1. At large difference ΔT M ¼ |T 2M À T 1M |, i.e., when this difference is much more
(by 1000 and more times) than the time coherence of the laser T c (and the
oscillation period of the generator), the frequency discriminator plays the role
of the converter of generator frequency into the phase fluctuations:
K 21 ¼ exp (ÀkT 2M À T 1M k/T c ) ! 0.
2. But at small difference T 2M À T 1M , i.e., comparable with the resonator time
constant T OF (and with the oscillation period of the generator), the frequency
discriminator plays the role of the ideal suppressor of phase fluctuations:
K 21 ¼ exp (À|T 2M À T 1M |/T OF ) ! 1. The suppression degree is defined by the
channels equalization accuracy in the optical power or by the irregularity coefficient, which effects on the relative phase delays in the channel transverse section.
In the optical range, the irregularity of the refraction index and microirregularities are deterministic from the point of view on the phase fluctuations’
suppression quality.
We take into consideration that, firstly, the law of the emission intensity variation,
which is passed from the laser to the MZ modulator input in the transverse section, is
closed to the “Gaussian function,” and phase delays of the coherent emission have
the difference phase shift on the transverse section. Moreover, the law of the
difference phase shift’s variation in the transverse section is close to the parabolic
one. Because of inaccuracies of manufacture of the optical waveguide MZ channels
and the spatial variations of the material refraction index at applying in the input of
the X-coupler, optical emissions are nonidentical in the intensity values in the
transverse section and in phase shifts. Because of this, at adding with taking into
account phase shifts in the MZ output, the intensity maximum is shifted. We note
that the intensity of the spontaneous emission passing in the MZ input is by several
ten times less than the coherent emission intensity (approximately, 10
À3 to 10
À4 for
the modern quantum-well laser diodes). The intensity of the spontaneous emission
passed to MZ input is uniformly distributed over the transverse section. Phase
fluctuations of the optical emission are determined by the exactly spontaneous
laser emission. Due to channel irregularities, the ratio in the transverse section of
the spontaneous emission intensity to the coherent emission intensity in the input and
in the output does not coincide. This leads to the imbalance of phase fluctuations’
levels in channels OC1 and OC2. The level of the spontaneous emission in channels
on the transverse section R remains almost unchanged, and the level of the optical
emission intensity P(R) in the transverse section of the optical emission channels
(passed on the PD area) is changed due to irregularities.
Now we can conclude: at nonsymmetry of optical channels (due to irregularity of
the permittivity) of 10
À3 , we can achieve the integral value reduction of the phase
noise in OEO MZ approximately by 40 times. The decrease of the permittivity
irregularity value in MZ channels should lead to larger suppression of the phase
noise.
As we see from Figs. 6.3, 6.4, and 6.6, the planar construction of modern
microwave modulators with the bandwidth up to 15–20 GHz is the bright manifestation of engineering advantages in the field of microwave engineering and in
6.2 The Construction and Operation Principle of OEO MZ
293
(by 1000 and more times) than the time coherence of the laser T c (and the
oscillation period of the generator), the frequency discriminator plays the role
of the converter of generator frequency into the phase fluctuations:
K 21 ¼ exp (ÀkT 2M À T 1M k/T c ) ! 0.
2. But at small difference T 2M À T 1M , i.e., comparable with the resonator time
constant T OF (and with the oscillation period of the generator), the frequency
discriminator plays the role of the ideal suppressor of phase fluctuations:
K 21 ¼ exp (À|T 2M À T 1M |/T OF ) ! 1. The suppression degree is defined by the
channels equalization accuracy in the optical power or by the irregularity coefficient, which effects on the relative phase delays in the channel transverse section.
In the optical range, the irregularity of the refraction index and microirregularities are deterministic from the point of view on the phase fluctuations’
suppression quality.
We take into consideration that, firstly, the law of the emission intensity variation,
which is passed from the laser to the MZ modulator input in the transverse section, is
closed to the “Gaussian function,” and phase delays of the coherent emission have
the difference phase shift on the transverse section. Moreover, the law of the
difference phase shift’s variation in the transverse section is close to the parabolic
one. Because of inaccuracies of manufacture of the optical waveguide MZ channels
and the spatial variations of the material refraction index at applying in the input of
the X-coupler, optical emissions are nonidentical in the intensity values in the
transverse section and in phase shifts. Because of this, at adding with taking into
account phase shifts in the MZ output, the intensity maximum is shifted. We note
that the intensity of the spontaneous emission passing in the MZ input is by several
ten times less than the coherent emission intensity (approximately, 10
À3 to 10
À4 for
the modern quantum-well laser diodes). The intensity of the spontaneous emission
passed to MZ input is uniformly distributed over the transverse section. Phase
fluctuations of the optical emission are determined by the exactly spontaneous
laser emission. Due to channel irregularities, the ratio in the transverse section of
the spontaneous emission intensity to the coherent emission intensity in the input and
in the output does not coincide. This leads to the imbalance of phase fluctuations’
levels in channels OC1 and OC2. The level of the spontaneous emission in channels
on the transverse section R remains almost unchanged, and the level of the optical
emission intensity P(R) in the transverse section of the optical emission channels
(passed on the PD area) is changed due to irregularities.
Now we can conclude: at nonsymmetry of optical channels (due to irregularity of
the permittivity) of 10
À3 , we can achieve the integral value reduction of the phase
noise in OEO MZ approximately by 40 times. The decrease of the permittivity
irregularity value in MZ channels should lead to larger suppression of the phase
noise.
As we see from Figs. 6.3, 6.4, and 6.6, the planar construction of modern
microwave modulators with the bandwidth up to 15–20 GHz is the bright manifestation of engineering advantages in the field of microwave engineering and in
6.2 The Construction and Operation Principle of OEO MZ
293