FODL at variation of the LD time constant for pumping current, which are higher
and lower than the threshold value. At increase of the pumping current in the region
of values, which are less than the threshold value, the time constant of LD increases
due to the growth of the barrier capacitance. In this current range, the LD optical
emission represents the spontaneous emission of photons. At that, the equivalent
circuit of the laser diode for pumping currents, which are less than the threshold
values, can be represented as the parallel-connected barrier capacitance C b and the
loss resistance R loss , and the time constant of LD (or the delay of the harmonic signal
in LD) is determined as T LD ¼ R loss C b , where C b ¼ C b0 exp (γ str I pump /I thr ), C b0 is the
value of the barrier capacitance at the zero pumping current, γ str is the real coefficient
defining by the geometry and the structure of the laser diode.
In the range of pumping current values, which are lower than the threshold value,
the LD operation is similar to the light emitting diode (LED). In the range of
pumping current values, which are higher than the threshold value, the optical
emission represents the laser generation. The influence on the time constant T LD of
the barrier capacitance of the junction becomes insignificant. The speed of the carrier
concentration achievement on the upper level to the threshold value, which is
directly connected with the level of the pumping exceed above the threshold
value, is the main factor, which determines of the LD time constant. Owing to the
growth of the carrier concentration speed, the delay in phase decreases of the
harmonic signal in LD. The delay time of the signal phase or the LD time constant
is determined by the approximated expression T LD ¼ τ e exp [À(I pump /I thr À 1)],
where τ e is the lifetime of electrons (carriers).
At current values equaled to the threshold value, the frequency function f(I pump )
has the minimum. The hysteresis character of this function at increase and decrease
of the pumping current is explained by the thermodynamic processes of heating of
cooling of the LD active region at small variations of the environment temperature.
The measured in experiments average slopes S f of the function f(I pump ) (at equal
offsets |I pump À I thr | versus the threshold value I thr ), in regions of the current
variations above and below of the threshold value, are approximately equal for
OEO with RF FODL and LD: S f ¼ Δf/ΔI pump ¼ 15 kHz/mA.
The phenomenon of the polarity change of the slope of LD time constant and the
slope S f of the function f(I pump ) for OEO with LD, which was for the first time
experimentally discovered and explained by authors by means of the theoretical
analysis for LD, gives a possibility to correctly select the operating pumping currents
of LD in OEO and the modulation signal amplitude, as well as to optimize the
construction of the LD modulator, of matching optical device with the optical fiber
and of the thermal stabilizing block.
7.3.6 Modern QWLDs and Their Characteristics
The QWLD construction, which analysis was presented in [9] on the base of
InGaAsP/InP with the output power about 7 mW introduced into the optical fiber
7.3 OEO DM Analysis on the Base of Abbreviated Differential Equations
405
and lower than the threshold value. At increase of the pumping current in the region
of values, which are less than the threshold value, the time constant of LD increases
due to the growth of the barrier capacitance. In this current range, the LD optical
emission represents the spontaneous emission of photons. At that, the equivalent
circuit of the laser diode for pumping currents, which are less than the threshold
values, can be represented as the parallel-connected barrier capacitance C b and the
loss resistance R loss , and the time constant of LD (or the delay of the harmonic signal
in LD) is determined as T LD ¼ R loss C b , where C b ¼ C b0 exp (γ str I pump /I thr ), C b0 is the
value of the barrier capacitance at the zero pumping current, γ str is the real coefficient
defining by the geometry and the structure of the laser diode.
In the range of pumping current values, which are lower than the threshold value,
the LD operation is similar to the light emitting diode (LED). In the range of
pumping current values, which are higher than the threshold value, the optical
emission represents the laser generation. The influence on the time constant T LD of
the barrier capacitance of the junction becomes insignificant. The speed of the carrier
concentration achievement on the upper level to the threshold value, which is
directly connected with the level of the pumping exceed above the threshold
value, is the main factor, which determines of the LD time constant. Owing to the
growth of the carrier concentration speed, the delay in phase decreases of the
harmonic signal in LD. The delay time of the signal phase or the LD time constant
is determined by the approximated expression T LD ¼ τ e exp [À(I pump /I thr À 1)],
where τ e is the lifetime of electrons (carriers).
At current values equaled to the threshold value, the frequency function f(I pump )
has the minimum. The hysteresis character of this function at increase and decrease
of the pumping current is explained by the thermodynamic processes of heating of
cooling of the LD active region at small variations of the environment temperature.
The measured in experiments average slopes S f of the function f(I pump ) (at equal
offsets |I pump À I thr | versus the threshold value I thr ), in regions of the current
variations above and below of the threshold value, are approximately equal for
OEO with RF FODL and LD: S f ¼ Δf/ΔI pump ¼ 15 kHz/mA.
The phenomenon of the polarity change of the slope of LD time constant and the
slope S f of the function f(I pump ) for OEO with LD, which was for the first time
experimentally discovered and explained by authors by means of the theoretical
analysis for LD, gives a possibility to correctly select the operating pumping currents
of LD in OEO and the modulation signal amplitude, as well as to optimize the
construction of the LD modulator, of matching optical device with the optical fiber
and of the thermal stabilizing block.
7.3.6 Modern QWLDs and Their Characteristics
The QWLD construction, which analysis was presented in [9] on the base of
InGaAsP/InP with the output power about 7 mW introduced into the optical fiber
7.3 OEO DM Analysis on the Base of Abbreviated Differential Equations
405