S 02 ¼ 0.4, a 0 ¼ 0, the double-lobe character of the directional pattern becomes more
expressed.
7.2.5 Plots of the Nonsymmetric Distribution of the Field
in the Far Zone
The case of the nonsymmetric distribution of the permittivity has the specific interest
for practical application. Figure 7.11 shows the functions of the module |E YL0 ( y)|
2
and the phase Φ YL0 ( y) ¼ Arg[E YL0 ( y)] of the function (Eq. 7.32) in the far zone at
nonsymmetric distribution (a 0 6 ¼ 0) at the transverse offset y ¼ k 0 l sin θ.
We should note (Figs. 7.12 and 7.13) that deviations of the symmetry parameter
a 0 of waveguide channels a 0 ¼ 0.2, a 0 ¼ 0.3 from the zero values leads not only to
deviations of the module |E YL0 ( y)|
2 maximum from the axis of y ¼ k 0 l sin θ ¼ 0, but
to the significant deviations of the phase Φ YL0 ( y) ¼ Arg[E YL0 ( y)]. At that, the phase
difference between minimal and maximal values varies from 60
to 120
, relatively,
at a 0 ¼ 0.2 and a 0 ¼ 0.3.
7.2.6 3D Plots of Symmetrical and Nonsymmetrical Field
Distribution in the Far Zone
Functions at symmetrical (a 0 ¼ 0) distribution of the module |E YL0 (x, y)|
2 for the
double-lobe laser directional pattern in the far zone are presented in Fig. 7.13. We
see 3D picture (plots (a–c)), which are calculated from Eq. (7.32) at transverse offset
y ¼ k 0 l sin θ for parameters S 01 ¼ 0.2 Á x, S 02 ¼ À 0.2. For the symmetric case
a 0 ¼ 0, the pictures are presented in Fig. 7.16a, b for different scales. Figure 7.16c
shows 3D picture for the nonsymmetrical case for parameters
S 01 ¼ 0.2 Á x, S 02 ¼ À 0.2.
Figure 7.13 shows possibilities of fields modeling for the complex physical
phenomena in lasers and coupled waveguides. We use the developed theoretical
model of the emission source with the finite dimensions of the emission area. The
case of the laser double-lobe pattern is examined. In the region of values at x ¼ 5, the
beginning of the first maximum formation is observed, while in the region of values
x ¼ À 10, the second maximum is observed and at x ¼ À 15: the small third
maximum. If the symmetry parameter is not equal to zero, in the plot of the contour
lines (Fig. 7.13e), the asymmetric turn of the pedestal by the angle of 30
is
observed.
The functions of |E YL0 (x, y)|
2 (a) and Φ YL0 ( y) ¼ Arg[E YL0 ( y)] (b) in 3D depiction
calculated, and their contour lines of the function (Eq. 7.32) calculated for the
nonsymmetric waveguide at dependence of asymmetry parameters from x or
a 0 ¼ 0.2 Á x at S 01 ¼ 0.4, S 02 ¼ 0.4, |E YL00 |
2
¼ 0.0001.
386
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
expressed.
7.2.5 Plots of the Nonsymmetric Distribution of the Field
in the Far Zone
The case of the nonsymmetric distribution of the permittivity has the specific interest
for practical application. Figure 7.11 shows the functions of the module |E YL0 ( y)|
2
and the phase Φ YL0 ( y) ¼ Arg[E YL0 ( y)] of the function (Eq. 7.32) in the far zone at
nonsymmetric distribution (a 0 6 ¼ 0) at the transverse offset y ¼ k 0 l sin θ.
We should note (Figs. 7.12 and 7.13) that deviations of the symmetry parameter
a 0 of waveguide channels a 0 ¼ 0.2, a 0 ¼ 0.3 from the zero values leads not only to
deviations of the module |E YL0 ( y)|
2 maximum from the axis of y ¼ k 0 l sin θ ¼ 0, but
to the significant deviations of the phase Φ YL0 ( y) ¼ Arg[E YL0 ( y)]. At that, the phase
difference between minimal and maximal values varies from 60
to 120
, relatively,
at a 0 ¼ 0.2 and a 0 ¼ 0.3.
7.2.6 3D Plots of Symmetrical and Nonsymmetrical Field
Distribution in the Far Zone
Functions at symmetrical (a 0 ¼ 0) distribution of the module |E YL0 (x, y)|
2 for the
double-lobe laser directional pattern in the far zone are presented in Fig. 7.13. We
see 3D picture (plots (a–c)), which are calculated from Eq. (7.32) at transverse offset
y ¼ k 0 l sin θ for parameters S 01 ¼ 0.2 Á x, S 02 ¼ À 0.2. For the symmetric case
a 0 ¼ 0, the pictures are presented in Fig. 7.16a, b for different scales. Figure 7.16c
shows 3D picture for the nonsymmetrical case for parameters
S 01 ¼ 0.2 Á x, S 02 ¼ À 0.2.
Figure 7.13 shows possibilities of fields modeling for the complex physical
phenomena in lasers and coupled waveguides. We use the developed theoretical
model of the emission source with the finite dimensions of the emission area. The
case of the laser double-lobe pattern is examined. In the region of values at x ¼ 5, the
beginning of the first maximum formation is observed, while in the region of values
x ¼ À 10, the second maximum is observed and at x ¼ À 15: the small third
maximum. If the symmetry parameter is not equal to zero, in the plot of the contour
lines (Fig. 7.13e), the asymmetric turn of the pedestal by the angle of 30
is
observed.
The functions of |E YL0 (x, y)|
2 (a) and Φ YL0 ( y) ¼ Arg[E YL0 ( y)] (b) in 3D depiction
calculated, and their contour lines of the function (Eq. 7.32) calculated for the
nonsymmetric waveguide at dependence of asymmetry parameters from x or
a 0 ¼ 0.2 Á x at S 01 ¼ 0.4, S 02 ¼ 0.4, |E YL00 |
2
¼ 0.0001.
386
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .