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Bend Losses

Definition: propagation losses in an optical fiber (or other waveguide) caused by bending

More general term: propagation losses

German: Biegeverluste

Category: fiber optics and waveguidesfiber optics and waveguides


Cite the article using its DOI: https://doi.org/10.61835/zje

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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.

bend losses in a large mode area fiber
Figure 1: Amplitude distribution in a large mode area fiber, which is bent more and more strongly towards the right side.

The fiber mode becomes substantially smaller and then very lossy; the light is coupled out into cladding modes. The numerical simulation has been done with the RP Fiber Power software.

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.

The magnitude of bend losses has some dependence on the polarization. This can be exploited, for example, for obtaining stable single-polarization emission from a fiber laser.

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.

Note that bending not only introduces losses, but can also reduce the effective mode area. This is particularly true for large mode area step-index fibers. Also, bending induces birefringence [3, 5].

Estimating Bend Losses

For estimating the magnitude of bend loss, the equivalent index method [4] 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. [6]) can include such effects, and thus predict the full wavelength dependence, but are complicated to handle.

Bend-insensitive Fibers

In some application areas of fibers, and particularly in optical fiber communications, it is of interest to have a relatively bend-insensitive fibers. This is particularly important in the area of fiber to the home (FTTH), where it is problematic to demand that any tight bending is avoided in the fiber installation. The G.657 standard for telecom fibers defines the characteristics of such fibers, with the main categories A for use in access networks and B for short distances, but with even stronger bending tolerance – in category B3 allowing a bend radius down to only 5 mm. For comparison, the more general category G.652 allows a bend radius only down to 30 mm.

Bend-insensitive fibers can be made with different designs. It is common to have trench-assisted fiber designs, containing a ring (trench) with relatively low refractive index around the fiber core. Another possibility are certain designs of photonic crystal fibers, which may be called hole-assisted.

Note that there are trade-offs between bend insensitivity and other properties, such as low propagation losses in the straight form. However, lowest propagation losses are not essential e.g. for FTTH, where only a relatively short transmission distances need to be realized.

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, with desired values of the bend radius of a few microns only, but limited by the issue of bend losses. For strong bending and thus particularly compact designs, waveguides with a relatively high numerical aperture, i.e., with a large refractive index contrast (i.e., a high numerical aperture), are needed, e.g. based on silicon-on-insulator (SOI) technology. Those, however, are tentatively more sensitive to propagation losses by scattering at non-perfect boundaries between core and cladding.

Case Study

See the tutorial Passive Fiber Optics, part 7: Propagation Losses

The following case study is available:

More to Learn

Encyclopedia articles:


[1]D. Marcuse, “Curvature loss formula for optical fibers”, J. Opt. Soc. Am. 66 (3), 216 (1976); https://doi.org/10.1364/JOSA.66.000216
[2]D. Marcuse, “Field deformation and loss caused by curvature of optical fibers”, J. Opt. Soc. Am. 66 (4), 311 (1976); https://doi.org/10.1364/JOSA.66.000311
[3]R. Ulrich et al., “Bending-induced birefringence in single-mode fibers”, Opt. Lett. 5 (6), 273 (1980); https://doi.org/10.1364/OL.5.000273
[4]D. Marcuse, “Influence of curvature on the losses of doubly clad fibers”, Appl. Opt. 21 (23), 4208 (1982); https://doi.org/10.1364/AO.21.004208
[5]S. J. Garth, “Birefringence in bent single-mode fibers”, IEEE J. Lightwave Technol. 6 (3), 445 (1988); https://doi.org/10.1109/50.4022
[6]L. Faustini and G. Martini, “Bend loss in single-mode fibers”, IEEE J. Lightwave Technol. 15 (4), 671 (1997); https://doi.org/10.1109/50.566689
[7]J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area”, “Opt. Express 14 (1), 69 (2006)”; https://doi.org/10.1364/OPEX.14.000069
[8]R. W. Smink et al., “Bending loss in optical fibers – a full-wave approach”, J. Opt. Soc. Am. B 24 (10), 2610 (2007); https://doi.org/10.1364/JOSAB.24.002610
[9]R. T. Schermer, “Improved bend loss formula verified for optical fiber by simulation and experiment”, IEEE J. Quantum Electron. 43 (10), 899 (2007); https://doi.org/10.1109/JQE.2007.903364
[10]R. T. Schermer, “Mode scalability in bent optical fibers”, Opt. Express 15 (24), 15674 (2007); https://doi.org/10.1364/OE.15.015674
[11]A. Argyros et al., “Bend loss in highly multimode fibres”, Opt. Express 16 (23), 18590 (2008); https://doi.org/10.1364/OE.16.018590
[12]J. M. Fini, “Large mode area fibers with asymmetric bend compensation”, Opt. Express 19 (22), 21866 (2011); https://doi.org/10.1364/OE.19.021866
[13]J. M. Fini, “Intuitive modeling of bend distortion in large-mode-area fibers”, Opt. Lett. 32 (12), 1632 (2007); https://doi.org/10.1364/OL.32.001632
[14]C. Schulze et al., “Mode resolved bend loss in few-mode optical fibers”, Opt. Express 21 (3), 3170 (2013); https://doi.org/10.1364/OE.21.003170

(Suggest additional literature!)

Questions and Comments from Users


How can one calculate the total usable wavelength range with single-mode guidance of a fiber – between cutoff wavelength and macro-bending cutoff wavelength of LP01 mode? Is it 500 nm wide?

The author's answer:

One can calculate it, but not easily, and it depends on the details of fiber design, and of course on the be bend radius and the tolerated level of propagation loss.

Similarly, there is a limit based on microbend losses; for calculating it, you would need to know how strong the irregularities in the fiber are.

Many single-mode fibers should work over a range of some hundreds of nanometers, maybe not always as much as 500 nm.


PM fiber (e.g. of PANDA type) will have loss as well as birefringence induced by the bending. Is it sensitive to the alignment of the stress rods? What practical rules of thumb should be used?

The author's answer:

For moderate bending, this should normally not be a problem. I imagine that for strong bending it may play a role how the stress rods are oriented, but that orientation is probably hard to control in practice.


For photonic integrated circuits, is there any formula or rule of thumb that can be used to obtain the optimal bending radius of curvature of the waveguide, i.e., is there a way of estimating the required bending radius of a waveguide of a particular material refractive index and waveguide dimension?

The author's answer:

Maybe under certain additional assumptions, but it is not so easy, as bend losses can depend on various details of the waveguide design.

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