Modeling of micro-diameter-scale liquid core
optical fiber filled with various liquids
Yonghao Xu, Xianfeng Chen*, and Yu Zhu
Department of Physics, the State Key Laboratory on Fiber Optic Local Area Communication Networks and Advanced
Optical Communication Systems, Shanghai Jiao Tong University, Shanghai 200240, China
* [email protected]
Abstract: This paper gives the simulation results on micro-diameter-scale
liquid core optical fiber (LCOF) filled with different kinds of liquids. The
nonlinear and group velocity dispersion (GVD) properties of the microdiameter-scale LCOF are achieved. The simulation of supercontinuum
generation of LCOF is also obtained. The calculations show that LOCF can
provide huge nonlinear parameter and large span of slow varying GVD
characteristics in the infrared region, which have potential applications in
optical communications and nonlinear optics. Besides, LOCF has advantage
of easy fabricating and robustness compared with silica nano-wire.
©2008 Optical Society of America
OCIS codes: (060.2280) Fiber design and fabrication; (190.4370) Nonlinear optics, fibers;
(260.2030) Dispersion.
References and Links
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
L. M. Tong, J. Y. Lou, and E. Mazur “Single-mode guiding properties of subwavelength-diameter silica
and silicon wire waveguides,” Opt. Express 12, 1025-1035 (2004).
J. Y. Lou, L. M. Tong, and Z. Ye, “Modeling of silica nanowires for optical sensing,” Opt. Express 12,
2135-2140 (2005).
K. Huang, S. Yang, and L. Tong, “Modeling of evanescent coupling between two parallel optical
nanowires,” Appl. Opt. 46, 1429-1434 (2007).
M. Rusu, S. Kivistö, C. Gawith, and O. Okhotnikov, “Red-green-blue (RGB) light generator using tapered
fiber pumped with a frequency-doubled Yb-fiber laser,” Opt. Express 13, 8547-8554 (2005).
S. Leon-Saval, T. Birks, W. Wadsworth, P. St. J. Russell, and M. Mason, “Supercontinuum generation in
submicron fibre waveguides,” Opt. Express 12, 2864-2869 (2004).
N. Karasawa, H. Kakehata, K. Mishina, J. Yamamoto, and S. Kobayashi, “Phase and amplitude comparison
between experiment and calculation of ultrabroad-band pulses generated in a taper fiber,” Photon. Technol.
Lett. 17, 31-34 (2005).
M. Foster and A. Gaeta, "Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,"
Opt. Express 12, 3137-3143 (2004).
R. Zhang, X. Zhang, D. Meiser, and H. Giessen, "Mode and group velocity dispersion evolution in the
tapered region of a single-mode tapered fiber," Opt. Express 12, 5840-5849 (2004).
G. S. He, R. Burzynski, and P. N. Prasad, “A novel nonlinear optical effect: Stimulated Raman–Kerr
scattering in a benzene liquid-core fiber,” J. Chem. Phys. 93, 7647-7655 (1990).
G. S. He and P. N. Prasad, “Stimulated Rayleight-Kerr scattering in a CS2 liquid-core fiber system,” Opt.
Commun. 73, 61-164 (1989).
G. S. He and G. C. Xu, “Efficient amplification of a broad-band optical signal through stimulated Kerr
scattering in a CS2 liquid-core fiber system,” J.Quantum Electron. 28, 323-329 (1992).
M. Saito, A. Honda, and K. Uchida, "Photochromic liquid-core fibers with nonlinear input-output
characteristics," J. Lightwave Technol. 21, 2255-2261 (2003).
J. C. Schaefer and I. Chabay, "Generation of enhanced coherent anti-stokes Raman spectroscopy signals in
liquid-filled waveguides," Opt. Lett. 4, 227-229 (1979).
G. S. He, M. Yoshida, J. D. Bhawalkar and P. N. Prasad, "Two-photon resonance-enhanced refractiveindex change and self-focusing in a dye-solution-filled hollow fiber system," Appl. Opt. 36, 1155-1163
(1997).
G. S. He, M. Casstevens, R. Burzynski, and X. Li, "Broadband, multiwavelength stimulated-emission
source based on stimulated Kerr and Raman scattering in a liquid-core fiber system," Appl. Opt. 34, 444454 (1995).
L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur,
“Subwavelenth-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816-819 (2003).
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9205
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
J. Lou, L. Tong, and Z. Ye, "Dispersion shifts in optical nanowires with thin dielectric coatings," Opt.
Express 14, 6993-6998 (2006).
R. Zhang, J. Teipel, and H. Giessen, "Theoretical design of a liquid-core photonic crystal fiber for
supercontinuum generation," Opt. Express 14, 6800-6812 (2006).
J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal
and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, "Group velocity dispersion of tapered fibers
immersed in different liquids," Opt. Express 12, 1700-1707 (2004).
Y. Zhu, X. Chen and Y. Xu, "Propagation Properties of Single-Mode Liquid-Core Optical Fibers With
Subwavelength Diameter" J. Lightwave Technol. 25, 3051-3056 (2007).
J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide
in ultraviolet, visible, and near-infrared” J. Appl. Phys. 94, 6167-6174 (2003).
G. P. Agrawal, Nonlinear Fiber Optics – Optics and Photonics, Third Edition, (Academic Press, New
York, 2001).
S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An
experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral
shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369,318-324 (2003).
P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, “2-regenerative
all-optical switch based on a highly nonlinear holey fiber,” Opt. Lett. 26, 1233-1235 (2001).
K. Kikuchi, “All-optical signal processing using fiber nonlinearity” Lasers and Electro-Optics Society 2,
428-429 (2002).
C. Martelli, J. Canning, K. Lyytikainen, and N. Groothoff, “Water-core Fresnel fiber,” Opt. Express, 13,
3890-3895 (2005).
Fuerbach, P. Steinvurzel, J. Bolger, and B. Eggleton, "Nonlinear pulse propagation at zero dispersion
wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005).
S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, and P. Roy, J. L.
Auguste, and J. M. Blondy, "Stimulated Raman scattering in an ethanol core microstructured optical fiber,"
Opt. Express 13, 4786-4791 (2005).
F. M. Cox, A. Argyros, and M. C. J. Large, "Liquid-filled hollow core microstructured polymer optical
fiber," Opt. Express 14, 4135-4140 (2006).
R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H.
Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231, 431-436 (2004)
K. B. Lodge and D. Danso, “The measurement of fugacity and the Henry’s law constant for volatile organic
compounds containing chromophores,” Fluid Phase Equilibria 253, 74–79 (2007)
1. Introduction
The single-mode guiding properties of micro- or submicro-diameter silica fibers show the
tight-confinement ability and a slow variation with small group velocity dispersion (GVD)
values in the anomalous dispersion [1]. It has a large number of applications in optical
sensing, pulse compression, optical frequency metrology and so on [2-7]. For applications in
nonlinear optics, lager nonlinear parameter (γ) is preferred. There are two methods to achieve
large nonlinear parameter (γ) in a fiber. One is to decrease the effective area of fiber, and the
other method is to choose the material with large nonlinear coefficient (n2). In the first
approach, photonic crystal fiber and tapered silica fiber are fabricated to decrease the effective
area, so that the nonlinear parameter (γ) can be greatly enhanced [1, 8]. Unfortunately, the
high cost of PCF and the fragileness of tapered fiber prevent them from large-scale
manufacturing and further commercial use. On the other hand, because the liquids have much
higher nonlinear optical coefficient, people filled the hollow fiber with high index liquids to
form a liquid core optical fiber (LCOF) [9]. Stimulated Raman Scattering and supercontinuum
are observed in LCOF owing to the large nonlinearity of the liquid [10-15]. The diameter of
the LCOF reported today is usually 10~100μm. It can be expected that when diameter of the
LCOF reaches to micrometer or sub-micrometer scale, huge nonlinear parameter (γ) can be
obtained owing to both small effective area and high nonlinear optical coefficient. As the
development of fabrication of taper silica fibers [16], the diameter of the hollow hole can also
easily reach to micro-diameter-scale while the outer silica diameter remains as large as about
ten micrometers. In additional, the GVD of the tapered fiber can be shifted by variation of the
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9206
diameter of fiber, and can also be adjusted by coated with thin dielectric or immersed into
different liquids [17-20,21].
In our previous work [21], we have investigated the propagation properties of microdiameter-scale LCOF and compare them with micro-diameter-scale tapered fiber. However, in
this paper, we pay more attentions on LCOF’s high nonlinear parameter and its potential use
in nonlinear optics, especially in supercontinuum generation. We theoretically demonstrate
the propagation properties of a new micro-diameter-scale fiber by filling different high index
liquids. By the numerical simulations of a 3-layer-structed cylindrical waveguide, we
compared the nonlinear parameter (γ) and GVD of the fundamental mode in the microdiameter-scale LCOF filled with four kinds of different high index liquids (carbon disulfide,
toluene, benzene, nitrobenzene). A simple way to enhance the nonlinear parameter (γ) or shift
the GVD of the fiber is provided by adjusting the diameter or making use of different liquids.
As a result, the supercontinuum generation can be controllable.
2. Mathematic model for micro-diameter-scale LCOF.
The mathematic model in our simulation is illustrated in Fig. 1. The micro-diameter-scale
liquid core optical fiber is a cylindrical structure of translation symmetry involving three
regions. (Fig. 1(a)): a liquid core (e.g. carbon disulfide) with radius a2, a silica cladding with
radius from a2 to a1 and the infinite air cladding, where the D represents the diameter of the
liquid core. As an example, we assume the ratio of a2 and a1 is 12.5/0.8 in our calculations.
The refractive indices of the liquid core, the silica cladding and the air cladding are n2, n1 and
n0, respectively. (Fig. 1(b)).
Fig. 1. Mathematic model of the micro-diameter-scale liquid core optical fiber. (a) Crosssection view and (b) refractive index profile of the fiber.
Solving Maxwell’s equation in cylindrical coordinates (r, Θ , z) leads to the expressions
for the components of the electromagnetic field for the mth mode. According to the boundary
condition, The longitudinal component of the electromagnetic field and the azimuthal
component of the electromagnetic field must be continuous at the inner and outer cylinder
surfaces (r=a1 and r=a2). Then we can get eight linear equations satisfied. This equation leads
a (8×8) matrix which determinant must be equal to zero to ensure a nontrivial solution. At
last, the dispersion equation can be obtained [22]. In this paper, only the features of
fundamental mode are discussed.
From the reference [18, 23], Sellmeier equations (1) were fitted for the refractive index
for the four kinds of liquids:
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9207
ncs2 (λ ) = 1.580826 +
1.52389 ×10−2
ntoluene (λ ) = 1.474775 +
λ
2
+
4.8578 ×10−4
0.699031 ×10 −2
nbenzene (λ ) = 1.475922 +
nnitrobenzene (λ ) = 1.5205 +
λ
2
0.967157 × 10 −2
λ
2
0.79 ×10 −2
λ
2
+
λ
+
−
4
−
8.2863 ×10−5
λ
2.1776 × 10 −4
λ
5.2538 ×10 −4
λ
1.670 ×10−3
λ
4
−
+
1.4619 ×10−5
λ8
;
(1)
;
4
4
6
+
8.5442 ×10 −5
3.1 ×10−4
λ
6
λ
+
6
−
3.0 ×10−5
λ8
2.6163 ×10 −5
λ8
;
;
3. GVD of the micro-diameter-scale LCOF filled with different kinds of liquids.
GVD of the fibers is given by the following equation (2) [24]:
Dispersion =
−2π c d 2 β
,
λ dω 2 .
(2)
Fig. 2. The GVD of the micro-diameter-scale LCOF filled for four different kinds of liquid.
Figure 2 shows the GVD curves as a function of wavelength for micro-diameter -scale
LCOF filled with four different kinds of liquids and different diameters. The nitrobenzene and
benzene have a strong absorption at wavelength larger than 1600nm. From the curves, the
GVD is usually thousands of ps·nm-1·km-1. This kind of fiber has the large negative GVD in
the visible region. In the infrared region the GVD varies slowly in a large wavelength area,
where shows a potential use in supercontinuum generation (further discussions in section 5).
For the same diameter, the micro-diameter-scale LCOF filled with carbon disulfide has the
maximum GVD value. The GVD (carbon disulfide) is about -1000ps·nm-1·km-1at the
wavelength of 800nm and diameter of 800nm. There are no zero dispersion points in the
region we presented. Generally, by adjusting the diameter or filling different liquids, the
tunable GVD can be obtained.
3. The nonlinear parameter (γ) of the fundamental mode.
The nonlinear parameter γ is important for investigating the nonlinear properties of the fiber.
Especially in some nonlinear process, such as self-phase-modulation, Stimulated Raman
Scattering and four wave mixing. It can be evaluated as following equation [24]:
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9208
γ=
n 2ω
,
cAeff
(3)
In this formula, the effective area of the mode Aeff can be obtained.
Aeff =
(∫ ∫
∞
−∞
∞
∫∫
−∞
2
F ( x, y ) dxdy ) 2
,
4
(4)
F ( x, y ) dxdy
Here, n2 hat is the nonlinear refractive index of the fiber material, the F(x, y) is the modal
field distribution function. c is the speed of the light in vacuum, and ω is the given frequency.
Among the four liquids we used, the n2 hat of tow liquids are available and presented as [25]
(they are obtained in the short pulse duration which is less than 200fs):
∧
carbon disulfide: n2 =1.2e-18 (m 2 /w)
∧
-19
,
(5)
2
toluene: n2 =1.3e (m /w)
(a)
(b)
Fig. 3. The effective area of the mode of the micro-diameter-scale liquid core optical fibers
filled with carbon disulfide or toluene (a) at the wavelength of 800nm; (b) at the wavelength of
1550nm.
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9209
(a)
(b)
Fig. 4. The nonlinear parameter of the micro-diameter-scale liquid core optical fibers filled
with carbon disulfide or toluene (a) at the wavelength of 800nm; (b) at the wavelength of
1550nm.
Figure 3 and 4 describes the value of the effective area of the mode and the nonlinear
parameter γ in the micro-diameter-scale LCOF filled with carbon disulfide or toluene at the
wavelength of 800nm and 1550nm, respectively. All the micro-diameter-scale LCOF filled
the two kinds of different liquid have a very large nonlinear parameter γ when the inner
diameter is around one micrometer. It is shown that there is a maximum value at a certain
diameter. For example, when the diameter is 0.5μm with the wavelength=800nm, the
nonlinear parameter of the micro-diameter-scale LCOF filled with the carbon disulfide shows
the maximum value which is about 18000W-1km-1. And with the wavelength=1550nm, 3250
w-1km-1, respectively. The fiber presents a stronger nonlinearity with the
wavelength=800nm. By filling different liquids or adjusting the diameter of the fiber, the
value of the nonlinear parameter (γ) can vary from about 50W-1km-1 to about 18000W-1km1
and with the wavelength=1550nm, the value of γ varying from about 10 w-1km-1 to about
3250W-1km-1. In the previous studies, the nonlinear coefficient γ of the some kinds of high
nonlinear fibers has been investigated. For example, the nonlinear coefficient γ is about 35 w1
km-1 in silica high nonlinear holey fiber, measured at 1550nm with a pulsed, dual-frequency
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9210
beat-signal nonlinear spectral enrichment technique [26]; typical values of γ of the Bi2O3 fiber
is 64W-1km-1 and for As2S3 the γ is measured as 162W-1km-1 [27]. The nonlinear parameter in
the micro-diameter-scale LCOF is expected to have a much larger value than traditional silica
fibers or other conventional highly nonlinear fibers.
4. Supercontinuum simulation
Considering the broad transparency and high nonlinear in infrared region, we simulate the SC
generation in micro-diameter-scale liquid core optical fiber filled with carbon disulfide. The
Nonlinear Schrödinger equation is expressed as follows:
2
⎡ 2 i 1 ∂
∂ A ⎤⎫
∂A ⎧
∂2 1
∂3 α ⎞
2
⎪⎛ i
⎪
= ⎨⎜ − β 2
+ β 3 3 − ⎟ + iγ ⎢ A +
A A − TR
⎥⎬ A
2
6 ∂T
2⎠
ω0 A ∂T
∂z ⎪⎝ 2 ∂T
∂T ⎥⎦ ⎪
⎣⎢
⎩
⎭
(
)
(6)
On the right side of equation (6), the first term represents dispersion and absorption of the
fiber and the second term shows the nonlinear effect, including self-steering and Raman
Effect. To simplify the calculation, we neglect absorption (α), the third-order of β (β3) and
Raman Effect (TR) in the equation. The absorption bands in UV range for the two liquid are
listed in the references [32-33]. By means of split-step Fourier Method, we successfully solve
equation (6) and give out the simulation result as following Fig. 5.
Fig. 5. The calculated output spectrum generated by a 1mm long LCOF with 0.6um inner
diameter full of (a) carbon disulfide and (b) toluene with a pump wavelength of 800nm, and a
pulse duration of 100fs, with different input peak power P
The SC spectrum generated by a 1mm long micro-diameter-scale LCOF with 0.6μm
inner diameter full of carbon disulfide and toluene with a pump wavelength of 800nm, and a
pulse duration of 100fs with different input peak power is shown in Fig. 5 (a) and (b). Here,
we neglected the effect of TPA and thermal lensing to the nonlinear response mainly because
of the short operation length and the relatively low peak power. Comparing with the previous
results in which 5cm long fiber is employed [18], the micro-diameter-scale LCOF needs much
shorter length on the same condition.
5. Conclusion
In this paper, we discussed the nonlinearity and GVD characterization of micro-diameterscale liquid core optical fiber filled with different kinds of liquids. These new kinds of microdiameter-scale LCOF are easier to fabricate than traditional taper fibers owing to the much
larger outer diameter. The fibers show huge nonlinear parameters (γ) and tunable GVD.
Because the technique to fill the tiny hole of a hollow fiber with liquids has been taken into
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9211
practice [28-31], we believe that micro-diameter-scale LCOF will have a potential application
in the communication and nonlinear optics.
Acknowledgment
This research was supported by the National Natural Science Foundation of China (No.
10574092); the National Basic Research Program “973” of China (No. 2007CB307000 and
2006CB806000)
#93962 - $15.00 USD
(C) 2008 OSA
Received 21 Mar 2008; revised 18 May 2008; accepted 27 May 2008; published 6 Jun 2008
9 June 2008 / Vol. 16, No. 12 / OPTICS EXPRESS 9212