Optics and Photonics Journal, 2013, 3, 61-65
doi:10.4236/opj.2013.32B015 Published Online June 2013 (http://www.scirp.org/journal/opj)
Description of the FDML Laser with Quasi-steady State
Model of the SOA
Zhi Wang, Limei Zhang, Lanlan Liu, Zhenchao Sun, Yingfeng Liu, Fu Wang
Institute of Optical Information, School of Science, Beijing, Jiaotong University,
Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing, China
Received 2013
ABSTRACT
Experiments and simulations demonstrate that an SOA-based ring cavity can operate as a tunable laser, wavelength-
swept laser or Fourier-domain-mode-locking laser according to the relation between the roundtrip frequency and the
sweeping frequency of the filter.
Keywords: Mode Locked Laser; Semiconductor Optical Amplifiers; Tunable Filter
1. Introduction
In the Fourier Domain Mode Locking laser (FD ML), which
was first presented by R. Huber [1,2], a narrowband op-
tical band pass filter is driven in resonance with the optical
roundtrip time of the laser cavity. The required resonator
length of several kilometers is realized by a long delay line
consisting of single mode fiber (SMF) and dispersion
management fibers. As each wavelength component cir-
culates in the cavity such that it is transmitted through
the filter at every pass, FDML represents a stationary
operating regime. Lasing does not have to build up re-
petitively as in conventionally wavelength swept laser
(WSL) sources, resulting in improved noise performance,
coherence length, output power and higher maximum
sweep repetition rates [1].
In spite of the numerous applications of FDML lasers
demonstrated [3-8] so far, up to now, only one model f or
the theoretical description of FDML is proposed by
Christian Jirauschek [9]. In their model, a dynamic equa-
tion is derived to identify the physical effects relevant for
FDML, and clarify the role of amplified spontaneous
emission (ASE) for self-starting and for the steady state
operation of FDML lasers. In 2012, they employed a
numerical simulation based on this model to investigate
the temporal evolution of the instantaneous power spec-
trum at different points in the laser cavity, and gained
deeper insight into the role of the physical effects gov-
erning FDML dynamics, such as gain recovery and
linewidth enhancement in the SOA, dispersion and self-
phase modulation (SPM) in the optical, and the filter
sweeping action [10].
However, there are a few defaults in Christian's model,
and a novel mechanism for SOA-based ring cavity
FDML laser (SOA-R-FDML) will be established based
on the quasi-steady state SOA [11] in this manuscript.
The improvement mainly comes from four aspects: first,
frequency dependence of the spectral gain (including the
material gain and absorption) are considered; second, the
gain properties of the SOA is simulated based on the
steady state model, which can give us the gain character-
istics for any incident frequency and power, including the
gain saturation; third, the ASE is always included in the
steady state model, accompanying with the resonance
light in the cavity and in the SOA; fourth, the FP trans-
mission function is used to accurately describe the sweep
filter.
2. Building up Laser Activity
Figure 1(a) is the basic structure of the SOA-R-FDML,
in which the SOA is the gain medium, the tunable filter
is driven by external signal, the coupler is for feedback
and output, isolators (ISO), polarization control (PC),
and dispersion management fibers are also included in
the cavity.
The cavity length of the SOA-R-FDML is about tens
of meters or kilometers, the roundtrip time of light in the
cavity is about hundreds of ns or us. The experiments
show that tens of roundtrips is necessary to build up the
laser from ASE with the amplifications by the SOA, so it
will cost about a few us or ms, which is much longer than
the gain recovery time of SOAs, which is abou t hundreds
of ps, so the SOA can be modeled as a steady-state ele-
ment.
When the injection curren t of the SOA is 200 mA, the
cavity is 20 m long, and the coupler is 70:30 (feedback :

Z. WANG ET AL.
62
output), the FWHM of the filter is about 0.146nm @
1560.52 nm, the building up activity in the SOA-R-FDML
can be simulated and shown in Figure 2. Figure 2(a)
shows the output spectra when the roundtrip is 1, 5, 10,
15, 20 and 50. Figure 2(b) shows the dependence of the
output peak power and the FWHM on the roundtrip in
the cavity, and the inset is the measured stationary spec-
tra. Figure 2(c) shows the relationship between the out-
put peak power (normalized to the saturation power of
the SOA) and the roundtrip, and the inset is the results
(by OSC) where every step corresponds to every round-
trip. From these figures, it can be seen that the peak
power increases and the linewidth becomes narrower till
to be unchanged after enough roundtrips, the cavity will
be a stationary laser with the output power of about 9.14
dBm and the FWHM of about 0.054 nm. It can be
counted from Figure 2(c) that the roundtrip is only 16 or
8 if the laser output about 95% or 80%, and the experi-
ments show that about 12 roundtrips (i.e. 12 steps) is
sufficient for lasing.
(a)
F
sweep
P
out
II III
F
round
/N
tu n e
F
round
/(NxN
tune
)
F
round
P
sat
I
P
ASE
(b)
Figure 1. (a) Structure of the SOA-R-FDML, (b) relation-
ship between the output peak power of the ring cavity and
the full band sweeping frequency.
1560.351560.41560.451560.51560.551560.61560.651560.7
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
wa v elength nm
output dB m
1
5
10
15
20
50
(a)
05 10 15 20 2530 35 4045 50
0. 06
0. 08
0. 1
0. 12
0. 14
0. 16
round trip
FW HM nm
05 10 15 20 2530 35 4045 50
-15
-10
-5
0
5
10
out
p
ut dBm
(b)
010 2030 40 5
0
0
20
40
60
80
100
round trip
output %
8
16
(c)
Figure 2. Building up laser activity in the cavity, (a) is the
evolution of the spectra, (b) is the evolution of the peak
power and the FWHM, (c) is the evolution of the normal-
ized peak power.
3. Three Operation Regimes
The center wavelength of the tunable filter varies with

Z. WANG ET AL. 63
time, and can be written as Eq. (1) for linear or sinusoidal
driver, where 

sweep=

max-

min,

avg=(

max+

min)/2,

min
and 
max are the min and max wavelength within the tun-
ing band, mod(t, Tsweep) is the modulus after t divided by
Tsweep, Fsweep (=1/Tsweep) is the full band sweeping fre-
quency.



 
min
sin
mod ,
sin 2mod,2
2
sweepsweep sweep
linear
avgsweep sweepsweep
tFtT
tFtT
 

 
 

 

For the ring cavity, the laser can be built up from the
A
3.1. WSL
Fround/(N·Ntune), the output of the ring cavity
) < Fsweep < Fround/Ntune, i.e., the
lig
en by a sinusoidal wave, the instan-
ta
SE of the SOA after N-times amplifications (the gain is
usually not same), it is also to say that light must propa-
gate N roundtrips in the cavity fo r lasing, so the building
up time can be written as Tbuild = NTround (building up
frequency Fbuild = Fround/N), where Tround is the roundtrip
time of the light (roundtrip frequency Fround = 1/Tround).
The effective tuning times in from 
min to

max is Ntune =


sweep/

FWHM, where 

FWHM, the FWHM of the tun-
able filter, is considered as the sweeping wavelength
resolution for the ring cavity, and the sweeping time
resolution is TFWHM = Tsweep/Ntune. The relationship be-
tween the output peak power and the full band sweeping
frequency Fsweep is obtained by this model and demon-
strated in Figure 1(b).
If Fsweep <<
is just the saturation power of the gain medium, i.e., it is
a tunable laser when the filter is very slowly tuned. If the
filter is continuously tuned faster, and Fsweep < Fround/
(N·Ntune), it is a common wavelength swept laser (WSL),
the output can be up to the saturation power of the SOA.
The region I in Figure 1(b) is for the regime of the tun-
able laser or WSL.
When Fround/(N·Ntune
ht propagates in the ring cavity less th an N roundtrips,
the ASE can't be amplified enough to build up laser, the
output peak power will be less than the saturation power
with a broad spectra linewidth. The ring cavity does not
operate as a laser in this regime, which is shown as the
region II in Figure 1(b), and the output power decreases
as Fsweep increasing.
If the filter is driv
neous sweeping frequency Fsweep t at different wave-
length can be derived from Eq. (1) and written as Eq. (2).
 
22
_14 .
s
weep tsweepavgsweep
FF    (2)
Fsweep_t is not exactly equal to Fsweep due to the nonlin-
ea
s
rity of the sinusoidal function. The relationship be-
tween Fsweep_t and the wavelength is shown on the right
axis of Figure 3(a), and the left axis is a part of Figure
1(b). Fsweep_t exactly equals to the driven frequency Fsweep
only at wavelength

1 and

2, and higher than Fsweep for
the wavelength in the range of (

1,

2) with the maxi-
mum Fsweep, for  < 
1 or
 > 
2, Fweep_t is lower than
Fsweep. The output power is greater on both end of the
sweeping range and smaller in the mid-band, which is
shown in Figure 3(b), and the spectra of both simula-
tions and experiments (inset figure) have good agree-
ments.
0 12 345
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
F
s w eep- t
/F
sweep
Power dBm

max

2

min

1
(a)
(b)
(c)
Figure 3. Properties of the W while the filter is driven by
drive waveform and output @ 1559.6 nm.
SL
a sinusoidal, (a) is the relationship between Fsweep_t and  , (b)
is the spectra of both simulation and experiment, (c) is the

Z. WANG ET AL.
64
In our setup, the ring cavity is about 12km long, the
tunable filter is driven by a sinusoidal function with fre-
quency of 22 .34 kHz and Vpp of 2.23 V, the output spec-
tra covers the band from 1556.1nm to 1565.4 nm. Figure
3(c) is th e waveform recorded b y an oscilloscop e following
a band pass filter @1559.6 nm at the ou tput of the WSL,
where the sinusoidal is the driver for the filter, the peak
and valley are corresponding to 1556.1 nm and 1565.4
nm, respectively. It shows that forward sweeps (shorter
to longer wavelength) have higher energy than backward
sweeps, this asymmetry is due to nonlinearities in the
SOA which tend to produce a downshift in energ y [2].
3.2. FDML
When Fsweep > Fround/Ntune, the ASE is always suppressed
passig th
model, a modified model based on
by the filter after ne SOA, so the output power is
even less than the ASE, the ring cavity does not work in
this regime. But, when Fsweep = M × Fround (M = 1, 2,
3......), i.e., the sweeping frequency of th e tunable filter is
exactly equal to the roundtrip frequency or its Mth order
harmonic, each wavelength component circulates in the
cavity such that it is transmitted through the filter and
feedback into the SOA for amplifying at every pass,
Lasing could build up not as in the conventional WSL.
Now, it is so-called Fourier domain mode locking laser
(FDML), which is shown as the red '+' in region III in
Figure 1( b).
In the simulations, the tunable filter is driven by a
sawtooth wave with frequency Fsweep = Fround, the wave-
length is swept from 1500 nm to 1600 nm, the injection
current of the SOA is 260 mA. Figure 4(a) shows the
relationships between the output peak power and the
roundtri p at wavel e n gt h 1 55 5 nm, 1560 nm and 156 5 nm,
it shows that the ring cavity will be a station ary operation
FDML after only 5 roundtrips. Figure 4(b) shows the
evolution of the spectra within a bandwidth of about
10nm, the roundtrip increases from lower to upper, and
the inset shows the spectra aroun d 10 dB m. The output of
the FDML shows tiny difference between different wave-
lengths due to the unflatness of the saturation of the SOA,
in the simulations, the unflatness is only about 0.03 dB
(about 0.7%) near 10dBm.
4. Conclusions
Against the current
the quasi-steady state SOA and segmentation method
with discrete frequencies is established for the frequency
domain mode locking lasers. With the consideration of
the tuning process of the filter and the feedback in the
ring cavity, the dyna mics of the building up laser activity
in the ring cavity are investigated. The relationship be-
tween the output peak power Pout and the full band
sweeping frequency Fsweep of the tunable filter is obtained
010 20 30 40 50
-20
-15
-10
-5
0
5
10
15
round t ri p
Power dBm
510 15 20 25 303540 45 50
10. 63
10.6 35
10. 64
10.6 45
10. 65
10.6 55
10. 66
1555nm
1560nm
1565nm
(a)
1556 1558 1560 1562 1564 1566
-20
-15
-10
-5
0
5
10
Wa vel ength nm
Power dBm
1556 1558 1560 1562 1564 1566
10. 63
10. 64
10. 65
10. 66
(b)
Figure 4. evolution of the output power (a) and the s
of the FDML (b).
ns of the amplified spontaneous emis-
on (ASE) and the gain properties of the SOA. The
dgements
the National Natural Sci-
1077048), Beijing Natural
CES
[1] R. Huber, M., “Fourier
Domain Modew Laser Operating
pectra
with the simulatio
si
SOA-R-FDML could operate at three different regimes,
which are tunable lasers, wavelength swept lasers (WSL)
and FDML lasers according to the relation between the
sweeping frequency Fsweep and the round trip frequency
Fround in the ring cavity. Some results for WSL and
FDML from both simulations and experiments agree well
to each other.
5. Acknowle
This work was supported by
ence Foundation of China (6
Science Foundation (4132035), Specialized Research
Fund for the Doctoral Program of Higher Education
(20120009110032), and by Beijing Jiaotong University
(2009JBM103, 2012 JBM103).
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