Abstract

Using the concept of leaky modes, we derive the minimum length of a single-mode fiber required to act as a spatial-mode filter of given quality. The degree of filter action is defined by the ratio of power carried by the fundamental mode to that carried by the leaky modes.

© 2002 Optical Society of America

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  1. A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
    [CrossRef]
  2. J. R. P. Angel, N. J. Wolf, “An imaging interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997).
    [CrossRef]
  3. M. Ollivier, J. M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
    [CrossRef] [PubMed]
  4. B. Mennesson, M. Ollivier, C. Ruilier, “Use of single-mode waveguides to correct the optical defects of a nulling interferometer,” J. Opt. Soc. Am. A 19, 596–602 (2002).
    [CrossRef]
  5. M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
    [CrossRef]
  6. E. Serabyn, J. K. Wallace, G. J. Hardy, E. G. H. Schmidtlin, H. T. Nguyen, “Deep nulling of visible laser light,” Appl. Opt. 38, 7128–7132 (1999).
    [CrossRef]
  7. C. Ruillier, F. Cassaing, “Coupling of large telescopes and single-mode waveguides: application to stellar interferometry,” J. Opt. Soc. Am. A 18, 143–149 (2001).
    [CrossRef]
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    [CrossRef]
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  10. F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
    [CrossRef]
  11. G. Perrin, M. Ollivier, V. Coudé du Foresto, “Spatial filtering with single-mode fibers for 10 µm interferometry,” in Interferometry in Optical Astronomy, P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 1007–1012 (2000).
    [CrossRef]
  12. R. Sammut, A. W. Snyder, “Leaky modes on circular optical waveguides,” Appl. Opt. 15, 477–482 (1976).
    [CrossRef] [PubMed]
  13. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  15. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252–2258 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. S. Shaklan, R. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2334–2338 (1988).
    [CrossRef] [PubMed]

2002 (1)

2001 (1)

1999 (2)

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

E. Serabyn, J. K. Wallace, G. J. Hardy, E. G. H. Schmidtlin, H. T. Nguyen, “Deep nulling of visible laser light,” Appl. Opt. 38, 7128–7132 (1999).
[CrossRef]

1997 (2)

J. R. P. Angel, N. J. Wolf, “An imaging interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997).
[CrossRef]

M. Ollivier, J. M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

1996 (1)

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

1988 (1)

1982 (1)

1976 (1)

1975 (1)

A. W. Snyder, C. Pask, “Optical fibre: spatial transient and steady state,” Opt. Commun. 15, 314–316 (1975).
[CrossRef]

1971 (1)

Angel, J. R. P.

J. R. P. Angel, N. J. Wolf, “An imaging interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997).
[CrossRef]

Benech, P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Berger, J.-P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Brunaud, J.

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

Cassaing, F.

Coudé du Foresto, V.

G. Perrin, M. Ollivier, V. Coudé du Foresto, “Spatial filtering with single-mode fibers for 10 µm interferometry,” in Interferometry in Optical Astronomy, P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 1007–1012 (2000).
[CrossRef]

Gloge, D.

Hardy, G. J.

Kern, P.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Léger, A.

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

Love, J. D.

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

Malbet, F.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

Mariotti, J. M.

M. Ollivier, J. M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

Mennesson, B.

B. Mennesson, M. Ollivier, C. Ruilier, “Use of single-mode waveguides to correct the optical defects of a nulling interferometer,” J. Opt. Soc. Am. A 19, 596–602 (2002).
[CrossRef]

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

B. Mennesson, “Thermal infrared stellar interferometry: observations of circumstellar environments using single-mode guided optics and contributions to the DARWIN space mission,” Ph.D. thesis (Université Paris, Paris, 1999).

Michel, G.

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

Nguyen, H. T.

Ollivier, M.

B. Mennesson, M. Ollivier, C. Ruilier, “Use of single-mode waveguides to correct the optical defects of a nulling interferometer,” J. Opt. Soc. Am. A 19, 596–602 (2002).
[CrossRef]

M. Ollivier, J. M. Mariotti, “Improvement in the rejection rate of a nulling interferometer by spatial filtering,” Appl. Opt. 36, 5340–5346 (1997).
[CrossRef] [PubMed]

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

G. Perrin, M. Ollivier, V. Coudé du Foresto, “Spatial filtering with single-mode fibers for 10 µm interferometry,” in Interferometry in Optical Astronomy, P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 1007–1012 (2000).
[CrossRef]

Pask, C.

A. W. Snyder, C. Pask, “Optical fibre: spatial transient and steady state,” Opt. Commun. 15, 314–316 (1975).
[CrossRef]

Perrin, G.

G. Perrin, M. Ollivier, V. Coudé du Foresto, “Spatial filtering with single-mode fibers for 10 µm interferometry,” in Interferometry in Optical Astronomy, P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 1007–1012 (2000).
[CrossRef]

Puget, J. L.

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

Roddier, R.

Rouan, D.

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

Rousselet-Perraut, K.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Ruilier, C.

Ruillier, C.

Sammut, R.

Schanen-Duport, I.

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Schmidtlin, E. G. H.

Schneider, J.

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

Sékulic, P.

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

Serabyn, E.

Shaklan, S.

Snyder, A. W.

R. Sammut, A. W. Snyder, “Leaky modes on circular optical waveguides,” Appl. Opt. 15, 477–482 (1976).
[CrossRef] [PubMed]

A. W. Snyder, C. Pask, “Optical fibre: spatial transient and steady state,” Opt. Commun. 15, 314–316 (1975).
[CrossRef]

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

Tomlinson, W. J.

Wagner, R. E.

Wallace, J. K.

Wolf, N. J.

J. R. P. Angel, N. J. Wolf, “An imaging interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997).
[CrossRef]

Appl. Opt. (6)

Astron. Astrophys. Suppl. Ser. (1)

F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999).
[CrossRef]

Astrophys. J. (1)

J. R. P. Angel, N. J. Wolf, “An imaging interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997).
[CrossRef]

Icarus (1)

A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, J. Schneider, “Could we search for primitive life on extrasolar planets in the near future? The DARWIN Project,” Icarus 123, 249–255 (1996).
[CrossRef]

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

Opt. Commun. (1)

A. W. Snyder, C. Pask, “Optical fibre: spatial transient and steady state,” Opt. Commun. 15, 314–316 (1975).
[CrossRef]

Other (5)

B. Mennesson, “Thermal infrared stellar interferometry: observations of circumstellar environments using single-mode guided optics and contributions to the DARWIN space mission,” Ph.D. thesis (Université Paris, Paris, 1999).

M. Ollivier, J. M. Mariotti, A. Léger, P. Sékulic, J. Brunaud, G. Michel, “Nulling interferometry for the DARWIN space mission,” in Interferometry in Optical Astronomy, P. J. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 354–358 (2000),reprinted in C. R. Acad Sci. Sér. D 2, 149–156 (2001).
[CrossRef]

G. Perrin, M. Ollivier, V. Coudé du Foresto, “Spatial filtering with single-mode fibers for 10 µm interferometry,” in Interferometry in Optical Astronomy, P. L. Léna, A. Quirrenbach, eds., Proc. SPIE4006, 1007–1012 (2000).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

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

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Figures (4)

Fig. 1
Fig. 1

Core parameter U as a function of the normalized frequency V=kρnco2Δ for some guided modes (dashed curves, real-valued Uguided) and leaky modes (solid curves, Uleaky=Uleakyr+jUleakyi).

Fig. 2
Fig. 2

Normalized attenuation coefficients αρ of the six leaky modes of Fig. 1 with lowest attenuation as a function of the normalized frequency V in the single-mode regime for a relative refractive-index difference of Δ=0.25%. The inset shows an enlargement of the V range in which the LP11 mode experiences very low attenuation.

Fig. 3
Fig. 3

In a single-mode fiber, the incident power (Pin) is distributed among the fiber’s fundamental mode (power PLP01) and the leaky modes (power PLM). In the nonabsorbing fiber the fundamental mode will propagate without attenuation, whereas the leaky modes are exponentially attenuated at a distance z0.

Fig. 4
Fig. 4

(a) Required minimum filter length z0, given in multiples of the fiber core radius ρ, as a function of the normalized frequency V for an attenuation coefficient A=106 and a relative refractive-index difference Δ=0.25%. The solid curve shows the case of minimum insertion loss, i.e., maximum coupling with η=0.78 for V=Vc=2.405; the dashed curve gives the case of high insertion loss, i.e., poor coupling with η=0.1 for V=Vc. A second pair of coordinate axes (at the top and at the right) is scaled in wavelengths λ and absolute values for z0, respectively. Here parameters of a silver halide mid-infrared fiber are assumed (core diameter, 19 µm; core refractive index, nco=2.18; and relative refractive-index difference, Δ=0.25%). (b) Ratio z0/ρ as a function of the attenuation coefficient A for V=1.5, 2, and 2.2 with Δ=0.25% and η(Vc)=0.78.

Equations (4)

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PLM(z)=PLM(0)exp(-αz),
η=|E(x, y)F*(x, y)dxdy|2|E(x, y)|2dxdy,
A=PLP01/PLM(z0).
z0ρ=1αρlnA(1-η)η.

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