An Erbium Doped Fiber Amplifier (EDFA) consists of a piece of fiber of length L, whose core is uniformly doped with Erbium ions. Such ions can be thought of as simple two-level systems, i.e., they can have only two energy states: 1) a fundamental state and 2) an excited state.

A strong ``pump'' laser light at the proper wavelength (usually 980 nm or 1480 nm) is propagated into the core of the fiber in order to excite its ions.

Excited ions, when ``hit'' by an input ``signal'' photon, have a certain probability (depending on the wavelength of the input photon) of releasing by stimulated emission a photon identical to the hitting one. The release of the energy of the stimulated photon brings the excited ion to its fundamental state.

Hence from one input ``signal'' photon we can obtain, by an avalanche process along the fiber core, an average of G photons at the fiber output, i.e., the signal photon has been amplified by a factor G, known as the Gain.

Since the probability of stimulated emission depends on the photon wavelength, so does the Gain.

The Gain clearly also depends on the total number of excited ions in the fiber, since the more the ions, the larger the average number of stimulated emissions per input photon.

In Optical Communication systems based on Wavelength Division Multiplexing, N signal laser beams at N different wavelengths (each carrying modulated user information) are coupled into the EDFA and propagate down the fiber along with the pump. While the pump ``loses'' photons to excite the ions as it propagates, the signals stimulate emission from the excited ions and ``gain'' photons

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