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Definition: a quantitative measure of the area which a waveguide or fiber mode effectively covers in the transverse dimensions
Modes of fibers or other waveguides have smooth transverse profiles where the definition of a mode area is not straightforward, particularly for complicated mode shapes where e.g. some 1/e2 intensity criterion as for Gaussian beams is not sensible. A useful definition for the effective mode area is
where E is the electric field amplitude and I is the optical intensity. For a Gaussian beam with radius w, the effective area is π w2, and the same equation is valid for relating the mode area to the effective mode radius. The equation would also hold for a rectangular (step-index) intensity profile with radius w.
Figure 1: A Gaussian mode and a rectangular profile with the same effective mode area.
Figure 1 shows a Gaussian mode and a rectangular profile with the same effective mode area. For the same optical power, the Gaussian mode has twice the peak intensity.
For a higher-order mode of a fiber (Figure 2), the intensity peaks are substantially higher than for the rectangular profile.
Figure 2: A higher-order mode (LP03) of a fiber and a rectangular profile with the same effective mode area.
From the effective mode area and the nonlinear index n2, one can calculate the nonlinear phase shift resulting from the Kerr effect:
where P is the optical power and L is the length of the medium. Note that this phase shift applies to the whole mode area, rather than e.g. only to the point with highest intensity, as the waveguide effect prevents the build-up of any significant transverse variations of the optical phase.
Typical single-mode fibers, as used e.g. for optical fiber communications, have effective mode areas of the order of 100 μm2. Large mode area fibers have several times higher mode areas, sometimes even above 1000 μm2. On the other hand, there are some photonic crystal fibers with mode areas below 10 μm2.
An important consequence of a small mode area is that the optical intensities for a given power level are high, so that nonlinearities become important. Also, small mode areas are usually the consequence of strong guiding, where bend losses and other effects of external disturbances are weak.
Note that the article on mode radius contains an equation that can be used for calculating the mode radius (and thus the effective mode area) for a step-index fiber.
See also: fibers, single-mode fibers, waveguides, modes, mode radius
Category: fibers and other waveguides
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