Suppressing the Effect of Dispersion Fluctuation on Broadband

Optical Parametric Amplification using Highly Nonlinear Tellurite

Microstructured Optical Fibers

Tong Hoang Tuan, Kawamura Harukata, Takenobu Suzuki and Yasutake Ohishi

Research Center for Advanced Photon Technology, Toyota Technological Institute,

2-12-1 Hisakata, Tempaku, Nagoya, 468-8511, Japan

Keywords: Optical Parametric Amplification, Dispersion Fluctuation, Microstructured Optical Fiber, Highly Nonlinear

Optical Fiber.

Abstract: The contribution of fiber nonlinearity to the signal gain spectrum of a fiber-optical parametric amplifier

(FOPA) in presence of fiber transverse geometry variation is numerically studied in this work. This is the

first time to demonstrate that the degradation of FOPA signal gain performance which is caused by fiber

diameter fluctuation and zero-dispersion wavelength (ZDW) variation can be suppressed by using highly

nonlinear optical fibers with short fiber length. By increasing the fiber nonlinear coefficient, the fiber length

which is required to have similar value of signal gain is reduced, the signal gain bandwidth can be

broadened and the spectral shape can be maintained. A tellurite microstructured optical fiber was fabricated

by using a developed tellurite glass 78TeO

–5ZnO-12Li

O-5Bi

mol%. The fiber outer-diameter

fluctuation is less than ±0.53 % and the corresponding ZDW varies less than ±2 nm over a 1-m-long section

of the fabricated fiber. The fiber nonlinear coefficient is calculated to be 676 W

-1

which is 23 times

larger than those values of highly nonlinear silica fibers. When the pump source is 5 W at 1557 nm, the

influence of ZDW fluctuation on signal gain spectra is almost suppressed.

1 INTRODUCTION

With the explosive spread of telecommunication

devices such as smartphones and computers in

recent years, the amount of information travelling

through the Internet is rapidly increasing and the

demand for high transmission capacity over global

telecommunication networks will continue to grow.

Currently, wavelength division multiplexing (WDM)

systems where different wavelengths propagate

simultaneously in an optical fiber are used for multi-

channel transmission. Although Erbium-doped fiber

amplifiers (EDFA) are widely used as gain media

for WDM systems, their gain bandwidths are as

narrow as 30 nm from 1530 to 1560 nm (T. Jose,

2015). In order to expand the WDM operating range,

fiber-optical parametric amplifiers (FOPAs) are very

promising candidates because they can provide

broad gain bandwidths and high signal gain in many

spectral bands where conventional EDFAs cannot

reach. FOPAs have been exploited for various

applications such as signal amplification, wave-

length conversion, phase-conjugation, slow and fast

lights, optical signal processing and biomedical

applications (M. E. Marhic, 2008).

The gain performance of FOPA is obtained by

employing four-wave mixing (FWM) process in

optical fibers. However, the phase-matching

condition which determines FWM gain properties is

very sensitive to the fluctuation of the chromatic

dispersion and zero-dispersion wavelength (ZDW)

which is caused by the fiber transverse geometry

variation. As a result, it reduces the achievable

parametric gain and gain bandwidth of FOPA and

restricts practical applications of FOPA. The gain

performances of FOPA in presence of dispersion

fluctuation have been investigated by using

conventional silica fiber. (M. Karlsson, 1998, M.

Farahmand et.al, 2004, B. P. Kuo et.al, 2012). Due

to their low nonlinearity, extremely long fibers (up

to a few kilometres) are required to obtain proper

values of parametric gain (G. Agrawal, 2007). In

these configurations, the effect of ZDW fluctuation

along the fiber length on FOPA gain spectra

becomes significant and unavoidable.

Tuan, T., Harukata, K., Suzuki, T. and Ohishi, Y.

Suppressing the Effect of Dispersion Fluctuation on Broadband Optical Parametric Ampliﬁcation using Highly Nonlinear Tellurite Microstructured Optical Fibers.

DOI: 10.5220/0006465800540058

In Proceedings of the 14th International Joint Conference on e-Business and Telecommunications (ICETE 2017) - Volume 3: OPTICS, pages 54-58

ISBN: 978-989-758-258-5

In this work, we proposed highly nonlinear

tellurite microstructured optical fibers as promising

candidates to shorten the required fiber length, and

considerably suppress the influence of fiber

transverse geometry variation and ZDW fluctuation

on FOPA gain performance for more practical

applications.

2 FIBER OPTICAL

PARAMETRIC

AMPLIFICATION

The gain performance of a single-pump FOPA

configuration can be calculated by using the theory

of a degenerated FWM process (G. Agrawal, 2007)

whose phase-matching condition is given by Eq. (1)

2 P

κβγ

=Δ +

(1)

where P is the pump power,

is the nonlinear

coefficient and the linear phase-mismatch Δ

defined by Eq. (2). Commonly, Δ

is calculated by

introducing the Taylor series expansion up to the

second term as in Eq. (3) where

and

are related

to the dispersion parameter

and

calculated at

the zero-dispersion frequency of the fiber as given in

Eqs. (4) and (5) (G. Agrawal, 2007) and

and

are pump and signal frequencies, respectively.

is p

ββ β β

Δ= + −

(2)

() ()

sp sp

ββωω βωω

Δ≈ − + −

(3)

230 0 40 0

()()

ββωω βωω

≈−+ −

(4)

440

ββ

≈

(5)

The optical signal gain (G

) is calculated by Eq. (6)

where L is the fiber length, P

(0) and P

(L) are the

signal power at the input and output of the fiber and

the parametric gain coefficient g is given by Eq. (7)

(Hansryd et al., 2002)

)(sinh)(1

)0(

)(

+==

(6)

22 2 2

()() ()( )

gP PP

κβ

γγγ

=−=−+

(7)

As an example, FOPA gain performance is

investigated by using a 2.5-km-long fiber with the

ZDW at 1550 nm such that

=0.1 ps

/km and

=10

-4

/km (G. Agrawal, 2007). The pump

wavelength is

=1550.2 nm, the pump power is P

=1.2 W and the nonlinear coefficient is

=2W

-1

The blue plot in Fig. 1 shows the gain spectrum

calculated by using the above parameter.

Assuming that the ZDW does not locate at 1550

nm but has a random value in the range 1550 ±1 nm,

the gain spectrum is modified and is plotted in Fig. 1

as shadow lines which show a considerable decrease

in both signal gain and gain bandwidth. However,

the distortion of FOPA signal gain spectra caused by

the random ZDW-fluctuation is suppressed as can be

seen in Fig. 2 when the nonlinear coefficient

becomes 10 times larger than the value in Fig. 1. In

addition, it is interesting to notice that the signal

gain bandwidth is broadened and the fiber length L

required to achieve similar parametric gain in Fig. 1

becomes 10 times shorter.

Figure 1: FOPA signal gain spectra with random ZDW-

fluctuation (1550 ±1 nm) when

=2 W

-1

and L =2.5

km.

Figure 2: FOPA signal gain spectra with random ZDW-

fluctuation (1550 ±1 nm) when

=20 W

-1

and L

=0.25 km.

Suppressing the Effect of Dispersion Fluctuation on Broadband Optical Parametric Ampliﬁcation using Highly Nonlinear Tellurite

Microstructured Optical Fibers

3 EFFECTS OF LONGITUDINAL

FLUCTUATION IN THE ZERO-

DISPERSION WAVELENGTH

3.1 Conventional Optical Fibers

To study FOPA performance in presence of ZDW

fluctuation along the fiber length, the parametric

gain is considered to be obtained from a multi-

section nonlinear fiber arrangement (L. Provino

et.al, 2003). Each section has different value of

ZDW. The ZDW fluctuation is considered to vary

continuously (M. Farahmand et.al, 2004). The

evolution of signal and idler amplitudes can be

described by integrating the propagation matrix in

which dispersion fluctuation is taken into account.

Figure 3: Example of a ZDW fluctuation map numerically

recorded along the fiber length.

As an example, a ZDW fluctuation map

numerically recorded along the fiber length is shown

in Fig. 3 (A. Mussot, 2006). The blue line represents

the ideal ZDW in a uniform fiber but the red line

indicates its actual fluctuation. Assuming that the

fiber mentioned in section 2 is subjected to this

ZDW fluctuation, its FOPA gain performance is

investigated with different values of

Figure 4: FOPA signal gain spectra with the effect of

ZDW fluctuation in Fig. 3 when

=2 W

-1

and L =2.5

km.

Figure 5: FOPA signal gain spectra with the effect of

ZDW fluctuation in Fig. 3 when

=20 W

-1

and L =0.1

km.

Figure 4 shows calculated FOPA signal gain

spectra which are related to

=2 W

-1

and L

=2.5 km. When

becomes 25 times larger,

calculated FOPA signal gain spectra in Fig. 5 show

that only a 0.1-km-long fiber is required to obtained

similar values of signal gain. In Figs. 4 and 5, the

blue lines (ideal) represent the ideal FOPA

performance in a perfectly uniform fiber and the red

lines (actual) show the gain performance with the

effect of ZDW fluctuation. As can be seen, the

actual FOPA performance in Fig. 4 is very different

from the ideal performance due to the effect of ZDW

fluctuation. But that difference is almost suppressed

as shown in Fig. 5. Moreover, the spectral

bandwidth is broadened from 100 to 230 nm. Those

features show that the influence of the ZDW

fluctuation on FOPA performance can be reduced

and the amplification band of FOPA can be

extended by using optical fibers with high

nonlinearity and short length.

3.2 Highly Nonlinear Tellurite

Microstructured Optical Fibers

Based on the idea in section 3.1, a highly nonlinear

tellurite microstructured optical fiber was designed

and fabricated. The fiber was made by using our

developed tellurite glass 78TeO

–5ZnO-12Li

O-

5Bi

(TZLB) mol%. The cross-sectional image of

the fiber was taken by a scanning electron

microscope (SEM) and is shown in Fig. 6. The

calculated nonlinear coefficient was

γ =

676 W

-1

This value is about 23 times larger than that of a

highly nonlinear silica fiber (M. Hirano et.al, 2016).

OPTICS 2017 - 8th International Conference on Optical Communication Systems

Figure 6: SEM cross-sectional image of the fabricated

tellurite MOF.

The outer-diameter fluctuation along a 1-m-long

section of the fabricated tellurite MOF is shown in

Fig. 7. Compared with the expected value, the

fluctuation is less than ±0.53 %. The corresponding

ZDW fluctuation which was calculated by a

commercial full-vectorial mode solver (Lumerical-

Mode Solution software) based on the finite element

method and the perfectly matched layer boundary

condition is shown in Fig. 8. The ZDW varies in the

range of 1557 ±2 nm. FOPA gain performance

regard to this ZDW fluctuation was calculated and

shown in Fig. 9. The pump source is 5 W at 1557

nm. As can be seen, FOPA signal gain spectra

spanned from approximately 1430 to 1710 nm (280-

nm bandwidth) and could be maintained although

ZDW fluctuation occurred.

Figure 7: Evolution of the fiber outer-diameter along a 1-

m-long section of the fabricated tellurite MOF.

Figure 8: Evolution of the calculated ZDW along a

1-m-long section of the fabricated tellurite MOF in Fig. 7.

Figure 9: Calculated FOPA signal gain spectra when the

ZDW fluctuation in Fig. 8 is taken into account.

4 CONCLUSIONS

For the first time, our simulations show that the

degradation of FOPA signal gain performance which

is caused by the fiber transverse geometry variation

can be suppressed by using highly nonlinear optical

fibers with short fiber length. Compared to silica

fibers, highly nonlinear tellurite MOFs with high

nonlinear coefficient and short fiber length are

expected to make FOPA performance more practical

by extending its amplification bands and

maintaining its signal gain spectra even in presence

of fiber transverse geometry variation.

ACKNOWLEDGEMENTS

This work was supported by the JSPS KAKENHI

Grant Number 15H02250 and by JSPS KAKENHI

Grant Number 17K14671.

REFERENCES

T. Jose and V. Narayanan, 2015. Design of a gain

flattened doped fiber amplifier with stabilized power

output for WDM transmissions, 2015 International

Conference on Microwave, Optical and Communication

Engineering (ICMOCE), Bhubaneswar, 193-196.

M. E. Marhic, 2008. Fiber optical parametric amplifiers

oscillators and related devices, Cambridge University

Press.

M. Karlsson, 1998. Four-wave mixing in fibers with

randomly varying zero-dispersion wavelength, J. Opt.

Soc. Am. B, 15, 2269-2275.

M. Farahmand and M. D. Sterke, 2004. Parametric

amplification in presence of dispersion fluctuations,

Opt. Express, 12, 136-142.

B. P. Kuo and S. Radic, 2012. Highly nonlinear fiber with

Suppressing the Effect of Dispersion Fluctuation on Broadband Optical Parametric Ampliﬁcation using Highly Nonlinear Tellurite

Microstructured Optical Fibers

dispersive characteristic invariant to fabrication

fluctuations, Opt. Express, 20, 7716-7725.

J. Hansryd, P. A. Andrekson, M. Westlund, Jie Li and

P. O. Hedekvist, 2002. Fiber-based optical parametric

amplifiers and their applications, IEEE J. Sel. Top.

Quantum Electron, 8, 3, 506-520.

G. P. Agrawal, 2007. Nonlinear fiber optics, Amsterdam,

London, Elsevier/Academic Press, 4

edition.

L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and

H. Maillotte, 2003. Broadband and flat parametric

amplifiers with a multisection dispersion-tailored

nonlinear fiber arrangement, J. Opt. Soc. Am. B 20,

1532-1537.

A. Mussot, E. Lantz, A. D. Legrand, C. Simonneau,

D. Bayart, T. Sylvestre and H. Maillotte, 2006.

Zero-dispersion wavelength mapping in short single-

mode optical fibers using parametric amplification,

IEEE Photonics Technology Letters, 18, 1, 22-24.

M. Hirano, Y. Yamamoto and T. Hasegawa, 2016.

Silica-based highly nonlinear fiber advances,

Proceeding of 2016 Optical Fiber Communications

Conference and Exhibition (OFC), Anaheim, CA, 1-3.

OPTICS 2017 - 8th International Conference on Optical Communication Systems