Abstract

The coupling efficiency of starlight into single and few-mode fibres fed with lenslet arrays to provide a continuous field of view is investigated. The single-mode field of view (FOV) and overall transmission is a highly complicated function of wavelength and fibre size leading to a continuous sample only in cases of poor throughput. Significant improvements are found in the few-mode regime with a continuous and efficient sample of the image plane shown to be possible with as few as 4 modes. This work is of direct relevance to the coupling of celestial light into photonic instrumentation and the removal of image scrambling and reduction of focal ratio degradation (FRD) using multi-mode fibre to single-mode fibre array converters.

© 2009 Optical Society of America

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References

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  1. Q1. J. Bland-Hawthorn & A. Horton, "Instruments without optics," SPIE 6269,62690N (2006).
    [CrossRef]
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  4. J. Corbett and J. Allington-Smith, "Coupling starlight into single-mode photonic crystal fiber using a field lens," Opt. Express 13, 6527-6540 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-17-6527.
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  7. Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
    [CrossRef]
  8. Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
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  12. Q4. T. Hunter and L. Ramsey "Scrambling properties of optical fibres and the performance of a double scrambler," Proc. Astro. Soc. Pacific 104, 1244-1251 (1992).
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  13. F. Roddier, Adaptive optics in astronomy (Cambridge, 1999).
    [CrossRef]

2007

J. Corbett, T. Butterley, and J. R. Allington-Smith, "Fibre modal power distributions and their application to OH-suppression fibres," Mon. Not. R. Astron. Soc. 378, 482-492 (2007).
[CrossRef]

A. J. Horton and J. Bland-Hawthorn, "Coupling light into few-mode optical fibres I: The diffraction limit," Opt. Express 15, 1443-1453 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-4-1443
[CrossRef] [PubMed]

2006

Q1. J. Bland-Hawthorn & A. Horton, "Instruments without optics," SPIE 6269,62690N (2006).
[CrossRef]

J. Corbett A. Dabirian, T. Butterley, N. A. Mortensen and J. R. Allington-Smith, "The coupling performance of photonic crystal fibres in fibre stellar interferometry," Mon. Not. R. Astron. Soc. 368, 203-210 (2006).

2005

2004

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

2002

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

1992

Q4. T. Hunter and L. Ramsey "Scrambling properties of optical fibres and the performance of a double scrambler," Proc. Astro. Soc. Pacific 104, 1244-1251 (1992).
[CrossRef]

1987

Albersen, M.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Allington-Smith, J.

Allington-Smith, J. R.

J. Corbett, T. Butterley, and J. R. Allington-Smith, "Fibre modal power distributions and their application to OH-suppression fibres," Mon. Not. R. Astron. Soc. 378, 482-492 (2007).
[CrossRef]

Birks, T.

Bjarklev, A.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Bland-Hawthorn, J.

Bonacinni, D.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Botton, L. C.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Butterley, T.

J. Corbett, T. Butterley, and J. R. Allington-Smith, "Fibre modal power distributions and their application to OH-suppression fibres," Mon. Not. R. Astron. Soc. 378, 482-492 (2007).
[CrossRef]

Corbett, J.

J. Corbett, T. Butterley, and J. R. Allington-Smith, "Fibre modal power distributions and their application to OH-suppression fibres," Mon. Not. R. Astron. Soc. 378, 482-492 (2007).
[CrossRef]

J. Corbett and J. Allington-Smith, "Coupling starlight into single-mode photonic crystal fiber using a field lens," Opt. Express 13, 6527-6540 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-17-6527.
[CrossRef] [PubMed]

Englund, M.

Folkenberg, J. R.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Horton, A.

Q1. J. Bland-Hawthorn & A. Horton, "Instruments without optics," SPIE 6269,62690N (2006).
[CrossRef]

Horton, A. J.

Hunter, T.

Q4. T. Hunter and L. Ramsey "Scrambling properties of optical fibres and the performance of a double scrambler," Proc. Astro. Soc. Pacific 104, 1244-1251 (1992).
[CrossRef]

Kuhlmey, B. T.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Leon-Saval, S. G.

Martijn de Sterke, C.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Maystre, D.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

McPhedran, R. C.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Mortensen, N. A.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Nielsen, M. D.

Q3. M. D. Nielsen, N. A. Mortensen, M. Albersen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, "Predicting macrobending loss for large-mode area photonic crystal fibres," Opt. Express 12, (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1775.
[CrossRef] [PubMed]

Ramsey, L.

Q4. T. Hunter and L. Ramsey "Scrambling properties of optical fibres and the performance of a double scrambler," Proc. Astro. Soc. Pacific 104, 1244-1251 (1992).
[CrossRef]

Renversez, G.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Roddier, F.

Shaklan, S.

White, T. P.

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. B

Q2. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botton, "Multipole method for microstructured optical fiber. I Formulation," J. Opt. Soc. Am. B 19, No 10 (2002).
[CrossRef]

Mon. Not. R. Astron. Soc.

J. Corbett A. Dabirian, T. Butterley, N. A. Mortensen and J. R. Allington-Smith, "The coupling performance of photonic crystal fibres in fibre stellar interferometry," Mon. Not. R. Astron. Soc. 368, 203-210 (2006).

J. Corbett, T. Butterley, and J. R. Allington-Smith, "Fibre modal power distributions and their application to OH-suppression fibres," Mon. Not. R. Astron. Soc. 378, 482-492 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Astro. Soc. Pacific

Q4. T. Hunter and L. Ramsey "Scrambling properties of optical fibres and the performance of a double scrambler," Proc. Astro. Soc. Pacific 104, 1244-1251 (1992).
[CrossRef]

SPIE

Q1. J. Bland-Hawthorn & A. Horton, "Instruments without optics," SPIE 6269,62690N (2006).
[CrossRef]

Other

F. Roddier, Adaptive optics in astronomy (Cambridge, 1999).
[CrossRef]

A. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 1983).

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

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Figures (13)

Fig. 1.
Fig. 1.

(a). Single spatial element feeding multiple, mass produced, photonic spectrographs, (b) Single spatial element feeding a single catadioptric spectrograph via a single mode converter to remove image scrambling

Fig. 2.
Fig. 2.

The telescope, lenslet array and fibre geometry

Fig. 3.
Fig. 3.

Section through the exit pupil image, E i , at various sampling constants, S

Fig. 4.
Fig. 4.

Normalised coupling efficiency into an LMA-20 fibre fed with the telescope pupil image via a field lens.

Fig. 5.
Fig. 5.

ρf (θ)for various S - Abscissa in direction A

Fig. 6.
Fig. 6.

ρL for various values of S - Abscissa in direction A

Fig. 7.
Fig. 7.

Total throughput (over all illuminated fibres in the 2D array) in direction A for S = (a) 0.5 - Red, (b) 1.0 - Green, (c) 4.0 - Blue. The grey and black lines are commented on below.

Fig. 8.
Fig. 8.

Total throughput (Hexagonal lenslet) as a function of S.

Fig. 9.
Fig. 9.

(a) Peak coupling efficiency (ρf at θ= 0) as a function of S, for α= 0.334 (Sopt =0.5), 0.665 (Sopt = 1.0) and α= 1.33 (Geometrical optimum), (b) Coupling field of view of various S when α= 0.665 and α= 1.33.

Fig. 10.
Fig. 10.

Plot of U against V for (a) a weakly guiding fibre (ncore nclad ) - scalar model, (b) a strongly guiding fibre (ncore >> nclad ) - corrected model

Fig. 11.
Fig. 11.

Fibre coupling efficiency, ρf , with input angle at the fibre for S = (a) 0.5, (b) 1.0, (c) 1.5, (d) 2.0 and (e) 4.0 (f) 4.0 comparison at various V - See text.

Fig. 12.
Fig. 12.

Total throughput (over all illuminated fibres) for S = 1.0

Fig. 13.
Fig. 13.

Total throughput as a function of the # of modes in the undersampled case

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

E i ( x , y ) = exp ( i k 0 2 f L ( x 2 + y 2 ) ) g ( x , y ) E ( x , y )
E ( x , y ) = P . exp ( k 0 n L )
g ( x , y ) = 1 2 π 2 xy
× { 3 x 3 x + y [ cos ( 2 3 π n L λ o F L y 3 x 1 + 2 ) cos ( 2 3 π n L λ o F L y 3 y 1 + 2 ) ]
+ 3 x 3 x + y [ cos ( 2 3 π n L λ o F L 2 y 1 + 2 ) cos ( 2 3 π n L λ o F L y 3 x 1 + 2 ) ] }
ρ F = ( A dA E i × h f * . μ z ) Re [ ( A dA E i × H f * . μ z ) ( A dA e f × h f * . μ z ) ]
ρ L = Hex dA I PSF A dA I PSF
χ . d T = 1 F L d p n L
d L = S × 1.22 F T λ o
S = d p n L 1.22 F L λ o
ρ f = ρ max · exp [ ( n L ∧θ ξ λ o ) 2 ]
λ opt 0.7911 F T
S opt n L α
NA = n core 2 n clad 2
h i = ( h x , y i + h z i ) exp ( i β i z )
Ψ h x , y i = β i 2 h x , y i
U = d f 2 ( k o 2 n core 2 β 2 )
V = k o ( d f 2 ) NA
U J l + 1 ( U ) J l ( U ) = W K l + 1 ( W ) J l ( W )
H E l + 1 , m ( Even ) h x , y = f l ( U m ) [ sin ( ) x ̂ + cos ( ) y ̂ ]
H E l + 1 , m ( Odd ) h x , y = f l ( U m ) [ cos ( ) x ̂ sin ( ) y ̂ ]
H E l - 1 , m ( Even ) h x , y = f l ( U m ) [ sin ( ) x ̂ cos ( ) y ̂ ]
H E l - 1 , m ( Odd ) h x , y = f l ( U m ) [ cos ( ) x ̂ + sin ( ) y ̂ ]
d p = 1.6 d f 2 ln V
S = V 2 lnV 1.6 n L 1.22 πNA F L

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