6.4 Characteristics and the Transfer Function of the MZ
Modulator in OEO
After passage of the optical emission through the modulator and FOS, on the PD
area, two optical emissions will be added, which passed through the MZ modulator
by the first E 1L and the second E 2L optical channels of the MZ modulator and FOS:
E 1L ¼ k 01 E 0L þ m L
ð
Þexp j2πν 0 t þ T 1M þ T FOS
ð
Þ À jφ 0L À jψ m1
½
,
ð6:4Þ
E 2L ¼ k 02 E 0L þ m L
ð
Þexp j2πν 0 t þ T 2M þ T FOS
ð
Þ À jφ 0L À jψ m2
½
:
ð6:5Þ
Excitation coefficients k 01 , k 02 of the first and second modulator channels, in the
general case, are relatively dependent upon the spatial index R and approximately
are: γ ¼ k 01 /k 02 .
Figure 6.9 shows the modulation characteristics of the MZ modulator.
Figure 6.10 shows the experimental functions of the optical power P O (U 0MZ /
U 0MZπ ) (curves 1 and 2 in Fig. 6.10a), the RF power P RF (U 0MZ /U 0MZπ ) on the
frequency f ¼ 10 GHz (curves 3 in (a) versus the DC bias voltage U 0MZ (a)) and
P O (λ) versus laser emission wavelength λ (Fig. 6.10b).
At the bias voltage U 0MZ ¼ U 0MZMIN ¼ U 0MZπ , the phase difference of optical
oscillations propagating via the optical channels OC1 and OC2 is equal to π.
We would like to know that the difference between minimal values of
ΔP OptRF ¼ P O (U 0MZ /U 0MZπ ) À P RF (U 0MZ /U 0MZπ ) % À 20 dB at U 0MZ /U 0MZπ ¼ 1
in Fig. 6.10 (curve 1 and curve 3). The difference ΔP OptRF between minimal values
is the important characteristic of the modulator. This cannot confuse with the
traditional characteristic, which is called the modulator contrast range. The contrast
range is the difference ΔP Opt : ΔP Opt ¼ P Omax À P Omin between maximal P Omax , for
example, at P Omax ¼ P O [(U 0MZ /U 0MZπ ) ¼ 0], and minimal values of P Omin , for
example, at P Omin ¼ P O [(U 0MZ /U 0MZπ ) ¼ 1] of the optimal power in the MZ
modulator output for different DC voltage on MZ. The contrast range ΔP Opt
determines the maximal level of power of the side optical harmonics at RF modulation. ΔP OptRF determines the final benefit as the result of statistical averaging over
fluctuations. As we see from Fig. 6.10, ΔP OptRF for the same type of the modulator
(curves 1 and 2) is by 20 dB lesser than ΔP Opt .
The plot P O (λ) versus the laser emission wavelength λ presented in Fig. 6.10b
gives a possibility to determine the function of the P O (λ) minimum displace at
variation of the DC bias voltage: 3 V/nm.
Figure 6.11a shows the power of RF oscillations P RFPD (P RFMZ ) of “detected”
optical emission in the PD load versus the microwave power P RFMZ in the electrical
input of MZ on the frequency f ¼ 10 GHz.
Experimental functions P RFPD (P RFMZ ) presented in Fig. 6.11a show that the ratio
of PF power P RFPD losses, which are applied to the electrical input of MZ in RF
FODL (which is MZ-FOS-PD), to the oscillation power P RFPD in the PD load is
about À20 dB.
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
299
Modulator in OEO
After passage of the optical emission through the modulator and FOS, on the PD
area, two optical emissions will be added, which passed through the MZ modulator
by the first E 1L and the second E 2L optical channels of the MZ modulator and FOS:
E 1L ¼ k 01 E 0L þ m L
ð
Þexp j2πν 0 t þ T 1M þ T FOS
ð
Þ À jφ 0L À jψ m1
½
,
ð6:4Þ
E 2L ¼ k 02 E 0L þ m L
ð
Þexp j2πν 0 t þ T 2M þ T FOS
ð
Þ À jφ 0L À jψ m2
½
:
ð6:5Þ
Excitation coefficients k 01 , k 02 of the first and second modulator channels, in the
general case, are relatively dependent upon the spatial index R and approximately
are: γ ¼ k 01 /k 02 .
Figure 6.9 shows the modulation characteristics of the MZ modulator.
Figure 6.10 shows the experimental functions of the optical power P O (U 0MZ /
U 0MZπ ) (curves 1 and 2 in Fig. 6.10a), the RF power P RF (U 0MZ /U 0MZπ ) on the
frequency f ¼ 10 GHz (curves 3 in (a) versus the DC bias voltage U 0MZ (a)) and
P O (λ) versus laser emission wavelength λ (Fig. 6.10b).
At the bias voltage U 0MZ ¼ U 0MZMIN ¼ U 0MZπ , the phase difference of optical
oscillations propagating via the optical channels OC1 and OC2 is equal to π.
We would like to know that the difference between minimal values of
ΔP OptRF ¼ P O (U 0MZ /U 0MZπ ) À P RF (U 0MZ /U 0MZπ ) % À 20 dB at U 0MZ /U 0MZπ ¼ 1
in Fig. 6.10 (curve 1 and curve 3). The difference ΔP OptRF between minimal values
is the important characteristic of the modulator. This cannot confuse with the
traditional characteristic, which is called the modulator contrast range. The contrast
range is the difference ΔP Opt : ΔP Opt ¼ P Omax À P Omin between maximal P Omax , for
example, at P Omax ¼ P O [(U 0MZ /U 0MZπ ) ¼ 0], and minimal values of P Omin , for
example, at P Omin ¼ P O [(U 0MZ /U 0MZπ ) ¼ 1] of the optimal power in the MZ
modulator output for different DC voltage on MZ. The contrast range ΔP Opt
determines the maximal level of power of the side optical harmonics at RF modulation. ΔP OptRF determines the final benefit as the result of statistical averaging over
fluctuations. As we see from Fig. 6.10, ΔP OptRF for the same type of the modulator
(curves 1 and 2) is by 20 dB lesser than ΔP Opt .
The plot P O (λ) versus the laser emission wavelength λ presented in Fig. 6.10b
gives a possibility to determine the function of the P O (λ) minimum displace at
variation of the DC bias voltage: 3 V/nm.
Figure 6.11a shows the power of RF oscillations P RFPD (P RFMZ ) of “detected”
optical emission in the PD load versus the microwave power P RFMZ in the electrical
input of MZ on the frequency f ¼ 10 GHz.
Experimental functions P RFPD (P RFMZ ) presented in Fig. 6.11a show that the ratio
of PF power P RFPD losses, which are applied to the electrical input of MZ in RF
FODL (which is MZ-FOS-PD), to the oscillation power P RFPD in the PD load is
about À20 dB.
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
299