Abstract

We determine the coupling characteristics of a large mode area (LMA) photonic crystal, single-mode fiber when fed with an on-axis field lens used to place an image of the telescope exit pupil at the fiber input. The maximum field of view is found to be approximately the same as that of feeding the fiber directly with the telescope PSF in the image plane. However, the field lens feed can be used to provide a flat, maximised coupling response over the entire visible-NIR which is not possible using either the highly wavelength dependent direct feed coupling to the LMA fiber or the attenuation spectrum limited step index fiber cases.

© 2005 Optical Society of America

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References

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  1. T. Birks, J. Knight and P St. J Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett., 22 p 961-963 (1997)
    [CrossRef] [PubMed]
  2. E.G. Neumann, Single-Mode Fibers �?? Fundamentals, (Springer-Verlag, 1988)
  3. A. Bjarklev, J. Broeng, A.S. Bjarklev, Photonic crystal fibers, (Kluwer, 2003)
    [CrossRef]
  4. Coude de Foresto, V. Ridgway S., Mariotti J.M, �??Deriving object visibilities from interferograms obtained with a fiber stellar interferometer,�??A&AS 121 379 (1997)
  5. G. Perrin, O. Lai, P. J. Lena, and V. Coude du Foresto, �??Fibered large interferometer on top of Mauna Kea: OHANA, the Optical Hawaiian Array for Nanoradian Astronomy,�?? in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE 4006, 708�??714 (2000).
    [CrossRef]
  6. M.D. Nielson, J.R. Folkenberg, N.A. Mortenson and A. Bjarklev, �??Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers,�?? Opt. Express 12, 430 (2004) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-430">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-430</a>
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  7. M.D. Nielsen, N.A. Mortensen, M. Albersen, J.R. Folkenberg, A. Bjarklev, D. Bonacinni, �??Predicting macrobending loss for large-mode area photonic crystal fibers,�?? Opt. Express 12, 1775 (2004) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775</a>
    [CrossRef] [PubMed]
  8. A.W. Snyder and J.D. Love, Optical waveguide Theory, (Chapman/Kluwer, 1983/ 2000)
  9. Joseph W Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996)
  10. T.P. White, B.T. Kuhlmey, R.C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, L.C. Botton, �??Multipole method for microstructured optical fiber. I Formulation,�?? J. Opt. Soc. Am. B 19 , No 10 (2002)
    [CrossRef]
  11. B.T. Kuhlmey, T.P. White, G. Renversez, D. Maystre, L.C. Botton, C. Martijn de Sterke, R.C. McPhedran, �??Multipole method for microstructured optical fiber. II Implementation and Results,�?? J. Opt. Soc. Am. B 19, No 10 (2002)
    [CrossRef]
  12. M.J Steel, T.P White, C. Martijn de Sterke, R.C. McPhedran, L.C. Botton, �??Symmetry and degeneracy in microstructered optical fibers,�?? Opt. Lett. 26 No.8 (2001).
    [CrossRef]
  13. D.T. Liu, B.M. Levine & M. Shao, �??Design and fabrication of a coherent array of single-mode optical fibers for the nulling coronograph,�?? Proc. SPIE 5170 Techniques and Instrumentation for detection of exoplanets. (2003)
  14. N.A. Mortensen and J.R. Folkenberg, �??Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,�?? Opt. Express 10, 475 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-475">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-475</a>
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  17. Equation (8) actually underestimates slightly �? < 0.40 for >f/4 and λ0 > 1000nm when coupling into the LMA-8 fiber however no simple model can account for the actual variation and direct recourse to Eq. (1) and (6) is required.
  18. Olivier Guyon, �??Wide-field interferometric imaging with single-mode fibers,�?? A&A 387, 366-378 (2002)

A&A

Olivier Guyon, �??Wide-field interferometric imaging with single-mode fibers,�?? A&A 387, 366-378 (2002)

A&AS

Coude de Foresto, V. Ridgway S., Mariotti J.M, �??Deriving object visibilities from interferograms obtained with a fiber stellar interferometer,�??A&AS 121 379 (1997)

IEEE Trans. MTT V NIT

A. Snyder, �??Excititation and scattering of modes on a dielectric optical fiber,�?? IEEE Trans. MTT V NIT-17 No.12 (1969)

J. Opt. Soc. Am. B

T.P. White, B.T. Kuhlmey, R.C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, L.C. Botton, �??Multipole method for microstructured optical fiber. I Formulation,�?? J. Opt. Soc. Am. B 19 , No 10 (2002)
[CrossRef]

B.T. Kuhlmey, T.P. White, G. Renversez, D. Maystre, L.C. Botton, C. Martijn de Sterke, R.C. McPhedran, �??Multipole method for microstructured optical fiber. II Implementation and Results,�?? J. Opt. Soc. Am. B 19, No 10 (2002)
[CrossRef]

Opt. Express

Opt. Lett.

T. Birks, J. Knight and P St. J Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett., 22 p 961-963 (1997)
[CrossRef] [PubMed]

M.J Steel, T.P White, C. Martijn de Sterke, R.C. McPhedran, L.C. Botton, �??Symmetry and degeneracy in microstructered optical fibers,�?? Opt. Lett. 26 No.8 (2001).
[CrossRef]

Proc. SPIE

D.T. Liu, B.M. Levine & M. Shao, �??Design and fabrication of a coherent array of single-mode optical fibers for the nulling coronograph,�?? Proc. SPIE 5170 Techniques and Instrumentation for detection of exoplanets. (2003)

G. Perrin, O. Lai, P. J. Lena, and V. Coude du Foresto, �??Fibered large interferometer on top of Mauna Kea: OHANA, the Optical Hawaiian Array for Nanoradian Astronomy,�?? in Interferometry in Optical Astronomy, P. J. Lena and A. Quirrenbach, eds., Proc. SPIE 4006, 708�??714 (2000).
[CrossRef]

Other

A.W. Snyder and J.D. Love, Optical waveguide Theory, (Chapman/Kluwer, 1983/ 2000)

Joseph W Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996)

Born and Wolf, Principles of optics 7th edition, (Cambridge University Press).

Equation (8) actually underestimates slightly �? < 0.40 for >f/4 and λ0 > 1000nm when coupling into the LMA-8 fiber however no simple model can account for the actual variation and direct recourse to Eq. (1) and (6) is required.

E.G. Neumann, Single-Mode Fibers �?? Fundamentals, (Springer-Verlag, 1988)

A. Bjarklev, J. Broeng, A.S. Bjarklev, Photonic crystal fibers, (Kluwer, 2003)
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Cross section of an LMA type fiber - Crystal Fiber A/S

Fig. 2.
Fig. 2.

The Telescope-Fiber feed (a) Schematic (b) Field assignment

Fig. 3.
Fig. 3.

Transverse field magnitude ∣E f∣, represented on a linear scale, showing Λ the characteristic length of the photonic structure and overplotted outline of E g(p,q), the geometric image of the exit pupil of the telescope shown at the correct scale of outer diameter ~ 1.33Λ for maximum coupling (Section 3.1)

Fig. 4.
Fig. 4.

Cross section through the fiber mode (∣E f∣ shown in 3D) and various images of the pupil at the endface of the fiber

Fig. 5.
Fig. 5.

(a) Maximum coupling, ρmax (i.e.on axis O, in fig 2) characteristics as a function of pupil image scale, (b) ρmax, as a function of telescope obscuration, (c) ρmax, as a function of pupil offset for geometric, diffracted and badly diffracted cases. For a lenslet not in contact with the fiber, these values must be reduced by the Fresnel coefficient at noted in section 2.0.

Fig. 6.
Fig. 6.

Effect of Gaussian pupil apodisation on the overall throughput. The three curve sets are for increasing values of dp, the diameter of the geometric pupil image, E g on the endface of the fiber wrt to the static mode field of the LMA fiber.

Fig. 7.
Fig. 7.

Coupling efficiencies as a function of input angle for (a) LMA-8, (b) LMA-15 for dp = 1.33Λ and (c) as a function of dp . All angles are given in degrees at the fiber endface.

Fig. 8.
Fig. 8.

(a) An overplot of ρf and ρs for FL = 2 and an LMA-8 fiber. (b) Overplot of the spectral response of lenslet and direct feed (on-axis) coupling into an LMA fiber for a 25% obscured pupil (c) Comparison of direct and lenslet feed FOV for ρ against θ.

Equations (17)

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ρ = A E i E f * dA 2 A E i 2 dA A E f 2 dA
E i ( r ) = J 1 ( k r 2 F ) ( k r 2 F ) ε 2 J 1 ( ε k r 2 F ) ( ε k r 2 F )
E i p q = h p q ε η E d ε η d ε d η
h p q ε η = exp ( i k o 2 z v ( p 2 + q 2 ) ) exp ( i k o 2 z U ( ε 2 + η 2 ) )
× A x y exp ( i k o 2 z v ( ( p M ε ) + ( q M p η ) ) ) dxdy
E d = E d exp ( i π λ f ( ε 2 + η 2 ) )
E i p q = h p q E g p q
ρ ( θ ) = ρ f ( θ ) . ρ s ( θ )
ρ f ( θ ) = ρ max . exp [ θ ( n n core ) 2 2 ( β ( λ o n Λ ) ) 2 ]
θ = n core n 2 β ( λ o Λ ) 2 ln ( 1 γ ρ max )
F fibre = 90 n 2 Λ β π n core λ o 2 ln ( 1 γ ρ max )
n d p n T d T = χ F fibre χ = ( n n T ) d p F fibre d T
χ = ( n core n . n T ) 1.33 β π λ o 2 ln ( 1 γ ρ max ) 90 d T
χ i R = ( n core n T ) 0.5263 2 ln ( 1 γ ρ max )
M ( n T n ) d L 1.33 Λ ( F L F T )
ρ s = Aperture U ( r δ r ) 2 d r Aperture U ( r ) 2 d r
S = χ i R F fibre F L = 1.0902 n F L ( Λ λ o )

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