mode (with the stepped and the gradient profile of the refraction index) become
relevant at information transmission.
In our investigation of the effect of refraction index variations versus the optical
frequency, we assume that the optical fiber in OEO MZ is dispersive, i.e., the delay
time in FOS is the function of the optical frequency T FOS (v).
In the vicinity of the central optical frequency ν L ¼ ν 0 ¼ ν of the laser emission,
the function of delay of the optical frequency T FOS (v) at Δv L ( f 0 is linear and can be
presented by the function:
T FOS v
ð Þ ¼ T FOS v 0
ð Þ þ v À v 0
ð
Þτ D ,
ð6:91Þ
where τ D is the retarding slope is determined by material and waveguide dispersion
of the optical fiber and for modern optical fibers is τ D ¼ dT/dv ¼ 10
À7 1/GHz.
Modern specially developed optical fibers for the dispersion correction have the
positive and negative dispersion with τ D ¼ À 10
À1
Á Á Á + 10
À1 1/GHz.
Taking into consideration the nonlinear variation of the refraction index, the
function of the refraction index versus the optical frequency can be approximated
by expanding this function into the Taylor series restricting in this expansion
by the first and second derivatives:
N FOS v
ð Þ ¼ N FOS v 0
ð Þ þ v À v 0
ð
Þ
dN FOS
dv
þ v À v 0
ð
Þ
2 d
2 N FOS
dv 2 :
ð6:92Þ
In our research of the analog model of OEO MZ, we studied how does the width
of the spectral line of the laser emission influence on the spectrum of RF oscillations
in OEO MZ. We studied the functions of PSD of the phase noise at variation of the
FOS refraction index from the laser optical frequency.
In computer investigations we have implemented the values of T FOS (ν) from 1 ns
to 100 μs, and τ D ¼ À 10
À1
Á Á Á + 10
À1 1/GHz. In OEO MZ with the dispersive
delay line, the increase of the width Δv (Fig. 6.32) by more than 10 GHz led at
modeling to the growth of PSD of the phase noise by four orders. At that, in the OEO
MZ spectrum, on offset frequencies by 0.1–1 kHz from the nominal frequency of
10 GHz, there are adjacent oscillation types, which do not “provide the generation
mode” (which alteration is defined by the delay time in the optical fiber) and the
spectrum has the comb structure—the periodic dependence upon the frequency
offset from the nominal generation frequency.
We can conclude that at increase of the laser line width Δv, the difference
between adjacent own types of oscillations of OEO MZ, which is indicated in the
plot as DF (Fig. 6.32) decreases and depends on the delay time in FOS T FOS (v) on the
laser average frequency v 0 and on the product of the dispersion slope τ D by the laser
emission bandwidth
Δv L ¼ Δv : DF ¼ 1 À Δv L Á τ D
ð
Þ =T FOS v 0
ð Þ:
ð6:93Þ
6.6 Analog Modeling of OEO MZ
353
relevant at information transmission.
In our investigation of the effect of refraction index variations versus the optical
frequency, we assume that the optical fiber in OEO MZ is dispersive, i.e., the delay
time in FOS is the function of the optical frequency T FOS (v).
In the vicinity of the central optical frequency ν L ¼ ν 0 ¼ ν of the laser emission,
the function of delay of the optical frequency T FOS (v) at Δv L ( f 0 is linear and can be
presented by the function:
T FOS v
ð Þ ¼ T FOS v 0
ð Þ þ v À v 0
ð
Þτ D ,
ð6:91Þ
where τ D is the retarding slope is determined by material and waveguide dispersion
of the optical fiber and for modern optical fibers is τ D ¼ dT/dv ¼ 10
À7 1/GHz.
Modern specially developed optical fibers for the dispersion correction have the
positive and negative dispersion with τ D ¼ À 10
À1
Á Á Á + 10
À1 1/GHz.
Taking into consideration the nonlinear variation of the refraction index, the
function of the refraction index versus the optical frequency can be approximated
by expanding this function into the Taylor series restricting in this expansion
by the first and second derivatives:
N FOS v
ð Þ ¼ N FOS v 0
ð Þ þ v À v 0
ð
Þ
dN FOS
dv
þ v À v 0
ð
Þ
2 d
2 N FOS
dv 2 :
ð6:92Þ
In our research of the analog model of OEO MZ, we studied how does the width
of the spectral line of the laser emission influence on the spectrum of RF oscillations
in OEO MZ. We studied the functions of PSD of the phase noise at variation of the
FOS refraction index from the laser optical frequency.
In computer investigations we have implemented the values of T FOS (ν) from 1 ns
to 100 μs, and τ D ¼ À 10
À1
Á Á Á + 10
À1 1/GHz. In OEO MZ with the dispersive
delay line, the increase of the width Δv (Fig. 6.32) by more than 10 GHz led at
modeling to the growth of PSD of the phase noise by four orders. At that, in the OEO
MZ spectrum, on offset frequencies by 0.1–1 kHz from the nominal frequency of
10 GHz, there are adjacent oscillation types, which do not “provide the generation
mode” (which alteration is defined by the delay time in the optical fiber) and the
spectrum has the comb structure—the periodic dependence upon the frequency
offset from the nominal generation frequency.
We can conclude that at increase of the laser line width Δv, the difference
between adjacent own types of oscillations of OEO MZ, which is indicated in the
plot as DF (Fig. 6.32) decreases and depends on the delay time in FOS T FOS (v) on the
laser average frequency v 0 and on the product of the dispersion slope τ D by the laser
emission bandwidth
Δv L ¼ Δv : DF ¼ 1 À Δv L Á τ D
ð
Þ =T FOS v 0
ð Þ:
ð6:93Þ
6.6 Analog Modeling of OEO MZ
353