average optical frequency of oscillations about 231 THz (the average wavelength is
1.3 μm).
Let us calculate the level of optical harmonics in the spectrum of the intensity
square of the output emission at modulation of the pumping current according to the
sine law.
At constant laser pumping current (bias current), for instance, 30–50 mA, and at
AC component amplitude, for example, 5–10 mA (Fig. 3.10a), the intensity
(or power) modulation of the laser output emission occurs. If to analyze the optical
spectrum of the laser output emission, then the square on output emission intensity
will represent the set of harmonics.
Let us determine the side harmonic levels at variation of the laser pumping (bias)
current according to the structure of Fig. 3.10 and the law J L ¼ J L0 + J L1 Á cos(2πf 0 t)
and, for instance, at values of normalized values J L0 ¼ 5, J L1 ¼ 1, 2πf 0 ¼ 10. To
calculate the harmonic level of the power spectral density S L of the laser, we may
apply the Wiener–Khinchin formula. For simplicity, to illustrate the principle of
DM, we make use the approximation by the function: E L ¼ 0, at I ¼ J 0L < J 0Lth ,
E L ¼ S 2L (J 0L À J 0Lth )
2 , at J 0L > J 0Lth .
Let us determine the side harmonic level at modulation by the harmonic oscillation (restricting by two harmonics on the left and right from the central frequency)
as:
S L ¼
ffiffiffiffiffiffiffiffiffiffi
1=2π
p
Z 1
À1
J L0 þ J L1 Á cos 2π f 0 t
ð
Þ
ð
Þ
2 Á exp À2πν 0 t
ð
Þdt
¼
1
2
ffiffiffiffiffiffiffi ffi
π=2
p
δ 2πν 0 À 2 Á 2π f 0
ð
Þ þ 20δ 2πν 0 À 2π f 0
ð
Þ
ð
þ102 Á δ 2πν 0
ð
Þþ20δ 2πν 0 þ 2π f 0
ð
Þþδ 2πν 0 þ 2 Á 2π f 0
ð
Þ Þ :
ð3:18Þ
The calculated spectrum of the QWLD squared emission intensity at modulation
absence is presented in Fig. 3.11a (second plot), Fig. 3.11b (second plot).
Figures 3.11a, b shows the calculated spectrum at modulation by the harmonic
oscillation. As we see, in the optical spectrum of intensity square, together with
the carrier frequency ν 0 , harmonics ν 0 Æ f 0 , ν 0 Æ 2f 0 and so on arise at modulation by
the current, which are spaced from the carrier by the multiples of the f 0 microwave
frequency of the harmonic modulation.
3.2.1.2 Harmonic Selection by the OF-2 Optical Filter
The optical filter OF-2 is shown in Fig. 3.10. In the pictures presented in Fig. 3.12 the
operation of the OF-2 optical filter located on the QWLD optical output is demonstrated: from five harmonics of the laser optical emission, the only two are extracted
(the carrier ν 0 and the right harmonic ν 0 À f 0 ), and other harmonic are suppressed.
96 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
1.3 μm).
Let us calculate the level of optical harmonics in the spectrum of the intensity
square of the output emission at modulation of the pumping current according to the
sine law.
At constant laser pumping current (bias current), for instance, 30–50 mA, and at
AC component amplitude, for example, 5–10 mA (Fig. 3.10a), the intensity
(or power) modulation of the laser output emission occurs. If to analyze the optical
spectrum of the laser output emission, then the square on output emission intensity
will represent the set of harmonics.
Let us determine the side harmonic levels at variation of the laser pumping (bias)
current according to the structure of Fig. 3.10 and the law J L ¼ J L0 + J L1 Á cos(2πf 0 t)
and, for instance, at values of normalized values J L0 ¼ 5, J L1 ¼ 1, 2πf 0 ¼ 10. To
calculate the harmonic level of the power spectral density S L of the laser, we may
apply the Wiener–Khinchin formula. For simplicity, to illustrate the principle of
DM, we make use the approximation by the function: E L ¼ 0, at I ¼ J 0L < J 0Lth ,
E L ¼ S 2L (J 0L À J 0Lth )
2 , at J 0L > J 0Lth .
Let us determine the side harmonic level at modulation by the harmonic oscillation (restricting by two harmonics on the left and right from the central frequency)
as:
S L ¼
ffiffiffiffiffiffiffiffiffiffi
1=2π
p
Z 1
À1
J L0 þ J L1 Á cos 2π f 0 t
ð
Þ
ð
Þ
2 Á exp À2πν 0 t
ð
Þdt
¼
1
2
ffiffiffiffiffiffiffi ffi
π=2
p
δ 2πν 0 À 2 Á 2π f 0
ð
Þ þ 20δ 2πν 0 À 2π f 0
ð
Þ
ð
þ102 Á δ 2πν 0
ð
Þþ20δ 2πν 0 þ 2π f 0
ð
Þþδ 2πν 0 þ 2 Á 2π f 0
ð
Þ Þ :
ð3:18Þ
The calculated spectrum of the QWLD squared emission intensity at modulation
absence is presented in Fig. 3.11a (second plot), Fig. 3.11b (second plot).
Figures 3.11a, b shows the calculated spectrum at modulation by the harmonic
oscillation. As we see, in the optical spectrum of intensity square, together with
the carrier frequency ν 0 , harmonics ν 0 Æ f 0 , ν 0 Æ 2f 0 and so on arise at modulation by
the current, which are spaced from the carrier by the multiples of the f 0 microwave
frequency of the harmonic modulation.
3.2.1.2 Harmonic Selection by the OF-2 Optical Filter
The optical filter OF-2 is shown in Fig. 3.10. In the pictures presented in Fig. 3.12 the
operation of the OF-2 optical filter located on the QWLD optical output is demonstrated: from five harmonics of the laser optical emission, the only two are extracted
(the carrier ν 0 and the right harmonic ν 0 À f 0 ), and other harmonic are suppressed.
96 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .