Abstract

We present optical fields formed by superposing nondiffracting parabolic beams with distinct longitudinal wave-vector components, generating light profiles that display intensity fluxes following parabolic paths in the transverse plane. Their propagation dynamics vary depending on the physical mechanism originating interference, where the possibilities include constructive and destructive interference between traveling parabolic beams, interference between stationary parabolic modes, and combinations of these. The dark parabolic region exhibited by parabolic beams permits a straightforward superposition of intensity fluxes, allowing formation of a variety of profiles, which can exhibit circular, elliptic, and other symmetries.

© 2013 Optical Society of America

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    [CrossRef]
  2. Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
    [CrossRef]
  3. M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
  4. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef]
  5. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [CrossRef]
  6. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
    [CrossRef]
  7. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  8. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
    [CrossRef]
  9. C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13, 2364–2369 (2005).
    [CrossRef]
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2010 (1)

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

2007 (1)

C. López-Mariscal and J. C. Gutiérrez-Vega, “The generation of nondiffracting beams using inexpensive computer-generated holograms,” Am. J. Phys. 75, 36–42 (2007).

2005 (4)

2004 (1)

2003 (1)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

2001 (1)

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

2000 (2)

1998 (1)

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1968 (1)

1967 (1)

Bandres, M. A.

Bouchal, Z.

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

Z. Bouchal and J. Wagner, “Self-reconstruction effect in free propagation wavefield,” Opt. Commun. 176, 299–307 (2000).
[CrossRef]

Chavez-Cerda, S.

Chávez-Cerda, S.

Christodoulides, D. N.

Dholakia, K.

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Gunn-Moore, F. J.

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

Gutiérrez-Vega, J. C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “The generation of nondiffracting beams using inexpensive computer-generated holograms,” Am. J. Phys. 75, 36–42 (2007).

C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13, 2364–2369 (2005).
[CrossRef]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Hicknann, J. M.

Iturbe-Castillo, M. D.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Kartashov, Y. V.

López-Mariscal, C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “The generation of nondiffracting beams using inexpensive computer-generated holograms,” Am. J. Phys. 75, 36–42 (2007).

C. López-Mariscal, M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Observation of parabolic nondiffracting optical fields,” Opt. Express 13, 2364–2369 (2005).
[CrossRef]

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Meneses-Nava, M. A.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Montgomery, W. D.

New, G. H. C.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Ramírez, G. A.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Rodríguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

Tepichín, E.

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Torner, L.

Vysloukh, V. A.

Wagner, J.

Z. Bouchal and J. Wagner, “Self-reconstruction effect in free propagation wavefield,” Opt. Commun. 176, 299–307 (2000).
[CrossRef]

Am. J. Phys. (1)

C. López-Mariscal and J. C. Gutiérrez-Vega, “The generation of nondiffracting beams using inexpensive computer-generated holograms,” Am. J. Phys. 75, 36–42 (2007).

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Czech. J. Phys. (1)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Laser Photon. Rev. (1)

M. Mazilu, D. J. Stevenson, F. J. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).

Opt. Commun. (2)

Z. Bouchal and J. Wagner, “Self-reconstruction effect in free propagation wavefield,” Opt. Commun. 176, 299–307 (2000).
[CrossRef]

J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Supplementary Material (5)

» Media 1: AVI (3858 KB)     
» Media 2: AVI (3858 KB)     
» Media 3: AVI (3858 KB)     
» Media 4: AVI (3858 KB)     
» Media 5: AVI (3858 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Intensity profiles for the (a) even and (b) odd fundamental stationary transverse modes (a=0) with their corresponding (c) and (d) traveling parabolic beams (+) at z=0. The previous profile arrangement is employed in the second row for (e)–(h) a=2. For all cases θ=0.50° and λ=632.8[nm] (He–Ne laser first emission line). Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Fig. 2.
Fig. 2.

Constructive interference DPB (a) intensity and (b) phase profiles at z=0 for a=3, θ1=0.50°, and θ2=0.40°, followed by the (c) and (d) propagation evolution of the intensity profile (Media 1). The previous profile arrangement is repeated in the second row for (e)–(h) θ2=0.47148°. The η coordinate for the local maximum of the traveling central parabolic arc is plotted against z in diverse scenarios for (i) fixed a and (j) fixed θ2. For all cases λ=632.8[nm]. Phase values are wrapped from π (black) to +π (white).

Fig. 3.
Fig. 3.

Destructive interference DPB (a) intensity and (b) phase profiles at z=0 for a=3, θ1=0.50° and θ2=0.47148°, followed by the (c) and (d) propagation evolution of the intensity profile (Media 2). The η coordinate for the local maximum of the traveling central parabolic arc is plotted against z in diverse scenarios for (e) fixed a and (f) fixed θ2. For all cases λ=632.8[nm]. Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Fig. 4.
Fig. 4.

Oscillatory DPBs constructed by superposing: (a)–(d) ESPB and OSPB with a=0 (Media 3), (e)–(h) two ESPBs with a=0, and (i)–(l) ESPB and OSPB with a=3. For all cases θ1=0.50°, θ2=0.47148°, and λ=632.8[nm]. Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Fig. 5.
Fig. 5.

Combination of: (a)–(d) co-flowing constructive and destructive interference DPBs, (e)–(h) counter-flowing constructive and destructive interference DPBs, and (i)–(l) three co-flowing constructive DPBs with θ3=0.44113°. For all cases θ1=0.50°, θ2=0.47148°, a=3, and λ=632.8[nm]. Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Fig. 6.
Fig. 6.

Compound DPBs constructed with (a)–(d) two (Media 4), (e)–(h) three (Media 5), and (i)–(l) four nonoverlapping parabolic intensity flows forming closed trajectories in the transverse plane. For all cases θ1=0.50°, θ2=0.47148°, and λ=632.8[nm]. Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Fig. 7.
Fig. 7.

Compound DPBs exhibiting (a)–(d) circular and (e)–(h) elliptic symmetries. For both cases θ1=0.50°, θ2=0.47148°, and λ=632.8[nm]. Green lines mark the x and y axes. Phase values are wrapped from π (black) to +π (white).

Equations (4)

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ϕe(rt;kt,a)=1π2|Γ1|2Pe(σξ;a)Pe(ση;a),
ϕo(rt;kt,a)=2π2|Γ3|2Po(σξ;a)Po(ση;a),
Ue,o(r;k,θ,a)=exp[ikcos(θ)z]ϕe,o[rt;ksin(θ),a],
U±(r;k,θ,a)=Ue(r;k,θ,a)±iUo(r;k,θ,a),

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