COL 9(5), 050603(2011) CHINESE OPTICS LETTERS May 10, 2011
Design procedure for photonic crystal fibers with
ultra-flattened chromatic dispersion
Huizhen Xu (徐徐徐惠惠惠真真真)
1,2∗
, Jian Wu (伍伍伍 剑剑剑)
1
, Yitang Dai (戴戴戴一一一堂堂堂)
1
,
Cong Xu (徐徐徐 聪聪聪)
1
, and Jintong Lin (林林林金金金桐桐桐)
1
1
Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts
and Telecommunications), Ministry of Education, Beijing 100876, China
2
College of Science, Jimei University, Xiamen 361021, China
∗
Corresp onding author: elimshee@gmail.com
Received November 1, 2010; accepted December 14, 2010; posted online April 18, 2011
A simple design procedure is used to generate photonic crystal fibers (PCFs) with ultra-flattened chromatic
disp ersion. Only four parameters are required, which not only considerably saves the computing time,
but also distinctly reduces the air-hole quantity. The influence of the air-hole diameters of each ring of
hexagonal PCFs (H-PCF, including 1-hole-missing and 7-hole-missing H-PCFs), circular PCFs (C-PCF),
square PCFs (S-PCF), and o ctagonal PCFs (O-PCF) is investigated through simulations. Results show
that regardless of the cross section structures of the PCFs, the 1st ring air-hole diameter has the greatest
influence on the dispersion curve followed by that of the 2nd ring. The 3rd ring diameter only affects
the dispersion curve within longer wavelengths, whereas the 4th and 5th rings have almost no influence
on the dispersion curve. The hole-to-hole pitch between rings changes the dispersion curve as a whole.
Based on the simulation results, a procedure is proposed to design PCFs with ultra-flattened dispersion.
Through the adjustment of air-hole diameters of the inner three rings and hole-to-hole pitch, a flattened
disp ersion of 0±0.5 ps/(nm·km) within a wavelength range of 1.239 – 2.083 µm for 5-ring 1-hole-missing
H-PCF, 1.248 – 1.992 µm for 5-ring C-PCF, 1.237 – 2.21 µm for 5-ring S-PCF, 1.149 – 1.926 µm for 5-ring
O-PCF, and 1.294 – 1.663 µm for 7-hole-missing H-PCF is achieved.
OCIS codes: 060.2280, 220.4000, 060.4005.
doi: 10.3788/COL201109.050603.
Since photonic crystal fibers (PCFs) were first reported
in 1996
[1]
, different kinds of PCF cross section structures,
such as hexagonal PCF (H-PCF)
[2]
, octagonal PCF (O-
PCF)
[3]
, square PCF (S-PCF)
[4]
, and so on, have been
developed. The dispersion properties of PCFs are sig-
nificantly different from those of conventional fibers be-
cause the cross section structures consisting of an array
of air holes allow for flexible tailoring of the dispersion
curves, which cannot be realized in conventional opti-
cal fibers. Control of the chromatic dispersion in PCFs
is of huge importance for applications in optical fiber
communications
[5]
, dispersion compensation, supercon-
tinuum generation
[6,7]
, and so on.
Many PCF designs have been proposed to achieve
ultra-flattened chromatic dispersion. In Ref. [8], the
chromatic dispersion in conventional PCFs was con-
trolled by changing the air holes, which are arrayed in
a regular hexagonal structure with the same diameters
in the cladding region. A PCF with a dispersion of
0±0.6 ps/(nm·km) from 1.24 to 1.44 µm was realized.
Because the air-filling fraction is too small to realize
ultra-flattened dispersion, more than 20 rings of air holes
(up to 455 holes) are required to significantly reduce the
confinement loss, thereby causing extreme complexity in
the manufacturing process. Moreover, the achievement of
this kind (same air-hole size) of ultra-flattened dispersion
over such a large wavelength range involves highly accu-
rate control of air-hole diameter and pitch
[9]
. To reduce
the quantity of air holes and realize ultra-flattened dis-
persion, many designs discussed in literature have the fol-
lowing characteristics: differently spaced rings of holes
[3]
and different sizes of holes
[10]
. In Ref. [3], the authors
presented an 8-ring O-PCF. After optimization of the di-
ameters of the 1st ring, the outer seven rings, and the air-
hole pitch, PCFs with a dispersion of 0± 0.5 ps/(nm·km)
in a wavelength range of 1.46–1.66 µm were obtained. In
Ref. [10], a new design with four or five rings of gradually
increasing air-hole diameters for each ring was proposed
for achieving ultra-flattened dispersion. Through opti-
mization, a four-ring PCF with a flattened dispersion of
0±0.5 ps/(nm·km) for a wavelength of 1.19 – 1.69 µm,
and a five-ring PCF with a flattened dispersion of 0±0.4
ps/(nm·km) for a wavelength 1.23 – 1.72 µm were pro-
posed. This design considerably reduces the ring number
of air holes, but the design procedure becomes compli-
cated because several geometrical parameters, five (four
air-hole diameters and one pitch) for the four-ring PCF
and six (five air-hole diameters and one pitch) for the
five-ring type, are needed to simultaneously optimize dis-
persion properties. Several studies have already used the
genetic algorithm to determine global minima for ultra-
flattened design
[11,12]
. However, the genetic algorithm
entails considerable computing time because it requires
numerous iterations. In Ref. [12], for example, the algo-
rithm required 40 individuals and 13 generations.
In this letter, a simple procedure for different kinds
of PCFs is presented to obtain ultra-flattened disper-
sion. This design procedure requires only four parame-
ters (three air-hole diameters and one hole-to-hole pitch),
considerably saving the computing time. In addition,
it requires only one array layout cross section structure
and four or five rings of air holes, tremendously reducing
the complexity in manufacturing process. This design
procedure is suitable not only for 1-hole-missing PCFs
1671-7694/2011/050603(4) 050603-1
c
° 2011 Chinese Optics Letters