2 n
m
m
n=1
+∞
2s
+ inφ ∑( 1
− ) n J
−
− ( F(ω )) cos[(2 n
1)ω t]}
0
2 n 1
m
m
n=1
where F(ωm) is the frequency response of the RF source and modulator. The detected power
of 2nd harmonic can be expressed as follows, in which Mp(ωm) denotes the frequency
response of the photodetector.
2
2
4
2
P
∝
ω
ω ∝
ω
ω
ω
J ( F(
)) M (2
) F (
) M (2
) (5)
2 m
2
m
p
m
m
p
m
When drive signal consists of a single tone at a low frequency ω1 low enough that Mp(ω1)=1,
the detected power of the signal at ω1 is (Huang & Zhu, 2006):
2
4
P ∝
∝
ω
ω
iω
F (
) (6)
1
1
m
Optical and Electrical Spectrum Analysis of Optoelectronic Devices
507
Substituting (6) into (5), the frequency response of the PD can be easily obtained by
normalizing the results. Fig. 1.7 shows the results when a 10 GHz modulator is employed. It
can be seen that the data after calibration fit well with the reference data. We can also see the
measurement range is doubled using harmonic analysis method compared to that using the
conventional swept frequency technique.
L ow
F requenc y
A M
Netw
t ork
A nalyz er
L iNbO3
L D
P D(DUT )
E S A
modulato
t r
Fig. 1.6. Schematic diagram of the measurement setup
0
)
-6
(dB 21 -12
de S -18
itu
VNA sweeping
-24
2nd order } After calibaration
1st order
Magn -30
2nd order
1st order } Before calibaration
-36
0.0
5.0
10.0
15.0
20.0
Frequency (GHz)
Fig. 1.7. Measurement results
2.3 Tuning characteristics of tunable lasers measurement
The lightwave wavelengths of semiconductor lasers vary with bias current and environment
temperature. The central wavelength can be easily obtained from optical spectrum analyzer.
With the bias current tuned, the wavelength variation of normal lasers is actually due to the
change of junction temperature. It is the heat induced change in refractive index that leads
to the changes in wavelength. This period is relatively slow and the response time is of the
order of milliseconds. However, the lightwave wavelength of DBR tunable laser varies fast
with phase section current, and the response time is of the order of nanoseconds. In practice,
fast tunable semiconductor lasers are considered to be the essential devices in optical packet
switching technique which is one of the key techniques of the next optical communication
network. The prerequisite of such lasers is the ability of fast switching in the limitation of
the order of nanometer. Thus, it is important to study the instantaneous properties of the
tunable laser. On the one hand, by studying the instantaneous characteristics one can
508
Optoelectronic Devices and Properties
achieve the wavelength switching time and the optimum time for the wavelength-stable
output. These parameters are important to judge whether a system meets requirement. On
the other hand, linewidth broadening is also a dynamic process. The linewidth of the
tunable laser in the tuning process is quite different from that in steady state. The linewidth
broadening will induce dispersion which will deteriorate the transmission. Therefore,
deeply studying the instantaneous characteristics of the tunable laser and the influence
factors is critical to the assessment and improvement of device properties.
The resolution of optical spectrum analyzer is of the order of 0.01 nm, which can not meet
the requirement of measuring the dynamic process, whereas by combining optical and
electrical spectrum analyses we can easily solve this problem. We introduce two methods to
measure the tuning speed. One is using optical filter to filter out one wavelength. Then after
detected by a photoelectric detector, the electric signal is observed using an oscilloscope.
Another method is using a reference laser and taking advantage of optical heterodyne
technique to generate a microwave beat signal. By detecting the beat signal’s varying speed
one can obtain the optical tuning speed. The time response of the beat signal is detected
using “zero span” function of the electrical spectrum analyzer.
2.4 Time-resolved optical spectrum measurement
In many applications, such as the transmission of AM and FM optical signal, channel switch
in FDM system, the transient characteristics of laser wavelength should be always taken into
account. Researchers have paid much attention in developing techniques to measure the
time-resolved optical spectra. One of them (Bergano, 1988) is based on an optical filter that is
used as a discriminator. The absorption coefficient of the filter is a function of the optical
wavelength, so that the variation of wavelength can be converted into intensity variation. In
this technique, the pass band of the optical filter is relatively wide. Another method (Yu &
O’Dowd, 2002) also uses an optical filter, but its pass band is narrow and only one
wavelength can be selected. After passing through this filter, an oscilloscope is used to
observe the intensity variation of the output. Commonly the signal under test is periodic, so
that when the frequency centre of the optical filter is changed, optical signals with other
frequencies can be measured. By combing all the data, the time-resolved optical spectrum
can be obtained. The schematic setup of these two methods is shown in Fig. 1.8(a).
O pti
t c al input
F ilte
t r
P hoto
t dete
t c to
t r
O s c illos c ope
(a)
O pti
t c al input
M-Z
P hotod
ot
ete
t c to
t r
O s c illos c ope
inte
t rferomete
t r
(b)
Fig. 1.8. Schematic setup for measuring time-resolved optical spectra
There is also a method that uses self-heterodyne technique (Joseph & Sadot, 2004), which
measuring the time-resolved optical spectra in electrical domain. The input optical signal is
divided into two branches, one of which is delayed. Then the beat signal of the two signals
Optical and Electrical Spectrum Analysis of Optoelectronic Devices
509
is measured, which is equivalent to obtain the autocorrelation function. After some
calculation, the time-resolved optical spectrum can be deduced. The schematic setup is
shown in Fig. 1.8(b).
V NA
D F B
L iN
i bO
E D F A
3
L Fib
i er
Mo
M dulato
t r
P D
Fig. 1.9. Experiment setup for measuring the chirp parameter and fibre dispersion
2.5 Measurement of chirp parameter and fiber dispersion
Almost all of the laser sources, including directly modulated semiconductor laser,
electroabsorption modulator, LiNbO3 modulator, have the characteristic of frequency chirp.
The chirp parameter indicates the relationship between the intensity variation and the phase
variation:
αδφ
δφ =
(7)
2 I
I is the optical intensity, Φ denotes the phase of the laser, α is the chirp parameter.
The chirp of the laser source together with the chromatic dispersion of single mode fibre
(SMF), which is simply a variation in the speed of propagation of a lightwave with a
wavelength, can severely affect the performance of optical communication systems based on
fibre. Consequently, characterizing these two parameters accurately plays an important role
in designing fibre based communication system.
0
1600
)m
1400
m -10
-1
) 1200
2
s (dB
1000
s (dB -20
-2
se
800
on
(GHz
on
2 n 600
-30
-3
f
esp
400
espR
200
-40
-4
I =125 mA
=125 m
LD
0
0
10
1
20
2
30
3
40
4
0
5
10
15
20
25
2
30
35
3
Fr
F eq
r uency (
eq
G
uency ( Hz)
G
n
(a)
(b)
Fig. 1.10. (a) Calibrated fibre transfer function. (b) The measured results according to (9)
510
Optoelectronic Devices and Properties
By using the sweep method based on VNA, the small-signal chirp parameter and the
dispersion coefficient can be measured simultaneously (Kowalski et al., 1999). The fibre
transfer function can be expressed as follows:
2
2
πλ DLf
I ∝ cos(
+ arctanα ) (8)
f
c
Firstly, the long fibre under test is replaced by a short length of fibre and the optical-to-
optical calibration is implemented to remove the impact induced by the VNA, the
modulator and the photodetector. Then the scattering parameter S21 of the long fibre is
measured. The square of the frequency fn according to the nth zero pole is proportional to
the reciprocal of the dispersion coefficient:
c
2
2
f L =
+ n −
α (9)
n
(1 2
arctan )
2
2 Dλ
π
The measurement setup is shown in Fig. 1.9. The results are shown in Fig. 1.10. As shown in
Fig. 1.10(b), we can obtain the fibre dispersion coefficient and the chirp parameter from the
slope and the intercept respectively according to (9). This method is accurate and simple.
The measurement uncertainty is about ±0.1.
3. Characterization based on optical spectrum analysis
In this section, we introduce the techniques for characterizing optoelectronic devices based
on optical spectrum analysis, which can be easily carried out with simple experimental
setups. The frequency responses of the lasers or modulators can be extracted from the
measured optical spectrum.
3.1 Frequency responses of broadband modulators
We use sideband calculating method which is proposed by Auracher and Keil for the first
time (Auracher & Keil, 1980), and developed by Shi and Willner et al. (Shi et al., 2003; Yan et
al., 2005; Yan et al., 2003; Kawanishi et al., 2001; Oikawa et al., 2003), to obtain the frequency
responses of modulators based on optical spectrum analysis. The sidebands produced by
direct or external modulation can be observed by OSA. The frequency modulation index can
be calculated from the intensities of the optical sidebands, and then the frequency response
of the modulator can be obtained. For a Mach-Zehnder modulator, the output optical field
can be written as:
E
i
j 0
E
e ω t e Φ e η U
ω t
e Φ
=
+
e η U
ω t (10)
o
( j 1 j 1 mcos m j 2 j 2 mcos m )
2
where Umcosωmt is the applied voltage, ω0 is the frequency of the lightwave, and Φ1、 Φ2, η1、 η2 are the inherent phase shifts and the phase modulation indices in two arms,
respectively.
Assuming that the incident optical field is equally split into two beams, and the applied
electrical fields in the two arms are with the same phase, the above equations can be
expanded into Fourier series by Bessel function as follows:
Optical and Electrical Spectrum Analysis of Optoelectronic Devices
511
E
∞
i
j 0
ω t
n
jΦ1
jΦ2
j n m
E =
e
∑ j ⎡e J U +
U
ω
η
η
⎤ ×
(11)
n (
) e J n(
)
e
t
o
1
m
2
m
2
⎣
⎦
n=−∞
From (11), we can see that the output optical field includes not only the carrier component
ω0, but also the infinite sidebands components ω0+nωm. The optical intensity of each
sideband can be expressed as:
I
i
2
2
I(ω + nω ) =
⎡J (η U ) + J (η U ) + 2J (η U )J (η U )cos(Φ − Φ )⎤
0
m
⎣
1
m
2
m
1
m
2
m
1
2
4 n
n
n
n
⎦ (12)
For M-Z interference intensity modulator, we have η1＝－ η2＝ η, and (12) can be rewritten
as:
I
i
2
I(ω + nω ) =
J ( U
η
)⎡1 + ( 1
− ) n
Φ − Φ ⎤
n
cos(
)
0
m
m ⎣
1
2
2
⎦ (13)
Under small-signal modulation, the Bessel function can be expanded as Taylor series. That is:
2
U
η
( U
η
)
m
m
J ( U
η
) ≈
, J ( U
η
) ≈
(14)
1
m
2
m
2
8
The modulation index can be obtained from the ratio between the intensities of the 1st and
2nd harmonic components,
2
J ( U
η
)
I(ω ± 2ω )
1
2
m
0
m
2
R (η) =
=
=
( U
η
) (15)
2 ,1
2
m
J ( U
η
)
I(ω ± ω )
16
1
m
0
m
These two intensities can be obtained from the measured optical spectra.
3.2 Frequency response of directly modulated lasers
Here we introduce the optical spectrum analysis method for frequency response measuring
of the directly modulated laser in detail. When a single-mode laser is modulated at ω m, the
electrical field can be written as (Henery et al., 1989; Bjerkan et al., 1996)
i[ 0
ω t+β sin(ω t+θ )]
(
E t) = E 1 + m cos(ω t)e
m
(16)
0
m
where E0 is the optical intensity without modulation, m is the intensity modulation index, ωm
is the angular frequency, β is the frequency modulation index, θ is the phase difference
between frequency modulation and intensity modulation.
Assuming that the intensity modulation index m<<1, the electrical intensity can be
expanded as:
+∞
ω + ω +θ
⎧
m
⎫
i[ 0 t p( t )]
m
−iθ
i
(
E t) = E ∑ e
× ⎨J
θ
β +
⎡
β
+
β
⎤ (17)
p (
)
J p− ( )e
J p+ ( )e
0
1
1
⎬
⎣
⎦
p=−∞
⎩
4
⎭
Hence the ratio between the intensities of 1st sideband and the carrier can be written as:
m
2
2
I
=
+
+ / I
J (β )(1
cosθ ) / J (β ) (18)
1
0
1
0
β
512
Optoelectronic Devices and Properties
m
2
2
I
=
−
− / I
J (β )(1
cosθ ) / J (β ) (19)
1
0
1
0
β
Then, we have
2
2
J (β ) / J (β ) = ( I +
×
+
I− ) /(2 I ) (20)
1
0
1
1
0
When the frequency modulation index β<<1, the equation above can be further simplified
as:
2
2
2
J (β ) / J (β ) ≈ 0.25β (21)
1