 π l x m Φ m ) = n = sinc ( π [ n l k d ] ) e i n Φ m l x m x .
f wr ( x ) = n = sinc ( π [ n l k d ] ) [ | f ( x 1 ) | e i n l Φ 1 δ ( x x 1 ) + | f ( x 2 ) | e i n l Φ 2 δ ( x x 2 ) + | f ( x 3 ) | e i n l Φ 3 δ ( x x 3 ) + ] ,
f wr ( x ) = | f ( x ) | n = sinc ( π [ n l k d ] ) e i n l Φ ( x ) .
g ( x ) = e i θ p x rect ( 2 p x ) n = δ ( x n p ) .
G ( X ) = 2 π δ ( X θ p ) sinc ( p 2 X ) × n = δ ( X 2 π n p ) = 2 π sinc ( p 2 [ X θ p ] ) × n = δ ( X 2 π n p ) = 2 π n = sinc ( p 2 [ 2 π n p θ p ] ) δ ( X 2 π n p ) = 2 π n = sinc ( π [ n θ 2 π ] ) δ ( X 2 π n p ) .
g ( x , θ , p ) = n = sinc ( π [ n θ 2 π ] ) e i 2 π n p x .
e i θ p x rect ( 2 p x ) n = δ ( x n p ) = n = sinc ( π [ n θ 2 π ] ) e i 2 π n p x ,

Metrics