Editing Optical amplifier (section)

=== Doped-fiber amplifiers ===
[[Image:Doped fibre amplifier.svg|thumb|right|300px|Schematic diagram of a simple doped-fiber amplifier]]
'''Doped-fiber amplifiers''' (DFAs) are optical amplifiers that use a [[dopant|doped]] [[optical fiber]] as a gain medium to amplify an optical signal.<ref name="pears1">{{cite book|last1=Pearsall|first1=Thomas|title=Photonics Essentials, 2nd edition|publisher=McGraw-Hill|date=2010|url=https://www.mheducation.com/highered/product/photonics-essentials-second-edition-pearsall/9780071629355.html|isbn=978-0-07-162935-5|access-date=2021-02-24|archive-date=2021-08-17|archive-url=https://web.archive.org/web/20210817005021/https://www.mheducation.com/highered/product/photonics-essentials-second-edition-pearsall/9780071629355.html|url-status=dead}}</ref> They are related to [[fiber laser]]s. The signal to be amplified and a pump laser are [[multiplexing|multiplexed]] into the doped fiber, and the signal is amplified through interaction with the doping [[ions]].

Amplification is achieved by stimulated emission of photons from dopant ions in the doped fiber. The pump laser excites ions into a higher energy from where they can decay via stimulated emission of a photon at the signal wavelength back to a lower energy level. The excited ions can also decay spontaneously (spontaneous emission) or even through nonradiative processes involving interactions with [[phonon]]s of the glass matrix. These last two decay mechanisms compete with stimulated emission reducing the efficiency of light amplification.

The ''amplification window'' of an optical amplifier is the range of optical wavelengths for which the amplifier yields a usable gain. The amplification window is determined by the spectroscopic properties of the dopant ions, the glass structure of the optical fiber, and the wavelength and power of the pump laser.

Although the electronic transitions of an isolated ion are very well defined, broadening of the energy levels occurs when the ions are incorporated into the glass of the optical fiber and thus the amplification window is also broadened. This broadening is both [[Homogeneous broadening|homogeneous]] (all ions exhibit the same broadened spectrum) and [[Inhomogeneous broadening|inhomogeneous]] (different ions in different glass locations exhibit different spectra). Homogeneous broadening arises from the interactions with [[phonon]]s of the glass, while inhomogeneous broadening is caused by differences in the glass sites where different ions are hosted. Different sites expose ions to different local electric fields, which shifts the energy levels via the [[Stark effect]]. In addition, the Stark effect also removes the degeneracy of energy states having the same total angular momentum (specified by the quantum number J). Thus, for example, the trivalent erbium ion (Er<sup>3+</sup>) has a ground state with J = 15/2, and in the presence of an electric field splits into J + 1/2 = 8 sublevels with slightly different energies. The first excited state has J = 13/2 and therefore a Stark manifold with 7 sublevels. Transitions from the J = 13/2 excited state to the J= 15/2 ground state are responsible for the gain at 1500&nbsp;nm wavelength. The gain spectrum of the EDFA has several peaks that are smeared by the above broadening mechanisms. The net result is a very broad spectrum (30&nbsp;nm in silica, typically). The broad gain-bandwidth of fiber amplifiers make them particularly useful in [[wavelength-division multiplexing|wavelength-division multiplexed]] communications systems as a single amplifier can be utilized to amplify all signals being carried on a fiber and whose wavelengths fall within the gain window.

An ''[[erbium-doped waveguide amplifier]]'' (EDWA) is an optical amplifier that uses a [[waveguide]] to boost an optical signal.

====Basic principle of EDFA====
A relatively high-powered beam of light is mixed with the input signal using a wavelength selective coupler (WSC). The input signal and the excitation light must be at significantly different wavelengths. The mixed light is guided into a section of fiber with erbium ions included in the core. This high-powered light beam excites the erbium ions to their higher-energy state. When the photons belonging to the signal at a different wavelength from the pump light meet the excited erbium ions, the erbium ions undergo stimulated emission and return to their lower-energy state.

A significant point is that the erbium gives up its energy in the form of additional photons which are exactly in the same phase and direction as the signal being amplified. So the signal is amplified along its direction of travel only. This is not unusual – when an atom "lases" it always gives up its energy in the same direction and phase as the incoming light. Thus all of the additional signal power is guided in the same fiber mode as the incoming signal. An [[optical isolator]] is usually placed at the output to prevent reflections returning from the attached fiber. Such reflections disrupt amplifier operation and in the extreme case can cause the amplifier to become a laser.

The erbium doped amplifier is a high gain amplifier.

====Noise====
The principal source of noise in DFAs is [[Amplified Spontaneous Emission|amplified spontaneous emission]] (ASE), which has a spectrum approximately the same as the gain spectrum of the amplifier. [[Noise figure]] in an ideal DFA is 3&nbsp;dB, while practical amplifiers can have noise figure as large as 6–8&nbsp;dB.

As well as decaying via stimulated emission, electrons in the upper energy level can also decay by spontaneous emission, which occurs at random, depending upon the glass structure and inversion level. Photons are emitted spontaneously in all directions, but a proportion of those will be emitted in a direction that falls within the [[numerical aperture]] of the fiber and are thus captured and guided by the fiber. Those photons captured may then interact with other dopant ions, and are thus amplified by stimulated emission. The initial spontaneous emission is therefore amplified in the same manner as the signals, hence the term a''mplified spontaneous emission''. ASE is emitted by the amplifier in both the forward and reverse directions, but only the forward ASE is a direct concern to system performance since that noise will co-propagate with the signal to the receiver where it degrades system performance. Counter-propagating ASE can, however, lead to degradation of the amplifier's performance since the ASE can deplete the inversion level and thereby reduce the gain of the amplifier and increase the noise produced relative to the desired signal gain.
 
Noise figure can be analyzed in both the optical domain and in the electrical domain.<ref>Baney, Douglas, M., Gallion, Philippe, Tucker, Rodney S., ”Theory and Measurement Techniques for the Noise Figure of Optical Amplifiers”, Optical Fiber Technology 6, 122 pp. 122-154 (2000)</ref> In the optical domain, measurement of the ASE, the optical signal gain, and signal wavelength using an optical spectrum analyzer permits calculation of the noise figure. For the electrical measurement method, the detected photocurrent noise is evaluated with a low-noise electrical spectrum analyzer, which along with measurement of the amplifier gain permits a noise figure measurement. Generally, the optical technique provides a more simple method, though it is not inclusive of excess noise effects captured by the electrical method such multi-path interference (MPI) noise generation. In both methods, attention to effects such as the spontaneous emission accompanying the input signal are critical to accurate measurement of noise figure.

====Gain saturation====
Gain is achieved in a DFA due to [[population inversion]] of the dopant ions. The inversion level of a DFA is set, primarily, by the power of the pump wavelength and the power at the amplified wavelengths. As the signal power increases, or the pump power decreases, the inversion level will reduce and thereby the gain of the amplifier will be reduced. This effect is known as gain saturation – as the signal level increases, the amplifier saturates and cannot produce any more output power, and therefore the gain reduces. Saturation is also commonly known as gain compression.

To achieve optimum noise performance DFAs are operated under a significant amount of gain compression (10&nbsp;dB typically), since that reduces the rate of spontaneous emission, thereby reducing ASE. Another advantage of operating the DFA in the gain saturation region is that small fluctuations in the input signal power are reduced in the output amplified signal: smaller input signal powers experience larger (less saturated) gain, while larger input powers see less gain.

The leading edge of the pulse is amplified, until the saturation energy of the gain medium is reached. In some condition, the width ([[FWHM]]) of the pulse is reduced.<ref name="Tutorial on Fiber Amplifiers">{{cite web|last=Paschotta|first=Rüdiger| title=Tutorial on Fiber Amplifiers| url=http://www.rp-photonics.com/tutorial_fiber_amplifiers.html| publisher=RP Photonics| access-date=10 October 2013}}</ref>

====Inhomogeneous broadening effects====
Due to the inhomogeneous portion of the linewidth broadening of the dopant ions, the gain spectrum has an inhomogeneous component and gain saturation occurs, to a small extent, in an inhomogeneous manner. This effect is known as ''[[spectral hole burning]]'' because a high power signal at one wavelength can 'burn' a hole in the gain for wavelengths close to that signal by saturation of the inhomogeneously broadened ions. Spectral holes vary in width depending on the characteristics of the optical fiber in question and the power of the burning signal, but are typically less than 1&nbsp;nm at the short wavelength end of the C-band, and a few nm at the long wavelength end of the C-band. The depth of the holes are very small, though, making it difficult to observe in practice.

====Polarization effects====
Although the DFA is essentially a polarization independent amplifier, a small proportion of the dopant ions interact preferentially with certain polarizations and a small dependence on the polarization of the input signal may occur (typically < 0.5&nbsp;dB). This is called polarization dependent gain (PDG).

The absorption and emission cross sections of the ions can be modeled as ellipsoids with the major axes aligned at random in all directions in different glass sites. The random distribution of the orientation of the ellipsoids in a glass produces a macroscopically isotropic medium, but a strong pump laser induces an anisotropic distribution by selectively exciting those ions that are more aligned with the optical field vector of the pump. Also, those excited ions aligned with the signal field produce more stimulated emission. The change in gain is thus dependent on the alignment of the polarizations of the pump and signal lasers – i.e. whether the two lasers are interacting with the same sub-set of dopant ions or not. 
In an ideal doped fiber without [[birefringence]], the PDG would be inconveniently large. Fortunately, in optical fibers small amounts of birefringence are always present and, furthermore, the fast and slow axes vary randomly along the fiber length. A typical DFA has several tens of meters, long enough to already show this randomness of the birefringence axes. These two combined effects (which in transmission fibers give rise to [[polarization mode dispersion]]) produce a misalignment of the relative polarizations of the signal and pump lasers along the fiber, thus tending to average out the PDG. The result is that PDG is very difficult to observe in a single amplifier (but is noticeable in links with several cascaded amplifiers).