3.2.1 Method of Direct Amplitude Modulation
Let us consider the case on direct amplitude modulation (DM) of the laser emission
by the pumping (bias) current. Structures of DM of the laser included in the OEO
structure are shown in Fig. 3.10a, b. In the structure of direct modulation of laser
emission, the pumping current can be presented in the form J L ¼ J L0 + J L1 Á Re[exp
( j2πf 0 )], where J L0 and J L1 are the DC and AC components of the pumping current,
relatively. The slope S 1L of the watt–ampere characteristic and the complex transfer
function of QWLD K L ( j2πf 0 , J 0L , J 0Lth ), which depends on the modulation frequency f 0 , the DC component of the pumping current J 0L , where J 0Lth is the
threshold value of QWLD pumping current, are attributed to the main QWLD
characteristics.
3.2.1.1 Watt–Ampere Characteristics of QWLD
The watt–ampere characteristics (WAC) of the laser diode is the function of the
normalized power of the photon flow density on the QWLD output P L ¼ E
2
LL versus
the DC pumping current J L0 . If we assume that spontaneous intensity noises are
small, WAC is approximated by the piecewise-linear curve: P ¼ P L ¼ 0, at
I ¼ J 0L < J 0Lth , P ¼ P L ¼ S 1L Á (J 0L À J 0Lth ), at J 0L > J 0Lth , where S 1L is the
slope of WAC at J 0L > J 0Lth . Let the intensity of output laser emission be described
at modulation absence by the last formula.
To obtain the harmonic amplitudes of the oscillation spectrum of the normalized
QWLD intensity, we present E L (J 0L ) by the function:
E L J 0L
ð Þ¼
0,
atI ¼J 0L
ð
Þ þ S 2EL J 0L ÀJ 0Lth
ð
Þ
2 ÀS 3EL J 0L ÀJ 0Lth
ð
Þ
3 , atJ 0L >J 0Lth
&
ð3:17Þ
where S 0EL , S 2EL , S 3EL are slopes of the nonlinear characteristics E L (J 0L ) at
J 0L > J 0Lth . The normalized emission power P L ¼ E
2
LL is P L t
ð Þ ¼ E
2
L t
ð Þ ¼
K C Á E L t
ð Þ Á E
Ã
L t À τ
ð
Þ
:
The power P L ¼ E
2
L at the resonator output can be presented in the form
P L ¼ P L0 + P L1 Á cos(2πf 0 t), where P L0 ¼ E
2
0L , P L1 ¼ E
2
10L are DC and AC
components on the optical QWLD output, 2πf 0 is the radio frequency of the
QWLD modulation current.
Figure 3.10 illustrates the principle of the direct modulation of the singlefrequency narrowband laser by means of the pumping current variations. This
method is called, for short, DM.
Figure 3.10 shows the experimental watt–ampere characteristic of the high-speed
QWLD (with the modulation radio-frequency band of 12 GHz) operating on the
94 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
Let us consider the case on direct amplitude modulation (DM) of the laser emission
by the pumping (bias) current. Structures of DM of the laser included in the OEO
structure are shown in Fig. 3.10a, b. In the structure of direct modulation of laser
emission, the pumping current can be presented in the form J L ¼ J L0 + J L1 Á Re[exp
( j2πf 0 )], where J L0 and J L1 are the DC and AC components of the pumping current,
relatively. The slope S 1L of the watt–ampere characteristic and the complex transfer
function of QWLD K L ( j2πf 0 , J 0L , J 0Lth ), which depends on the modulation frequency f 0 , the DC component of the pumping current J 0L , where J 0Lth is the
threshold value of QWLD pumping current, are attributed to the main QWLD
characteristics.
3.2.1.1 Watt–Ampere Characteristics of QWLD
The watt–ampere characteristics (WAC) of the laser diode is the function of the
normalized power of the photon flow density on the QWLD output P L ¼ E
2
LL versus
the DC pumping current J L0 . If we assume that spontaneous intensity noises are
small, WAC is approximated by the piecewise-linear curve: P ¼ P L ¼ 0, at
I ¼ J 0L < J 0Lth , P ¼ P L ¼ S 1L Á (J 0L À J 0Lth ), at J 0L > J 0Lth , where S 1L is the
slope of WAC at J 0L > J 0Lth . Let the intensity of output laser emission be described
at modulation absence by the last formula.
To obtain the harmonic amplitudes of the oscillation spectrum of the normalized
QWLD intensity, we present E L (J 0L ) by the function:
E L J 0L
ð Þ¼
0,
atI ¼J 0L
ð
Þ þ S 2EL J 0L ÀJ 0Lth
ð
Þ
2 ÀS 3EL J 0L ÀJ 0Lth
ð
Þ
3 , atJ 0L >J 0Lth
&
ð3:17Þ
where S 0EL , S 2EL , S 3EL are slopes of the nonlinear characteristics E L (J 0L ) at
J 0L > J 0Lth . The normalized emission power P L ¼ E
2
LL is P L t
ð Þ ¼ E
2
L t
ð Þ ¼
K C Á E L t
ð Þ Á E
Ã
L t À τ
ð
Þ
:
The power P L ¼ E
2
L at the resonator output can be presented in the form
P L ¼ P L0 + P L1 Á cos(2πf 0 t), where P L0 ¼ E
2
0L , P L1 ¼ E
2
10L are DC and AC
components on the optical QWLD output, 2πf 0 is the radio frequency of the
QWLD modulation current.
Figure 3.10 illustrates the principle of the direct modulation of the singlefrequency narrowband laser by means of the pumping current variations. This
method is called, for short, DM.
Figure 3.10 shows the experimental watt–ampere characteristic of the high-speed
QWLD (with the modulation radio-frequency band of 12 GHz) operating on the
94 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .