Optics and Photonics Journal, 2013, 3, 57-60
doi:10.4236/opj.2013.32B014 Published Online June 2013 (http://www.scirp.org/journal/opj)
High Performance Asymmetric Three
Corrugation-Pitch-Modulated DFB Lasers Suitable for
Stable Single Longitudinal Mode Operation
Qiang Zuo*, Jianyi Zhao, Zhihao Wang, Xin Chen, Wen Liu
Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information,
Huazhong University of Science and Technology, Wuhan 430074, China
Email: 2004zuoyou@163.com
Received 2013
This paper presents an optimized asymmetric three corrugation-pitch-modulated DFB laser (3CPM-DFB) with ex-
tremely high mode selectivity(L
= 0.97) and low flatness(F = 0.009), which are two key parameters to indicate the
laser’s single longitudinal mode(SLM) performance. In threshold analysis, the optimization process based on transfer
matrix method is demonstrated to maximize L
and minimize F simultaneously. In the above-threshold regime, the
evolutions of L
and longitudinal distribution of photon density with injection current are evaluated. More impor-
tantly, nanoimprint lithography which was proved an efficient way to fabricate DFB gratings can provide completely
same simple fabrication procedure for both 3CPM grating and conventional uniform grating. So the big practical value
of 3CPM-DFB can be expected because of its advanced performance and easy manufacturability.
Keywords: Corrugation-Pitch-Modulated; Distributed Feedback Laser; Mode Selectivity; Flatness
1. Introduction
With the development requirements of metro and access
networks, low cost and high stable single longitudinal
mode (SLM) oscillation DFB lasers are desired
strongly[1]. The diffraction grating structure is one of the
key parts deciding the laser’s SLM performance, which
usually indicated by two parameters: mode selectivity
) and cavity field flatness factor (F). Actually, to
avoid the degradation of SLM operation of conventional
quarterly-wavelength shifted (QWS) grating DFB laser
induced by spatial hole burning (SHB) effect, there is a
long research history of grating optimization design.
Mainly they are classified into four categories:(1)gain
coupling grating[2]; (2)distributed coupling coefficient
(DCC) grating[3]; (3)corrugation pitch modulated (CPM)
grating[4]; (4) multiple phase-shift (MPS) grating[5]. Of
course, appropriate combination of phase-shift or CPM
and DCC grating can give better SLM performance, de-
spite the fact that the difficulties of manufacture increase
The major drawback of gain coupling grating and DCC
grating is fabrication difficulties, making them hard to
implement. As far as manufacturing method of diffrac-
tion grating is concerned, nanoimprint lithography (NIL),
as a promising nano-structure fabrication method with
high resolution, high throughput and low cost, was pro-
posed to fabricate diffraction gratings of DFB laser re-
cently [7-8]. The characteristics of NIL make it provide
completely apparent manufacturing processes to MPS
type and CPM type grating with no more complexity. To
the authors’ knowledge, however, there hasn’t been ac-
curate optimization research of multiple CPM grating DFB
laser up to now. In this work, an asymmetric three CPM
grating is optimized to improve the laser’s SLM per-
formance. Results show that 3CPM-DFB can give much
bigger L
and smaller F than 3PS-DFB, namely,
more stable SLM performance. In Section 2, the classical
transfer matrix method (TMM) is used for threshold
analysis and grating structure optimization. Then above
threshold analysis of the optimized 3CPM-DFB is inves-
tigated in Section 3. The variations of L
and longi-
tudinal distribution of photon density versus injection
current are calculated. Finally, Section 4 summarizes the
main conclusions.
2. 3CPM Grating Structure and Optimization
2.1. 3CPM Grating Structure
Figure 1 schematically shows the 3CPM grating struc-
ture under analysis. Both ends of the grating are perfectly
anti-reflection coated and the coupling coefficient is uni-
form along the axis. The unique character of 3CPM grat-
Copyright © 2013 SciRes. OPJ
ing is that there are three Bragg-detuned sections with the
grating period bigger than that of the other parts, namely,
the basic period. As shown in Figure 1, 1
rar de-
fined as the center of the three CPM parts respectively
and length of the three CPM parts are 1,2, 3.
All these parameters are normalized to the total cavity
length L.
Lc LcLc
jj  are the grating period of the three CPM
parts respectively. 0
is the basic period. Define the rela-
tive pitch difference of three CPM parts to basic period
as follows:
Here the center of the second CPM part is limited to
the center of the cavity. That means 2
r 0.5. So the rest
of parameters need to be optimized are 1, 3, 1,
2,3, ,2,3 and normalized coupling
coefficient (). Think of the fact that the effect of rela-
tive pitch difference to device performance is periodic[4],
the varying range of relative pitch difference is limited
between 0 and is limited between 1 and 3.
The constraints of 1,3,1,2,3 are to avoid the
overlap of the three CPM parts. The other laser parame-
ters used in this paper are summarized in Table 1.
r rLc
Lc Lc 1
KL 
r r
Lc Lc Lc
Figure 1. A simplified schematic diagram for the 3CPM-DFB
laser structure.
Table 1. Summary of laser parameters.
Laser parameters Value
Materials parameters
Spontaneous emission rate, A 2.5 × 108 s-1
Bimolecular recombination coefficient, B 1.0 × 10-16 m3·s-1
Auger recombination coefficient, C 3.0 × 10-41 m6·s-1
Differential gain, A0 2.7 × 10-20 m2
Gain curvature, A1 1.5 × 1019 m-3
Differential peak wavelength, A2 2.7 × 10-32 m4
Internal loss, αloss 4.0 × 103 m-1
Effective index at zero injection, n0 3.41351524
Carrier density at transparency, N0 1.5 × 1024 m-3
Differential index, dn/dN -1.8 × 10-26 m3
Group velocity, νg 8.1 × 107 s-1
Nonlinear gain coefficient, ε 1.5 × 10-23 m3
Structure parameters
Active layer width, w 1.5 μm
Active layer thickness, d 0.12 μm
Cavity length, L 500 μm
Optical confinement factor, Г 0.35
Grating period, Λ 227.039 nm
2.2. Grating Structure Optimization
To do the threshold analysis, sophisticated TMM-based
laser model is used [5-6]. The cavity is divided into
seven concatenated sections to ensure structure parame-
ters in each section are constant. For a given set of struc-
ture parameters, the entire lasing mode and their thresh-
old gain can be obtained based on TMM model. Then the
mode selectivity and field flatness can be calculated.
They are defined by
 
z (2)
Where th L
and L
are the normalized gain of the
lasing mode and the main side mode respectively.
is the normalized electric field intensity at position z and
I is its average value along the cavity. The set of struc-
ture parameters mentioned in section 2.1 are scanned and
updated with the similar step by step procedures that are
clearly presented in reference [5,6]. In every step, the big-
ger L
and smaller F than the previous step can be
picked out and the corresponding structure parameters
can be updated. Then other parameters are ready to opti-
mized. This process is repeated until no improvements on
and F are achieved.
The final results are summarized in Table 2 and com-
pared with that of the 3PS-DFB reported in literature [5]
and QWS-DFB. It is clear that the optimized asymmetric
3CPM-DFB have big advantages with much higher
and extremely low F. And the optimized structure
parameters are as follows: = 0.135, 3= 0.78, 1=
0.26, = 0.23, = 0.29, = 1.7,
2.3 1
0 ,
 2
3. , 4 3
3, 1.4 10
 Figure
2 shows the mode distribution of this optimized structure.
Table 2.
L, F and for several laser structures.
Laser Structure
F th
Optimized 3CPM-DFB 0.97 0.009 1.14
QWS-DFB 0.73 0.3 0.7
Optimized 3PS-DFB[5] 0.78 0.01 1.18
Figure 2. Mode distribution of the optimized structure.
Copyright © 2013 SciRes. OPJ
Q. ZUO ET AL. 59
3. Above Threshold Analysis
Even if the threshold analysis presents a good perform-
ance of the optimized 3CPM-DFB, an above threshold
analysis is essential to assess the effect of SHB on the
laser performance with the increasing injection current.
In the above threshold regime, the longitudinal inho-
mogeneities of the photo density, the carrier density and
the refractive index have to be considered. The basic
model is TMM together with rate equation. The details of
lasing mode and side mode analysis are clearly presented
in reference [5-6].
Figure 3 shows the longitudinal distribution of the
photon density in the optimized asymmetric 3CPM-DFB
laser under different biasing currents. Due to the stimu-
lated emission, gradual increase of the photon number in
the whole structure can be observed. The meaningful
feature is that the difference between the central photon
density and the escaping photon densities at the facets is
very small. This is beneficial when taking the emitted
power into consider.
The mode selectivity of the optimized asymmetric
3CPM-DFB versus biasing current is shown in Figure 4,
compared with that of the optimized 3PS-DFB in refer-
ence [5] and QWS-DFB. Undoubtedly, the optimized
3CPM-DFB is the best and very stable. On the contrary,
there are different degrees decreasing of mode selectivity
versus current both in 3PS-DFB and QWS-DFB. This
represents the optimized 3CPM-DFB is immune to the
4. Conclusions
An asymmetric 3CPM-DFB laser grating structure has
been proposed and analyzed in the threshold and above
threshold regime. The optimized 3CPM-DFB has ex-
tremely high mode selectivity and low field flatness. The
Figure 3. Longitudinal distribution of the photon de nsity in
the optimized structure under different biasing currents.
Figure 4. Mode selectivity vs. current injection of the opti-
mized structure, the optimized 3PS-DFB of reference [5]
and the QWS-DFB laser structures.
above threshold analysis shows the longitudinal distribu-
tion of photon density is still flat enough and mode selec-
tivity is still very high even under 5th
, representing this
optimized 3CPM-DFB laser is immune to SHB with high
stable single mode operation and very suitable to modern
optical communication system.
5. Acknowledgements
This work was supported by the Special Project on De-
velopment of national key scientific instruments and
equipment of China (Grant No. 2011YQ16000205); the
National key technology R&D program of China (Grant
No. 2009BAH49B01), and the Chinese National Science
and Technology Plan 863 (No 2011AA010304).
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