generation frequency and the OEO MZ frequency differs by 10,000 times. At
modeling of the phase noises, we use the Leeson phase noise model [5] and the
approach to the noise synthesis using the Langevinian equations. We assume that the
optical fiber in OEO MZ is excited by the laser, which PSD of the phase noise is
close to the Lorentzian curve, and the laser emission spectral line is equal to Δv L ¼ Δv
and is for different modeling conditions of 1 kHz, 10 kHz, 10 MHz, 100 MHz,
1 GHz, 10 GHz, 30 GHz, 100 GHz, the average generation frequency of the laser is
v L ¼ v 0 ¼ v and is 128 THz.
The laser included in the OEO MZ structure is formed by enclosed into the loop
of the optical nonlinear amplifier (OA), the narrowband optical filter, and RF FODL.
The laser is modeled in the operational mathematical system with the help of
standard blocks (integrators, multipliers, adders, filtering blocks, amplifying blocks,
nonlinear blocks, etc.), which models the instantaneous values of the strength
oscillations of the laser optical oscillations E(t) of the nonlinear differential equation
of the type 1: the differential equation (5.60).
The closed loop of OEO MZ (the RF oscillator) is modeled with the help of the
standard blocks (integrators, multipliers, adders, filtering blocks, nonlinearity
blocks, etc.) for RF oscillations of OEO u(t) (instantaneous values), which models
the differential nonlinear equation of the type 2: the differential equation (6.28).
In the differential equation (6.28), E
2
0L is the normalized laser output, E 0P is the
strength of the electrical field of the laser pumping, S ONA , S NA are AE nonlinear
functions, relatively, of the optical amplifier and the RF amplifier in OEO MZ, K OA
is the transfer function of the optical amplifier in the laser, K FODL is the RF FODL
transfer function, v OF , f F0 are natural frequency of the lased optical resonator and the
RF filter, relatively, T OL and T FOS are delay time in the laser and in RF oscillator,
relatively, T OF , T F ¼ T EF are time constants of the laser optical resonator and the RF
filter, relatively. The “Langevinian” noise sources ξ n , ψ n of the field strength in the
laser and the electrical oscillation voltage in OEO MZ are modeled by the standard
blocks of the white noise with a possibility to change the noise level within the limits
for 10
À15 to 10
À1 . MZ is modeled by the parallel-connected delay lines. At that, the
delay time of the single delay line is changed at variation of the modulating signal.
PD is modeled by the multiplication block.
The time scale is chosen taking into account that the laser oscillation frequency
would be by 1000–10,000 times more than the frequency of RF oscillations of OEO,
and the oscillation period in OEO is about 0.01–0.1 s. During modeling, the laser’s
generation line width is varied (with the help of the level variation of the “white
noise” block) and the dispersion slope of FOS is τ D ¼ À 10
À1 Á Á Á + 10
À1 1/GHz.
350
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .
modeling of the phase noises, we use the Leeson phase noise model [5] and the
approach to the noise synthesis using the Langevinian equations. We assume that the
optical fiber in OEO MZ is excited by the laser, which PSD of the phase noise is
close to the Lorentzian curve, and the laser emission spectral line is equal to Δv L ¼ Δv
and is for different modeling conditions of 1 kHz, 10 kHz, 10 MHz, 100 MHz,
1 GHz, 10 GHz, 30 GHz, 100 GHz, the average generation frequency of the laser is
v L ¼ v 0 ¼ v and is 128 THz.
The laser included in the OEO MZ structure is formed by enclosed into the loop
of the optical nonlinear amplifier (OA), the narrowband optical filter, and RF FODL.
The laser is modeled in the operational mathematical system with the help of
standard blocks (integrators, multipliers, adders, filtering blocks, amplifying blocks,
nonlinear blocks, etc.), which models the instantaneous values of the strength
oscillations of the laser optical oscillations E(t) of the nonlinear differential equation
of the type 1: the differential equation (5.60).
The closed loop of OEO MZ (the RF oscillator) is modeled with the help of the
standard blocks (integrators, multipliers, adders, filtering blocks, nonlinearity
blocks, etc.) for RF oscillations of OEO u(t) (instantaneous values), which models
the differential nonlinear equation of the type 2: the differential equation (6.28).
In the differential equation (6.28), E
2
0L is the normalized laser output, E 0P is the
strength of the electrical field of the laser pumping, S ONA , S NA are AE nonlinear
functions, relatively, of the optical amplifier and the RF amplifier in OEO MZ, K OA
is the transfer function of the optical amplifier in the laser, K FODL is the RF FODL
transfer function, v OF , f F0 are natural frequency of the lased optical resonator and the
RF filter, relatively, T OL and T FOS are delay time in the laser and in RF oscillator,
relatively, T OF , T F ¼ T EF are time constants of the laser optical resonator and the RF
filter, relatively. The “Langevinian” noise sources ξ n , ψ n of the field strength in the
laser and the electrical oscillation voltage in OEO MZ are modeled by the standard
blocks of the white noise with a possibility to change the noise level within the limits
for 10
À15 to 10
À1 . MZ is modeled by the parallel-connected delay lines. At that, the
delay time of the single delay line is changed at variation of the modulating signal.
PD is modeled by the multiplication block.
The time scale is chosen taking into account that the laser oscillation frequency
would be by 1000–10,000 times more than the frequency of RF oscillations of OEO,
and the oscillation period in OEO is about 0.01–0.1 s. During modeling, the laser’s
generation line width is varied (with the help of the level variation of the “white
noise” block) and the dispersion slope of FOS is τ D ¼ À 10
À1 Á Á Á + 10
À1 1/GHz.
350
6 Operation Analysis of Optoelectronic oscillator (OEO) with External. . .