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fiber mode

Typically, the intensity distribution of light propagating in an optical fiber changes during propagation. It even often develops in rather complex ways. For example, see what happens if we inject a Gaussian beam (tilted 20° relative to the beam axis) into a fiber with a core radius of 20 μm and an NA of 0.3:

Figure 1: Evolution of strength in a multimode fiber simulated using RP Fiber Power software. Inject a Gaussian beam at an angle of 20° to the beam axis into the light

(Note that here we only show the intensity distribution, since the large spatial region shown makes it difficult to visualize the wavefront.)

The interference effects that occur when the beam reaches the core/cladding interface and is reflected there can be clearly seen. Finally, the transverse beam profile is shown in Figure 2:

Figure 2: Beam profile in fiber after propagation beyond 100 μm.

We have seen that intensity distributions often evolve in complex ways. However, there are certain amplitude distributions (i.e. distributions of electric field magnitudes) where the intensity distribution remains constant during propagation (assuming a lossless fiber). This field distribution is called the mode of the fiber. The simplest of these basic patterns, also known as the LP 01 pattern, is shown below for the fiber in the current example:

Figure 3: Intensity distribution of the fundamental mode in a mode fiber. Gray circles indicate core/cladding boundaries.

This is a higher order mode, the LP 37 mode:

Figure 4: Intensity distribution of the LP 37 mode in a multimode fiber.

As for the fundamental pattern, the natural divergence is exactly offset by the uneven exponential distribution.

Note that especially higher-order modes can have profiles that extend significantly into the cladding.

The figure below shows the amplitude distribution of all guided modes of a fiber, sorted by their mode indices: