Abstract

A linearly polarized Bessel beam, whose spatial frequencies correspond to the Brewster angle, impinging at normal incidence on a higher refractive-index interface is shown to lead to a reflected field that can be used to produce an azimuthally polarized optical vector beam.

© 2012 Optical Society of America

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References

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  1. D. G. Hall, Opt. Lett. 21, 9 (1996).
    [CrossRef]
  2. P. L. Greene and D. G. Hall, J. Opt. Soc. Am. A 15, 3020 (1998).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  4. K. C. Toussaint, S. Park, J. E. Jureller, and N. F. Scherer, Opt. Lett. 30, 2846 (2005).
    [CrossRef]
  5. Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
    [CrossRef]
  6. D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
    [CrossRef]

2005 (1)

1998 (1)

1996 (1)

1972 (2)

Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Greene, P. L.

Hall, D. G.

Jureller, J. E.

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Nakajima, N. Y.

Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Park, S.

Pohl, D.

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Scherer, N. F.

Toussaint, K. C.

Appl. Phys. Lett. (1)

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

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

Opt. Lett. (2)

Proc. IEEE (1)

Y. Mushiake, K. Matsumura, and N. Y. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of geometry. Linearly polarized Bessel beam is normally incident from the z direction in the z=ζ<0 object plane (OP), and is reflected off a beam splitter (BS) before impinging on the interface at z=0. The reflected beam from the interface passes through the BS and subsequently the converging lens (CL) at z=g>0 and produces an azimuthally polarized OVB at the focal backplane (FB) of the converging lens at z=f+g. z is measured along the beam path.

Fig. 2.
Fig. 2.

Azimuthally polarized OVB in focal backplane z=f+g (see Fig. 1) for an incident x-polarized, ν=0-order Bessel beam with (k/κ)f=2 and w=0.3. Axes in units of k/κ.

Fig. 3.
Fig. 3.

Magnitude of the optical intensity associated with the (a) radial and (b) azimuthal components of the beam as a function of position Δz with respect to the Fourier plane f+g along the optical axis. Parameters are the same as in Fig. 2.

Equations (7)

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U˜i(k,ζ)=d2ρeik·ρU(ρ,ζ)=U0eikzζx^d2ρeik·ρJν(kρ)eiνϕ=U0eikzζx^0ρdρJν(kρ)02πdΦeikρcosΦeiνϕ,
U˜i(k,ζ)=U0eikzζeiνϕkx^0ρdρJν(kρ)02πdΦeikρcosΦiνΦ=2πU0eikzζeiνϕkx^0ρdρJν(kρ)Jν(kρ)=2πkU0eikzζeiνϕkδ(kk)x^=2πkU0eikzζeiνϕkδ(kk)[cosϕkρ^ksinϕkϕ^k],
U˜r(k,ζ)=2πkU0eikzζeiνϕkδ(kk)×[rpcosϕkρ^krssinϕkϕ^k],
rp=n1n21(n1n2sinθ)2cosθn1n21(n1n2sinθ)2+cosθ,rs=n1n2cosθ1(n1n2sinθ)2n1n2cosθ+1(n1n2sinθ)2,
U˜r(k,ζ)=2πkU0rseikzζeiνϕkδ(kk)sinϕkϕ^k.
Uf(ρ,f+g)=1iλfeiκfeiκ2fρ2U˜r(ρκf,g)=ikU0rseikz(f+g)eiνϕδ(ρkκf)sinϕϕ^,
Uf(ρ,f+g)=ikU0rseikz(f+g)eiνϕ×wπ(ρkκf)2+w2sinϕϕ^.

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