Abstract

The superposition of multiple plane waves with appropriate propagation vectors generates a periodic or quasi-periodic non-diffractive optical field. We show that the Fourier spectrum of the phase modulation of this field is formed by two disjoint parts, one of which is proportional to the Fourier spectrum of the field itself. Based on this result we prove that the non-diffractive field can be generated, with remarkable high accuracy and efficiency, in a Fourier domain spatial filtering setup, using a synthetic phase hologram whose transmittance is the phase modulation of the field. In a couple of cases this result is presented analytically, and in other cases the proof is computational and experimental.

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References

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  21. SLM HEO 1080 P, HOLOEYE Photonics AG.

2010 (1)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

2009 (3)

2008 (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).

2007 (3)

2005 (2)

2003 (2)

P. Xie and Z. Q. Zhang, “Multifrequency gap solitons in nonlinear photonic crystals,” Phys. Rev. Lett. 91(21), 213904 (2003).
[PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28(9), 710–712 (2003).
[PubMed]

2002 (1)

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43(4), 241–258 (2002).

2000 (1)

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000).
[PubMed]

1999 (1)

1998 (1)

1994 (1)

1989 (1)

1987 (1)

1971 (1)

Arrizón, V.

Boguslawski, M.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

Campos, J.

Carrada, R.

Chavez-Cerda, S.

Chávez-Cerda, S.

Cohn, R. W.

Cottrell, D. M.

Davis, J. A.

Denz, C.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34(17), 2625–2627 (2009).
[PubMed]

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37(1), 42–55 (2007).

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).

Dong, J. W.

Durnin, J.

González, L. A.

Gu, M.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37(1), 42–55 (2007).

Hickmann, J. M.

Indebetouw, G.

Jáuregui, R.

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).

Jones, A. L.

Joseph, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34(17), 2625–2627 (2009).
[PubMed]

Juskaitis, R.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000).
[PubMed]

Kirk, J. P.

Kivshar, Y.

Krolikowski, W.

Liang, G. Q.

Liang, M.

Mao, W. D.

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).

Méndez, G.

Meneses-Nava, M. A.

Molloy, J.

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43(4), 241–258 (2002).

Moreno, I.

Neil, M. A. A.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000).
[PubMed]

Neshev, D.

Ostrovskaya, E.

Padgett, M.

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43(4), 241–258 (2002).

Reece, P.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37(1), 42–55 (2007).

Rose, P.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34(17), 2625–2627 (2009).
[PubMed]

Ruiz, U.

Sánchez-de-la-Llave, D.

Terhalle, B.

Volke-Sepúlveda, K.

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).

Wang, H. Z.

Wilson, T.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000).
[PubMed]

Xavier, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34(17), 2625–2627 (2009).
[PubMed]

Xie, P.

P. Xie and Z. Q. Zhang, “Multifrequency gap solitons in nonlinear photonic crystals,” Phys. Rev. Lett. 91(21), 213904 (2003).
[PubMed]

Yzuel, M. J.

Zhang, Z. Q.

P. Xie and Z. Q. Zhang, “Multifrequency gap solitons in nonlinear photonic crystals,” Phys. Rev. Lett. 91(21), 213904 (2003).
[PubMed]

Zhong, Y. C.

Adv. Mater. (Deerfield Beach Fla.) (1)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. (Deerfield Beach Fla.) 22(3), 356–360 (2010).

Appl. Opt. (2)

Chem. Soc. Rev. (1)

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipulation,” Chem. Soc. Rev. 37(1), 42–55 (2007).

Contemp. Phys. (1)

J. Molloy and M. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43(4), 241–258 (2002).

J. Microsc. (1)

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197(3), 219–223 (2000).
[PubMed]

J. Nanophotonics (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2(1), 021875 (2008).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys. At. Mol. Opt. Phys. (1)

K. Volke-Sepúlveda and R. Jáuregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

P. Xie and Z. Q. Zhang, “Multifrequency gap solitons in nonlinear photonic crystals,” Phys. Rev. Lett. 91(21), 213904 (2003).
[PubMed]

Other (1)

SLM HEO 1080 P, HOLOEYE Photonics AG.

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Figures (11)

Fig. 1
Fig. 1

Partial view of (a) the modulus and (b) the phase of the NDOF with parameters (Q = 5, p = 0). The modulus and the phase of the NDOF with parameters (Q = 6, p = 1) are respectively shown at parts (c) and (d) of the figure.

Fig. 2
Fig. 2

Modulation of the kinoform for the one dimensional NDOF cos(2πρ0x).

Fig. 3
Fig. 3

(a) Modulus and (b) phase in the basic cell of the NDOF with parameters (Q = 4, p = 0) and a shift π/4 in θ. The Fourier spectra correspond respectively to (c) the NDOF h(x,y), (d) the kinoform hK(x,y), and (e) the error function e(x,y) = hK(x,y)-βh(x,y).

Fig. 4
Fig. 4

Fourier spectra of (a) the NDOF h(x,y) with parameters (Q = 6, p = 1), (b) the corresponding kinoform hK(x,y), and (c) the error function e(x,y) = hK(x,y)-βh(x,y).

Fig. 5
Fig. 5

Modules in the Fourier spectra of (a) the NDOF h(x,y) with parameters (Q = 5, p = 0), and (b) its kinoform hK(x,y). The phases of these Fourier spectra are respectively shown at parts (c) and (d) of the figure.

Fig. 6
Fig. 6

Modules in the Fourier spectra of (a) the NDOF h(x,y) with parameters (Q = 8, p = 0), and (b) its kinoform hK(x,y). The phases of these Fourier spectra are respectively shown at parts (c) and (d) of the figure.

Fig. 7
Fig. 7

Modules in the Fourier spectra of (a) the NDOF h(x,y) with parameters (Q = 25, p = 0), and (b) its kinoform hK(x,y). The phases of these Fourier spectra are respectively shown at parts (c) and (d) of the figure.

Fig. 8
Fig. 8

Modules of the NDOFs with topological charge p = 1 and number of interfering waves (a) Q = 15, (b) Q = 30, and (c) Q = 50. Note that the NDOF acquires the structure of a Bessel beam of order 1 when Q increases.

Fig. 9
Fig. 9

(a) Modulus and (b) phase of a NDOF with parameters (Q = 5, p = 0), obtained by numerical simulation of the kinoform in a spatial filtering setup. The modulus and phase numerically obtained for the NDOF with parameters (Q = 6, p = 1), are respectively shown at parts (c) and (d) of the figure.

Fig. 10
Fig. 10

Scheme of the experimental optical setup employed to generate a NDOF using its kinoform in a spatial filtering setup. The input laser beam, conditioned by the beam expander (BE) arrives to the phase SLM in an oblique direction.

Fig. 11
Fig. 11

Modules of the experimentally recorded Fourier spectra of the kinoforms for the NDOFs with indices (a) (Q = 5, p = 0) and (b) (Q = 6, p = 1). The modules of the respective experimentally generated NDOFs are displayed in the parts (c) and (d) of the figure.

Tables (1)

Tables Icon

Table 1 Amplitude and Efficiency Gains of Kinoforms for Several NDOFs

Equations (9)

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f ( r , θ ) = C n = 0 Q 1 exp ( i θ n ) exp [ i 2 π ρ 0 r cos ( θ n Δ θ ) ] ,
η f = Ω | h ( x , y ) | 2 d x d y Ω d x d y ,
h K ( x , y ) = exp [ i φ ( x , y ) ]     .
h K ( x , y ) = β h ( x , y ) + e ( x , y ) ,
G K = η K / η f = β 2 .
h K ( x , y ) = m = 1 c m cos [ 2 π ( m ρ 0 ) x ]
h ( x , y ) = 1 2 cos [ 2 π ρ 0 ( x + y ) ] + 1 2 cos [ 2 π ρ 0 ( x y ) ] .
h ( x , y ) = cos [ 2 π ρ 0 x ] cos [ 2 π ρ 0 y ] .
h K ( x . y ) = m = 1 q = 1 c m q h ( m x , q y )

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