Abstract

Whereas nodal points having zero amplitude are well-known wave phenomena, destructive interference across a continuous area is rare. In fact, these strange states seem to defy nature’s “abhorrence of nothingness.” Philosophizing aside, we report general schemes for constructing a nodal area in a spatially coherent beam of light by use of a lossless phase mask. Theoretical, numerical, and experimental results are presented. Nodal areas are important for high contrast imaging, laser surfacing, radiation shielding, and other structured light applications. Moreover, these results transcend optics and open the possibility of achieving nodal area wave functions in quantum, acoustic, and other coherent wave systems.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  5. D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
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2013 (2)

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

G. J. Ruane, G. A. Swartzlander, Appl. Opt. 52, 171 (2013).
[Crossref]

2011 (2)

2009 (1)

G. A. Swartzlander, J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
[Crossref]

2008 (1)

K. C. Wright, L. S. Leslie, N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[Crossref]

2007 (1)

G. A. Swartzlander, R. I. Hernandez-Aranda, Phys. Rev. Lett. 99, 163901 (2007).
[Crossref]

2006 (1)

L. Marrucci, C. Manzo, D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

2005 (4)

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

V. Westphal, S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

R. Soummer, Astrophys. J. 618, L161 (2005).
[Crossref]

G. Foo, D. M. Palacios, G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
[Crossref]

2004 (1)

M. V. Berry, M. R. Dennis, J. Opt. A Pure Appl. Opt. 6, S178 (2004).
[Crossref]

2003 (1)

O. Guyon, Astron. Astrophys. 404, 379 (2003).
[Crossref]

2002 (2)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

2000 (1)

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

1992 (2)

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

1989 (1)

P. Coullet, L. Gil, F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

1982 (1)

1974 (1)

J. F. Nye, M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[Crossref]

1972 (1)

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

1961 (1)

L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

1958 (1)

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)].

1941 (1)

L. Landau, Phys. Rev. 60, 356 (1941).
[Crossref]

Absil, O.

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

Allen, L.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Barnett, S. M.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Berry, M. V.

M. V. Berry, M. R. Dennis, J. Opt. A Pure Appl. Opt. 6, S178 (2004).
[Crossref]

M. V. Berry, Phys. Today 55(5), 10 (2002).
[Crossref]

J. F. Nye, M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[Crossref]

Biener, G.

Bigelow, N. P.

K. C. Wright, L. S. Leslie, N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[Crossref]

Boccaletti, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Bomzon, Z.

Carlotti, A.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

A. Carlotti, R. Vanderbei, N. J. Kasdin, Opt. Express 19, 26796 (2011).
[Crossref]

Chigrinov, V.

Clénet, Y.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Coullet, P.

P. Coullet, L. Gil, F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Dennis, M. R.

M. V. Berry, M. R. Dennis, J. Opt. A Pure Appl. Opt. 6, S178 (2004).
[Crossref]

Du, T.

Fienup, J. R.

Foo, G.

Gerchberg, R. W.

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

Gil, L.

P. Coullet, L. Gil, F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Ginzburg, V. L.

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)].

Guyon, O.

O. Guyon, Astron. Astrophys. 404, 379 (2003).
[Crossref]

Hasman, E.

Hell, S. W.

V. Westphal, S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

Hernandez-Aranda, R. I.

G. A. Swartzlander, R. I. Hernandez-Aranda, Phys. Rev. Lett. 99, 163901 (2007).
[Crossref]

Kasdin, N. J.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

Kleiner, V.

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

Labeyrie, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Landau, L.

L. Landau, Phys. Rev. 60, 356 (1941).
[Crossref]

Law, C. T.

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref]

Leslie, L. S.

K. C. Wright, L. S. Leslie, N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[Crossref]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Marrucci, L.

Mawet, D.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

Mennesson, B.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

Murauski, A.

Nye, J. F.

J. F. Nye, M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[Crossref]

Padgett, M. J.

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Palacios, D. M.

Paparo, D.

L. Marrucci, C. Manzo, D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Pitaevskii, L. P.

L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)].

Pueyo, L.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

Riaud, P.

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Rocca, F.

P. Coullet, L. Gil, F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Rouan, D.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Ruane, G. J.

Santamato, E.

Saxton, W. O.

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

Serabyn, E.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

Slussarenko, S.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

Soskin, M. S.

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Soummer, R.

R. Soummer, Astrophys. J. 618, L161 (2005).
[Crossref]

Surdej, J.

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

Swartzlander, G. A.

G. J. Ruane, G. A. Swartzlander, Appl. Opt. 52, 171 (2013).
[Crossref]

G. A. Swartzlander, J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
[Crossref]

G. A. Swartzlander, R. I. Hernandez-Aranda, Phys. Rev. Lett. 99, 163901 (2007).
[Crossref]

G. Foo, D. M. Palacios, G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
[Crossref]

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

Vanderbei, R.

Vasnetsov, M. V.

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

Wallace, J. K.

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

Westphal, V.

V. Westphal, S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

Wright, K. C.

K. C. Wright, L. S. Leslie, N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[Crossref]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (1)

O. Guyon, Astron. Astrophys. 404, 379 (2003).
[Crossref]

Astrophys. J. (2)

R. Soummer, Astrophys. J. 618, L161 (2005).
[Crossref]

D. Mawet, P. Riaud, O. Absil, J. Surdej, Astrophys. J. 633, 1191 (2005).
[Crossref]

Astrophys. J. Suppl. Ser. (1)

D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J. K. Wallace, Astrophys. J. Suppl. Ser. 209, 7 (2013).
[Crossref]

J. Mod. Opt. (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[Crossref]

J. Opt. A Pure Appl. Opt. (2)

M. V. Berry, M. R. Dennis, J. Opt. A Pure Appl. Opt. 6, S178 (2004).
[Crossref]

G. A. Swartzlander, J. Opt. A Pure Appl. Opt. 11, 094022 (2009).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, Nature 412, 313 (2001).
[Crossref]

Opt. Commun. (1)

P. Coullet, L. Gil, F. Rocca, Opt. Commun. 73, 403 (1989).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optik (1)

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

Phys. Rev. (1)

L. Landau, Phys. Rev. 60, 356 (1941).
[Crossref]

Phys. Rev. A (1)

K. C. Wright, L. S. Leslie, N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[Crossref]

Phys. Rev. Lett. (4)

V. Westphal, S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[Crossref]

L. Marrucci, C. Manzo, D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

G. A. Swartzlander, C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[Crossref]

G. A. Swartzlander, R. I. Hernandez-Aranda, Phys. Rev. Lett. 99, 163901 (2007).
[Crossref]

Phys. Today (1)

M. V. Berry, Phys. Today 55(5), 10 (2002).
[Crossref]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)].

Proc. R. Soc. A (1)

J. F. Nye, M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[Crossref]

Publ. Astron. Soc. Pac. (1)

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, A. Labeyrie, Publ. Astron. Soc. Pac. 112, 1479 (2000).
[Crossref]

Zh. Eks. Teor. Fiz. (2)

V. L. Ginzburg, L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)].

L. P. Pitaevskii, Zh. Eks. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

Other (1)

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Supplementary Material (1)

» Supplement 1: PDF (4887 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Optical configuration for producing a nodal area with a q -plate (QP). Uniform laser light that is circularly polarized by polarizing optics P1 enters an aperture AP at the x , y plane. Lens L1 focuses the transmitted light onto QP. Lens L2 forms the exit pupil at the x , y plane. The second set of polarizing optics, P2, is circularly cross polarized to P1. The nodal area appears at the x , y plane, where an image is captured by a CCD.

Fig. 2.
Fig. 2.

Experimental verification of an elliptical nodal area. Image of the elliptical aperture (a) without and (b) with the elliptical vortex q -plate.

Fig. 3.
Fig. 3.

(a) An apodized annular aperture matched with (b) an m = 6 vortex phase element generates (c) a dark region with radius equal to the outer radius of the aperture. (d)–(f) Same as (a)–(c), but with (d) an annular aperture, (e) the numerically computed element, and (f) the corresponding nodal area.

Equations (1)

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A ˜ ( r ) = n = 0 N c n R n 0 ( s ) ,

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