Vol.3, No.5, 401-407 (2011) Natural Science
Copyright © 2011 SciRes. OPEN ACCESS
Design of supercontinuum generating photonic crystal
fiber at 1.06, 1.31 and 1.55 µm wavelengths for medical
imaging and optical transmission systems
Feroza Begum*, Yoshinori Namihira
Graduate School of Engineering and Science, University of the Ryukyus, Okinawa, Japan; *Corresponding Author:
Received 29 March 2011; revised 14 April 2011; accepted 20 April 2011.
We propose broad supercontinuum spectrum
generating highly nonlinear photonic crystal
fiber (HN-PCF) which can be used in ultrahigh-
resolution optical coherence tomography and
optical transmission systems. Using full vector
finite difference method, we investigated the
different properties of HN-PCF. Broadband su-
percontinuum spectrum is numerically calcu-
lated by using nonlinear Schrödinger equation.
Investigation showed that it is possible to ob-
tain longitudinal resolution in a biological tissue
of 1.3 μm, 1.2 μm and 1.1 μm by using pico-
second continuum light at center wavelengths
of 1.06 μm, 1.31 μm and 1.55 μm, respectively.
Keywords: Photonic Crystal Fibers (PCFs);
Finite Difference Method; Chromatic Dispersion;
Supercontinuum Spectrum;
Optical Coherence Tomography
Photonic crystal fibers (PCFs) are new class of optical
waveguide in recent years. PCF consists of a thread of
silica with a lattice of microscopic air capillaries running
along the entire length of the fiber. The design freedom
of photonic crystal fibers (PCFs) can be used to tailor
and extend the range of optical parameters like disper-
sion and nonlinearity [1]. Owing to the high index dif-
ference between silica core and air hole cladding, PCFs
allow much stronger mode confinement, and thereby
much higher nonlinearities. The reduced effective area
Aeff is achieved by stronger mode confinement in the
core with small core diameter, as a result nonlinearity γ
can be increased. From the nonlinearity equation γ =
2πn/λAeff, it is clearly shown that nonlinearity is inversely
proportional to the fiber’s effective area. The zero
dispersion wavelengths can thus be shifted toward the
visible to near IR and matched with the operating wave-
length of a large variety of nanosecond to femtosecond
high peak power lasers, yielding broadband continuum
[2]. The broadband supercontinuum (SC) generation in
optical fibers currently attracts a lot of attention because
of the high potential for applications in the fields of the
optical communications, optical coherence tomography
(OCT), optical metrology, time resolved absorption and
spectroscopy [3-7]. OCT enables micron-scale, cross-
-sectional and three-dimensional imaging of biological
tissues in situ and in real time. Ultrahigh-resolution OCT
imaging in the spectral region from 1.0 to 1.6 μm re-
quires extremely broad bandwidths because coherence
length depends on the longitudinal resolution. However,
this spectral region is of particular interest for OCT be-
cause it penetrates deeply into biological tissue and per-
mits spectrally resolved imaging of water absorption
bands. In this spectral region, attenuation is minimum
due to absorption and scattering. It should be noted that
scattering decreases at longer wavelengths in proportion
to 1/λ4, indicating that the scattering magnitude at
1.0 μm - 1.6 μm wavelengths is lower than at the visible
wavelengths [8]. Superluminescent diodes (SLDs) are
often used for OCT imaging and typically have 10 -
15 μm longitudinal resolution [9]. This resolution is in-
sufficient for identifying individual cells or assessing
subcellular structures such as nuclei. Ultrahigh-resolution
OCT in biological tissue, achieving high longitudinal res-
olution at center wavelength near 1.0 μm [10-12], 1.3 μm
[13,14] and 1.55 μm [15], has been demonstrated with
femtosecond lasers as low coherence light sources. On
the other hand, telecommunication window (around
1.55 μm) is the most attractive window in optical com-
munication systems, dispersion compensation and non-
linear optics because of the minimum transmission loss
of the fiber. Chromatic dispersion controlling and simul-
taneously keeping the confinement loss to a level below
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
the Rayleigh scattering limit in conventional fiber is very
important for any optical systems. Recently, we have
reported that it is possible to achieve broad superconti-
num spectrum, high longitudinal resolution in biological
tissue by using HN-PCF with ultraflattened chromatic
dispersion properties [16].
Therefore, as part of the ongoing efforts in pursuit of
simple structures in PCFs for SCG light sources, in this
paper, we further demonstrate an HN-PCF with an ultra-
flattened chromatic dispersion over a wider wavelength
range, broad supercontinum spectrum, and high longitu-
dinal resolution. In this paper, we explore the possibility
of generating supercontinuum spectrum by using pico-
second pulses in six-ringed highly nonlinear photonic
crystal fiber (HN-PCF) ultrahigh-resolution OCT and
optical transmission systems. The three different sizes
air hole diameters are used in order to simplify the
structure and decrease the fabrication difficulties. From
numerical simulation results we achieve very high non-
linear coefficients with ultra-flattened chromatic dis-
persion, low dispersion slope, broadband SC spectrum,
ultra-high resolution, high power and low confinement
loss, simultaneously. We realize longitudinal resolution
in biological tissue of 1.3 μm, 1.2 μm and 1.1 μm at the
center wavelengths of 1.06 μm, 1.31 μm and 1.55 μm for
the application of OCT system. This is, to our knowl-
edge, the highest resolution achieved to date for bio-
logical imaging in these wavelengths. Moreover, pico-
second pulse laser source is cheaper than that of femto-
second laser source in this case it attracts in practical
Figure 1(a) shows the transverse geometry of hex-
agonal PCF (H-PCF). For the purpose of simplicity only
two rings are shown. The air holes are arranged with a
hexagonal symmetry across the cross section where Λ is
the center-to-center spacing between the air holes, d is
the air hole diameter, and the core diameter is 2a. The
H-PCF is constructed by repeating the unit equal lateral
triangular lattice with vertex angle of 60˚ shown in Fig-
ure 1(b). The air holes of diameter d are located at each
corner of the equilateral triangle. A cross-section of the
proposed HN-PCF structure is illustrated in Figure 1(c).
In this design, first ring air hole diameter is d1, second
and third ring air hole diameter is d2, fourth to sixth ring
air hole diameter is d. PCFs possess artificially-periodic
cladding consisting of micrometer-sized air holes allow
flexible tailoring of the dispersion curves. As a conse-
quence we need to incorporate much more sophisticated
structure with more degrees of freedom regarding the
total number of design parameters in order to achieve
Figure 1. Transverse geometry of the H-PCF: (a)
Structure with two rings and (b) a unit equal lateral
triangular lattice and (c) Geometry of the proposed six
ring HN-PCF.
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
flat dispersion, small effective area, while keeping the
confinement losses as low as possible. For index-guiding
PCFs as periodic lattice arrangement for the air holes are
not absolutely necessary to achieve guidance of light in
the core region [3]. The proposed HN-PCF is designed
following this principle to control the dispersion and
dispersion slope in wide wavelength range. Therefore, in
the proposed structure, we break the uniformity of the
cladding region and the diameter of the first ring air hole
is reduced to d1 to obtain near zero flat dispersion, while
the diameter of other air hole rings d is selected large for
keeping low confinement loss value.
The full-vector finite difference method (FDM) [17,18]
with anisotropic perfectly matched boundary layers
(PMLs) is used to calculate the different properties of
PCFs. Anisotropic PMLs absorbing boundary are posi-
tioned outside the outermost ring of air holes in order to
reduce the simulation window and to evaluate the con-
finement loss of the proposed fiber with a finite number
of air hole rings. The material dispersion given by Sell-
meier equation is directly included in the calculation.
Therefore, chromatic dispersion in References [17,18]
corresponds to the total dispersion of the PCFs. Chro-
matic dispersion is an important phenomenon in the
propagation of short pulses in optical fibers. Temporally
short pulses have a large spectral bandwidth. The differ-
ent spectral components of the pulse travel through the
medium at slightly different group velocities because of
chromatic dispersion, which can result in a temporal
broadening of the light pulses with no effect on their
spectral compositions. Once the modal effective indices
is obtained by solving an eigenvalue problem drawn
from the Maxwell’s equations using the FDM, the pa-
rameter chromatic dispersion, confinement loss and ef-
fective area can be calculated by [17,18]
d1 2π
where, vg is group velocity, β2 is group velocity disper-
sion, λ is the wavelength, c is the velocity of light in va-
cuum, Re(neff) is the real part of neff.
10 0
20log e8.686Im
 (2)
where, Im(neff) is the imaginary part of neff, k0 = 2π/λ is
the free space wave number.
  
 
ExyExy xy
Exy Exyxy
where, E is the transverse electric field derived by solving
Maxwell’s equations. We can know that the effective area
depends on two factors: the refractive index difference
between the cores and the cladding, the dimension of the
Since amorphous silica can be treated as a homoge-
neous material, the lowest-order nonlinear coefficient is
the third-order susceptibility χ(3) [8]. Most of the nonlin-
ear effects in optical fibers therefore originate from
nonlinear refraction, a phenomenon that refers to the
intensity dependence of the refractive index resulting
from the contribution of χ(3), i.e., the refractive index of
the fiber becomes
nn nE (4)
where n1 is the linear part, 2
Eis the optical intensity
inside the fiber, n2 is the nonlinear refractive index related
to χ(3) by the following relation
where Re stands for the real part. Nonlinear coefficient is
calculated with following equation [8].
eff eff
cA A
 
 
 
 
 
 
 
where γ is the nonlinear coefficient, ω is the angular
frequency, n2 is the nonlinear refractive index, λ is the
wavelength of the light, (n2/Aeff) is the nonlinear constant.
Two ways to enhance the nonlinearity is to reduce the
effective area through a smaller core diameter and higher
index contrast. By appropriate choice of size and pattern
of PCF section, the effective area can be reduced; there-
by the nonlinearity of the fiber can be increased by in-
creasing the intensity inside the fiber which increases the
nonlinear phase change during propagation.
The wavelength dependence properties of chromatic
dispersion, dispersion slope, effective area, nonlinear
coefficient and confinement loss for the six-ring
HN-PCF in Figure 1(c) are shown in Figure 2, where
center-to-center spacing Λ = 0.87 μm, the relative sizes
of air holes are d1 = 0.33 μm, d2 = 0.78 μm, d = 0.84 μm.
The proposed HN-PCF show ultra-flattened chromatic
dispersion of 0 ± 4.0 ps/(nm·km) is from 1.06 to 1.68
μm wavelength range (620 nm band). The chromatic
dispersion slopes variation is 0 ± 0.04 ps/(nm2·km) in
expected wavelength range. In OCT window, the effec-
tive area of the HN-PCF is 1.78 μm2 and 2.1 μm2 at 1.06
μm and 1.31 μm, respectively. And the corresponding
nonlinear coefficients are more than 102.0 [Wkm]1 and
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
Figure 2. (a) Chromatic dispersion and dispersion slope, (b)
Effective area and nonlinear coefficient and (c) Confinement
loss characteristics.
70.0 [Wkm]1 at 1.06 μm and 1.31 μm, respectively. On
the other hand, in telecommunication window, the effec-
tive area of the proposed HN-PCF is 2.45 μm2 at 1.55 μm
and the corresponding nonlinear coefficients are more
than 51.0 [Wkm]1. These nonlinear coefficients values
are higher than those ones reported in References [2-4,11,
12,17]. The confinement losses are less than 101 dB/km
in the targeted wavelength range which is lower than
Rayleigh scattering loss in conventional fiber [8].
For numerical calculation of SC spectra, the nonlinear
Schrödinger equation (NLSE) is used and this NLSE is
solved by using split-step Fourier method [8].
22 6
cT T
 
 
where A is the complex amplitude of the optical field, α
is the attenuation constant of the fiber, βi (i =1 to 3) are
the i-th order of the Taylor series expansion of the pro-
pagation constant around the carrier frequency, γ is the
nonlinear coefficient, λc is the center wavelength, and TR
is the Raman scattering parameter, respectively.
SC generation in the proposed HN-PCF is numerically
calculated which is shown in Figures 3(a), (b) and (c).
In Figure 3, we consider the propagation of the sech2
waveform with the full width at half maximum (FWHM)
TFWHM and the Raman scattering parameters TR are 1.0 ps
and 3.0 fs, respectively, through the proposed HN-PCF.
The input power Pin of the incident pulse are 43.0 W, 8.0
W and 40.0 W, at center wavelength λc of 1.06 μm,
1.31 μm and 1.55 μm, respectively. Calculated β2 and β3
values are shown in table 1 for the center wavelength
1.06 μm, 1.31 μm and 1.55 μm. From Table 1, it is ob-
served that β2 value at 1.31 μm wavelength is lower than
that of 1.06 μm and 1.55 μm wavelengths. If we increase
incident power at 1.31 μm wavelength, then would need
to increase β2 value as well. However, in our calculation
we found β2 value of this fiber to be 0.23 [ps2/km] at the
1.31 μm wavelength. Moreover, it is seen that broad
FWHM of SC spectrum and short fiber length LF is
achieved at center wavelength λc = 1.55 μm and λc =
1.06 μm, respectively.
If a Gaussian source line shape is assumed, then the
coherence length lc of an OCT system is given by [12].
This lc is very important for estimating the longitudinal
resolution lr in air and biological tissue. After calculating
lc, longitudinal resolution in air and biological tissue can
be estimated [12]. For ultrahigh-resolution OCT imaging
lc should be low value because lr is proportional with lc.
where λc is the center wavelength and Δλ is the FWHM
spectral width, ntissue is the refractive index of the bio-
logical tissue.
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
Figure 3. Intensity spectrum of the proposed HN-PCF at (a)
1.06 μm, (b) 1.31 μm and (c) 1.55 μm.
For ultrahigh-resolution OCT imaging lc should be
low value because lr is proportional with lc. The calcu-
lated lc and lr values are shown in table 1 when typical
ntissue is 1.44 at 1.06 μm, and 1.65 at 1.31 μm and 1.55 μm,
respectively [19]. These calculated lr values are lower
than that of reported in References [5,9,10,13-15]. From
the calculated data of Table 1, it is found that among
three center wavelengths, the highest resolution is ob-
tained at 1.55 μm wavelength.
Figures 4 (a), (b) and (c) represents the intensity
spectra of the proposed HN-PCF at center wavelengths
1.06, 1.31 and 1.55 μm, respectively in different input
powers. From these figures, it is seen that intensity spec-
tra are gradually broadening with increasing the input
power, Pin at the particular wavelength.
The wavelength dependence of chromatic dispersion
variation after changing air hole diameter d1 and d2 for the
HN-PCF in Figure 1(c) is depicted in Figures 5 (a) and
(b), respectively. It is reported that the air hole diameter
of the first ring is particularly important for the overall
dispersion flatness [20] and it may vary within ± 1%
during the fabrication process [21]. To take this matter
into consideration, the air hole diameter d1 of the first ring
is varied up to ± 5% from the optimum value as can be
shown in Figure 5(a). From the Figure 5(a) results, it is
found that the chromatic dispersion remains unchanged
until ±4% variation of the diameter d1. In Figure 5(a), it
is observed that chromatic dispersion curves shift down-
ward and upward from the optimum one in +5% and
5% variation of d1, respectively, in longer wavelengths.
On the other hand, from Figure 5(b), it is depicted that
after changing air hole diameter d2 at 0.84 μm value, the
chromatic dispersion curve is shifted upward from the
optimum curve. From this result, it is confirmed that air
hole diameter d2 is very important to obtain the optimum
result. Hence, it is crucial to select air hole diameter d2
value very carefully.
We have proposed broadband SC generating phonic
crystal fiber as a light source for ultrahigh-resolution
OCT imaging system by using picosecond pulses. We
Table 1. Calculated coherence lengths and longitudinal resolu-
Paramters λc = 1.06 [μm] λc = 1.31 [μm] λc = 1.55 [μm]
β2 [ps2/km] 2.98 0.23 1.01
β3 [ps3/km 0.01 0.0 0.01
TR [fs] 3.0 3.0 3.0
Pin [W] 43.0 8.0 40.0
LF [m] 7.0 70.0 18.0
FWHM [nm]260.0 374.0 585.0
lc [μm] 1.9 2.0 1.8
lr [μm] 1.3 1.2 1.1
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
Figure 4. Intensity spectrum at center wavelength (a) 1.06 μm,
(b) 1.31 μm and (c) 1.55 μm of the proposed HN-PCF in dif-
ferent input powers.
Figure 5. (a) Plot of chromatic dispersion tolerances and (b)
Chromatic dispersion properties after changing the air hole
diameter of second and third rings of the proposed HN-PCF.
achieved high longitudinal resolution in a biological
tissue of 1.3 μm, 1.2 μm and 1.1 μm at center wave-
length of 1.06, 1.31 and 1.55 μm, respectively. From
numerical simulation results, it was found that the pro-
posed HN-PCF exhibits high nonlinear coefficients with
ultra-flattened chromatic dispersion, low dispersion
slopes, broadband SC spectrum, ultra-high resolution,
high power and very low confinement losses, simulta-
neously. The broad SC bandwidth of the light source
will permit in both high resolution and improve the di-
agnosis of diseases from 1.0 to 1.6 μm wavelength
ranges. The design procedure of the proposed HN-PCF
structure could be more efficient and easier because for
optimization relatively fewer geometrical parameters are
needed. Moreover, it should be noted that the picosecond
light source is relatively cheaper; hence, the proposed
HN-PCF would be useful in practical applications. Such
F. Begum et al. / Natural Science 3 (2011) 401-407
Copyright © 2011 SciRes. OPEN ACCESS
broadband supercontinuum generated HN-PCF will be
useful in the precise measurement of optical frequencies,
high resolution noninvasive medical imaging (optical
coherence tomography), atomic spectroscopy and tele-
communication dense wavelength division multiplexing.
Authors gratefully acknowledge to the Japan Society for Promotion
of Science (JSPS) for their support in carrying out this research work,
JSPS ID number P 09078. Dr. Feroza Begum is a JSPS research fellow.
[1] Russel, P.St.J. (2003) Photonic crystal fibers. Science,
299, 358-362. doi:10.1126/science.1079280
[2] Champert, P.-A., Couderc, V., Leproux, P., Février, S.,
Tombelaine, V., Labonté, L., Roy, P., Froehly, C. and
Nérin, P. (2004) White-light supercontinuum generation in
normally dispersive optical fiber using original mul-
ti-wavelength pumping system. Optics Express, 12, 4366-
4371. doi:10.1364/OPEX.12.004366
[3] Saitoh, K. and Koshiba, M. (2004) Highly nonlinear
dispersion-flattened photonic crystal fibers for supercon-
tinuum generation in a telecommuinication window. Op-
tics Express, 12, 2027-2032.
[4] Yamamoto, T., Kubota, H., Kawanishi, S., Tanaka, M.
and Yamaguchi, S. (2003) Supercontinuum generation at
1.55 μm in a dispersion-flattened polarization-maintai-
ning photonic crystal fiber. Optics Express, 11, 1537-
1540. doi:10.1364/OE.11.001537
[5] Hartl, I., Li, X.D., Chudoba, C., Ghanta, R.K., Ko, T.H.,
Fujimoto, J.G., Ranka, J.K. and Windeler, R.S. (2001)
Ultrahigh-resolution optical coherence tomography using
continuum generation in an air-silica microstructure op-
tical fiber. Optics Letters, 26, 608-610.
[6] Sotobayashi, H., Chujo, W. and Kitayama, K. (2002)
Photonic gateway: multiplexing formate conversions of
OCDM-to-WDM and WDM-to-OCDM at 40 Gb/s (4 ×
10 Gb/s). Journal of Lightwave Technology, 20, 2022-
2028. doi:10.1109/JLT.2002.806769
[7] He, G.S., Lin, T.C., Prasad, P.N., Kannan, R., Vaia, R.A.
and Tan, L.-S. (2002) New technic for degenerated two-
photon absorption spectral measurements using femtose-
cond continuum generation. Optics Express, 10, 566-574.
[8] Agrawal, G.P. (1995). Nonlinear fiber optics. Academic
Press, San Diego.
[9] Youngquist, R.C., Carr, S. and Davies, D.E.N. (1987)
Optical coherence-domain reflectometry: A new optical
evaluation technique. Optics Letters, 12, 158-160.
[10] Lim, H., Jiang, Y., Wang, Y., Huang, Y.-C., Chen, Z. and
Wise, F.W. (2005) Ultrahigh-resolution optical coherence
tomography with a fiber laser source at 1 μm. Optics
Letters, 30, 1171-1173. doi:10.1364/OL.30.001171
[11] Tse, M.L.V., Horak, P., Poletti, F., Broderick, N.G.R.,
Price, J.H.V., Hayes, J.R. and Richardson, D.J. (2006)
Supercontinuum generation at 1.06 μm in holey fibers
with dispersion flattened profiles. Optics Express, 14,
4445- 4451. doi:10.1364/OE.14.004445
[12] Kinjo, T., Namihira, Y., Arakaki, K., Koga, T., Kaijage,
S.F., Razzak, S.M.A., Begum, F., Nozaki, S. and Higa, H.
(2010) Design of highly nonlinear dispersion-flattened
square photonic crystal fiber for medical applications.
Optics Review, 17, 61-65.
[13] Colston, B.W., Jr., Sathyam, U.S., DaSilva, L.B., Everett,
M.J., Stroeve, P. and Otis, L.L. (1998) Dental OCT. Op-
tics Express, 3, 230-238. doi:10.1364/OE.3.000230
[14] Boppart, S.A., Bouma, B.E., Pitris, C., Southern, J.F.,
Brezinski, M.E. and Fujimoto, J.G. (1998) In vivo cellular
optical coherence tomography imaging. Nature Medicine,
4, 861-865. doi:10.1038/nm0798-861
[15] Lee, J.H., Jung, E.J. and Kim, C.-S. (2009) Incoherent,
CW supercontinuum source based on Erbium fiber ASE
for optical coherence tomography imaging. Proceedings
of OptoEelectronics and Communication Conference,
Hong- kong, 13-17 July 2009, 1-2.
[16] Begum, F., Namihira, Y., Kinjo, T. and Kaijage, S. (2010)
Supercontinuum generation in photonic crystal fibers at
1.06, 1.31 and 1.55 μm wavelengths. Electronics Letter,
46, 1518-1520. doi:10.1049/el.2010.2133
[17] Begum, F., Namihira, Y., Kaijage, S., Razzak, S.M.A.,
Hai, N.H., Kinjo, T., Miyagi, K. and Zou, N. (2009) De-
sign and analysis of novel highly nonlinear photonic
crystal fibers with ultra-flattened chromatic dispersion.
Optics communications, 282, 1416-1421.
[18] Shen, L.-P., Huang, W.-P. and Jian, S.-S. (2003) Design
of photonic crystal fibers for dispersion-related applica-
tions. Journal of Lightwave Technology, 21, 1644-1651.
[19] Ohmi, M., Ohnishi, Y., Yoden, K. and Haruna, M. (2000)
In vitro simultaneous measurement of refractive index
and thickness of biological tissue by the low coherence
interferometry. IEEE Transactions on Biomedical Engi-
neering, 47, 1266-1270. doi:10.1109/10.867961
[20] Reeves, W.H., Knight, J.C., Russell, P.St.J. and Roberts,
P.J. (2002) Demonstration of ultra-flattened dispersion in
photonic crystal fibers. Optics Express, 10, 609-613.
[21] Poletti, F., Finazzi, V., Monro, T.M., Broderick, N.G.R.,
Tse, V. and Richardson, D.J. (2005) Inverse design and
fabrication tolarences of ultra-flattened dispersion holey
fibers. Optics Express, 13, 3728-3736.