page_title: Double-clad fiber
section_title: Spiral shape
hierarchical_section_title: Double-clad fiber / Fiber for amplifiers and fiber lasers / Chaotic fibers / Spiral shape
context_page_description: Double-clad fiber is a class of optical fiber with a structure consisting of three layers of optical material instead of the usual two. The inner-most layer is called the core. It is surrounded by the inner cladding, which is surrounded by the outer cladding. The three layers are made of materials with different refractive indices.
  There are two different kinds of double-clad fibers. The first was developed early in optical fiber history with the purpose of engineering the dispersion of optical fibers. In these fibers, the core carries the majority of the light, and the inner and outer cladding alter the waveguide dispersion of the core-guided signal. The second kind of fiber was developed in the late 1980s for use with high power fiber amplifiers and fiber lasers. In these fibers, the core is doped with active dopant material; it both guides and amplifies the signal light. The inner cladding and core together guide the pump light, which provides the energy needed to allow amplification in the core. In these fibers, the core has the highest refractive index and the outer cladding has the lowest. In most cases the outer cladding is made of a polymer material rather than glass.
context_section_description: An almost-circular shape with small spiral deformation seems to be the most efficient for chaotic 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", at which the spiral curve is broken (see figure at right). The core, placed in vicinity of this chunk, is intercepted more regularly by all the rays compared to other chaotic fibers. This behavior of rays has an analogy in wave optics. In the language of modes, all the modes have non-zero derivative in vicinity of the chunk, and cannot avoid the core if it is placed there. One example of modes is shown in the figure below and to the right. Although some of modes show scarring and wide voids, none of these voids cover the core.
  The property of DCFs with spiral-shaped cladding can be interpreted as conservation of angular momentum. The square of the derivative of a mode at the boundary can be interpreted as pressure. Modes (as well as rays) touching the spiral-shaped boundary transfer some angular momentum to it. This transfer of angular momentum should be compensated by pressure at the chunk. Therefore, no one mode can avoid the chunk. Modes can show strong scarring along the classical trajectories (rays) and wide voids, but at least one of scars should approach the chunk to compensate for the angular momentum transferred by the spiral part.
  The interpretation in terms of angular momentum indicates the optimum size of the chunk. There is no reason to make the chunk larger than the core; a large chunk would not localize the scars sufficiently to provide coupling with the core. There is no reason to localize the scars within an angle smaller than the core: the small derivative to the radius makes the manufacturing less robust; the larger  is, the larger the fluctuations of shape that are allowed without breaking the condition . Therefore, the size of the chunk should be of the same order as the size of the core.
  More rigorously, the property of the spiral-shaped domain follows from the theorem about boundary behavior of modes of the Dirichlet Laplacian. Although this theorem is formulated for the core-less domain, it prohibits the modes avoiding the core. A mode avoiding the core, then, should be similar to that of the core-less domain.
  Stochastic optimization of the cladding shape confirms that an almost-circular spiral realizes the best coupling of pump into the core.
caption: Spiral-shaped cladding (blue), its chunk (red), and 3 segments of a ray (green).
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