Double-clad fiber

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In fiber optics, a double-clad fiber (or doubly clad fiber) is an optical fiber that has a relatively small-diameter core and two layers of large-diameter cladding. Usually, both cladding layers have lower refractive index than the core, and the inner cladding layer has lower refractive index than the outer layer. This allows the inner cladding to carry multimode light of a different wavelength from that carried in the core of the fiber. This type of fiber is also called depressed-inner-cladding fiber and W-profile fiber (from the fact that a symmetrical plot of its refractive index profile superficially resembles the letter W).

1 Applications
2 Notes and references

[edit] Applications

Fig.1. Cross-section of circular double-clad fiber with offset core.

Fig.2. Cross-section of double-clad fiber with rectangular inner cladding

[edit] Fiber lasers and optical amplifiers

Double-clad fibers often are used for fiber lasers and optical amplifiers, because the core can be doped to act as the gain medium while the inner cladding layer carries a pump beam used to maintan the population inversion in the core. For such applications, the core may be single-mode or may be multimode with a low numerical aperture. The use of double-clad fibers allows fiber lasers to be scaled to higher powers than can otherwise be achieved.

The shape of the cladding is very important at narrow core and wide cladding. Circular symmetry in a double-clad fiber seems to be the worst solution for a fiber laser; in this case, many modes of the light in the cladding miss the core and hence cannot be used to pump it. ^[1]. On the language of geometrical optics, most of rays of pump just walk around the core without to pump it. The ray tracing ^[2] , simulations of the paraxial propagaiton ^[3] and the mode analysis ^[4] give similar results.

[edit] Chaotic fibers

Fig.3. Shape of the of the spiral-shaped cladding (blue), its chunk (red), and 3 segments of a ray (green).

In general, modes of a waveguide have scars, which correspond to the classical trajectories. The scars may avoid the core, then the mode is not coupled, and it is vain to excite such a mode in the double-clad fiber amplifier. The scars can be distributed more or less uniformly in so-called chaotic fibers ^[5] have more complicated cross-sectional shape and provide more uniform distribution of intensity in the inner cladding, allowing efficient use of the pump light. However, the scaring takes place even in chaotic fibers. An almost-circular shape with small spiral deformation seems to be the most efficient forchaotic fibers. In such a fiber, the angular momentum of a ray increases at each reflection from the smooth wall, until the ray hits the chunk [fig.3] of the spiral curve. The core placed in viciniti of this chunk is visited by all the rays more regularly, than in other cahotic fibers . This behavior of rays has analogy in the wave optics. On the language of modes, all the modes have non-zero derivative in vicinity of the chunk, and cannot avoid the core placed there. Such behavior of modes follows from the theorem about boundary behavior of modes of the Dirichlet Laplacian ^[6].

[edit] Filling factor

Fig.4. Estimates of the pump efficiency in a double-clad fiber with

F = 0.8

(blue) and

F = 0.9

(red) , discussed in ^[7] compared to the results of the ray tracing simulations ^[2](black curves).

The efficiency of absorption of pumping energy in the fiber is an important parameter of a double-clad fiber laser. In many cases this efficiency can be approximated with ^[7]

$1- \exp\left( - F \frac{\pi r^2}{S}\alpha L \right) ,$

where

$~S~$ is the cross-sectional area of the cladding

$~r~$ is the radius of the core (which is taken to be circular)

$~\alpha~$ is the absorption coefficient of pump light in the core

$~L~$ is the length of the double-clad fiber, and

$~F~$ is a dimensionless adjusting parameter, which is sometimes called the "filling factor"; $~0<F<1~$ .

The filling factor may depend on the initial distribution of the pump light, the shape of the cladding, and the position of the core within it.

The exponential behavior of the efficiency of absorption of pump in the core is not obvious. We could expect, that some modes of the cladding (or some rays) are better coupled to the core than others; therefore, the "true" dependence could be combination of several exponentials; and the only comparison with simulations (Fig.4) justifies this approximation for fibers with broken circular symmetry. In particular, this approximation does not work for circular fibers, see the initial work by Bedo et all, cited below. For chaotic fibers, $~F~$ approaches unity. The value of $~F~$ can be estimated by numerical analysis with propagation of waves, expansion by modes or by geometrical optics ray tracing, and values 0.8 and 0.9 are only empiric adjusitng parameters, which provide good egreement of the simple esitmate with numerical simulations for two specific classes of douple-cald fibers, circular ofset and rectangular. Obviously, the simple estimate above fails, as the ofset parameter becomes small compared to the size of cladding.

The filling factor $~F~$ approaches unity especially quickly in the spiral-shaped cladding, due to the special boundary behavior of the modes of the Dirichlet Laplacian, [1]. Designers of double-clad fiber have to find a reasonable compromise between the optimized shape (for the efficient couplung of pump into the core) and the simplicity of the manufacturing of the preform used to draw the fibers.

[edit] Alternative structures

The planar waveguides with gain medium take an intermediate position between conventional solid-state lasers and the conventional fouble-clad lasers. The planar waveduide may confine milti-mode pump and high-quality signal, allowing the efficient coupling of pump and the diffraction-limited output ^[8] , ^[3],

[edit] Other applications

A double-clad fiber has the advantage of very low microbending losses. It also has two zero-dispersion points, and low dispersion over a much wider wavelength range than a singly-clad fiber. Double-clad fibers can also be used for the compensation of chromatic dispersion in optical communications and other applications.