pumping currents, the phase-frequency characteristic has a large slope in the frequency region corresponding to the clearly expressed resonance peaks in AFC with
the natural frequency ω 0 in the frequency range from 1 to 5 GHz.
Depending on AFC, the “resonance peak” is caused by the phenomenon of the
“electron–photon” resonance, which is demonstrated in injection semiconductor
lasers in the region of the microwave modulation. The “electron–photon” resonance
arises at equality of the pumping oscillation period and the own relaxation time of
excited particles in QWLD. The resonance frequency of QWLD modulation f res
depends on the pumping exceed above the threshold value, on the electron lifetime τ e
and the photon lifetime τ p in the resonator and determined by the expression:
f res ¼ 1=τ e
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
τ e =τ p
À
Á
I 0 =I th À 1
ð
Þ
q
.
In the region of the large pumping currents from 50 to 80 mA, the phasefrequency characteristic φ(ω) approaches to linear and is described by the expression
to accuracy to the constant φ 0 : φ(ω) ¼ 2π fR LD C LD + Arg[K LD ( jω)].
For demonstration of phase offsets on the fixed radio frequency, the functions of
the phase differences for different small offsets of the constant pumping current are
calculated. An analysis shows that the pumping current influence on the PFC slope
in the whole frequency region is different. At small exceeds of the pumping current
(1.2–2.0) at variation of the pumping current of 1 mA, the maximal slope of PFC is
30–70
/mA at fixed radio frequency in the range 1.0–5.0 GHz. At large pumping
currents, the maximal PFC slope is 1–5
/mA at fixed frequency in the range
5.0–10.0 GHz.
From these calculated data, we can conclude that at providing of stabilization of
the constant QWLD pumping current is not worse than 10
À4 (which corresponds to
absolute current offsets of 7.5 Â 10
À3 mA at the pumping current of 75 mA), the
absolute variations of time constant of QWLD under investigation, owing to DC
pumping current variations, are about 2 Â 10
À3 ps/mA at modulation in the radiofrequency range of 8–12 GHz.
Thus, obtained calculated and experimental values of PFC and QWLD time
constant (or the PFC values on the modulation frequency f mod dividing by the
value of the given frequency) T LD ¼ φ LD /(2πf mod ) variations give the possibility to
perform measurements of the light time delays (with utilization of these types of
QWLDs as the modulated light source) in fiber-optical systems and in light-guiding
fibers with the help of oscillator methods [13, 14] not worse than 2 Â 10
À3 ps, which
is equivalent, for instance, to registration of geometrical lengthening of the optical
fiber on the level 0.2 μm. Therefore, such QWLD is expedient to use in the highsensitive oscillator fiber-optical sensors as well as in oscillators with RF FODL for
generation of the high-stable harmonic radio signal.
On the other hand, at transmission of the harmonic microwave radio signal, for
example, in lines by the phased active arrays (PAA), the absolute phase offsets on
the frequency of 10 GHz, due to the instability of the QWLD DC pumping current,
are 0.72 Â 10
À2 degrees. The application of these types of QWLDs in PAA is also
promising.
400
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
the natural frequency ω 0 in the frequency range from 1 to 5 GHz.
Depending on AFC, the “resonance peak” is caused by the phenomenon of the
“electron–photon” resonance, which is demonstrated in injection semiconductor
lasers in the region of the microwave modulation. The “electron–photon” resonance
arises at equality of the pumping oscillation period and the own relaxation time of
excited particles in QWLD. The resonance frequency of QWLD modulation f res
depends on the pumping exceed above the threshold value, on the electron lifetime τ e
and the photon lifetime τ p in the resonator and determined by the expression:
f res ¼ 1=τ e
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
τ e =τ p
À
Á
I 0 =I th À 1
ð
Þ
q
.
In the region of the large pumping currents from 50 to 80 mA, the phasefrequency characteristic φ(ω) approaches to linear and is described by the expression
to accuracy to the constant φ 0 : φ(ω) ¼ 2π fR LD C LD + Arg[K LD ( jω)].
For demonstration of phase offsets on the fixed radio frequency, the functions of
the phase differences for different small offsets of the constant pumping current are
calculated. An analysis shows that the pumping current influence on the PFC slope
in the whole frequency region is different. At small exceeds of the pumping current
(1.2–2.0) at variation of the pumping current of 1 mA, the maximal slope of PFC is
30–70
/mA at fixed radio frequency in the range 1.0–5.0 GHz. At large pumping
currents, the maximal PFC slope is 1–5
/mA at fixed frequency in the range
5.0–10.0 GHz.
From these calculated data, we can conclude that at providing of stabilization of
the constant QWLD pumping current is not worse than 10
À4 (which corresponds to
absolute current offsets of 7.5 Â 10
À3 mA at the pumping current of 75 mA), the
absolute variations of time constant of QWLD under investigation, owing to DC
pumping current variations, are about 2 Â 10
À3 ps/mA at modulation in the radiofrequency range of 8–12 GHz.
Thus, obtained calculated and experimental values of PFC and QWLD time
constant (or the PFC values on the modulation frequency f mod dividing by the
value of the given frequency) T LD ¼ φ LD /(2πf mod ) variations give the possibility to
perform measurements of the light time delays (with utilization of these types of
QWLDs as the modulated light source) in fiber-optical systems and in light-guiding
fibers with the help of oscillator methods [13, 14] not worse than 2 Â 10
À3 ps, which
is equivalent, for instance, to registration of geometrical lengthening of the optical
fiber on the level 0.2 μm. Therefore, such QWLD is expedient to use in the highsensitive oscillator fiber-optical sensors as well as in oscillators with RF FODL for
generation of the high-stable harmonic radio signal.
On the other hand, at transmission of the harmonic microwave radio signal, for
example, in lines by the phased active arrays (PAA), the absolute phase offsets on
the frequency of 10 GHz, due to the instability of the QWLD DC pumping current,
are 0.72 Â 10
À2 degrees. The application of these types of QWLDs in PAA is also
promising.
400
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .