resonance peak is determined by the chosen laser type as well as by constant
pumping current. So, lasers with the width of the emission spectral line from 10 to
1000 kHz have the resonance peak, which is defined by the own frequency of the
photon–electron resonance on the appropriate offset frequencies.
6.7.4 Limit Values of PSD of the Phase Noise
Now we examine the limit values of PSD of the phase noise and the natural
generation line of OEO MZ taking into account the spontaneous emission of
QWLD and the transverse spatial irregularity of the MZ optical channels. Utilization
in OEO MZ of QWLD is kindly reported on the OEO overall sizes. The limit OEO
values of the natural generation line are defined, as it follows from deduced expressions in this chapter, by the value of S βFN : the quadrature component of the laser
spontaneous emission. We know that the integral index of spontaneous emission in
the laser mode (coefficient of spontaneous emission) for semiconductor lasers with
the hetero-structure (not QWLD) can change in wide limits from 10
À1 to 10
À5
depending on sizes of the active region and the laser resonator.
Spontaneous laser emission plays the principal role in such phenomena as natural
widening of single-frequency generation line, formation of the ultra-luminescence
spectrum, as well as in generation dynamics at instantaneous switching-on of
generation development. At least, in semiconductor laser, if the one of resonator
dimensions is commensurable or smaller of the wavelength. In addition, the values
of amplification (absorption) are high enough in order to the approximation of the
uniform plane waves would be unacceptable. In this situation, the finding of the
emission part into the laser mode from the separate active dipole within the limits of
conventional approach, which is used for other types of lasers, is not adequate
enough for semiconductor lasers, on which, as we know, the attention was attracted
in publications.
Besides, QWLD has low values of the output level of spontaneous emission in the
generated laser mode. PSD of the output spontaneous emission level S β depends on
the carrier lifetime on the upper level, on the generation level, on the emission
polarization, etc.
Let us take for QWLD the integral index of spontaneous emission (the ratio of the
gain of stimulated emission and spontaneous emission) into the laser mode equaled
β ¼ 10
À3 , at the width of the spectral line of spontaneous emission of Δv ¼ 10
10 Hz
(we cannot confuse of this characteristic with the width of the laser spectral line,
which is equal 1–10 kHz for the best samples). Then PSD of the QWLD phase noise
at offset 1 kHz is S β % β/Δν ¼ 10
À12 [À120 dB/Hz]. At accepted values of QWLD
parameters and taking into account that relative deviations of material refraction
index of MZ modulator (in the transverse section, at distance between the optical
channels not more than 60 μm, G 22 ¼ Δε/ε ¼ 10
À3
) , at the optical fiber length of
2–5 km, PSD of the phase noise in OEO MZ at offset 1 kHz from the generated
frequency 10 GHz is equal S ΨAG (F ¼ 10
3 1/s) % 10
À12
– 10
À17 [1/Hz].
6.7 Formation of the OEO MZ Oscillation Spectrum
363
pumping current. So, lasers with the width of the emission spectral line from 10 to
1000 kHz have the resonance peak, which is defined by the own frequency of the
photon–electron resonance on the appropriate offset frequencies.
6.7.4 Limit Values of PSD of the Phase Noise
Now we examine the limit values of PSD of the phase noise and the natural
generation line of OEO MZ taking into account the spontaneous emission of
QWLD and the transverse spatial irregularity of the MZ optical channels. Utilization
in OEO MZ of QWLD is kindly reported on the OEO overall sizes. The limit OEO
values of the natural generation line are defined, as it follows from deduced expressions in this chapter, by the value of S βFN : the quadrature component of the laser
spontaneous emission. We know that the integral index of spontaneous emission in
the laser mode (coefficient of spontaneous emission) for semiconductor lasers with
the hetero-structure (not QWLD) can change in wide limits from 10
À1 to 10
À5
depending on sizes of the active region and the laser resonator.
Spontaneous laser emission plays the principal role in such phenomena as natural
widening of single-frequency generation line, formation of the ultra-luminescence
spectrum, as well as in generation dynamics at instantaneous switching-on of
generation development. At least, in semiconductor laser, if the one of resonator
dimensions is commensurable or smaller of the wavelength. In addition, the values
of amplification (absorption) are high enough in order to the approximation of the
uniform plane waves would be unacceptable. In this situation, the finding of the
emission part into the laser mode from the separate active dipole within the limits of
conventional approach, which is used for other types of lasers, is not adequate
enough for semiconductor lasers, on which, as we know, the attention was attracted
in publications.
Besides, QWLD has low values of the output level of spontaneous emission in the
generated laser mode. PSD of the output spontaneous emission level S β depends on
the carrier lifetime on the upper level, on the generation level, on the emission
polarization, etc.
Let us take for QWLD the integral index of spontaneous emission (the ratio of the
gain of stimulated emission and spontaneous emission) into the laser mode equaled
β ¼ 10
À3 , at the width of the spectral line of spontaneous emission of Δv ¼ 10
10 Hz
(we cannot confuse of this characteristic with the width of the laser spectral line,
which is equal 1–10 kHz for the best samples). Then PSD of the QWLD phase noise
at offset 1 kHz is S β % β/Δν ¼ 10
À12 [À120 dB/Hz]. At accepted values of QWLD
parameters and taking into account that relative deviations of material refraction
index of MZ modulator (in the transverse section, at distance between the optical
channels not more than 60 μm, G 22 ¼ Δε/ε ¼ 10
À3
) , at the optical fiber length of
2–5 km, PSD of the phase noise in OEO MZ at offset 1 kHz from the generated
frequency 10 GHz is equal S ΨAG (F ¼ 10
3 1/s) % 10
À12
– 10
À17 [1/Hz].
6.7 Formation of the OEO MZ Oscillation Spectrum
363