Abstract

We present a method for efficient and versatile generation of beams whose intensity and phase are prescribed along arbitrary 3D curves. It comprises a non-iterative beam shaping technique that does not require solving inversion problems of light propagation. The generated beams have diffraction-limited focusing with high intensity and controlled phase gradients useful for applications such as laser micro-machining and optical trapping. Its performance and feasibility are experimentally demonstrated on several examples including multiple trapping of micron-sized particles.

© 2013 Optical Society of America

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2012

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[CrossRef]

2011

2010

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express18, 6988–6993 (2010).
[CrossRef] [PubMed]

F. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010).
[CrossRef]

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics4, 188–193 (2010).
[CrossRef]

2008

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]

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Physics4, 716–720 (2008).
[CrossRef]

2007

2006

2005

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg–Saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

2004

2002

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

2000

M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys.41, 275–285 (2000).
[CrossRef]

1999

1987

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi47, 1177–1203 (2004).
[CrossRef]

Alieva, T.

Allebach, J. P.

Allen, L.

M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys.41, 275–285 (2000).
[CrossRef]

Alpmann, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[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]

Bernet, S.

Bouwmeester, D.

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Physics4, 716–720 (2008).
[CrossRef]

Calvo, M. L.

Cámara, A.

Campos, J.

Cheben, P.

Cottrell, D. M.

Courtial, J.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg–Saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

Davis, J. A.

Denz, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[CrossRef]

Dholakia, K.

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

Esseling, M.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[CrossRef]

Fahrbach, F.

F. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010).
[CrossRef]

Fürhapter, S.

Garces-Chavez, V.

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

Gerke, T. D.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics4, 188–193 (2010).
[CrossRef]

Grier, D.

Grier, D. G.

E. R. Shanblatt and D. G. Grier, “Extended and knotted optical traps in three dimensions,” Opt. Express19, 5833–5838 (2011).
[CrossRef] [PubMed]

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express18, 6988–6993 (2010).
[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, “Three-dimensional holographic ring traps,” Proc. SPIE6483, 64830F (2007).
[CrossRef]

Irvine, W. T. M.

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Physics4, 716–720 (2008).
[CrossRef]

Jesacher, A.

Ladavac, K.

Lee, S.-H.

Martínez-Matos, O.

Maurer, C.

McGloin, D.

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

Melville, H.

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

Moreno, I.

Oddershede, L. B.

Padgett, M.

M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys.41, 275–285 (2000).
[CrossRef]

Piestun, R.

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics4, 188–193 (2010).
[CrossRef]

Reihani, S. N. S.

Ritsch-Marte, M.

Rodrigo, J. A.

Rohrbach, A.

F. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010).
[CrossRef]

Roichman, Y.

S.-H. Lee, Y. Roichman, and D. G. Grier, “Optical solenoid beams,” Opt. Express18, 6988–6993 (2010).
[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, 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, “Three-dimensional holographic ring traps,” Proc. SPIE6483, 64830F (2007).
[CrossRef]

Seldowitz, M. A.

Shanblatt, E. R.

Sibbett, W.

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

Simon, P.

F. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010).
[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]

Sweeney, D. W.

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi47, 1177–1203 (2004).
[CrossRef]

Whyte, G.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg–Saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

Woerdemann, M.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[CrossRef]

Yzuel, M. J.

Appl. Opt.

Contemp. Phys.

M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys.41, 275–285 (2000).
[CrossRef]

Laser Photonics Rev.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev.1–16 (2012).
[CrossRef]

Nat.

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

Nat. Photonics

F. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics4, 780–785 (2010).
[CrossRef]

T. D. Gerke and R. Piestun, “Aperiodic volume optics,” Nat. Photonics4, 188–193 (2010).
[CrossRef]

Nat. Physics

W. T. M. Irvine and D. Bouwmeester, “Linked and knotted beams of light,” Nat. Physics4, 716–720 (2008).
[CrossRef]

New J. Phys.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg–Saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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]

Physics-Uspekhi

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi47, 1177–1203 (2004).
[CrossRef]

Proc. SPIE

Y. Roichman and D. G. Grier, “Three-dimensional holographic ring traps,” Proc. SPIE6483, 64830F (2007).
[CrossRef]

Other

V. A. Soifer, ed., Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

Supplementary Material (6)

» Media 1: MOV (2624 KB)     
» Media 2: MOV (2690 KB)     
» Media 3: MOV (1736 KB)     
» Media 4: MOV (2241 KB)     
» Media 5: MOV (3227 KB)     
» Media 6: MOV (1042 KB)     

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Figures (6)

Fig. 1
Fig. 1

(a) Setup for projecting a curve light beam in the focal region, z ∈ [−d, d], of the focusing lens (FL). A ring-shaped beam exhibiting Gaussian and HIG intensity profiles [(b), red and blue color lines, respectively] is considered. The beam propagation in the yz–plane is displayed for each case, (c) and (d), correspondingly. The beam intensity at the focal plane (z = 0) is also shown. (e) Intensity of G (r|c2) for several types of curves c2.

Fig. 2
Fig. 2

(a)–(d) Intensity distribution of the beam projected in the focal plane (z = 0) according to several closed and open 2D curves. First and second row correspond to the expected and experimental beams. The experimental beam propagation is shown in ( Media 1) for each case. Third row displays the phase of the theoretical beams shown in (a), (c) and (d). Axis units are given in mm.

Fig. 3
Fig. 3

Experimental results. Intensity distribution of the beams designed along 3D curves: (a) tilted ring, (b) Viviani’s curve, (c) an Archimedean spiral, and a trefoil-knotted curve (d). Second, third, and fourth row display the beam propagated before, at, and after the focal plane, respectively. The overall beam prorogation was measured and stored in ( Media 2) for each case. Units are given in mm.

Fig. 4
Fig. 4

Experimental results. Intensity distribution of the beams designed along 3D curves: (a) tilted ring, (b) Viviani’s curve, (c) an Archimedean spiral, and a trefoil-knotted curve (d). These volumetric reconstructions were obtained from the measured beam propagations shown in ( Media 2).

Fig. 5
Fig. 5

Optical vortex traps shaped in different 3D configurations. The particles are trapped 10 μm in deep into the sample, black arrows indicate particles in free diffusion at the chamber bottom. The traps (a)–(d) are correspondingly shown in ( Media 3, Media 4, Media 5, and Media 6).

Fig. 6
Fig. 6

Sketch of the optical trapping setup. The hologram is addressed into the SLM, which is illuminated by a collimated laser beam. The resulting beam, H (r|c3), is projected into the back-aperture of the microscope objective (MO), by using the relay lenses (RL1 and RL2 are set as a Keplerian telescope). A dichroic-mirror filter (DF) and the tube lens (TL) are set to image the sample on the CMOS camera.

Tables (1)

Tables Icon

Table 1 Parametric curves c3(t)

Equations (10)

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F ( r , 0 | c 2 ( t ) , t [ 0 , T ] ) = 1 L 0 T exp ( [ x x 0 ( t ) ] 2 + [ y y 0 ( t ) ] 2 2 w 0 2 ) Φ ( r , t ) | c 2 ( t ) | d t ,
L = 0 T | c 2 ( t ) | d t
Φ ( r , t ) = exp ( i w 0 2 [ y x 0 ( t ) x y 0 ( t ) ] + i σ w 0 2 0 t [ x 0 ( τ ) y 0 ( τ ) y 0 ( τ ) x 0 ( τ ) ] d τ ) ,
G ( r , 0 | c 2 ( t ) , t [ 0 , T ] ) = 1 L 0 T Φ ( r , t ) | c 2 ( t ) | d t ,
φ ( r , t ) = exp ( i π [ x x 0 ( t ) ] 2 + [ y y 0 ( t ) ] 2 λ f 2 z 0 ( t ) ) ,
H ( r , 0 | c 3 ( t ) , t [ 0 , T ] ) = 1 L 0 T φ ( r , t ) Φ ( r , t ) | c 2 ( t ) | d t ,
Ψ ( r ) = exp { i ψ [ a ( r ) , ϕ ( r ) ] } .
G ( r | c 2 ) = 1 2 π 0 2 π exp ( i [ σ R 0 2 w 0 2 t R 0 w 0 2 r sin ( t θ ) ] ) d t .
J m ( ρ ) = 1 2 π 0 2 π exp ( i [ m t ρ sin t ] ) d t ,
G ( r | c 2 ) = J m ( R 0 w 0 2 r ) exp ( i m θ ) = J m ( k r ) exp ( i m θ ) .

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