Abstract

Bessel beams of the evanescent kind are presented and analyzed. They rapidly decay with propagation but retain their original transversal shape. A physical method of generation is proposed in the form of propagation of an ordinary (nonevanescent) Bessel beam across an interface between two different dielectric media. Transmission and reflection coefficients are calculated for this type of beam. The analysis is vectorial and is fully consistent with Maxwell’s equations. Apodized beams of Gauss–Bessel and Circ–Bessel types are propagated by numerical simulation and are shown also to retain a narrow central lobe. Beams of these types have evident advantages in near-field applications, microscopy, and high-density data storage with subwavelength resolution.

© 1998 Optical Society of America

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References

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  1. A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
    [CrossRef]
  2. D. W. Pohl, “Scanning near-field optical microscopy,” Adv. Opt. Electron. Microscopy 12, 243–312 (1991).
  3. S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990); B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
    [CrossRef]
  4. J. Durnin, “Exact solutions for nondiffractive beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  5. F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  6. S. Ruschin, “Modified Bessel nondiffracting beams,” J. Opt. Soc. Am. A 11, 3224–3228 (1994).
    [CrossRef]
  7. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
  8. R. R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
    [CrossRef]
  9. Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
    [CrossRef]

1996 (1)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

1995 (1)

Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

1994 (1)

1991 (2)

R. R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

D. W. Pohl, “Scanning near-field optical microscopy,” Adv. Opt. Electron. Microscopy 12, 243–312 (1991).

1990 (1)

S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990); B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

1987 (2)

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

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

1984 (1)

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

Bagini, V.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Bouchal, Z.

Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

Durnin, J.

Frezza, F.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Gori, F.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Harotoonian, A.

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

Isaacson, M.

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

Kino, G. S.

S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990); B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

Lewis, A.

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

Mansfield, S. M.

S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990); B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

Mishra, R. R.

R. R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Murray, M.

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

Olivik, M.

Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Pohl, D. W.

D. W. Pohl, “Scanning near-field optical microscopy,” Adv. Opt. Electron. Microscopy 12, 243–312 (1991).

Ruschin, S.

Santarsiero, M.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Schettini, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Schiripa Spangolos, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Adv. Opt. Electron. Microscopy (1)

D. W. Pohl, “Scanning near-field optical microscopy,” Adv. Opt. Electron. Microscopy 12, 243–312 (1991).

Appl. Phys. Lett. (1)

S. M. Mansfield, G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990); B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phys. Lett. 68, 141–143 (1996).
[CrossRef]

J. Mod. Opt. (2)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, G. Schiripa Spangolos, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

R. R. Mishra, “A vector analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Ultramicroscopy (1)

A. Lewis, M. Isaacson, A. Harotoonian, M. Murray, “Development of a 500Å spatial resolution light microscope,” Ultramicroscopy 13, 227–232 (1984).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Power distribution of a TM Bessel beam at the interface between two propagating media of refractive indices n1=2.2 and n2=1. Dotted curves, transversal part of the electrical energy; dashed curves, longitudinal part; solid curves, total electrical energy. Note the change in scales and the different partition ratios between the different components for the two cases. The incident beam is a normal Bessel beam with parameters α1 =1.9k0, β1=1.1k0. The transmitted beam is of evanescent type (α1=1.9k0, β1=i1.62k0).

Fig. 2
Fig. 2

Propagation of a Gauss–Bessel evanescent beam compared with propagation of a pure Gaussian beam of the same initial size as the central lobe of the Bessel function. Transverse profiles are normalized and calculated at different distances from the entrance plane. All units are in wavelengths. In this example α=15, and the apodization Gaussian has w=1.5; the pure Gaussian beam has w=0.12.

Fig. 3
Fig. 3

Propagation of a Gauss–Bessel evanescent beam compared with propagation of an initially circular beam of the same size as the central lobe of the Bessel function. Transversal profiles are normalized and calculated at different distances from the entrance plane. All units are in wavelengths. In this example α=15, and the apodization Gaussian has w=1.5, the initial radius of the circular beam is b=0.12.

Fig. 4
Fig. 4

Decay of power density at axis for beams of different shape types. C, circular, G, Gaussian, BC, Bessel–circular; BG, Bessel–Gaussian; E, exponential decay. Beam parameters correspond to those of Figs. 2 and 3.

Fig. 5
Fig. 5

Decay of power density at axis for Bessel–Gauss beams of different types: evanescent (solid curves), critical (dotted curves), and propagating (dashed curves). Parameters in (a) are (α, w0, k0)=(15,1.5,2π), (15, 1.5, 15), (15, 1.5, 30). Parameters in (b) are (α, w0, k0)=(15,0.75,2π), (2π, 1.5, 2π) (1, 5, 2π).

Equations (29)

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α2<n2k02.
Un(r, ϕ, z)=exp(iϕn)Jn(αr)exp(-βz)
α2>n2k02,
β=α2-n2k02.
Er=iβJ1(αr)exp(-iβz),Hr=0,
Eϕ=0,Hϕ=i ωcJ1(αr)exp(-iβz),
Ez=αJ0(αr)exp(-iβz),Hz=0.
Er=0,Hr=βμk0J1(αr)exp(-iβz),
Ez=0,Hz=-iαμk0J0(αr)exp(-iβz),
Eϕ=-J1(αr)exp(-iβz),Hϕ=0.
αr=αt=αi=α,
-βr=βi=ω02c2n12-α2,
βt=ω02c2n22-α2,
(βi)2<(n12-n22) ω02c2.
R=n22βi-n12βtn22βi+n12βt,T=2βin12n22βi+n12βt,
R=βi-βtβi+βt,T=2βiβi+βt.
βi=k0 n12(n12+n22)1/2.
U(ρ, z)=0ymaxyf(y)J0(ρy)exp(-izk2-y2)dy,
f(y)=0ρmaxρU(ρ, 0)J0(ρy)dρ.
y=k sin θ.
U(ρ, 0)=exp-ρ2w2J0(αρ),
f(y)=w22I0αw22 yexp-w24(α2+y2).
U(ρ, 0)=J0(aρ)η(b-ρ),
f(y)=bα2-y2(αJ0(yb)J1(αb)-yJ0(αb)J1(yb).
Er=0,Eϕ=0,Ez=kJ0(kr),
Hr=0,Hϕ=i ωcJ1(kr),Hz=0.
Er=0,Eϕ=-J1(kr),Ez=0,
Hr=0,Hϕ=0,Hz=-i μJ0(kr).
[βi2]cr=(n12-n22) ω02c2.

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