Bend losses are a frequently encountered problem in the context of waveguides, and in particular in fiber optics, since fibers can be easily bent. Bend losses mean that optical fibers exhibit additional propagation losses by coupling light from core modes (guided modes) to cladding modes when they are bent. Typically, these losses rise very quickly once a certain critical bend radius is reached. This critical radius can be very small (a few millimeters) for fibers with robust guiding characteristics (high numerical aperture), whereas it is much larger (often tens of centimeters) for single-mode fibers with large mode areas.
Generally, bend losses increase strongly for longer wavelengths, although the wavelength dependence is often strongly oscillatory due to interference with light reflected at the cladding/coating boundary, and/or at the outer coating surface. The increasing bend losses at longer wavelengths often limit the usable wavelength range of a single-mode fiber. For example, a fiber with a single-mode cut-off wavelength of 800 nm, as is suitable for operation in the 1-μm region, may not be usable at 1500 nm, because they would exhibit excessive bend losses. Note that even without macroscopic bending of a fiber, bend losses can occur as a result of microbends, i.e., microscopic disturbances in the fiber, which can be caused by imperfect fabrication conditions.
In multimode fibers, bend losses are usually strongly mode-dependent. The critical bend radius is typically larger for higher-order transverse modes. By properly adjusting the bend radius, it is possible to introduce significant losses for higher-order modes without affecting the lowest-order mode. This can be useful e.g. for the design of high-power fiber amplifiers and fiber lasers where a higher effective mode area can be achieved when using a fiber with multiple transverse modes.
Photonic crystal fibers can have very low bend losses even far beyond the single-mode cutoff wavelength. Therefore, they can be “endlessly single-mode”, i.e., they exhibit usable single-mode characteristics over a very large wavelength range.
Estimating Bend Losses
For estimating the magnitude of bend loss, the equivalent index method  can be used. The basic idea behind this technique is to calculate the mode distributions for an effective index which contains a term accounting for the modified path lengths at different transverse positions. An elasto-optic correction term (taking into account local modifications of the refractive index by mechanical stress) leads to an effectively weaker “tilt” of the refractive index profile than when considering the geometrical effect alone [3, 9].
Such a method of calculating bend losses is convenient and usually a good approximation, provided that there is no light reflected e.g. from the outer cladding surface back to the fiber core. More sophisticated models (see e.g. Ref. ) can include such effects, and thus predict the full wavelength dependence, but are complicated to handle.
Bend Losses in Photonic Integrated Circuits
Bend losses are important not only in fiber optics, but also in the context of photonic integrated circuits. Compact circuits designs often require strong bending of waveguides on such chips, but the issue of bend losses often limits the usable radius of curvature. For strong bending and thus particularly compact designs, waveguides with a relatively high numerical aperture, i.e., with a large refractive index contrast, are needed. Those, however, are tentatively more sensitive to propagation losses by scattering at non-perfect boundaries between core and cladding.
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