Introduction
A graded-index (GRIN) fiber is an optical fiber whose core refractive index decreases gradually as the radial distance from the fiber’s central axis increases. This varying index profile causes light rays to follow sinusoidal paths along the fiber.
In graded-index fibers, the refractive index near the core center is higher than near the cladding. The most common refractive index profile is nearly parabolic, which continuously refocuses the rays and significantly reduces modal dispersion. Both graded-index and step-index profiles may be used in multimode fiber design.
Multimode fibers can be manufactured with either step-index or graded-index profiles. Compared to step-index fibers, multimode graded-index fibers provide much lower modal dispersion. Modal dispersion can be reduced even further using single-mode step-index fibers with very small core diameters (typically less than 5–10 μm).
In graded-index fibers, the cladding refractive index remains constant, while the core’s refractive index has a parabolic variation. In contrast, step-index fibers have uniform refractive indices in both core and cladding.
Ray transmission in graded-index fiber: Light rays bend toward the core due to continuous refraction, causing curved propagation paths.
Mathematical Expression of Refractive Index
The refractive index of a graded-index fiber is given by:
n(r) = n1 [1 – 2Δ (r/a)α ]1/2
Where:
- a = core radius
- r = radial distance from the fiber axis
- α = refractive index profile parameter
- n1 and n2 = core and cladding refractive indices
When α = 2, the fiber exhibits a parabolic refractive index profile, which provides optimal reduction of modal dispersion.
Graded-Index Multimode Fiber
Multimode fibers support multiple transverse guided modes for a given optical frequency and polarization. The number of supported modes depends on wavelength and the refractive index profile of the fiber.
For step-index fibers, the number of modes is determined by the V-number. At large V values, the number of modes is approximately:
Number of modes ≈ V² / 2
Multimode fibers often have large core diameters and higher numerical aperture (typically 0.2–0.3). This provides strong light-guiding properties even under tight bends but increases scattering losses due to irregularities at the core-cladding boundary.
Common Multimode Fiber Sizes
- 50/125 μm
- 62.5/125 μm
These fibers can support hundreds of guided modes. Larger-core fibers with diameters of several hundred micrometers are also available.
Multimode fibers allow easier light launching due to relaxed alignment tolerances. However, they offer lower spatial coherence and more complex output field patterns compared to single-mode fibers.
Advantages
- Capable of transmitting large amounts of data
- Lower distortion than step-index multimode fibers
Disadvantages
- Lower light-coupling efficiency
- More expensive compared to step-index fibers
Applications
- Used in short-distance, lower-bandwidth applications such as LANs operating at 1 Gbps or less
- Used where reduced modal dispersion is required in multimode systems
- Step-index single-mode fibers are preferred for long-haul, high-bandwidth communication such as carrier backbone networks