Bending Loss Formula Research Articles

Theoretical macrobending loss in single-mode transmission through a uniform index fiber-optic cable

The macrobending loss of propagating waves in optical fibers is studied here by employing simple toroidal coordinates (r, θ, ϕ) for the governing Maxwell equations of electromagnetism, the solution for which is expressed by the central axial component Π ϕ of the Hertz vector Π. The refractive indices of the core and its cladding are supposed uniform all along the length of the cable. Effects of coating, Jacketing and the effect of elastic strain in the fiber are not considered. Knowing that the bending losses are of different nature when the radius of curvature R exceeds or is less than a certain critical value R c , the study is accordingly divided in to two parts. Firstly, when R > R c wave guide action holds, and it is shown through an example that it is small, varying linearly with the bending angle ϕ of the cable and practically independent of R. On the other hand, when R < R c , leaking waves are propagated and the problem is remodeled by a leaking ring source of EM waves in a medium consisting of the cladding only. The analysis of the model results in a bending loss formula that varies as ϕ3 and depends on R by a factor of the form e−αR/R.

A Security Detection Scheme Based on TTD for NG-PON2 Fiber Links

For improving the physical layer security of next generation passive optical network (NG-PON2), we propose a security detection scheme by detecting the terminal thermal distribution (TTD) at the optical fiber end face on the optical network unit (ONU), when the fiber link is tapped. The principle of the scheme is given that the thermal energy always exists in fiber links and the TTD at the optical fiber end face can be detected. When the link tapping occurs, the leaking light energy induced by bending converts into the thermal energy, which changes the TTD at the optical fiber end face on ONU of NG-PON2. The TTD models of core and cladding layers at the optical fiber end face owing to bending are built with the double cylindrical coordinate systems, based on the bending loss formula of optical fiber and thermodynamic coupling theory. Then, the simulations for the TTD models are carried out under the different conditions of input power, bending radius and distant of detected point from the center of optical fiber end face, respectively. The simulation results indicate three conditions above are the main factors affecting the TTD changes. Finally, we set up an experimental system in the lab, using a light-emitting diode at 1550nm, and a thermal microscope (Telops-FAST-IR). The experimental results show the TTD of core layer at the optical fiber (G.652D) end face changes 72.5% at the input power of 1dBm with the bending radius from 10mm to 5mm, and are consistent with the simulation ones.

A semi-analytical calculation method of bending loss for large-mode-area fibers with arbitrary refractive-index profile

Predicting mode-dependent bending loss is important for large-mode-area (LMA) fibers to strip out unwanted modes. In order to seek a reasonable calculation method, a new bending loss formula that allows for both mode field distortion and weaker mode confinement was derived in detail. Based on the formula, a semi-analytical method was introduced to calculate the mode bending loss for LMA fibers. By combining the applications of the finite element method, discrete Fourier transforms and numerical integral, the method is valid for LMA fibers with arbitrary refractive index profile. The obtained loss characteristics are basically consistent with the previous results. This accordance demonstrates the feasibility and generality of the semi-analytical method.

Bending Loss Evaluations of Holey Fibers Having a Core Consisting of an Elliptical-Hole Lattice by Various Approaches

In general, an accurate evaluation of the bending loss of an optical fiber with an arbitrary refractive index profile is a cumbersome task, especially for holey fibers (HFs). In this paper, various approaches are applied and compared for the bending loss evaluations of single-polarization elliptical-hole core circular-hole HFs (EC-CHFs), which are circular-hole HFs having a core with an elliptical-hole lattice structure. Our simulation results show that when bending loss formulas for weakly guiding circular fibers are applied to a HF by regarding it as an approximate circular fiber having an equivalent step-index (SI) profile, the definition of the core region is the most crucial issue. Moreover, we also show that the results obtained by the approximate approach based on the bending loss formulas for the equivalent SI circular fiber are in good agreement with direct approaches with numerical simulations for the real EC-CHF structure, if the equivalent core radius is suitably defined for the real cross section.

Improved Bend Loss Formula Verified for Optical Fiber by Simulation and Experiment

This paper presents an improved curvature loss formula for optical waveguides, which is shown to accurately predict the bend loss of both single-mode and multimode fibers. The formula expands upon a previous formula derived by Marcuse, greatly improving its accuracy for the case of multimode fiber. Also presented are the results of bent fiber simulations using the beam propagation method (BPM), and experimental measurements of bend loss. Agreement among simulation, formula and measurement support the validity of both theoretical methods. BPM simulations showed that the lowest order modes of the bent fiber were reduced to their linearly polarized constituents prior to the onset of significant bend loss. This implies that certain LP mode orientations should propagate with much lower loss than previously expected, and should impact the mode stripping ability of bent large mode area fibers, as employed in fiber lasers and amplifiers.

Simplified Formula of Bending Loss for Optical Fiber Sensors

A simple fiber-optic bending loss formula is achieved for optical fiber sensors. This simple formula considers various bending radii, number of turns, extra bending angle, and wavelength and has good agreement with theoretical and experimental data. We also propose a simplified formula for sensitivity of the fiber-optic bending loss in this article. The defined sensitivity formula has the benefit of showing parameters for fiber-optic bending sensor systems.

Bend loss in single-mode fibers

In this paper, we present the results of extensive single-radius bend loss measurements for two different fibers over wide ranges of wavelength (800-1600 nm) and curvature radius (13.5-27.5 mm). A new bend loss formula is also derived, allowing a good fit of experimental data over the whole range of both parameters. Using an equivalent step-index (ESI) approach we obtain a good agreement between estimated and real parameters: e.g., cutoff wavelengths are within 1%.

New bending loss formula explaining bends on loss curve

A new bending loss formula for single-mode fibres is presented. Comparison with measurements and conventional theory shows good agreement. Reported bends on the loss curves for matched- and depressed-clad fibres are explained.

Single-polarization operation in highly birefringent optical fibers

Single-polarization characteristics in highly birefringent fibers have been investigated by considering the photoelastic effect in the entire cross section of the fiber. It has been shown by stress analysis that the stress-induced birefringence between the two orthogonal polarization modes in the cladding is much smaller than that in the core and the vicinity of the core–cladding interface, which causes differential bending loss for the two polarization modes. A bending loss formula, which takes into account the photoelastic effect, has been derived for each polarization mode. Differential attenuation characteristics and extinction ratios have been investigated for several bending radii using the bending loss formula.

Dispersion-free single-mode doubly clad fibres with small pure bend losses

A pure bend loss formula for doubly clad profiles is used to investigate the limitations and tolerances induced in the design of dispersion-free W-fibres by keeping the radiation losses below an acceptable level.

Analytical bending loss formula of optical fibers with field deformation

Bending losses in a radially inhomogeneous profile fiber were studied, taking into account bend‐induced field deformation to the first‐order perturbation. Analytical bending loss formulas are given for arbitrary mode numbers in step‐index fibers. Polarization degeneracy in bending loss still exists even when field deformation effects are taken into account. The bending loss in a step‐index single‐mode fiber increases by 36% at υ = 2.4 and ℜ = RΔ/a = 10 as compared with that without field deformation.

Bending loss formulas for step‐index optical fiber and their applicable regions

AbstractThis paper presents a method for analyzing bending loss formula for the hybrid mode propagating in a uniform bend. As a hybrid mode, we chose the LP mode and found dependency of the bending loss formula on the directional angle, propagation constant and the amplitude ratio and phase difference of the constituent mode. The results contain those previously obtained and are applicable to more cases. We found that the bending loss of a general LP mode depends on the amplitude ratio and phase difference of the constituent mode, the directional angle, and the propagation constant. A linearly polarized LP mode has its bending loss dependent on the directional angle but not on the polarization angle. The bending loss of the HE and EH modes does not depend on the directional angle. Based on the condition for which the deviation of the field distribution due to the bend is negligible, we found the applicable range of the bending loss formula.

Bending loss formulas for step-index optical fiber and their applicable regions

Bending loss formulas for step-index optical fiber and their applicable regions

Bent asymmetric dielectric slab waveguides: a detailed analysis

Analytic expressions for the field and propagation constants of the mode along a uniformly curved three-layered slab waveguide are presented in terms of the power series of the curvature. To compare the accuracy of approximate solutions, numerical analysis is carried out. New bending loss formulas are also derived which consider the field deformation and the change of the propagation constant. It is shown that they are very accurate over a wide range of normalized frequency.

Simplified bending loss formula for single-mode optical fibers

Simplified bending loss formula for single-mode optical fibers

Bending losses of coated single-mode optical fibers

Peaks appear in bending losses of coated single-mode fibers due to interference between the guided mode and rays which are radiated from the guided mode and are reflected at cladding-coating boundary. This paper reports derivation of bending loss formulas for coated slab waveguides and coated fibers. Plane wave concepts are also used to explain the appearance of the loss peaks. Measurements were performed by using two coated single-mode fibers. The agreement between theory and experimental results is found to be excellent. It is possible to obtain the refractive index difference from measured peak wavelengths.

Bending loss of propagation modes in arbitrary-index profile optical fibers

A bending loss formula for optical fibers with an axially symmetric arbitrary-index profile is derived by approximating the refractive-index profile with a staircase function. The permissible bending radius R* defined for a given value of bending loss is derived. It is deduced that R* is nearly proportional to wavelength lambda when the normalized frequency nu and the refractive-index difference Delta are fixed. The ratio of R* at two different values of nu depends only on the ratio of nu. The influence of an index dip and profile smoothing on R* is numerically evaluated.

Bending losses of dielectric rectangular waveguides for integrated optics

A new bending-loss formula for dielectric waveguides with rectangular cross section is obtained. Some important differences are shown, compared with the existing formula obtained from a slab-waveguide model.

Bending losses of dielectric slab optical waveguide with double or multiple claddings: theory

Bending-loss formulas of a multilayer planar optical waveguide are obtained on the basis of continuation of wave functions without solving the complicated eigenvalue equation. We then consider the bending losses of a doubly clad slab waveguide in which the core has the largest refractive index, and the inner cladding has the lowest. Bending losses are shown to be drastically reduced by inserting low-index inner claddings between the core and the outer cladding.

Bending Losses of the Asymmetric Slab Waveguide

The bending losses of the asymmetric slab waveguide are computed. The computation is based on the knowledge of the exact form of the solution of Maxwell's equations of the bent structure and the additional assumption that the field near the bent waveguide can be approximated by the field of the straight waveguide. The result of this theory is in good agreement with an existing theory. It appears that the bending loss formula can be used to estimate the bending losses of the round optical fiber if the mode parameters entering the formula are replaced by the corresponding mode parameters of the round fiber. We present curves that allow the numerical evaluation of the bending loss of the lowest order even TE mode of the symmetric slab waveguide.