of the optical carrier frequency 128 THz to the frequency of the microwave
subcarrier of 10 GHz, which is 12,800. Obtaining in OEO on the microwave
subcarrier of 10 GHz of PSD of the phase noise less than À120 dB/Hz for offset
1 kHz is quite realizable.
2.5 OEO with Self-Heterodyne Mixing as the Oscillator
Containing the Phase Fluctuation Correlator
in the Feedback Loop
OEO with the direct and external modulation has a following feature: at application
of two optical fibers or two optical channels (as in the case of OEO with the MZ
modulator) and arrangement of optical filters, the suppression of the one harmonic
happens together with alignment of undepressed harmonic amplitudes with the help
of attenuators. In this case, OEO with RF FODL of such a type contains the
frequency discriminator or a correlator (Fig. 2.4a). The frequency discriminator
method is applied in radio electronics and optoelectronics to measure the phase
noise and laser spectra. This method is a version of the phase detector method with
the difference that here we need not the reference source. Figure 2.4a illustrates the
principle of the frequency discriminator method, which uses a delay line. Here, the
signal from the generator G is divided into two channels. The signal of the one
channel is delayed with the respect of the second channel by the time ΔT M ¼ |
T 2M À T 1M |. The delay line transforms the frequency fluctuations into phase fluctuations. The quadrature phase shift of signals passed to inputs of the mixer (phasedetector) (i.e., the 90
-phase shift between oscillations in channels) is settled by
adjustment of the delay line or the phase shifter.
Then the phase detector transforms the phase fluctuations into the voltage fluctuations, which can be further interpreted by the spectrum analyzer in the bandwidth
of the modulating signal as the frequency noise. The frequency noise is then
transformed into phase noise values of the device under consideration. This method
is perfectly used for the LC oscillators or the cavity oscillators [25–30].
OEO, shown in Figs. 2.1, 2.2, and 2.3 includes the above-mentioned circuit
(Fig. 2.4), which illustrates operation principles of the correlator and the frequency
discriminator methods. The laser is used as the reference generator in OEO, the
optical fiber or channels in the MZ modulator is used as the delay line, the
photodetector is used as the phase detector.
At small relative delays in Figs. 2.1, 2.2, and 2.3, the phase dispersion σ
2
PD at
output of the phase detector (or in the photocurrent of the photodetector) is
determined as σ
2
PD ¼ σ
2
1L þ σ
2
1L À 2
A 2
A 1
K 21 σ 1L σ 2L , where σ
2
1L , σ
2
2L are dispersions
of the optical phase fluctuations, relatively, at input of optical channels OC1 and
OC2, K 21 is the auto-correlation function of the random process K 21 % exp
(À2Δν L Á ΔT M ) ¼ exp(À2ΔT M /T c ), Δν L % 1/T c is the natural width of the
spectral line of the reference generator (a laser) emission, T c is the time of laser
2.5 OEO with Self-Heterodyne Mixing as the Oscillator Containing the Phase. . .
31
subcarrier of 10 GHz, which is 12,800. Obtaining in OEO on the microwave
subcarrier of 10 GHz of PSD of the phase noise less than À120 dB/Hz for offset
1 kHz is quite realizable.
2.5 OEO with Self-Heterodyne Mixing as the Oscillator
Containing the Phase Fluctuation Correlator
in the Feedback Loop
OEO with the direct and external modulation has a following feature: at application
of two optical fibers or two optical channels (as in the case of OEO with the MZ
modulator) and arrangement of optical filters, the suppression of the one harmonic
happens together with alignment of undepressed harmonic amplitudes with the help
of attenuators. In this case, OEO with RF FODL of such a type contains the
frequency discriminator or a correlator (Fig. 2.4a). The frequency discriminator
method is applied in radio electronics and optoelectronics to measure the phase
noise and laser spectra. This method is a version of the phase detector method with
the difference that here we need not the reference source. Figure 2.4a illustrates the
principle of the frequency discriminator method, which uses a delay line. Here, the
signal from the generator G is divided into two channels. The signal of the one
channel is delayed with the respect of the second channel by the time ΔT M ¼ |
T 2M À T 1M |. The delay line transforms the frequency fluctuations into phase fluctuations. The quadrature phase shift of signals passed to inputs of the mixer (phasedetector) (i.e., the 90
-phase shift between oscillations in channels) is settled by
adjustment of the delay line or the phase shifter.
Then the phase detector transforms the phase fluctuations into the voltage fluctuations, which can be further interpreted by the spectrum analyzer in the bandwidth
of the modulating signal as the frequency noise. The frequency noise is then
transformed into phase noise values of the device under consideration. This method
is perfectly used for the LC oscillators or the cavity oscillators [25–30].
OEO, shown in Figs. 2.1, 2.2, and 2.3 includes the above-mentioned circuit
(Fig. 2.4), which illustrates operation principles of the correlator and the frequency
discriminator methods. The laser is used as the reference generator in OEO, the
optical fiber or channels in the MZ modulator is used as the delay line, the
photodetector is used as the phase detector.
At small relative delays in Figs. 2.1, 2.2, and 2.3, the phase dispersion σ
2
PD at
output of the phase detector (or in the photocurrent of the photodetector) is
determined as σ
2
PD ¼ σ
2
1L þ σ
2
1L À 2
A 2
A 1
K 21 σ 1L σ 2L , where σ
2
1L , σ
2
2L are dispersions
of the optical phase fluctuations, relatively, at input of optical channels OC1 and
OC2, K 21 is the auto-correlation function of the random process K 21 % exp
(À2Δν L Á ΔT M ) ¼ exp(À2ΔT M /T c ), Δν L % 1/T c is the natural width of the
spectral line of the reference generator (a laser) emission, T c is the time of laser
2.5 OEO with Self-Heterodyne Mixing as the Oscillator Containing the Phase. . .
31