Abstract

Frozen waves (FWs) are very interesting particular cases of nondiffracting beams whose envelopes are static and whose longitudinal intensity patterns can be chosen a priori. We present here for the first time (that we know of) the experimental generation of FWs. The experimental realization of these FWs was obtained using a holographic setup for the optical reconstruction of computer generated holograms (CGH), based on a 4-f Fourier filtering system and a nematic liquid crystal spatial light modulator (LC-SLM), where FW CGHs were first computationally implemented, and later electronically implemented, on the LC-SLM for optical reconstruction. The experimental results are in agreement with the corresponding theoretical analytical solutions and hold excellent prospects for implementation in scientific and technological applications.

© 2012 Optical Society of America

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References

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2010

2006

2005

2004

2003

2002

1989

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Abate, V.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Ambrosio, L. A.

Arrizón, V.

Bouchal, Z.

Dartora, C. A.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Figueroa, H. E. H.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Friberg, A.

Goodman, J. W.

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

Hernandez-Figueroa, H. E.

Mattiuzzi, M.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Méndez, G.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Nobrega, K. Z.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Rached, M. Z.

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Recami, E.

M. Zamboni-Rached, E. Recami, and H. E. Hernandez-Figueroa, J. Opt. Soc. Am. A 22, 2465 (2005).
[CrossRef]

H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, Localized Waves (Wiley, 2008).

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

Sánchez-de-La-Llave, D.

Turunen, J.

Vasara, A.

Zamboni-Rached, M.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Other

H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, Localized Waves (Wiley, 2008).

E. Recami, M. Z. Rached, H. E. H. Figueroa, V. Abate, C. A. Dartora, K. Z. Nobrega, and M. Mattiuzzi, “Method and apparatus for producing stationary (intense) wavefields of arbitrary shape,” U.S. patent application 20110100880-A1 (May5, 2011).

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

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Figures (7)

Fig. 1.
Fig. 1.

Experimental holographic setup for FW generation.

Fig. 2.
Fig. 2.

(a) Comparison of desired longitudinal intensity function (blue line), theoretical prediction by Ψ(ρ,z) (black line), and experimental result (red line) for a step function; and (b) 3D plot of experimental intensity.

Fig. 3.
Fig. 3.

Orthogonal projection and transverse section (in detail) of the FW square intensity: (a) theoretical and (b) experimental results.

Fig. 4.
Fig. 4.

(a) Comparison of desired longitudinal intensity function, theoretical prediction by Ψ(ρ,z), and experimental result for an exponential behavior; and (b) 3D plot of experimental intensity.

Fig. 5.
Fig. 5.

Orthogonal projection and transverse section (in detail) of an FW with exponential intensity: (a) theoretical and (b) experimental results.

Fig. 6.
Fig. 6.

3D plot of experimental FW order 2 Bessel beams.

Fig. 7.
Fig. 7.

Orthogonal projection and transverse section (in detail) of a FW with order 2 Bessel beam intensity: (a) theoretical and (b) experimental results.

Equations (6)

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Ψ(ρ,ϕ,z,t)=eiωtn=NNAnJν(kρnρ)eikznzeiνϕ
An=1L0LF(z)ei2πLnzdz
(ddρJν(ρω2/c2Q2))|ρ=ρ0=0.
H(x,y)=1/2{β(x,y)+α(x,y)cos[φ(x,y)2π(ξx+ηy)]},
F(z)={1forl1<z<l20elsewhere
F(z)={exp(qz)forl1<z<l20elsewhere,

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