Abstract

The power density in the vicinity of a tapered fiber is calculated, with the vectorial model of step-index circular waveguides. For the fundamental HE11 mode carrying a power of 1 Watt, we show that it is possible to obtain theoretical densities in the range of 108 W/cm2 at the fiber surface. The promising use of such intense evanescent fields as “atomic mirrors” is considered, and the feasibility of these guides is investigated.

© 1999 Optical Society of America

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References

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  1. R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.
  2. S. Lacroix, F. Gonthier, J. Bures, “All-fiber wavelength filter from successive biconical tapers,” Opt. Lett. 11, 671–673 (1986).
    [CrossRef] [PubMed]
  3. S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).
  4. F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
    [CrossRef]
  5. W. Henry, “Evanescent field devices: a comparison between tapered optical fibres and polished or D-fibres,” Opt. Quantum Electron. 26, S261–S272 (1994).
    [CrossRef]
  6. R. J. Cook, R. K. Hill, “An electromagnetic mirror for neutral atoms,” Opt. Commun. 43, 258–260 (1982).
    [CrossRef]
  7. V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
    [CrossRef] [PubMed]
  8. A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
    [CrossRef] [PubMed]
  9. A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
    [CrossRef] [PubMed]
  10. P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wiggley, G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
    [CrossRef] [PubMed]
  11. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 12.
  12. Reference 11, Chap. 24.
  13. C. Vassalo, “Pseudo-modes et guides optiques,” Ann. Telecommun. 43, 48–65 (1988).

1996 (2)

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

1994 (1)

W. Henry, “Evanescent field devices: a comparison between tapered optical fibres and polished or D-fibres,” Opt. Quantum Electron. 26, S261–S272 (1994).
[CrossRef]

1993 (1)

1989 (1)

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

1988 (3)

S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

C. Vassalo, “Pseudo-modes et guides optiques,” Ann. Telecommun. 43, 48–65 (1988).

1986 (1)

1982 (1)

R. J. Cook, R. K. Hill, “An electromagnetic mirror for neutral atoms,” Opt. Commun. 43, 258–260 (1982).
[CrossRef]

Aspect, A.

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

Balykin, V. I.

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

Black, R. J.

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

Bures, J.

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wiggley, G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).

S. Lacroix, F. Gonthier, J. Bures, “All-fiber wavelength filter from successive biconical tapers,” Opt. Lett. 11, 671–673 (1986).
[CrossRef] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

Cook, R. J.

R. J. Cook, R. K. Hill, “An electromagnetic mirror for neutral atoms,” Opt. Commun. 43, 258–260 (1982).
[CrossRef]

Courtois, J-Y.

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Daxhelet, X.

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

Dumais, P.

Gonthier, F.

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wiggley, G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).

S. Lacroix, F. Gonthier, J. Bures, “All-fiber wavelength filter from successive biconical tapers,” Opt. Lett. 11, 671–673 (1986).
[CrossRef] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

Henkel, C.

Henry, W.

W. Henry, “Evanescent field devices: a comparison between tapered optical fibres and polished or D-fibres,” Opt. Quantum Electron. 26, S261–S272 (1994).
[CrossRef]

Hill, R. K.

R. J. Cook, R. K. Hill, “An electromagnetic mirror for neutral atoms,” Opt. Commun. 43, 258–260 (1982).
[CrossRef]

Kaiser, R.

Labeyrie, G.

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

Lacroix, S.

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wiggley, G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
[CrossRef] [PubMed]

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).

S. Lacroix, F. Gonthier, J. Bures, “All-fiber wavelength filter from successive biconical tapers,” Opt. Lett. 11, 671–673 (1986).
[CrossRef] [PubMed]

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

Landragin, A.

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

Lapierre, J.

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

Lethokov, V. C.

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 12.

Ovchinnikov, Y. B.

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

Sidorov, A. I.

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 12.

Stegeman, G. I.

Vansteenkiste, N.

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

Vassalo, C.

C. Vassalo, “Pseudo-modes et guides optiques,” Ann. Telecommun. 43, 48–65 (1988).

Villeneuve, A.

Westbrook, C. I.

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

A. Landragin, G. Labeyrie, C. Henkel, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Specular versus diffuse reflection of atoms from an evanescent-wave mirror,” Opt. Lett. 21, 1591–1593 (1996).
[CrossRef] [PubMed]

Wiggley, P. G. J.

Ann. Telecommun. (2)

S. Lacroix, F. Gonthier, J. Bures, “Fibres unimodales effilées,” Ann. Telecommun. 43, 43–47 (1988).

C. Vassalo, “Pseudo-modes et guides optiques,” Ann. Telecommun. 43, 48–65 (1988).

Appl. Phys. Lett. (1)

F. Gonthier, S. Lacroix, X. Daxhelet, R. J. Black, J. Bures, “Broadband all-fiber filters for wavelength division multiplexing applications,” Appl. Phys. Lett. 54, 1290–1292 (1989).
[CrossRef]

Opt. Commun. (1)

R. J. Cook, R. K. Hill, “An electromagnetic mirror for neutral atoms,” Opt. Commun. 43, 258–260 (1982).
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

W. Henry, “Evanescent field devices: a comparison between tapered optical fibres and polished or D-fibres,” Opt. Quantum Electron. 26, S261–S272 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

A. Landragin, J-Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, A. Aspect, “Measurement of the van der Waals force in an atomic mirror,” Phys. Rev. Lett. 77, 1464–1467 (1996).
[CrossRef] [PubMed]

V. I. Balykin, V. C. Lethokov, Y. B. Ovchinnikov, A. I. Sidorov, “Quantum-state-selective mirror reflection of atoms by laser light,” Phys. Rev. Lett. 60, 2137–2140 (1988).
[CrossRef] [PubMed]

Other (3)

R. J. Black, F. Gonthier, S. Lacroix, J. Lapierre, J. Bures, “Abruptly tapered fibers: index response for sensor application,” in Technical Digest, Postdeadline Papers, 4th International Conference on Optical Fiber Sensors (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), Pd.-3-1–Pd.-3-4.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 12.

Reference 11, Chap. 24.

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Figures (8)

Fig. 1
Fig. 1

Evolution of power density log10(D) as a function of radius ρ of the fiber for λ=780 nm, at different distances X (μm) of the fiber–air interface and for both polarization directions of the even HE11 mode: (a) ϕ=0°, (b) ϕ=90°. D is expressed in watts per square centimeter for a total incident power of 1 W.

Fig. 2
Fig. 2

Radius ρ of the fiber as a function of wavelength showing the limit of the single-mode propagation regime (V2.405).

Fig. 3
Fig. 3

Evolution of the maxima of the power density log10(D) and the corresponding radii ρ as a function of wavelength, for both polarization directions (a) ϕ=0°, (b) ϕ=90°.

Fig. 4
Fig. 4

Fraction of the power carried by the HE11 mode outside the fiber as a function of radius ρ, for a few common wavelengths. Also indicated are the loci of maximum density at the core–cladding interface and the limit of the single-mode regime.

Fig. 5
Fig. 5

Density evolution along the normalized radial direction r/ρ at λ=780 nm, for different radii ρ of the fiber and both polarization directions: (a) ϕ=0°, (b) ϕ=90°. The interface discontinuities are due to that of the radial component er of the electric field.

Fig. 6
Fig. 6

Equal power-density curves of even HE11 (arbitrary linear scale from 2 to 10) in the vicinity of the fiber for ρ=0.17 μm and λ=780 nm. The dashed circle indicates the fiber–air interface. Note the circular asymmetries due to field polarization. Polarization directions ϕ=0° and ϕ=90° are along the horizontal and vertical axes, respectively.

Fig. 7
Fig. 7

Theoretical calculation of the beat lengths Zb(ρ) between HE11TE01, HE11TM01, HE11HE21 (vectorial theory) and LP01LP11 (scalar theory) as a function of ρ for λ=633 nm. Values for radii ρc and normalized cutoff frequencies Vc are given in the legend.

Fig. 8
Fig. 8

Relative transmitted power at λ=633 nm by HE11 at the end of the stretching process. Inside the figure is an enlargement of the beats between HE11 and the TE01, TM01, and HE21 group: The rapid oscillations locally determine Zb from which is deduced ρ by using the Zb (LP01LP11) curve of Fig. 7. The regime becomes single mode for ρ<0.23 μm, and the leaky modes are responsible for the observed loss for an elongation >7.3 mm.

Tables (1)

Tables Icon

Table 1 Values of Maximum Density for Both Polarization Directions (ϕ=0 and 90°) at Different Distances X (μm) of the Fiber–Air Interface and Corresponding Radii ρ from Fig. 1

Equations (13)

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eˆ=eN=[rˆer(R, ϕ)+Φˆeϕ(R, ϕ)+zˆez(R, ϕ)]N,
hˆ=hN=[rˆhr(R, ϕ)+Φˆhϕ(R, ϕ)+zˆhz(R, ϕ)]N,
N=12 Re S(e×h*)zˆdS,
P=12 Re S(eˆ×h^*)zˆdS=1.
U2+W2=V2=2πρλ2(nc2-ng2),
D(R, ϕ)=dPdS=12 Re(eˆ×h^*)zˆ=12 (erhϕ-eϕhr)N.
D(R, ϕ)=1πρ2 f(R, ϕ)M,
f(R>1, ϕ)={a1a5K02(WR)+a2a6K22(WR)(a1a6+a2a5)×K0(WR)K2(WR)cos 2ϕ}{U/WK1(W)}2,
f(R1, ϕ)={a1a3J02(UR)+a2a4J22(UR)(a1a4+a2a3)×J0(UR)J2(UR)cos 2ϕ}{1/J1(U)}2,
M={a1a3[J02(U)+J12(U)]+a2a4[J22(U)-J1(U)J3(U)]}{1/J1(U)}2-{a1a5[K02(W)+K12(W)]+a2a6[K22(W)-K1(W)K3(W)]}×{U/K1(U)}2,
D(R>1)1πρ2 UK0(WR)VK1(W)2,
D(R1)1πρ2 WJ0(UR)VJ1(U)2.
F(λ, ρ)=12 Re 02πρ(eˆ×h^*)zˆrdrdϕ

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