suppressing coefficient G 12 , the physical sense of which is opened by the mechanism
of “statistical” noise suppression at self-heterodyning in the Mach–Zehnder interferometer. The coefficient G 12 ¼ 1 À (A 1 /A 2 ) Á exp (ÀT FOS /T c ) is lesser for the
higher time and spatial coherence of the laser and for lesser the difference of two MZ
optical channels in the difference of refraction indices of the core and the envelope
and in overall sizes of channels. The growth of the laser power, as we see from
Eq. (6.68), leads to the decrease of PSD of the phase noise in OEO MZ not only due
to the reduction of coefficients K
2
ΓPN Á K
2
PD , K
2
ΓPN , but is determined by the third term
in expression (6.68). The delay growth T FOS in RF FODL with the single optical
fiber at increase of the geometrical FOS length in OEO MZ leads to reduction of PSD
of the phase noise, but as we see from Eq. (6.68), this reduction is defined by the term
in the denominator equaled to (1 + σ U ) cos [FT FOS ] and therefore, this decrease is
restricted and is, as a rule, not more than 8–11 dB/Hz.
PSD of the phase noise in OEO MZ significantly decreases at utilization of the
so-called “two-arms” or the mutual microwave modulation of refraction index in two
optical channels of MZ modulator.
6.5.12 Modulations of Two Channels in MZ
We can significantly reduce of PSD of the phase noise in OEO MZ by using at
optical phase modulation in both optical channels of the MZ interferometer. At that,
the relative phase shift in radio frequency between channel electrodes is 90–180
.
Figure 6.24a shows the structure of OEO MZ with the external PD at modulation
of MZ in both optical channels. Besides the modulation circuit in both channels of
the single MZ modulator, at present, we can use commercially available modulators,
in which the modulation methods in different optical channels are used, which are
included in different MZ.
Let us consider the calculation features of PSD of the phase noise in this case,
taking into account the noises of the laser, PD and NA. In PD area, the components
passed the MZ modulator through the first E 1L ¼ E 1L (R) and the second E 2L ¼ E 2L (R)
optical channels of MZ and FOS, have a form (Fig. 6.24a):
E 1L ¼ k 01 E 0L þ m SL
ð
ÞRe exp j2πν 0 t þ T M1 þ T FOS
ð
Þ À jφ 10L À jψ sm1
½
f
g ,
ð6:69Þ
E 2L ¼ k 02 E 0L þ m SL
ð
Þexp j2πν 0 t þ T M2 þ T FOS
ð
Þ À jφ 20L À jψ Sm2
½
, ð6:70Þ
where m SL are fluctuations of the electrical component strength amplitude of EMF,
ψ sm1 and ψ Sm2 are fluctuations of the optical phase of the electrical component
strength in the output of first and second optical channels of FOS, k 01 and k 02 is the
excitation coefficients of the optical channel OC1 and OC2 in the MZ modulator. At
RF modulation, as shown in Chap. 5, in OEO MZ after the optical filter (which is
334
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
of “statistical” noise suppression at self-heterodyning in the Mach–Zehnder interferometer. The coefficient G 12 ¼ 1 À (A 1 /A 2 ) Á exp (ÀT FOS /T c ) is lesser for the
higher time and spatial coherence of the laser and for lesser the difference of two MZ
optical channels in the difference of refraction indices of the core and the envelope
and in overall sizes of channels. The growth of the laser power, as we see from
Eq. (6.68), leads to the decrease of PSD of the phase noise in OEO MZ not only due
to the reduction of coefficients K
2
ΓPN Á K
2
PD , K
2
ΓPN , but is determined by the third term
in expression (6.68). The delay growth T FOS in RF FODL with the single optical
fiber at increase of the geometrical FOS length in OEO MZ leads to reduction of PSD
of the phase noise, but as we see from Eq. (6.68), this reduction is defined by the term
in the denominator equaled to (1 + σ U ) cos [FT FOS ] and therefore, this decrease is
restricted and is, as a rule, not more than 8–11 dB/Hz.
PSD of the phase noise in OEO MZ significantly decreases at utilization of the
so-called “two-arms” or the mutual microwave modulation of refraction index in two
optical channels of MZ modulator.
6.5.12 Modulations of Two Channels in MZ
We can significantly reduce of PSD of the phase noise in OEO MZ by using at
optical phase modulation in both optical channels of the MZ interferometer. At that,
the relative phase shift in radio frequency between channel electrodes is 90–180
.
Figure 6.24a shows the structure of OEO MZ with the external PD at modulation
of MZ in both optical channels. Besides the modulation circuit in both channels of
the single MZ modulator, at present, we can use commercially available modulators,
in which the modulation methods in different optical channels are used, which are
included in different MZ.
Let us consider the calculation features of PSD of the phase noise in this case,
taking into account the noises of the laser, PD and NA. In PD area, the components
passed the MZ modulator through the first E 1L ¼ E 1L (R) and the second E 2L ¼ E 2L (R)
optical channels of MZ and FOS, have a form (Fig. 6.24a):
E 1L ¼ k 01 E 0L þ m SL
ð
ÞRe exp j2πν 0 t þ T M1 þ T FOS
ð
Þ À jφ 10L À jψ sm1
½
f
g ,
ð6:69Þ
E 2L ¼ k 02 E 0L þ m SL
ð
Þexp j2πν 0 t þ T M2 þ T FOS
ð
Þ À jφ 20L À jψ Sm2
½
, ð6:70Þ
where m SL are fluctuations of the electrical component strength amplitude of EMF,
ψ sm1 and ψ Sm2 are fluctuations of the optical phase of the electrical component
strength in the output of first and second optical channels of FOS, k 01 and k 02 is the
excitation coefficients of the optical channel OC1 and OC2 in the MZ modulator. At
RF modulation, as shown in Chap. 5, in OEO MZ after the optical filter (which is
334
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .