a new lp02 mode dispersion compensation scheme based on mode converter using hollow optical fiber

Optics Communications 222 (2003) 213–219

www.elsevier.com/locate/optcom

A new LP02 mode dispersion compensation scheme basedon mode converter using hollow optical fiber

S. Choi, K. Oh*

Department of Information and Communications, Kwangju Institute of Science and Technology, 1 Oryong-dong, Buk-gu,

Kwangju 500-712, Republic of Korea

Received 26 January 2003; received in revised form 19 April 2003; accepted 2 May 2003

Abstract

We report on a novel dispersion compensation technique using the LP02 mode of a ring-core dispersion compen-

sating fiber along with a compact mode converter based on hollow optical fiber. Design parameters of both the mode

converter and the matching dispersion compensating fiber are numerically analyzed. Evaluation of mode conversion

efficiency, total dispersion, dispersion slope, and modal delay are discussed. It is predicted that 1.31 km of proposed

dispersion compensating fiber can compensate the chromatic dispersion accumulated in 60 km conventional single-

mode fiber with the average dispersion below �1 ps/nm/km in the entire conventional band, 1.53–1.57 lm.

� 2003 Published by Elsevier Science B.V.

PACS: 42.79 Gn; 42.25 B; 42.79.Sz

Keywords: Optical waveguide; Dispersion compensation; Optical communication

1. Introduction

With the advent of erbium-doped fiber ampli-

fiers (EDFAs), limitations due to fiber attenuation

have been virtually removed in the gain-band andchromatic dispersion plays a critical role to de-

termine overall transmission capacity. Simulta-

neous compensation of dispersion and dispersion

slope for a conventional single-mode fiber (SMF)

or a non-zero dispersion-shifted fiber (NZDSF) in

the gain-band of EDFAs has been required for the

* Corresponding author. Tel.: +82-62-970-2213; fax: +82-62-

970-2237.

E-mail address: koh@kjist.ac.kr (K. Oh).

0030-4018/03/$ - see front matter � 2003 Published by Elsevier Scien

doi:10.1016/S0030-4018(03)01574-8

improvement of performance in high-speed long-

haul wavelength-division-multiplexing (WDM)

transmission systems [1,2]. For broadband com-

pensation, various techniques such as dispersion

compensating fibers (DCFs) using a single-mode[3–5] or higher-order modes (HOMs) [6,7,9], fiber

Bragg-grating devices [10,11], and virtually imaged

phased-array devices [12] have been reported.

Among these techniques, the single-mode DCF is

widely used due to its low loss, flexible waveguide

design for the fundamental LP01 mode [13], and

established manufacturing processes. However,

single-mode DCFs suffer from non-linear effectssuch as four-wave-mixing and cross-phase modu-

lation due to their small effective core areas

ce B.V.

214 S. Choi, K. Oh / Optics Communications 222 (2003) 213–219

(Aeff : 15–20 lm2). This results in signal distortion

among the adjacent WDM channels. On the while,

HOM-DCF techniques are based on the large

negative chromatic dispersion of the HOMs near

cut-off in few-mode fibers along with spatial mode

converter (MC) pairs [6,8]. The main advantage ofusing HOMs is the ability to achieve a very large

negative dispersion in a shorter length of DCF.

This provides a lower insertion loss and a higher

figure of merit. Furthermore, the larger effective

area of HOMs can significantly reduce non-linear

effects. Despite these merits, HOM-DCF tech-

niques face the technical challenge of coupling the

LP01 mode back and forth to the desired HOM. Itrequires a mode converter pair with a high-con-

version efficiency, broadband operation, and low

insertion loss. Various mode converters such as

LP01 $ LP11 and LP01 $ LP02 have been reported

using periodic stress [14], microbending [15,16],

and photo-induced index change [17,18] in optical

fibers. These devices, however, suffer from high

sensitivity to environmental perturbation such asstrain and temperature changes due to their in-

herent periodic nature. Recently, a ring type mode

converter based on a tapered hollow optical fiber

(HOF) [19] and an HOM dispersion compensation

technique in LP02 mode DCF [20] have been re-

ported by the authors.

In this paper, we report on a broadband LP02

mode dispersion compensating scheme based on

(a)

(b)

Fig. 1. Dispersion compensation scheme: (a) transmission links casca

hollow-core mode converters.

an HOF mode converter in a ring-core index

HOM-DCF. Based on the adiabatic transforma-

tion of optical modes without periodic perturba-

tion structure, the proposed mode converter is

inherently immune to environmental influences.

Furthermore, it can be spliced with low loss toconventional single-mode fibers. Design parame-

ters of both the ring-core DCF and the mating

mode converter are discussed to optimize com-

pensation of both chromatic dispersion and its

slope in the conventional band (C-band) of EDFA

from 1.53 to 1.57 lm. The modal delay between

LP01 and LP02 modes is also analyzed to estimate

the penalty of incomplete mode conversion.

2. Design and analysis

An HOM dispersion-compensating module re-

quires two mode converters and a HOM-DCF of a

certain length. The schematic block diagram of the

proposed dispersion compensation technique isshown in Fig. 1(a). The shaded regions of each

fiber segment represent the core of the optical fi-

ber. One end of the HOF is adiabatically tapered

to a solid core that matches the conventional SMF

core. The other end maintains a hollow core. The

input mode converter, concatenated serially to an

SMF, converts the incident LP01 mode into a ring-

shaped mode, which couples efficiently to the LP02

ded with SMF-HOF MC-LP02 DCF and (b) structures of two

Fig. 3. Refractive index profile: (a) hollow optical fiber and (b)

LP02 dispersion compensating fiber.

S. Choi, K. Oh / Optics Communications 222 (2003) 213–219 215

mode in a ring-core LP02 mode DCF. After the

accumulated chromatic dispersion in the SMF is

compensated by the DCF, the output mode con-

verter converts the LP02 mode of the DCF back

into the LP01 mode of the output SMF. The

structure of the mode converters is shown inFig. 1(b). The HOFs can be fabricated using

modified chemical vapor deposition (MCVD)

process and hole sizes of HOFs can be precisely

controlled in both preform collapse and fiber

drawing process [19]. The ring waveguide design

parameters were adjusted to maintain a funda-

mental mode of the HOF and to efficiently couple

to the LP02 mode in the DCF. One end of the HOFwas designed to the adiabatically tapered solid

fiber and then connected to the SMF. The SMF

end was also designed by the tapered structure to

minimize the insertion loss with that of the tapered

HOF end. The cross-section area at the open end

of the HOF is shown in Fig. 2. The HOF structure

is an air-hole (Ha) in the center, a circular ring-core

(Hb), and an outer silica cladding (Hc). Here, d1and d2 represent the diameter of air-hole and the

thickness of the core, respectively. The refractive

index profile of the proposed HOF is shown

schematically in Fig. 3(a). The relative index dif-

ference, D, designated as ðncore � ncladdingÞ=ncladdingwas about 1%. For the given HOF parameters, the

Fig. 2. Cross-section area of a hollow optical fiber.

matching LP02 mode DCF was designed as a ring-

core structure in order to effectively couple the ring

mode out of the HOF to the LP02 mode in the

DCF. The design parameters were primarily cho-sen to maximize the overlap between the two fields

which minimize modal interference. Its refractive

index profile, shown in Fig. 3(b), consists of a

high-index core with the relative index of Dþ and a

core diameter of 2b. A depressed cladding with the

relative index of D� exists at diameters of 2a and

2c. Surrounding this is an outer cladding. Design

parameters of the DCF are summarized in Table 1.The waveguide structure was further tailored to

obtain a large negative dispersion near its LP02

mode cut-off (kc ¼ 1:60 lm). For conventional

SMF, a step index structure with the core diameter

of 8.2 lm and the relative index difference of

D ¼ 0:34% was assumed for theoretical analysis

and comparison with the proposed DCF. The total

chromatic dispersion, DðkÞ, including both thematerial and the waveguide dispersion, was ob-

tained from the effective index, neff . Numerical

mode analysis of the following Eq. (1) was used:

Dk ¼ � kc� d

2neffdk2

ðps=nm=kmÞ; ð1Þ

Table 1

Design parameters of LP02 ring-core dispersion compensating fiber

Parameter Diameter (lm) Refractive index difference (%) LP02 kc (lm)

Specification 2a 2b 2c Dþ D�

1.2 7.4 7.9 1.96786 0.06437 1.60

Fig. 4. Total chromatic dispersion curve for the SMF and the

LP02 DCF in the conventional band.

216 S. Choi, K. Oh / Optics Communications 222 (2003) 213–219

where c is the velocity of light in free space and k is

the wavelength. Dispersion slope was calculated bySðkÞ ¼ dDðkÞ=dk (ps/nm2/km). Total chromatic

dispersion at 1.55 lm was calculated as 16 ps/nm/

km for the LP01 mode in the SMF and )769.34 ps/

nm/km for the LP02 mode in the DCF, respec-

tively. Relative dispersion slope (RDS, defined as

the ratio of dispersion slope to dispersion), which

is an indicator for broadband compensation, was

0.00356 nm�1 for the SMF and 0.00695 nm�1 forthe DCF, respectively. Dispersion curves for the

LP01 mode of SMF and the LP02 mode of DCF in

the entire C-band are shown in Fig. 4.

Fig. 5. Power coupling efficiency between the HOF and the

LP02 DCF as a function of the hole radius.

3. Results and discussion

The proposed DCF can guide four linear po-larized modes such as LP01, LP11, LP21, and LP02.

Of these, the fundamental mode of the HOF

cannot couple to the anti-symmetric LP11 and LP21

modes due to mode orthogonality. The ring mode

from the HOF, therefore, can couple to either the

LP02 or the LP01 mode. The waveguide parameters

for both HOF and DCF should be optimized such

that the coupling to the LP01 mode is suppressed as

much as possible. To analyze the modal excitationin the DCF by the ring mode in the HOF, the

power coupling efficiency, g, into individual fiber

mode was obtained by calculating the overlap in-

tegral between the electric field of the fundamental

HOF mode and that of the DCF modes using

Eq. (2) [21]:

g ¼jR R

ELP01ðHOFÞELP0iðDCFÞ

rdrdhj2R R

jELP01ðHOFÞ j2rdrdh

R RjELP0iðDCFÞ j

2rdrdh;

ð2Þ

where E is the electric field and i ¼ 1; 2 denotes theLP01 and the LP02 modes in the DCF, respectively.

Fig. 5 shows the power coupling efficiency between

the fundamental mode of the HOF and LP01, LP02

modes of the DCF as a function of HOF hole

S. Choi, K. Oh / Optics Communications 222 (2003) 213–219 217

radius. The cut-off wavelengths for the two HOFs

were 1.40 and 1.42 lm, respectively. From Eq. (2),

maximum coupling efficiency of 83–87% into the

LP02 mode of the DCF was predicted for the hole

radius of 2.0–2.5 lm in the HOF, whereas cou-pling into the LP01 mode of the DCF was esti-

mated as less than 13%. In the case of incomplete

mode conversion, co-propagating LP01 and LP02

modes can induce modal delay impairments [22].

For the proposed HOM-DCF, we calculated the

differential modal delay between the LP01 and LP02

modes as a function of wavelength [22] as shown in

Eq. (3):

Fig. 6. Differential modal delay between the LP01 and the LP02

mode in the DCF.

Fig. 7. The total dispersion and dispersion slope compens

DsL

¼ DðsLP02 � sLP01Þ

L

¼ ðnLP02e � nLP01e Þ

c� k

c� dðn

LP02e � nLP01

e Þdk

ðns=kmÞ:

ð3ÞNote that in this calculation, we could estimate

the worst-case impact of modal delay, where both

the LP01 and the LP02 modes are excited an equalamount. Numerical analysis results in the differ-

ential modal delay between LP01 and LP02 modes

of 51.78–82.27 ns/km over the C-band as shown

in Fig. 6.

Multi-path interference (MPI) has been a

practical limiting factor in applications using dis-

persion compensating fibers with a few modes as

well as distributed Raman amplifiers [23,24]. Inorder to minimize the MPI in HOM dispersion

compensating schemes based on HOF mode con-

verters, it is important to increase the coupling

efficiency to the LP02 mode and suppress the LP01

mode. In the proposed design, the LP01 mode

coupling could be further reduced by implement-

ing methods such as LP01 mode rejection long

period fiber gratings, mode selective couplers,and selective doping of absorbing ions in the

core, resulting in the higher intensity of the LP02

mode.

The total compensated dispersion, DT, was nu-

merically estimated for the cascaded transmission

ated for the cascaded SMF-DCF transmission links.

218 S. Choi, K. Oh / Optics Communications 222 (2003) 213–219

links composed of SMF and the proposed DCF as

Eq. (4):

DT ¼ DDCFLDCF þ DSMFLSMF

LDCF þ LSMF

ðps=nm=kmÞ; ð4Þ

where D is the dispersion computed from the

fiber structures in Fig. 4 and L is the fiber length.

Here, we have assumed the complete mode

conversion from LP01 to LP02 modes, which will

give us an estimate of the best range of disper-sion compensation. The total dispersion nor-

malized to the SMF for the cascaded SMF-DCF

transmission links is plotted in Fig. 7. The ac-

cumulated dispersion at 1.55 lm of the SMF can

be compensated by the LP02 DCF when the

numerator of Eq. (4) reaches zero [25]. In addi-

tion, by controlling the length of the DCF, the

dispersion slope as well as the dispersion can bemanaged within a certain range over the entire

C-band. The transmission link composed of 60

km SMF and 1.247 km proposed DCF showed a

total compensated dispersion between )0.18 and

1.58 ps/nm/km, with zero dispersion at 1.55 lm.

As the length of proposed DCF further increased

to 1.31 km the total dispersion was kept less

than �1 ps/nm/km, and the dispersion slopebetween )0.09 and 0.3 ps/nm2/km in the entire

C-band.

4. Conclusions

We have proposed a novel LP02 mode disper-

sion compensation technique based on a hollow

optical fiber mode converter. This mode con-

verter showed inherent broadband operation with

the coupling efficiency of 87% from the LP01

mode of the SMF to the LP02 mode in the ring-core DCF. Design parameters for the HOF and

the matching ring-core DCF have been opti-

mized, resulting in an average dispersion of )750ps/nm/km in the C-band. Compensation of the

dispersion within �1 ps/nm/km and the disper-

sion slope within the range of )0.09 to 0.3 ps/

nm2/km was predicted using 1.31 km of DCF for

the 60 km long SMF. Further improvements inLP01 mode coupling suppression are being stud-

ied by the authors.

Acknowledgements

The authors thank Dr. H.S. Seo and Mr. W.

Shin for their help in the numerical analysis. This

work was supported in part by the Korea Scienceand Engineering Foundation through the UFON

Research Center, the Ministry of Education

through the BK21 Program, and the Ministry of

Information and Communication through the

ITRC-CHOAN program.

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