7.2 The Model of the Dielectric Waveguide Structure
of the Laser and the Optical Channel
One of the main differences of modulators of the optical range from the RF
modulators is the adequacy of the optical wavelength with the transverse dimensions
of optical channels. We can often forget about this difference and represent the ideal
model of the optical device without speaking about spatial distribution of the optical
field. The numerical modeling of MZ optical channels with account of spatial
channel dimensions shows that the wave propagating through the optical channel
cannot be considered as the plane wave. In the transverse section, not only the
intensity or the power of emission varies nonuniformly, but the optical phase as well.
At that, variations of the optical phase achieves from 100
to 300
depending on the
type of the optical channel, its length and irregularity.
Further, we consider the spatial model of the waveguide structure of the laser and
the optical channel.
Deriving of the formulas for amplitude and phase calculation of RF oscillations in
OEO MZ from the abbreviated equations (Fig. 7.1a) is performed in Chaps. 3 and 5.
In these formulas, there are the module and the argument of the MZ transfer function.
At variation of the module and the argument of the MZ transfer function, the
amplitude and the frequency of MZ will oscillate. To take into consideration the
influence on the module and the MZ transfer function of the symmetry disturbances
in the transverse section, we form and analyze the model of the dielectric waveguide
structure of the laser and the optical channel of the MZ modulator.
Figure 7.5a, b shows the structure of OEO MZ on the base of Y- and X-optical
couplers with the spatial filter SF (a), the structure of OEO MZ with dividing optical
plates (mirrors) and the spatial filter (“M” is the lens).
The one of the aims of investigations in this section is studying of the effect of the
optical channel asymmetry upon the amplitude square and the phase shift in the
transverse section in the MZ output. The asymmetry in the waveguide optical
channels, as shown below, exposes the essential influence on the distribution of
the amplitude and the phase of oscillations not only in the transverse section of the
separated channel ОC-1 or ОC-2. The waveguide asymmetry is the reason of the
asymmetric distribution of the amplitude square (or intensity) after summation of the
output emissions in the near and far zone on the photodetector area. The presence of
the waveguide channel asymmetry in MZ is the one of reasons of the nonzero level
of DC of the optical emission on the PD.
Figure 7.5c–f shows the spatial pictures of the amplitude square of the electromagnetic field in the transverse section in the output of the MZ modulator, after
summation of two optical oscillations passed via OC-1 and OC-2 optical channels of
MZ (Fig. 7.5a, b). In Fig. 7.5c, we see results of the structural equation modeling and
patterns of the contour lines of the amplitude square of the electromagnetic field in
the transverse section in the output of the MZ modulator in the case of the full
symmetry of waveguide channels, and in Fig. 7.5d–f we see similar results of the
structural equation modeling and patterns of contour lines in the case of the asymmetry of waveguide channels. So, Fig. 7.5d–f show that due to asymmetry of
7.2 The Model of the Dielectric Waveguide Structure of the Laser and the Optical. . .
375
of the Laser and the Optical Channel
One of the main differences of modulators of the optical range from the RF
modulators is the adequacy of the optical wavelength with the transverse dimensions
of optical channels. We can often forget about this difference and represent the ideal
model of the optical device without speaking about spatial distribution of the optical
field. The numerical modeling of MZ optical channels with account of spatial
channel dimensions shows that the wave propagating through the optical channel
cannot be considered as the plane wave. In the transverse section, not only the
intensity or the power of emission varies nonuniformly, but the optical phase as well.
At that, variations of the optical phase achieves from 100
to 300
depending on the
type of the optical channel, its length and irregularity.
Further, we consider the spatial model of the waveguide structure of the laser and
the optical channel.
Deriving of the formulas for amplitude and phase calculation of RF oscillations in
OEO MZ from the abbreviated equations (Fig. 7.1a) is performed in Chaps. 3 and 5.
In these formulas, there are the module and the argument of the MZ transfer function.
At variation of the module and the argument of the MZ transfer function, the
amplitude and the frequency of MZ will oscillate. To take into consideration the
influence on the module and the MZ transfer function of the symmetry disturbances
in the transverse section, we form and analyze the model of the dielectric waveguide
structure of the laser and the optical channel of the MZ modulator.
Figure 7.5a, b shows the structure of OEO MZ on the base of Y- and X-optical
couplers with the spatial filter SF (a), the structure of OEO MZ with dividing optical
plates (mirrors) and the spatial filter (“M” is the lens).
The one of the aims of investigations in this section is studying of the effect of the
optical channel asymmetry upon the amplitude square and the phase shift in the
transverse section in the MZ output. The asymmetry in the waveguide optical
channels, as shown below, exposes the essential influence on the distribution of
the amplitude and the phase of oscillations not only in the transverse section of the
separated channel ОC-1 or ОC-2. The waveguide asymmetry is the reason of the
asymmetric distribution of the amplitude square (or intensity) after summation of the
output emissions in the near and far zone on the photodetector area. The presence of
the waveguide channel asymmetry in MZ is the one of reasons of the nonzero level
of DC of the optical emission on the PD.
Figure 7.5c–f shows the spatial pictures of the amplitude square of the electromagnetic field in the transverse section in the output of the MZ modulator, after
summation of two optical oscillations passed via OC-1 and OC-2 optical channels of
MZ (Fig. 7.5a, b). In Fig. 7.5c, we see results of the structural equation modeling and
patterns of the contour lines of the amplitude square of the electromagnetic field in
the transverse section in the output of the MZ modulator in the case of the full
symmetry of waveguide channels, and in Fig. 7.5d–f we see similar results of the
structural equation modeling and patterns of contour lines in the case of the asymmetry of waveguide channels. So, Fig. 7.5d–f show that due to asymmetry of
7.2 The Model of the Dielectric Waveguide Structure of the Laser and the Optical. . .
375