Abstract

We propose a novel method for generating both propagating and evanescent Bessel beams. To generate propagating Bessel beams we propose using a pair of distributed Bragg reflectors (DBRs) with a resonant point source on one side of the system. Those modes that couple with the localized modes supported by the DBR system will be selectively transmitted. This is used to produce a single narrow band of transmission in κ space that, combined with the circular symmetry of the system, yields a propagating Bessel beam. We present numerical simulations showing that a propagating Bessel beam with central spot size of 0.5λ0 can be maintained for a distance in excess of 3000λ0. To generate evanescent Bessel beams we propose using transmission of a resonant point source through a thin film. A transmission resonance is produced as a result of the multiple scattering occurring between the interfaces. This narrow resonance combined with the circular symmetry of the system corresponds to an evanescent Bessel beam. Because propagating modes are also transmitted, although the evanescent transmission resonance is many orders of magnitude greater than the transmission for the propagating modes, within a certain distance the propagating modes swamp the exponentially decaying evanescent ones. Thus there is only a certain regime in which evanescent Bessel beams dominate. However, within this regime the central spot size of the beam can be made significantly smaller than the wavelength of light used. Thus evanescent Bessel beams may have technical application, in high-density recording for example. We present numerical simulations showing that with a simple glass thin film an evanescent Bessel beam with central spot size of 0.34λ0 can be maintained for a distance of 0.14λ0. By choice of different material parameters, the central spot size can be made smaller still.

© 2005 Optical Society of America

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  2. J. Durnin, “Exact solutions for nondiffracting beams.  I.  The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  3. J. Durnin, J. H. Eberly, “Diffraction-free arrangement,” U.S. patent 4,852,973 (1 August 1989).
  4. J. Eberly, Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (personal communication, 2004).
  5. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  6. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  7. S. Ruschin, A. Leizer, “Evanescent Bessel beams,” J. Opt. Soc. Am. A 15, 1139–1143 (1998).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).
  9. W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
    [CrossRef]
  10. J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).
  11. V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
    [CrossRef]
  12. D. McGloin, V. Garcés-Chávez, K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
    [CrossRef] [PubMed]

2003 (1)

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

1999 (1)

1998 (1)

1991 (1)

1989 (1)

1987 (2)

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

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).

Dholakia, K.

D. McGloin, V. Garcés-Chávez, K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Durnin, J.

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

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

J. Durnin, J. H. Eberly, “Diffraction-free arrangement,” U.S. patent 4,852,973 (1 August 1989).

Eberly, J.

J. Eberly, Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (personal communication, 2004).

Eberly, J. H.

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

J. Durnin, J. H. Eberly, “Diffraction-free arrangement,” U.S. patent 4,852,973 (1 August 1989).

Friberg, A. T.

Garcés-Chávez, V.

D. McGloin, V. Garcés-Chávez, K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Herman, R. M.

Leizer, A.

McGloin, D.

D. McGloin, V. Garcés-Chávez, K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28, 657–659 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Miceli, J. J.

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

Pendry, J. B.

J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).

Robertson, W. M.

Ruschin, S.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Turunen, J.

Vasara, A.

Wiggins, T. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (4)

Nature (London) (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature (London) 419, 145–147 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).

J. Durnin, J. H. Eberly, “Diffraction-free arrangement,” U.S. patent 4,852,973 (1 August 1989).

J. Eberly, Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (personal communication, 2004).

J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).

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Figures (14)

Fig. 1
Fig. 1

Wave vectors lying on the surface of a cone.

Fig. 2
Fig. 2

Distributed Bragg reflectors with field decaying into Bragg stacks and localized mode in the cavity.

Fig. 3
Fig. 3

(a) Narrow band of k r corresponding to a localized mode. (b) Narrow bands of k r corresponding to two localized modes.

Fig. 4
Fig. 4

Two-dimensional schematic of the wave field created with DBR arrangement.

Fig. 5
Fig. 5

(a) When the cavity is of finite size then the mode has a fixed lateral extent and its intensity as a function of r is approximated by a top-hat function. (b) When the cavity is unbounded the mode has an intensity that decays with radial distance.

Fig. 6
Fig. 6

Band structure of Ti O 2 Si O 2 Bragg reflector. The horizontal line corresponds to the fixed frequency of light used. The vertical line corresponds to the cutoff between propagating and evanescent modes. All propagating modes lie within the bandgap.

Fig. 7
Fig. 7

Transmission as a function of k r for a DBR arrangement with Ti O 2 Si O 2 Bragg reflectors.

Fig. 8
Fig. 8

(a) Transmitted intensity as a function of radial distance for a DBR with Ti O 2 Si O 2 Bragg reflectors. (b) Normalized transmitted intensity as a function of radial distance for a DBR with Ti O 2 Si O 2 Bragg reflectors.

Fig. 9
Fig. 9

Intensity plotted against z for fixed r = 0 and r = 0.72 λ 0 showing paradoxical exponential decay of intensity for a propagating Bessel beam generated when the cavity is unbounded in the plane.

Fig. 10
Fig. 10

Transmission through a thin dielectric film to generate an evanescent Bessel beam.

Fig. 11
Fig. 11

Transmission as a function of k r for a thin film with ε f = 1.96 + 0.0001 i and d f = 0.357 λ 0 .

Fig. 12
Fig. 12

(a) Normalized transmitted intensity as a function of radial distance for thin film with ε f = 1.96 + 0.0001 i and d f = 0.357 λ 0 for fixed z values up to z = 0.27 λ 0 . (b) Normalized transmitted intensity as a function of radial distance for thin film with ε f = 1.96 + 0.0001 i and d f = 0.357 λ 0 for fixed z values up to z = 3 λ 0 .

Fig. 13
Fig. 13

T 2 exp ( k z z ) for a thin film with ε f = 1.96 + 0.0001 i and d f = 0.357 λ 0 .

Fig. 14
Fig. 14

Normalized transmitted intensity as a function of radial distance for thin film with ε f = 100.0 + 0.0001 i and d f = 0.05 λ 0 for fixed z values up to z = 0.10 λ 0 .

Tables (1)

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Table 1 Parameters for a DBR Arrangement in Air

Equations (1)

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T = t 21 t 32 exp ( i k z d f ) + t 21 r 32 r 12 t 32 exp ( 3 i k z d f ) + = t 21 t 32 exp ( i k z d f ) 1 r 32 r 12 exp ( 2 i k z d f ) ,

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