Abstract: It is often believed that a fiber amplifier with large core and/or higher NA exhibits stronger ASE. However, this is not true for single-mode amplifiers. The article explains why.
There are models for calculating the power of amplified spontaneous emission (ASE) in a fiber amplifier, which are using a kind of “capture fraction” for spontaneous emission. The idea is simple: spontaneous emission goes in all directions, and only some fraction of the total power, which goes into a certain cone around the fiber axis, will be guided because all other light either has a too large angle of incidence at the core/cladding interface to experience total internal reflection, or simply travels in backward direction. So one expects a higher ASE power for an active fiber with higher numerical aperture (NA), and also for fibers with large core area.
Although all this looks pretty reasonable, the application of such a model to a single-mode fiber is totally wrong, and this is often overlooked. If the fiber is single-mode, and for simplicity we consider a loss-less fiber with a four-level gain medium (as for a neodymium-doped fiber), the power spectral density of ASE depends only on the magnitude of the generated gain. This means that if you slowly increase the core diameter or the NA, the ASE power stays constant as long as single-mode guidance is preserved! At that point, you get a jump in ASE power, as in a multimode fiber the above statement applies to very single mode. As you go to a strongly multimode fiber, you get into a regime where the above-mentioned capture fraction model becomes a good approximation.
So what is the problem with that model in single-mode or few-mode situations? It is of course that effectively one uses a simple ray picture, disregarding the wave nature of light. What also helps is of course a basic knowledge of quantum noise phenomena.
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