located in FOS in Figs. 2.4 and 4.10), two optical harmonics pass on the photodetector area with frequencies ν 0L and ν 0L + f 0 , which strengths are equal, relatively, to:
– First harmonic E 10L t
ð Þ ¼
ffiffiffiffiffi
A 1
p
E 0L cos 2πν 0L t þ φ 0L þ φ 10Lm t
ð Þ
½
,
– Second harmonicE 20L t
ð Þ ¼
ffiffiffiffiffi
A 2
p
E 0L cos 2π ν 0L þ f 0
ð
Þ t þ φ 0L þ φ 20Lm t
ð Þ
½
.
Here A 1 andA 2 , as introduced in Chaps. 2 and 5, show the level of optical
harmonic amplitudes.
In modern MZ modulators (for example, showed in Fig. 6.8b, c) the mutual
modulation of both channels OC1 and OC2 is used. This is possible owing to
existence of the differential phase delay φ 20L À φ 10L ¼ π of optical oscillations E 1L
and E 2L , which propagate in different optical channels OC1 and OC2. Linearly
polarized spatial oscillations in inputs of different optical channels OC1 and OC2
have the phase shift of 180
(Fig. 6.4c).
A modulation in MZ showing in Fig. 6.24b is another type of effective modulation. Two modulators MZ1 and MZ2 (Fig. 6.24b) are located on the single substrate.
Powers of optical emissions E 1MZL , E 2MZL , which pass in MZ1 and MZ2, are
proportional, relatively, to coefficients k 0MZ1 and k 0MZ2 : k 01 ¼ P MZ1 /P 0L and
k 02 ¼ P MZ2 /P 0L , where P MZ1 and P MZ2 are the optical powers in the modulator
MZ1 and MZ2. P 0L is the total optical power in the input before splitting. Optical
emissions modulated in MZ1 and MZ2 modulators pass to the photodetector area.
Statistical averaging at photodetection (Chap. 5) leads to the phase noise decrease of
RF oscillations at level equalization of optical power in MZ1 and MZ2 modulators.
MZ1 and MZ2 are mounted on the single substrate and are excited from the single
laser. Figure 6.24b shows the schematic diagram of the amplitude double modulator
MXIQ-LN-40 of iXBlue Photonics Company. Two sets of RF electrodes RF1 and
RF2 are included in this diagrams, electrodes of the DC bias DC1 and DC2, and
electrodes of DC bias DC3, which regulate the phase difference between emissions
in two modulators MZ1 and MZ2. Figure 5.24с shows the double MZ modulator
from EOspace Company.
Let us examine the diagram in Fig. 6.24a and we show which benefit in RF
oscillations’ phase noise we can obtain in OEO at the double-channel modulation.
We remind, as shown in Chap. 5, the statistical averaging of phase fluctuations of
detected laser noises leads to suppression of phase fluctuations of OEO RF
oscillations.
Phase fluctuations ψ sm1 and ψ Sm2 in Eqs. (6.69) and (6.70) are defined not only by
the laser phase noise but the amplified (in NA and NA1) phase noises of PD (PD or
PD2) and amplified thermal RF noises (in NA). As the result of photodetection by
the external PD2 located outside OEO MZ, we obtain for PSD of the phase noise in
the photo-current of PD2 for OC1 and OC2, relatively from Eqs. (6.67) and (6.68),
two following equations:
336
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
– First harmonic E 10L t
ð Þ ¼
ffiffiffiffiffi
A 1
p
E 0L cos 2πν 0L t þ φ 0L þ φ 10Lm t
ð Þ
½
,
– Second harmonicE 20L t
ð Þ ¼
ffiffiffiffiffi
A 2
p
E 0L cos 2π ν 0L þ f 0
ð
Þ t þ φ 0L þ φ 20Lm t
ð Þ
½
.
Here A 1 andA 2 , as introduced in Chaps. 2 and 5, show the level of optical
harmonic amplitudes.
In modern MZ modulators (for example, showed in Fig. 6.8b, c) the mutual
modulation of both channels OC1 and OC2 is used. This is possible owing to
existence of the differential phase delay φ 20L À φ 10L ¼ π of optical oscillations E 1L
and E 2L , which propagate in different optical channels OC1 and OC2. Linearly
polarized spatial oscillations in inputs of different optical channels OC1 and OC2
have the phase shift of 180
(Fig. 6.4c).
A modulation in MZ showing in Fig. 6.24b is another type of effective modulation. Two modulators MZ1 and MZ2 (Fig. 6.24b) are located on the single substrate.
Powers of optical emissions E 1MZL , E 2MZL , which pass in MZ1 and MZ2, are
proportional, relatively, to coefficients k 0MZ1 and k 0MZ2 : k 01 ¼ P MZ1 /P 0L and
k 02 ¼ P MZ2 /P 0L , where P MZ1 and P MZ2 are the optical powers in the modulator
MZ1 and MZ2. P 0L is the total optical power in the input before splitting. Optical
emissions modulated in MZ1 and MZ2 modulators pass to the photodetector area.
Statistical averaging at photodetection (Chap. 5) leads to the phase noise decrease of
RF oscillations at level equalization of optical power in MZ1 and MZ2 modulators.
MZ1 and MZ2 are mounted on the single substrate and are excited from the single
laser. Figure 6.24b shows the schematic diagram of the amplitude double modulator
MXIQ-LN-40 of iXBlue Photonics Company. Two sets of RF electrodes RF1 and
RF2 are included in this diagrams, electrodes of the DC bias DC1 and DC2, and
electrodes of DC bias DC3, which regulate the phase difference between emissions
in two modulators MZ1 and MZ2. Figure 5.24с shows the double MZ modulator
from EOspace Company.
Let us examine the diagram in Fig. 6.24a and we show which benefit in RF
oscillations’ phase noise we can obtain in OEO at the double-channel modulation.
We remind, as shown in Chap. 5, the statistical averaging of phase fluctuations of
detected laser noises leads to suppression of phase fluctuations of OEO RF
oscillations.
Phase fluctuations ψ sm1 and ψ Sm2 in Eqs. (6.69) and (6.70) are defined not only by
the laser phase noise but the amplified (in NA and NA1) phase noises of PD (PD or
PD2) and amplified thermal RF noises (in NA). As the result of photodetection by
the external PD2 located outside OEO MZ, we obtain for PSD of the phase noise in
the photo-current of PD2 for OC1 and OC2, relatively from Eqs. (6.67) and (6.68),
two following equations:
336
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .