Technical Parameters of EDFA
The key parameters that characterize EDFA are defined
below:
saturation power
gain
amplified spontaneous emission power
noise factor
Saturation output power
Formula 018 - determines the maximum output power of the amplifier. A larger
power value allows you to increase the distance of the non-relay section. This
setting varies depending on the model of optical amplifier. For powerful EDFAs,
it can exceed 36 dBm (4 W).
Gain G
The gain is determined from the ratio:
Formula 019
where Formula 020 and Formula 021 are the power (useful) signals at the input
and output of the amplifier, and the logarithmic equivalent is determined by the
formula Formula 022 (dB). The magnitude of the gain depends on the input power
and tend to its maximum limit as the input power decreases.
Amplified spontaneous emission power ASE
In the absence of an input signal, the EDFA is a source of spontaneous emission
of photons. The emission spectrum depends on the shape of the energy band of
erbium atoms and on the statistical distribution of the populations of the zone
levels. Spontaneously formed photons propagating through the fiber in the active
zone of the EDFA amplifier are replicated, resulting in the creation of
secondary photons at the same wavelength, with the same phase, polarization and
direction of propagation. The resulting spectrum of spontaneous photons is
called amplified spontaneous emission. Its power is normalized per 1 Hz and has
a dimension of W / Hz.
If a signal is supplied to the amplifier input from a laser, then a certain
fraction of energy transitions, which previously worked on amplified spontaneous
emission, begins to occur under the influence of a signal from the laser,
amplifying the input signal. Thus, not only the gain of the useful input signal
occurs, but also the attenuation of the ASE.
When a multiplex signal is applied to the input, there is a further outflow of
power from the ASE in favor of amplified multiplex channels. Amplifiers
typically operate in saturation with respect to the output signal. This creates
a natural alignment of signal levels in the channels, which is extremely
desirable especially for long lines with a large number of serial amplifiers.
If the laser preceding the amplifier generates radiation in the spectral window
of Formula 023 (Formula 024, where Formula 025 is the speed of light), and
accordingly the filter in the receiving optoelectronic module passes the signal
in the same window, then the contribution to the noise power at the output is
due to amplified spontaneous emission will be equal to Formula 026. Thus,
optical lines with the cascade of EDFA perform better when the multiplex signal
is represented by spectrally narrower individual channels. The use of
narrow-band filters directly in front of the receiving optoelectronic module
tuned to the operating wavelength also helps to reduce the noise level from
amplified spontaneous emission.
The large intrinsic time constants of EDFA — the time constant of the transition
to the metastable state of ~ 1 μs, the lifetime of the metastable state of ~ 10
μs — eliminate ASE cross-modulation in the amplifier and make the cascade of
optical amplifiers more stable. The power of the amplified spontaneous emission
is related to the gain by the formula:
Noise figure NF
The noise factor is defined as the signal-to-noise ratio at the input () to the
signal-to-noise ratio at the output ():
It is important to note that the input noise power is a quantum-limited minimum
and is determined by zero fluctuations of the vacuum. The output noise power
consists of the sum of the amplified spontaneous emission power and the noise
power of zero vacuum fluctuations that pass through the amplifier without
change:. , then the noise factor can be expressed in terms of the gain and power
of the amplified spontaneous emission:
, (4)
Often when describing EDFA, the noise figure is indicated in dB:. The minimum
noise factor is 1 (0 dB) and is achieved at or at. This means that the amplifier
introduces minimal noise equal to the noise of an ideal optical amplifier. In
practice, it is necessary to immediately increase by 3 dB (), since there are
two directions of polarization (two modes), and therefore, typical values are
5.5 dB.
The closer the noise factor is to 1, the less additional noise the amplifier
makes. At the same time, when using a cascade of several amplifiers, the total
noise factor increases. We find the total noise factor of two amplifiers,
characterized by amplification and noise factors, respectively. The noise output
after two stages is recorded as
where the quantum noise of the vacuum is taken into account, which occurs only
at the output of the amplifier chain, and the signal at the output
whence the total noise factor is equal
As with RF amplifiers, the best way to obtain a device with low noise
characteristics is to use a low noise high gain amplifier as the first stage and
a high power noise amplifier as the second stage. The first stage also
determines the noise response of a multi-stage amplifier.
The power of amplified spontaneous emission is of practical importance when a
useful signal is applied to the EFDA input. Therefore, ASE should be measured
precisely in the presence of such a signal. The analyzer measures the power in
the window (for example, 100 MHz, 50 MHz or less) and is reduced to 1 Hz. Since
the output signal is linearly polarized (its polarization coincides with the
polarization of the signal at the input from the laser), the polarizer can
completely eliminate this component of the useful signal by passing noise only
with normal polarization, which is measured experimentally (first measurement).
Noise, unlike a useful signal, is not polarized, i.e. The total noise takes into
account the contributions from two normal polarizations. The useful signal is
calculated by the formula. Measurement - of the total output signal - occurs
when the axis of the polarizer coincides with the direction of linear
polarization of the useful signal (second measurement). Then, using the
analyzer, the signal power at the input is directly measured, that is, the
signal in the absence of an amplifier (third measurement). Now you can determine
the gain