Optics and Photonics Journal, 2013, 3, 197-201
doi:10.4236/opj.2013.32B047 Published Online June 2013 (http://www.scirp.org/journal/opj)
Design of Seven-core Photonic Crystal Fiber with Flat
In-phase Mode for Yb: Fiber Laser Pumping
Ruijuan Dong1, Peiguang Yan1*, Gelin Zhang1, Huiquan Li1, Shuangchen Ruan1,
Huifeng Wei2, Jie Luo2
1Shenzhen key laboratory of laser engineering, Shenzhen University,
College of Electronic Science and Technology,ShenZhen, China
2State Key Laboratory of Optical Fiber and Cable Manufacture Technology,
Yangtze Optical Fiber and Cable Company Ltd. R&D center, Wuhan, China
Email: *yanpg@szu.edu.cn
Received 2013
We numerically investigate the seven-core photonic crystal fiber (PCF) with the zero dispersion wavelength designed in
the range of 1000 - 1080 nm, particularly suitable for the ytterbium-doped fiber laser pumping. Also, the PCFs are well
designed for obtaining a flat in-phase mode by carefully adjusting the diameter of inner layer six holes, and the corre-
sponding empirical values of fiber structure are summarized and listed. The variations of inner six holes to the ampli-
tude of in-phase mode are further investigated, and our results show that a better tolerance can be achieved in the fiber
structures with lower filling ratio configuration.
Keywords: Photonic Crystal Fiber (PCF); In-phase Mode (IPM); Supercontinuum Generation (SCG)
1. Introduction
The supercontinuum generation (SCG) in photonic crys-
tal fiber (PCF) is an intensively research topic in optical
and photonic science in the last decade [1-4]. Along with
the research of SCG, the corresponding SC sources have
already found their applications in optical coherence to-
mography (OCT), pump-probe spectroscopy, metrology
or non-linear microscopy. Recently, high power SC
source becomes a new research trend and exhibits strong
attraction because of the high spectral power density. The
ytterbium fiber (Yb:fiber) laser system has the merits of
high efficiency, reliability and compatibility with PCF,
rendering them almost ideal candidates for compact
sources of SC radiation [5-8]. H. Chen [7] reported a 35
W high power all fiber SC source based on PCF with
picosecond laser, and X. Hu [8] reported a 50W strictly
single mode all-fiber SC source spanning from 500 nm to
over 1700 nm by using a 5-m-long commercially PCF.
However, it is particularly challenging to further improve
the SC power that limited by the low coupling efficiency
from the large mode area Yb:fiber into the highly
nonlinear PCF. The mismatch between their core diame-
ters causes a high splicing loss, and the leaked power is
enough to destroy the splicing point at high pump power.
Simply increasing the core size of PCF would cause the
zero dispersion wavelength (ZDW) shift to longer wave-
length, hence unfavorable for spectral broadening ac-
cording to the soliton mechanism. A feasible method is
the PCF mode-field expanders [9], but the fabrication
process is complicated and the large convert ratio of
mode field is more challenging in itself. Several recent
researches focused on the high pulse energy phase-locking
multicore Yb-doped PCF laser [10-12], and SC genera-
tion has reported with 5.4 W output power in a seven-
ore PCF with femtosecond Yb:fiber laser system [13],
but the fundamental supermode is not optimal in that
fiber design.
Among all supermodes, only the in-phase mode (IPM)
where all cores have the same phase has the best Gaus-
sian-like far field intensity distribution resulting in good
beam quality [14-17]. A. Mafi [14-15] has presented a
recipe for constructing custom-shaped modes based on
perturbation theory of coupled modes, but the recipe is
not intuitive. In this paper, our aim is to design the seven-
ore PCFs with well flat IPM while keeping the ZDW in
1000 - 1080 nm for Yb:fiber laser pumping. The corre-
sponding empirical values of fiber structure are summa-
rized and listed. The variations of inner six holes to the
amplitude of IPM are further investigated, and our results
show that a better tolerance can be achieved in the fiber
structures with lower filling ratio configuration.
*Corresponding author.
Copyright © 2013 SciRes. OPJ
2. The Fiber Structure
Figure 1 is the cross section of seven-core PCF with the
enlarged microstructure region. The air holes are ar-
ranged in a hexagonal pattern. Around the central core,
the adjacent six air holes are missed to form a seven-core
PCF, and each core is marked out with number. The lat-
tice constant is set to Λ, the inner six air holes around
central core have a diameter of d1 and air filling ratio of
F1, while the other air holes have a diameter of d2 and
filling ratio of F2. We utilize the full-vectorial finite ele-
ment method to simulate the mode field distribution and
fiber parameters of the seven-core PCF e.g. dispersion
parameter D, nonlinear coefficient γ and effective mode
area Aeff. Material dispersion of silica is included in our
simulation [18].
3. Results and Discussion
In our calculation, the filling ratio F2 is set in the range of
0.45 - 0.55. These F2 values are slightly higher than the
single mode condition [19], but can also achieve a high
beam quality as has been proved in single core PCFs [20].
Also, a slightly higher F2 has the merits of mode con-
finement. We check the lattice constant Λ from 2.8μm to
3.4μm, and adjust the filling ratio F1 to get the flat IPM.
The corresponding values are organized in Table 1. It
can be seen the F1 are 0.497, 0.577 for F2 = 0.45, 0.55 at
Λ = 2.8 μm, while the corresponding value of F1 are
0.4928, 0.5728 at Λ = 3.4 μm. We notice that the F1 in-
creases by ~0.008 when the F2 increases by 0.01 for a
fixed Λ value in concerned range. Furthermore, the F1
decreases by ~0.0007 when the Λ increases by 0.1μm for
a fixed F2. We then test the other Λ and F2 in the con-
cerned range, and find that good flat IPM can be
achieved based on the above mentioned empirical rela-
tion. Figure 2 shows the 3-D flattened IPM distribution
for Λ = 2.8 μm, 3.4 μm and F2 = 0.45, 0.55, respectively.
It is evidently that all the lobes of the IPMs are of equal
Figure 1. The fiber structure.
Table 1. The calculated F1 for flattened IPMs in the concerned range of Λ and F2.
2.8 2.9 3.0 3.1 3.2 3.3 3.4
F2=0.45 0.497 0.49630.49560.49490.49420.4935 0.4928
F2=0.46 0.505 0.50430.50360.50290.50220.5015 0.5008
F2=0.47 0.513 0.51230.51160.51090.51020.5095 0.5088
F2=0.48 0.521 0.52030.51960.51890.51820.5175 0.5168
F2=0.49 0.529 0.52830.52760.52690.52620.5255 0.5248
F2=0.50 0.537 0.53630.53560.53490.53420.5335 0.5328
F2=0.51 0.545 0.54430.54360.54290.54220.5415 0.5408
F2=0.52 0.553 0.55230.55160.55090.55020.5495 0.5488
F2=0.53 0.561 0.56030.55960.55890.55820.5575 0.5568
F2=0.54 0.569 0.56830.56760.56690.56620.5655 0.5648
F2=0.55 0.577 0.57630.57560.57490.57420.5735 0.5728
(a) (b) (c) (d)
Figure 2. The flattened 3-D IPMs, here, (a) is for Λ = 2.8 μm and F2 = 0.45, (b) is for Λ = 2.8 μm and F2 = 0.55; (c) is for Λ=3.4
μm and F2 = 0.45, while (d) is for Λ = 3.4 μm and F2 = 0.55.
Copyright © 2013 SciRes. OPJ
R. J. DONG ET AL. 199
Considering that the ZDW range of fiber structures in
Table 1 can be determined by the fiber structures at the
low left corner and the top right corner, we calculate the
dispersion profiles of the two fiber structures as shown in
Figure 3 (a). The inset clearly shows the ZDW position
is in our desired range of 1000 nm-1080 nm, meeting our
design purpose. Figure 3 (b) shows the calculated
nonlinear coefficient γ and effective mode area Aeff at
wavelength of 1060 nm at the different F2. Here we only
display the values for Λ = 2.8 μm and 3.4 μm, it is
enough for determining the γ and Aeff range for the other
Λ in Table 1. It can be expected that the Aeff is sevenfold
larger than the single core PCF with the same Λ and F2.
Hence the pump coupling efficiency can be enhanced
but with a sacrifice of γ. As for the fiber structure of Λ =
3.4 μm, F1 = 0.5728 and F2 = 0.55, the γ value is
1.67W-1km-1, about one seventh of the single core PCF
with similar structure in reference [20].
Since the flattened IPM is controlled by engineering
the air-hole size between the cores, a tolerance analysis is
necessary to study how robust the fiber design is to per-
turbations. Through a change of the first layer filling
Figure 3. The properties for the flattened IPMs with
structure of Λ = 2.8 μm, F2 = 0.55 and Λ = 3.4 μm, F2 = 0.45.
Here, (a) is dispersion profiles, and (b) is for γ and Aeff
calculated at 1060nm.
ratio F1, a tolerance comparison is given in Figure 4. The
curves are obtained by extracting out the x component of
electric field Ex across the cores marked with 5, 1, 2.
Figure 4 (a) is for the fiber structure of Λ = 2.8 μm and
F2 = 0.55, while Figure 4 (b) is for the same Λ but with a
lower filling ratio F2 = 0.45. We can see that the Ex curve
changes significantly for the case of F2 = 0.55 at the
variations of ± 5%. However, the MCPCF with a lower
filling ratio of F2 = 0.45 and Λ = 2.8 μm exhibits high
resistance to the perturbations, hence benefiting for the
flat IPM control in actual fabrication process.
It is necessary to analyze the IPM distribution at the
different wavelengths, since the SC usually covers a
broad spectral range. Figure 5 shows the calculated 3-D
field distribution for the case of Λ = 2.8 μm, F1 = 0.497
and F2 = 0.45. Although the wavelength spans from 600
nm to 1800 nm, the Ex amplitude difference between the
central lobe and surround lobes is still in an acceptable
level. Consequently, the IPMs of MCPCF are more fa-
vorable for the high power coherent SC source. It is also
noticed that the central lobe is slightly lower at the short
wavelength but higher at the long wavelength as we
compare the field distribution at 600 nm with that at
1800 nm, hence the visible parts in the generated spec-
trum would be gathered in outside six lobes when this
MCPCF is applied in SCG.
Figure 4. The Ex tolerance of IPMs with the variations of ±
5% for the inner six air holes, here (a) is for Λ = 2.8 μm and
F2 = 0.45, while (b) is for Λ = 2.8 μm and F2 = 0.55.
Copyright © 2013 SciRes. OPJ
(a) (b)
(c) (d)
Figure 5. The 3-D IPMs at wavelength 600 nm, 1060 nm,
1400, 1800 nm from (a) to (b), respectively. The fiber has a
structure of Λ = 2.8 μm, F1 = 0.497 and F2 = 0.45.
4. Conclusions
In conclusion, we firstly numerically investigate the
seven-core PCF with the ZDW designed in the range of
1000 - 1080 nm for the purpose of high power SC source
pumped by the Yb: fiber laser. Also, the PCFs are well
designed for obtaining a flat in-phase mode by carefully
adjusting the diameter of inner layer six holes, and the
corresponding empirical values of fiber structure are
summarized and listed. The variations of inner six holes
to the amplitude of in-phase mode are further investi-
gated, and our results show that a better tolerance can be
achieved in the fiber structures with lower filling ratio
configuration. These results are helpful for design of
seven-core PCF for high power SCG.
5. Acknowledgements
Supported by NSFC (Nos.61007054, 61275144), Doctoral
Program of Higher Education Research Fund (No.2010
408110002), the Improvement and Development Project
of Shenzhen Key Lab (Nos.CXB201005240014A, ZDSY
0120612094924467), the Science and technology project
of Shenzhen City (No. JC201105170693A), the Science
and technology project of Shenzhen University (No.2012
1) and the Science and technology project of Shenzhen
City (Nos.ZYC20100690103A, 2011PTZZ0125).
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