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, 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]

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)

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).

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