Impact of profile design on macrobending losses

This is a continuation from the previous tutorial - single element lens.

1. The Depressed Cladding Fiber Design

Historically both matched and depressed clad single-mode optical fibers have been widely deployed in telecommunications networks. For example, the original AT&T standard single-mode fiber was a depressed clad fiber with \(\text{MFD}=8.8\) μm.

A depressed cladding design has an annular ring of \(\Delta\lt0\), often called a trench, between the raised index core and the silica cladding. In this case, the effective \(\Delta\) should be measured between the up-doped core and down-doped trench, so that the depressed clad design has a higher effective \(\Delta\) than the matched clad design.

Referring to the diagram of Fig. 2.5, the difference between \(n_\text{eff}\) of the LP₀₁ mode and the depressed cladding index level is greater than the difference between \(n_\text{eff}\) and the index of the pure silica outer cladding.

Therefore, the transverse propagation constant (refer to Eq. [2.9c]) in the depressed cladding region will be a larger imaginary number compared to that in the outer cladding, so that the field decays most rapidly per unit distance in the depressed cladding region.

Referring again to the analogy with a particle in a potential energy well, this corresponds to having a repulsive barrier around the central attractive potential well.

The depressed cladding region, therefore, decreases the coupling between optical power in the core and optical power in the outer cladding. This reduction in coupling can be used to reduce the sensitivity of a fiber to macrobending losses.

Macrobending refers to the loss of power propagating in a guided mode of the fiber when the fiber is held in a curved geometry. In general, macrobending is minimized for waveguides in which optical power is tightly confined to the core of the fiber and when the evanescent wave in the cladding is most rapidly damped. An equivalent condition is to say that the mode in question should have a high effective index \(n_\text{eff}\).

Confinement of the fundamental LP₀₁ mode in the core of a step-index fiber can be increased by raising either the core radius \(a\) or the index \(\Delta\). However, either change decreases the macrobending loss of higher order modes as well, raising the effective cutoff wavelength of the fiber, as described in the previous section.

The undesirable increase in cutoff can be mitigated by introducing the depressed cladding feature to the waveguide design. A careful study shows that the matched cladding design can be reoptimized for improved macrobending loss performance using the higher effective \(\Delta\) to pull the field into the core for a slightly smaller \(\text{MFD}\) of \(8.8\) μm, while using a depressed cladding to maintain the cable cutoff less than 1260 nm.

2. Phenomenology of Macrobending Loss

Macrobending occurs in a large deflection of the fiber axis, where large is defined relative to the fiber core diameter, such as that associated with spooling or the presence of loops. The resulting loss consists of the transition loss and pure bending loss.

The transition loss occurs at the transitions from straight to bent sections of the fiber and is the result of the mismatch of the field shapes in the straight and the bent fiber.

The pure bending loss occurs because of energy radiating in the radial direction along a section of fiber bent at constant radius of curvature. Macrobending is a deterministic problem in a bend at constant radius of curvature, as opposed to the stochastic microbending problem discussed later.

Phenomenologically, for small variations around a given profile design, there is a strong and linear correlation between the log of macrobending loss (at fixed radius of curvature \(R\)) and the so-called MAC factor, defined as \(\text{MAC}=\text{MFC}\text{(μm)}/\lambda_\text{c}\text{(μm)}\). Either the fiber or cable effective cutoff can be used to calculate the MAC factor.

A rigorous and exact calculation of the macrobending loss of a fiber under constant curvature is computationally very intensive. One simple approximate method results from the realization that by employing a coordinate system transformation, a fiber bent at a constant radius of curvature has equivalent behavior to a straight fiber with index profile that has been altered from that of the bent fiber by a simple linear transformation.

The so-called ‘‘tilted index profile’’ model calculates the loss of the equivalent straight fiber with refractive index profile in the plane of the bend as follows:

\[\tag{2.18}n_s^2(r)=n_o^2(r)+2n_o^2(o)r/R\]

where \(n_o(r)\) is the index profile of the unperturbed fiber and \(R\) is the radius of curvature of the bend.

Figure 2.5 shows graphically the tilted profile macrobending model for a specific bend radius using both matched (black lines) and depressed clad (red lines) designs.

The effective indices are indicated by dashed lines using the same color scheme. The depressed cladding design shown here has a trench radius five times the core radius.

Far away from the core, at radii more than 19 microns, the effective indices of both profiles are lower than the tilted cladding index level. Thus, the bent fiber supports only a leaky mode instead of a pure guided mode.

Bending loss, thus, occurs by the tunneling of the power from core to the cladding. The point at which the effective index becomes lower than the equivalent straight index (tilted profile) of the bent fiber is the so-called ‘‘radiation caustic.’’

Macrobending loss is proportional to the integral of mode power outside the radiation caustic. As the bend radius \(R\) decreases, the slope of the tipped index profile increases, and the radiation caustic moves in toward smaller radii.

In that case, the fraction of power falling outside the radiation caustic increases, and therefore, the bending loss increases. Clearly for a given bend radius \(R\), a fiber with a higher effective index will be less sensitive to macrobending.

Because of the presence of the depressed index trench, the radiation caustic for the depressed clad fiber is located in this example at approximately 18.8 microns, while that for the matched clad fiber is at about 15.2 microns.

This means that in the depressed clad case, the electric field will have decayed to a smaller amplitude when it crosses the cladding index and begins to couple to radiation modes.

This is shown quantitatively in Fig. 2.6, where the electric fields for the two cases are plotted on a log scale. The radiation caustics determined from the tilted profile case of Fig. 2.5 are marked to show that the electric field for the depressed clad fiber has decayed by an additional factor of five to six times relative to the matched clad fiber at the point at which power begins to be lost.

To continue the analogy with the particle in a potential well, we note that the triangular region between the effective index line and the tilted profile, between 5 microns and the radiation caustic, represents a tunneling barrier of greater area in the case of the depressed cladding fiber.

Depressed cladding fibers can improve performance in scenarios where low bending losses are important, such as indoor optical wiring, access networks,
jumpers, ribbon corner fibers, cables with tight packing densities, and cables intended for very low temperature applications.

High quality matched clad fibers are usually specified as having less than 0.05 dB/100 turns for loops of radius \(R=25\) and \(30\) mm at 1625 nm and less than 0.05 dB/turn for loop of radius \(R=16\) mm at 1550 nm.

Depressed clad G.652 fibers can give improved performance for loops of this size range, but from the point of view of system performance, losses for modern fibers of either matched or depressed clad designs are rather low in absolute terms for 25 and 30 mm radii.

The performance of depressed clad fibers begins to diverge significantly from that of matched clad fibers for radii of \(R\) ~ 16mm or less, where bending losses of commercial matched clad fibers are not currently specified.

A single loop of a high-quality G.652-matched clad fiber with radius 10 mm can have bending loss of several decibels. At these tight bending radii, depressed clad fiber may have 5–10 times better macrobending loss performance than matched clad fiber.

The next tutorial discusses about stimulated atomic emissions.