Description of the FDML Laser with Quasi-steady State Model of the SOA

doi:10.4236/opj.2013.32B015

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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

Email: [email protected]

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.

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)

sweep

out

II III

round

tu n e

round

/(NxN

tune

)

round

sat

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

wa v elength nm

output dB m

(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

out

ut dBm

(b)

010 2030 40 5

100

round trip

output %

(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

sweepsweep sweep

linear

avgsweep sweepsweep

tFtT

 



 

 



 



For the ring cavity, the laser can be built up from the

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-

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).



_14 .

weep tsweepavgsweep

 

 (2)

Fsweep_t is not exactly equal to Fsweep due to the nonlin-

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 (



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

s w eep- t

sweep

Power dBm



max



min



(a)

(b)

(c)

Figure 3. Properties of the W while the filter is driven by

drive waveform and output @ 1559.6 nm.

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.

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

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

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

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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