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Coupling light into few-mode optical fibres I: The diffraction limit

Anthony J. Horton and Joss Bland-Hawthorn

Open Access Open Access

Abstract

Multimode fibres are widely used in astronomy because of the ease of coupling light into them at a telescope focus. The photonics industry has given rise to a broad range of products but these are almost exclusively restricted to single-mode fibres, although some can be adapted for use in fibres that allow several modes to propagate. Now that astronomical telescopes are moving toward diffraction-limited performance through the use of adaptive optics (AO), we address the problem of coupling light into a few-mode fibre (FMF). We find that fibres with as few as ∼5 guided modes share important characterisitcs with multimode fibres, in particular high coupling efficiency. We anticipate that future astronomical instruments at an AO-corrected focus will be able to exploit a broad class of photonic devices.

©2007 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. Maximum coupling efficiency versus core diameter for an NA = 0.1 fibre at a wavelength of 1.5μm. The overall coupling efficiency and the contributions from each fibre mode are shown for (a) α = 0 and (b) α = 0.2.

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Fig. 2.
Fig. 2. Optimal focal ratio versus core diameter for an NA = 0.1 fibre at a wavelength of 1.5μm. The focal ratio corresponding to maximum coupling efficiency is shown for (a) α = 0 and (b) α = 0.2.

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Fig. 3.
Fig. 3. Coupling efficiency versus focal ratio for an NA = 0.1 fibre at a wavelength of 1.5μm. Coupling efficiency is shown for core diameters of 10, 25, 40 and 55μm with (a) α = 0 and (b) α = 0.2.

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Fig. 4.
Fig. 4. Coupling efficiency versus decentring of the image centre from the fibre axis. Coupling efficiency is shown for NA = 0.1 fibres with 10, 25, 40 and 55μm core diameters at a wavelength of 1.5μm and with α = 0.

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Fig. 5.
Fig. 5. Coupling efficiency versus wavelength for NA = 0.1 fibres with core diameters of 10, 25, 40 and 55μm, and with α = 0. For each diameter the focal ratio was fixed at the optimal value for a wavelength of 1.6μm.

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Tables (1)

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Table 1. Cutoff frequencies for the linearly polarised modes of a step index fibre.

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Equations (10)

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E lm ρ θ = A lm sin lθ cos lθ J l ( u lm ρ ) J l ( u lm ) ρ ≤ 1
A lm sin lθ cos lθ K l ( w lm ρ ) K l ( w lm ) ρ > 1 ,
V = ( u 2 + w 2 ) 1 2
u J l − 1 ( u ) J l ( u ) + w K l − 1 ( w ) K l ( w ) = 0 .
E focus ( r ) ∝ E ˜ pupil ( r λf )
E pupil ( r ' ) = E ٭ P ( r ' ) Ψ ( r ' )
E focus = E 0 [ 2 J 1 ( s ) s − α 2 2 J 1 ( αs ) αs , ]
ε lm = ∣ ∫ ∞ E focus * ∙ E lm d A ∣ 2 ∫ ∞ ∣ E focus ∣ 2 d A ∫ ∞ ∣ E lm ∣ 2 d A .
ε lm = ∣ 〈 E focus | E lm 〉 ∣ 2 〈 E focus | E focus 〉 〈 E lm | E lm 〉
ε ext = ∫ ∞ ε psf ( r ) I ext ( r f ) dA ∫ ∞ I ext ( r f ) dA
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