The calculated dependences of the transfer function module shown in Fig. 6.15
are well agreed with the typical experimental characteristics for this class of MZ
modulators, which have the modulation frequency band of 20–35 GHz (Fig. 2.11c in
Chap. 2).
We calculated by Eq. (6.8) (а) and Eq. (6.9) (b) dependences of the module |M eZ |
and the argument argM eZ of the MZ transfer function in the small-signal mode
calculated accordingly by Eqs. (6.8) and (6.9) at for various geometrical length of
electrodes L e ¼ 1000, 3000, 5000 μm and for various loss parameters for
(a) α 1m ¼ 0.27 dB/cm, n M ¼ 2.4, (b) α 1m ¼ 0.41 dB/cm, n M ¼ 3.18, (c) α 1m ¼ 0.68
dB/cm, n M ¼ 4.24. α 1m ¼ 0.27 – 0.68 dB/cm.
From our calculation of the MZ transfer function and the analysis of the plots
presented in Fig. 6.11b, we can make the following conclusion. The growth of the
electrode lengths leads to the rejection character of the function of the module |M eZ |
with clearly expressed minima of the transfer characteristic, which corresponds to
adding of the out-of-phase direct wave and reflected wave from the end boundary of
the strip, and the slope of function argM eZ versus the modulation frequency is
determined by the losses α 1m .
6.4.2 The Total MZ Transfer Function with Account
of the Transfer Function of the Radio-Frequency
Electrodes of MZ
The MZ has the specific feature: its transfer function depends not only on the radiofrequency electrodes (their length, configuration, etc.) but upon the transfer function
of the MZ optical system M Z , which is determined by its differential structure.
In Fig. 3.14a, b (Chap. 3) we show the calculated functions of the module |M Z |
and the argument argM Z versus the phase difference value in the optical channels
OC1 and OC2: 2πν(T 2M À T 1M ) (ν is the laser optical frequency) of the MZ transfer
function (а) for different values of the excitation coefficient k 01 ¼ А ¼ α for
k 02 ¼ В ¼ 1 À А. These functions are calculated by formulas η ¼
Δφ 0M2
U 0MZ L ¼
2πΔn eff
λU 0M
and α ch ¼
Δn ef Re
Δn efIm
¼
2Δφ 0M2
Δα pt L M
. From the plots analysis shown in Fig. 2.14а, we can make
a conclusion that the module |M Z | and the argument argM Z depend upon the
excitation coefficient k 01 . The total MZ transfer function (taking into consideration
of the radio-frequency electrodes and the MZ differential structure) is determined
with the accuracy to the constant coefficient at small-signal modulation:
M ZZ % M Z Á M eZ .
The total transfer function of RF FODL defined as a ratio of the first harmonic
voltage amplitude in the RF FODL output to the amplitude of the first harmonic
voltage in the RF FODL input is determined as:
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
305
are well agreed with the typical experimental characteristics for this class of MZ
modulators, which have the modulation frequency band of 20–35 GHz (Fig. 2.11c in
Chap. 2).
We calculated by Eq. (6.8) (а) and Eq. (6.9) (b) dependences of the module |M eZ |
and the argument argM eZ of the MZ transfer function in the small-signal mode
calculated accordingly by Eqs. (6.8) and (6.9) at for various geometrical length of
electrodes L e ¼ 1000, 3000, 5000 μm and for various loss parameters for
(a) α 1m ¼ 0.27 dB/cm, n M ¼ 2.4, (b) α 1m ¼ 0.41 dB/cm, n M ¼ 3.18, (c) α 1m ¼ 0.68
dB/cm, n M ¼ 4.24. α 1m ¼ 0.27 – 0.68 dB/cm.
From our calculation of the MZ transfer function and the analysis of the plots
presented in Fig. 6.11b, we can make the following conclusion. The growth of the
electrode lengths leads to the rejection character of the function of the module |M eZ |
with clearly expressed minima of the transfer characteristic, which corresponds to
adding of the out-of-phase direct wave and reflected wave from the end boundary of
the strip, and the slope of function argM eZ versus the modulation frequency is
determined by the losses α 1m .
6.4.2 The Total MZ Transfer Function with Account
of the Transfer Function of the Radio-Frequency
Electrodes of MZ
The MZ has the specific feature: its transfer function depends not only on the radiofrequency electrodes (their length, configuration, etc.) but upon the transfer function
of the MZ optical system M Z , which is determined by its differential structure.
In Fig. 3.14a, b (Chap. 3) we show the calculated functions of the module |M Z |
and the argument argM Z versus the phase difference value in the optical channels
OC1 and OC2: 2πν(T 2M À T 1M ) (ν is the laser optical frequency) of the MZ transfer
function (а) for different values of the excitation coefficient k 01 ¼ А ¼ α for
k 02 ¼ В ¼ 1 À А. These functions are calculated by formulas η ¼
Δφ 0M2
U 0MZ L ¼
2πΔn eff
λU 0M
and α ch ¼
Δn ef Re
Δn efIm
¼
2Δφ 0M2
Δα pt L M
. From the plots analysis shown in Fig. 2.14а, we can make
a conclusion that the module |M Z | and the argument argM Z depend upon the
excitation coefficient k 01 . The total MZ transfer function (taking into consideration
of the radio-frequency electrodes and the MZ differential structure) is determined
with the accuracy to the constant coefficient at small-signal modulation:
M ZZ % M Z Á M eZ .
The total transfer function of RF FODL defined as a ratio of the first harmonic
voltage amplitude in the RF FODL output to the amplitude of the first harmonic
voltage in the RF FODL input is determined as:
6.4 Characteristics and the Transfer Function of the MZ Modulator in OEO
305