Abstract

We present an analytical solution for the phase introduced by a phase-only spatial light modulator to generate far-field phase and amplitude distributions within a domain of interest. The solution is demonstrated experimentally and shown to enable excellent control of the far-field amplitude and phase.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. von Freymann, “Three-dimensional laser lithography: finer features faster,” presented at CLEO-Europe, Munich, Germany, May12–16, 2013.
  2. L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Opt. Lett. 37, 2415 (2012).
    [CrossRef]
  3. L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
    [CrossRef]
  4. D. Walter, T. Pfeifer, C. Winterfeldt, R. Kemmer, R. Spitzenpfeil, G. Gerber, and C. Spielmann, Opt. Express 14, 3433 (2006).
    [CrossRef]
  5. N. Sannerand, N. Huot, and E. Audouard, Opt. Lett. 30, 1479 (2005).
    [CrossRef]
  6. M. M. Wefers and K. Nelson, Opt. Lett. 20, 1047 (1995).
    [CrossRef]
  7. A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, Opt. Express 16, 2597 (2008).
    [CrossRef]
  8. R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).
  9. M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).
  10. J. A. Davis, K. O. Valadez, and D. M. Cottrell, Appl. Opt. 42, 2003 (2003).
    [CrossRef]
  11. C. K. Hsueh and A. A. Sawchuk, Appl. Opt. 17, 3874 (1978).
    [CrossRef]
  12. J. A. Vaughan, T. Hornung, T. Feurer, and K. Nelson, Opt. Lett. 30, 323 (2005).
    [CrossRef]
  13. V. Bagnoud and J. D. Zuege, Opt. Lett. 29, 295 (2004).
    [CrossRef]
  14. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
    [CrossRef]
  15. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  16. B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
    [CrossRef]

2013 (3)

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
[CrossRef]

2012 (1)

2008 (1)

2006 (1)

2005 (2)

2004 (1)

2003 (1)

2002 (1)

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

1995 (1)

1982 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Audouard, E.

Bagnoud, V.

Batan, N. A. D.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Bernardo, A. D.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Bernet, S.

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Cottrell, D. M.

Courtois, C.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Cros, B.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Davis, J. A.

de la Cruz, A. R.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Feurer, T.

Forbes, A.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Galvan-Sosa, M.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Gerber, G.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Hernandez-Rueda, J.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Hooker, S. M.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
[CrossRef]

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Opt. Lett. 37, 2415 (2012).
[CrossRef]

Hornung, T.

Hsueh, C. K.

Huot, N.

Ina, H.

Jesacher, A.

Kemmer, R.

Kobayashi, S.

Kuznetsov, S.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Liu, L. Z.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
[CrossRef]

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Opt. Lett. 37, 2415 (2012).
[CrossRef]

Matthieussent, G.

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Maurer, C.

Moreno, L.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Nelson, K.

Ngcobo, S.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

O’Keeffe, K.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
[CrossRef]

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Opt. Lett. 37, 2415 (2012).
[CrossRef]

Pfeifer, T.

Portilla, J.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Ritsch-Marte, M.

Sannerand, N.

Sawchuk, A. A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Schwaighofer, A.

Siegel, J.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Solis, J.

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

Spielmann, C.

Spitzenpfeil, R.

Takeda, M.

Valadez, K. O.

Vaughan, J. A.

von Freymann, G.

G. von Freymann, “Three-dimensional laser lithography: finer features faster,” presented at CLEO-Europe, Munich, Germany, May12–16, 2013.

Walter, D.

Wefers, M. M.

Winterfeldt, C.

Zuege, J. D.

Appl. Opt. (2)

Appl. Phys. A (1)

M. Galvan-Sosa, J. Portilla, J. Hernandez-Rueda, J. Siegel, L. Moreno, A. R. de la Cruz, and J. Solis, Appl. Phys. A 114, 1007 (2013).

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2289 (2013).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Optik (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Phys. Rev. A (1)

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, Phys. Rev. A 87, 023810 (2013).
[CrossRef]

Phys. Rev. E (1)

B. Cros, C. Courtois, G. Matthieussent, A. D. Bernardo, N. A. D. Batan, and S. Kuznetsov, Phys. Rev. E 65, 026405 (2002).
[CrossRef]

Other (1)

G. von Freymann, “Three-dimensional laser lithography: finer features faster,” presented at CLEO-Europe, Munich, Germany, May12–16, 2013.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Illustrative domains for the focal plane, where SP is the domain of interest and SQ is outside of that. The value a is defined as the maximum distance from the origin of the boundary between SP and SQ.

Fig. 2.
Fig. 2.

General schematic for the demonstration experiment. Note that the interferometry arm is blocked for intensity measurements.

Fig. 3.
Fig. 3.

Measured far-field intensity profiles for generation of (a) text and (b) a portrait of Joseph Fourier.

Fig. 4.
Fig. 4.

Generation of the EH13 mode by a phase-only SLM. (a) shows the intensity profile, on an arbitrary logarithmic scale, inside and outside the domain of interest; the boundary between these domains is indicated by the white circle. (b) and (c) show, respectively, the measured profiles in the axial region of the transverse profiles of the intensity in arbitrary units and phase in units of π. (d) and (e) compare lineouts of the (d) measured (blue, solid) and target (red, dashed) real part of the field amplitude in arbitrary units, and (e) phase in units of π.

Fig. 5.
Fig. 5.

Demonstration of simultaneous control of amplitude and phase by generating (left) a circle of uniform intensity, within which is a circular region with a phase of π/2 relative to the surrounding annulus; (right) a square, within which is a triangular region with a phase shifted by π relative to the surrounding region. The measured transverse intensity and phase profiles are shown in (a) and (b), respectively. We also note that the phase in (b) was set to zero, if the intensity was below 10% of maximum.

Equations (5)

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

{U(X,Y)=eikX2+Y2+f2λfdxdy×u(x,y)eikf(xX+yY)u(x,y)=dXdY×U(X,Y)eikX2+Y2+f2e+ikf(xX+yY),
u(x,y)=SPdXdYUP(X,Y)eikX2+Y2+f2e+ikf(xX+yY)+SQdXdYUQ(X,Y)eikX2+Y2+f2e+ikf(xX+yY)
=P(x,y)+Q(x,y),
Q02+(Peiϕ+P*e+iϕ)Q0+(PP*u02)=0,
|u0|eiψ0T=P+e+iϕ{R[Peiϕ]±R[Peiϕ]2(|P|2|u0|2)},

Metrics