Influence of soliton interaction on optical communication systems

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VNU. JOURNAL OF SCIENCE. Mathematics - Physics. T.xx. N„3AP, 2004

INFLUENCE OF SOLITON INTERACTION ON OPTICAL

COMMUNICATION SYSTEMS

H o a n g C hi H ieu , T rinh Đ in h C h ien
D epartm ent o f Physics, College o f Science, V N U

Abstract. In this paper, we used numerical method to investigate the two-soliton
interaction in optical fiber communication systems, in the case of in-phase and
equal amplitude solitons. With some difference initial separation of two-solitons,
separation between neighboring solitons in a digital bit stream, we obtain limit
values of bit rate and maximum transmission distances of soliton communication
system respectively.

1. In tro d u c tio n

The existence of fiber solitons is the result of a balance between group velocity 
dispersion (GVD) and self-phase modulation (SPM) ill dispersive nonlinear medium. So 
soliton pulses can propagate undistorted over long distance and remain unaffected after 
collision with each other. Thus the soliton communication system s have ultra-high bit rate 
and extremely long propagate distance. However, soliton light-wave system s were not 
commercially available, now. Because, they have some limitations, example: soliton 
interaction, soliton collision, pulse chirp... In this paper, we consider the two-soliton 
interaction with initial equal-phase and amplitudes. By the Matlap software, we showed 
the evolutionary process of two solitons with difference initial pulse separation
2. B a sic p ro p a g a tio n eq u a tio n

The mathematical description of one fiber soliton is solution of the nonlinear 
Schrodinger equation (NSE) [1] [2] [3].

j£E + i - £ J i + |u|2u = 0 , with u(0,t) = sech(ĩ). (1)
d ị 2

This equation was solved by inverse scattering method (2] [3]. And with two-soliton. 
initial condition is: u(0,x) = s e c h ( t- Yo)+ rsech{r(ĩ + Yo)}exp(j0). So we have two-soliton 
solution in fiber with arbitrary initial phase and separation is [4] :

|q |c o s h (a l +

16

^ ' ^ + | a

2

|c o s h (a

2

+ i e

2

)ei+l

a -jC o s h a j c o s h a 2 - a 4[cosh(a1 + a2) - c o s h(<|>2 — <t>X )J

where: <{>1.2 =

Ị'

— - ^1.2j + (*o)i,2 ’ »1.2 = n u ( t + x^i.a)+(ao)l,2.

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Influence of soliton interaction on...

fr 1

2

r\ ± 2A^ 1

[[ni.2 AÇ2 + n2 _ AÇ2 +r|2 j

AÇ = ỗ 2 n - n i -n a

u(x.t) is the normalized form of two-soliton envelope amplitude

3. T h e tw o -s o lito n in te r a c tio n w ith in itia l eq u a l p h a s e s a n d a m p litu d e
With two-solitons are launched whose amplitudes and phases are equal, we have: 0=0 
and Ẹ,,=4,=0. And then substituting into equation (2), it become:

q{t,x) = Q|rii sechri] (t + Yo)ein' x/2 + n-2 sechr)2( x - y 0)ein-x/2|

_2 2

1 r\ 1 2 “ Hi

where: Q = — ---5--- --- :

rji +Ï12 - r i 1ri2[tanha1 tan h a2 -s e c h a j sech a2 COSVJ/J

1 9 1 )k _ , 2x0 t u x
^ n u = l + _ ;Ju o. — sech(x0)

(3)

> = 1 + _ J ? Ĩ 2 _

sin h 2 t0

Where Yu is Initial separation,T is normalized time, X is normalized propagate 
distance. The two-soliton solution Eq. 3 describes the interaction of two solitons with above 
initial condition. We investigate the soliton

communication system s with parameters in 
Table 1. Because X is normalized with respect

to L|„ so each u n it of X is 50km. We
investigate the two-soliton interaction when 
the value of initial separation y0 varies from

1.5 to 6.5. Thus, from Eq.3, we have evolutionary process of two solitons is shown in Fig. 1. 
Because bit rate is B=(y0Tn)'1, so B varies from 15,4 Gb/s to 67 Gb/s.

Table 1

Pulse width T„= 5ps

Dispersion parameter p : =-0.5 ps:/km
Dispersion length L|)= 50 km

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6 2

Hoang Chi Hieu, Trinh Dinh Chien

F ig .l. Soliton interaction with initial equal amplitude and phase
Fig. 1 displays the evolution pattern showing periodic collapse o f a soliton pair for 
various pulse separation. The periodic collapse of neighboring soỉitons is undesirable from

the system standpoint. One T bl 2

way to avoid the interaction 
problem is to increase Yu such 
that the collapse distance, ZM
is much larger than the

transmission distance Lf. From the results in the Fig 1, we can measure the collapse 
distance ZM at each difference pulse separation Yu and thus we have table 2.

I0 1,5 2,5 3,5 4,5 5,5 6,5

B (Gb/s) 67 40 28,6 22,2 18,2 15.4

z „ (km) 105 460 1750 3850 10500 ] 7250

4 . C o n clu sio n

The curve shown in Figure 2 is very useful 
for us to use as a guideline to choose the optimum 
pulse separation given a certain transmission 
distance. Pulse separation has to be minimized in 
order to achieve high bit rate transmission.

With initial condition are equal phase and 
amplitude, the soliton interaction investigated is the 
strongest. Actually, we can choose the value of 
initial phase and amplitude to decrease "solium 
interaction force” to the minimum. We will 
investigate this problem in later papers.

Fig.2. ZM as a functio 
initial separation.

R efer en ces

1. H.C.Hieu. T.D.Chien and Nguyen Manh Hung, Investigatings about the ultra-short pulsef 
in soliton form. 3rd National Optic & Spectroscopy Conference,8. 2002, pp 41-45.
2. G.P.Agrawa), Fiber-Optic Communication System s, New York: Willey, 1998.
3. Le Nguyen Binh and al. Optical Fiber Communication Systems, Mocss, 1996

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