How low can I go with refractive index to still have optical fiber without high loss and banding loss at single mode optical fiber?
Thanks
Use the Snell-Descartes law to determine the critical angle for total internal refraction. That will give you a ratio of optical indexes between the core and the cladding. In your case, the lowest critical angle achievable is your intended maximum bending angle.
While Dr Hurth's suggestion might be appropriate for large core multimode optical waveguides, it is a poor predictor of bend performance in single mode optical fibre.
For example Corning SMF 28e+ standard single mode fibre has a core-clad relative index difference of 0.0036.
http://www.corning.com/media/worldwide/global/documents/sfiber%20Corning%20Specialty%20Fiber%20Product%20Information%20Sheets%20111913.pdf
Applying Snell's law, the complement of the critical angle is 0.085 radian (NA 0.12), so predicted minimum bend radius with an 8.2 micron core diameter would be around 0.1 mm. In practice, this fibre shows significant attenuation for bend radii of a few millimetres.
Geometric optics predictions are independent of wavelength, and suggest that smaller core radii will tolerate tighter bends - counter to practical experience, and the predictions of a more complete analysis.
A wave analysis shows that the bend loss has an exponential dependence on the ratio of bend radius to core radius and on the core-cladding index difference. There is a strong wavelength dependence, with bend loss increasing with wavelength.
Small core-clad index differences are usable if the fibre is operated at high normalised frequency (V-number). For single wavelength operation, the fibre should be designed with a single mode cut-off wavelength close to (or possibly longer than) the operating wavelength. If the core-clad refractive index is reduced, the core diameter should be increased to maintain or increase the V-number and cut-off wavelength.
If microbending loss is a concern, good cabling practice will help, as will use of a large silica cladding diameter such as 250 microns, rather than the 125 micron commonly used for standard single mode fibres.
If the requirement is a low value for the absolute refractive index, then a low cladding index will allow the core index to be reduced while still maintaining an index difference which gives acceptable bend performance. Doping a silica cladding with fluorine and/or boron oxide will help, though boron does degrade the attenuation at 1300 nm and longer wavelengths.
Article Radiation from bent optical waveguides
Nice complement of information, Alan.
Obviously, geometric optics only work in approximation and as your rightfully pointed out do not take wavelength dependency.
Could you provide a full text for your paper. I'd be interested in more details.
Cedric
Cedric,
I don't have an electronic copy of the paper, but there is also a description in: Allan W. Snyder & John. D. Love, "Optical Waveguide Theory", Chapter 23 (1983).
An alternative treatment is mentioned in Chapter 3 of S. E. Miller & A. G. Chynoweth "Optical Fiber Telecommunications" (1979). They refer to an earlier paper
E.A. Marcatilli & S.E.Miller "Improved relations describing directional control in electromagnetic wave guidance", Bell Syst. Tech J. vol 48, pp 2103-2132.
Also, D. Marcuse "Curvature loss formula for optical fiber", JOSA vol. 66, p 216 (1976) https://www.osapublishing.org/josa/abstract.cfm?uri=josa-66-3-216
In the same chapter, Marcuse et. al. also mention another treatment in which a transformation of coordinates produces an effective refractive index profile
n = n(r) { 1 + r/Rc) cos(phi) }
Bending the fibre makes the mode field behave as if the refractive index increases linearly with displacement outwards from the axis of curvature. From this it becomes apparent that all modes on a bent fibre are leaky. The loss is determined by the tunnelling of the evanescent wave through the region of the cladding where the transformed refractive index is lower than the mode effective index.
M. Heiblum & J.H. Harris "Analysis of curved optical waveguides by conformal transformation", IEEE J. Quantum Electron. QE-11 pp 130-138 (1975).
This approach has been used by numerous authors since then.
Regards,
Alan.
Article Absolute Measurement of the Nonlinear Refractive Indices of ...
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