5.4 Fluctuation Differential Equations of OEO
with the Langevinian Noise Sources
We described in detail in Sects. 5.1 and 5.2 the calculation procedure of the OEO
DM and OEO MZ steady-state mode. Now we transfer to the fluctuation analysis of
the oscillation amplitude and phase of OEO.
Under influence of noises of the laser active element, the deviations of amplitude
and phase arise in OEO from the steady-state values. Before the start of the analysis,
we describe the main positions of the fluctuation model of the laser.
5.4.1 Main Regulations of the Fluctuation Laser Model
and Langevinian Noise Sources
The semiclassical laser theory considered in Chap. 3 leads to the deterministic
motion equation for the field amplitude, and the problems concerning the spectral
line width and fluctuations remain beyond the scope of this theory. Noises in
differential equations can be taken into consideration by means of introduction of
Langevinian noise sources, which is the procedure for which it is not easy to find the
strict substantiation and the truth of which can be justified, to a great extent, by the
coordination with other approaches. One of such approaches is the quantum-field
approach, which is not used here, but it serves as the more consistent basis for the
laser theory. It permits to answer of questions, which are not defined within the limits
of the semiclassical theory, for instance, how much photons do exist at the threshold? Our task includes the investigation of OEO operation at large amplitudes of
laser oscillation within the limits of semiclassical laser theory taking into account
fluctuations.
The main regulations of the fluctuation model of the laser adopted at the OEO
analysis can be formulated in the form of ten points, which are discussed below:
1. The random fluctuations of the oscillation phase of the laser optical emission are
the main reason of laser spectral line widening.
2. The laser has the narrow spectral line and the high temperature stability.
3. Fluctuations of the laser field are caused by the spontaneous emission.
4. Owing to the relatively high average power, which falls on the PD area, and the
large number of the random acts of spontaneous emission (according to the
central limit theorem), the probability density has (in magnitude) the Gaussian
or normal distribution law. The small value of phase fluctuations allows the
linearization of the fluctuation equations. The equation for the field phase
becomes similar to the equation for the random wandering under an impact of
the Gaussian random Langevinian forces.
5. The distribution density of the phase increments of the laser emission has the
Gaussian law.
5.4 Fluctuation Differential Equations of OEO with the Langevinian Noise Sources
233
with the Langevinian Noise Sources
We described in detail in Sects. 5.1 and 5.2 the calculation procedure of the OEO
DM and OEO MZ steady-state mode. Now we transfer to the fluctuation analysis of
the oscillation amplitude and phase of OEO.
Under influence of noises of the laser active element, the deviations of amplitude
and phase arise in OEO from the steady-state values. Before the start of the analysis,
we describe the main positions of the fluctuation model of the laser.
5.4.1 Main Regulations of the Fluctuation Laser Model
and Langevinian Noise Sources
The semiclassical laser theory considered in Chap. 3 leads to the deterministic
motion equation for the field amplitude, and the problems concerning the spectral
line width and fluctuations remain beyond the scope of this theory. Noises in
differential equations can be taken into consideration by means of introduction of
Langevinian noise sources, which is the procedure for which it is not easy to find the
strict substantiation and the truth of which can be justified, to a great extent, by the
coordination with other approaches. One of such approaches is the quantum-field
approach, which is not used here, but it serves as the more consistent basis for the
laser theory. It permits to answer of questions, which are not defined within the limits
of the semiclassical theory, for instance, how much photons do exist at the threshold? Our task includes the investigation of OEO operation at large amplitudes of
laser oscillation within the limits of semiclassical laser theory taking into account
fluctuations.
The main regulations of the fluctuation model of the laser adopted at the OEO
analysis can be formulated in the form of ten points, which are discussed below:
1. The random fluctuations of the oscillation phase of the laser optical emission are
the main reason of laser spectral line widening.
2. The laser has the narrow spectral line and the high temperature stability.
3. Fluctuations of the laser field are caused by the spontaneous emission.
4. Owing to the relatively high average power, which falls on the PD area, and the
large number of the random acts of spontaneous emission (according to the
central limit theorem), the probability density has (in magnitude) the Gaussian
or normal distribution law. The small value of phase fluctuations allows the
linearization of the fluctuation equations. The equation for the field phase
becomes similar to the equation for the random wandering under an impact of
the Gaussian random Langevinian forces.
5. The distribution density of the phase increments of the laser emission has the
Gaussian law.
5.4 Fluctuation Differential Equations of OEO with the Langevinian Noise Sources
233