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Modeling photonic crystal fiber for ef ficient soliton pulse propagation at 850 nm

R. Vasantha Jayakantha Raja a, K. Porsezian a,⁎, Shailendra K. Varshney b, S. Sivabalan c

a Department of Physics, Pondicherry University, Puducherry, 605 014, Indiab Department of Electronics and Electrical Communication Engineering and Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur, 721 302, Indiac School of Electrical Engineering, VIT University, Vellore, 632 014, Tamil Nadu, India

a b s t r a c ta r t i c l e i n f o

 Article history:

Received 14 May 2010

Received in revised form 11 July 2010Accepted 11 July 2010

We numerically investigate the dynamics of soliton propagation at 850 nm in chloroform filled liquid core

photonic crystal fiber (LCPCF) by using both finite element method (FEM) and split step Fourier method

(SSFM). We propose a novel chloroform filled PCF structure that operates as a single mode at 850 nm

featuring an enhanced dispersion and nonlinearity for ef ficient soliton propagation with low input pulse

energy and low loss over small distances. We adopt the projection operator method (POM) to derive the

pulse parameter equations which clearly describes the impact of fourth order dispersion on the pulse

propagation in the proposed PCF. To analyse the quality of the pulse, we perform the stability analysis of 

pulse propagation numerically and compare our results of the newly designed chloroform filled PCF with

that of standard silica PCF. From the stability analysis, we infer that the soliton pulse propagation in modi fied

chloroform filled PCF is highly stable against the perturbation.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, intensive investigations of PCFs have receivedgreat deal of scientific attention because of its numerous invaluable

nonlinear applications in sensor and communication fields [1,2]. The

arrangement of air holes in the cladding region gained more

importance due to optical properties of PCF such as high nonlinearity,

highly birefringence, large mode-field area, high numerical aperture,

ultra flattened dispersion, adjustable zero dispersion, etc [1–4]. InPCF,

the refractive index difference between core and cladding is much

higher than in conventional fiber which can be obtained by changing

the size of the air hole. These modifications further provide high

nonlinearity and zero dispersion at visible wavelength and low loss.

This significant variation of air hole diameter, pitch and design of the

PCF have several applications like wavelength conversion using four

wave mixing, optimization of the pump spectra to achieve flat-Raman

gain, minimization of noise figure of the PCF amplifier, Raman lasing

characteristics, narrow or broad bandpass filters, etc. [5–9].

The recent widespread research on soliton propagation in PCF was

mainly motivated by its numerous invaluable nonlinear applications

in supercontinuum generation, pulse compression, optical switching,

fiber laser, parametric amplifier, modulational instability, etc

[1,10,11]. Among these applications, the combination of engineered

dispersion induced frequency chirp and elevated nonlinearity induced

frequency have led to the soliton pulse propagation at the short

wavelength in PCF [12] which has attracted many researchers due to

its wide variety of applications in spectroscopy and materialprocessing. For instance, Wadsworth, et al. [13] and Luan, et al. [14]

had investigated the soliton propagation in the near visible regime

using Ti:Sapphire laser. A crucial problem faced in the optical soliton

transmission lines is to obtain an ef ficient soliton propagation in PCF

with single mode, low loss, and high nonlinear coef ficient. It is well

known that the linearlength and nonlinear length should be balanced

to obtain the soliton pulse propagation. As the dispersion is inversely

proportional to linear length, one can obtain soliton at short distance

using high ‘dispersion PCF’ and the required input power can be

reduced by choosing ‘high nonlinear PCF’. In general, there are two

proven ways to enhance the nonlinearity and dispersion in fibers.

First, one can modify the design of PCF with large air hole size leading

to high nonlinearity and large dispersion. But, if we design PCF to

enhance the nonlinearity, the single mode does not exist for large air

hole size. In the second method, non-silica technology such as SF6,

TF10, CS2, nitrobenzene, etc, have now emerged as the most exciting

prospects in the development of PCFs, as they amount to high

nonlinearity for soliton propagation with low input energy of the

pulse [1,15]. But in these structures also, due to the high index

contrast between core and cladding refractive index, obtaining a

single mode PCF and anomalous dispersion at visible regime is very

dif ficult. Recently, Zhang et al. [16] have reported the supercontinuum

generation in chloroform filled core PCF which has both single mode

existence and zero dispersion at visible regime. This high nonlinearity

in chloroform filled LCPCF can modify the dynamics of soliton

propagation, which makes the soliton dynamics in LCPCF interesting

Optics Communications 283 (2010) 5000–5006

⁎ Corresponding author.

E-mail addresses: rvjraja@yahoo.com (R. Vasantha Jayakantha Raja),

ponzsol@yahoo.com (K. Porsezian), skvarshney_10@yahoo.co.uk (S.K. Varshney),

ssivabalan@vit.ac.in (S. Sivabalan).

0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.optcom.2010.07.025

Contents lists available at ScienceDirect

Optics Communications

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from the fundamental point of view. Considering the above discussed

important investigations, we have reported in this paper a novel PCF

structure to achieve high ef ficient soliton pulse propagation at

850 nm, which would have found wide applications in optical

coherence tomography and frequency metrology [1]. To the best of 

our knowledge, in this paper, we have succeeded in achieving highly

stable soliton at 850 nm in a very short distance using low power.

In addition to the design of PCF for ef ficient soliton propagation, we

concentrate more in analysing the dynamics of the pulse propagationthrough newly designed PCF. Among the several analytical and

numerical techniques like the Lagrangian variational method [17],

Hamiltonian method [18], projection operator method (POM) [19,20],

non-Lagrangian collective variable approach [21], collective variable

technique [22] and the moment method [23] to study the pulse

dynamicsinfiber systems,we choose thegeneralized POMto investigate

thesolitonpropagationin PCFat 850 nm. Because,the POMis considered

to be more versatile as it does not require the complex procedure of 

derivation of the Lagrangian. The POM for complex nonlinear partial

differential equations wasproposed by Nakkeeran andWai as a meansto

derivethe ordinary differentialequations that could be derived eitherby

the Lagrangian variational method or the bare approximation of the

collective variable theory [19,20]. Since then it has motivated many

researchers to analyse the pulse propagation with various linear and

nonlinear physical coef ficients in single mode and birefringent fibers

using Gaussian/hyperbolic ansatz [19,22]. Even though several authors

have reported the various dynamical patterns with various physical

coef ficients, to our knowledge, there is no pulse parameter equations

using POM for higher order NLSE in the presence of fourth order

dispersion. But, it is noteworthy that the higher order dispersion also

plays a major role in the pulse dynamics in PCF during the pulse

propagation. So we intent to derive the pulse parameter equation with

the influence of fourth order dispersion using POM.

In this paper, the finite element method (FEM) scheme is

employed to obtain accurate results of designing PCF which is

required to analyse the pulse propagation in PCF. The numerical

method FEM solves the vector wave equations and split step Fourier

method (SSFM) solves a generalized nonlinear Schrödinger equation

(NLSE) for the different core material. In order to investigate thedynamics of soliton propagation in the proposed PCF, we have carried

out POM with the detailed numerical simulations. Finally, we have

also analysed the stability of soliton for the newly proposed structure.

2. Designing chloroform filled photonic crystal fiber 

At the outset, we intend to study the role of four important

parameters such as single mode, linear length, nonlinear length and

confinement loss in PCF to study the soliton propagation. It is evident

from the theory of PCF that large dispersion and a high nonlinearity in

the visible regime can be achieved by designing PCF with large air hole

diameter (d) andsmall pitch (Λ ) constant [1]. However, it is noteworthy

that, after attaining certain value of normalized air hole size (d /Λ ), the

fiber may not be a single mode. Hence, the single mode will not exist at850 nm for high nonlinear PCF by choosing large air hole diameter.

So, we have started our discussion from designing PCF for possibility of 

single mode existence at the maximum possible large air hole diameter

and low pitch. The spectral variation of the V-parameter for different

d /Λ  at Λ =1 μ m for both silica (solid curves) and chloroform-core

(dashedcurves) PCFis shown in Fig. 1, where, ds,Λ s and dc ,Λ c represent

diameter of air hole, pitch of silica and chloroform PCF respectively. We

have used FEM [24] to simulate our designed PCF structures. The

valueof nonlinear refractiveindex n2of chloroform is 1.7× 10−18 m2 /W

[16] and the refractive index of chloroform is given by [25]

nCHCl3= 1:431364 + 5632:41 × λ

−2−2:0805 × 108

× λ

−4

+ 1:2613 × 10

13

× λ

−6

:

where λ is the wavelength in nm. We can observe from Fig. 1

that the single mode exists up to dc /Λ c =0.85 in the case of chloro-

form-core PCF, whereas in the silica-core PCF it exists only up to

ds /Λ s=0.6 at 850 nm. In order to achieve high nonlinear coef ficient

to obtain the soliton pulse propagation with low power in LCPCF, we

have further modified our PCF structure by increasing the size of air

hole in the first ring as demonstrated in Fig. 2 (b) where the idea has

come from ref. [8]. In Fig. 2 (a) and (b) we have shown the

schematics of a silica-core PCF (SPCF) and the chloroform-core PCF

(CPCF), respectively. The modified CPCF has dc /Λ c =0.9 in the first

ring and dc /Λ c =0.8 in the successive rings with Λ c = 1 μ m and the

core diameter D equals to the diameter of air hole in the outer ring dc 

i.e. D= dc .

3. Analysis of linear and nonlinear length scales

In order to achieve the soliton at very short length, we have

analysed linear length scale which is inversely proportional to

dispersion. Fig. 3 illustrates the obtained group velocity dispersion

(GVD) characteristics for both fibers SPCF and CPCF using FEM. It can

be seen that the zero dispersion is located at 742 nm for SPCF and

680 nm for CPCF. It is also shown in Fig. 3 that the obtained GVD value

110.26 ps/nm/kmin CPCF at 850 nm is 4 times greater than that of the

GVD value of 27.34 ps/nm/km in SPCF. Since the calculated linear

length for the input pulse width 200 fs in SPCF is 1.22 m and CPCF is

0.3 m, the soliton can be obtained at a length four times shorter in

CPCF than that of SPCF. The calculated confinement loss through FEM

at 850 nm for SPCF and CPCF are 0.019 dB/m and 3.4×10−8 dB/m,

respectively.

To understand thedynamicsof nonlinearpulsepropagationin PCF,we have considered the NLSE of the following form [1]:

∂U 

∂ z +

α

2U  + ∑

4

n =2 β n

in−1

n!

∂nU 

∂T n= iγ j U j

2U  +

i

ω0

∂ðj U j2

U Þ

∂T −T RU 

∂ jU j2

∂T 

!

ð1Þ

where U is the slowlyvarying envelope amplitude of the wave, z is the

longitudinal coordinate along the fiber in meter, T  is the time in the

reference frame in ps. The parameter β n is the n(=2,3,4)-th order

dispersion coef ficient. The parameter γ  is the Kerr nonlinear

coef ficient and T R is the delayed Raman response.

In order to analyse thenonlinear evolutionof pulse in PCF, we have

considered a physical situation wherein SPM effect is alone present,

Fig. 1. V eff  as a function of λ for silica-core (solid line) and chloroform-filled (dashed)

PCF for different diameter of air hole at pitch= 1 μ m.

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while the dispersion effects and loss are neglected. To observe the

action of the SPM on PCF alone, we turned off the dispersive term in

NLSE. So the Eq. (1) becomes simply

∂ A∂ z 

=ie−α z 

LNL

j A j2 A: ð2Þ

A is the normalized amplitude defined as

 Að z ;τÞ = √P 0expð−α z = 2ÞU ð z ; τÞ ð3Þ

where τ =T 

T 0and P 0 is the input power. The nonlinear length

LNL =1

γP 0provides the distance at which the nonlinear effects are

important. To study the effect of SPM in PCF, we have considered

the Gaussian pulse of width T 0= 200 fs with corresponding calculated

γ  values through FEM equal to 0.1518 W−1m−1 for SPCF and

27.99 W−

1m−

1 for CPCF at 850 nm respectively. Calculated frequen-cy spectra are shown in Fig. 4 for Gaussian pulse at the fiber length

L =20 m with peak powers of 20 W and 0.1 W for SPCF and CPCF,

respectively. Since the nonlinearity of CPCF is almost 200 times larger

than that of SPCF, it is clear that CPCF can attain the same spectral

broadening with 200 times lower power values than that of SPCF.

Thus one can achieve ef ficient pulse broadening at 850 nm in CPCF

with low input power and low confinement loss.

4. Ef ficient soliton propagation in photonic crystal fiber 

The physical process of a fundamental soliton propagation can be

explained by considering the effect of SPM and GVD. Even though the

higher order dispersion coef ficients play major role in PCF, there is no

significant change in soliton pulse propagation for sixth order dispersion.

Hence, we have analysed the effects of group velocity dispersion up to

fourth order dispersiononly. To investigate thesolitonpropagation in PCF,

we have numerically solved theEq.(1)using (SSFM)with initial envelope

of sech-shaped pulse at z =0. The value of Raman response parameter T Rof silicais 5 fs. Tothe best ofour knowledge,the T Rvalue of chloroformhas

notbeen reported. Hence,we calculatetheT R value of chloroformby using

the following formula as in [17],

T R ≈ f R ∫∞

0

t ⁎ hRðt Þdt  ð4Þ

where f R represents the fractional contribution of the delayed Raman

response and hR is theRaman response function which canbe given by

an approximate formula as

hR =τ

21 + τ22

τ1τ22

sint 

τ1

exp − t 

τ2

ð5Þ

Fig.2. Schematicdiagram of (a)silica-corePCF (SPCF) with ds/Λ s=0.6and(b)themodified chloroformfilledPCF (CPCF) whoseparameters aredc /Λ c =0.9inthefirstring, dc /Λ c =0.8in

the rest rings and diameter of the core D= dc . pitch=1 μ m for both SPCF and CPCF.

Fig. 4. Calculated SPM-broadened spectra in PCF for an unchirped Gaussian pulse

T 0=200 fs, β n=0, λ=850 nm.Fig. 3. Calculated GVD for fundamental mode as a function of  λ for SPCF and CPCF.

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where τ 1 and τ 2 are adjusting parameters. We have used experimen-

tal data from [26] to calculate the τ 1 and τ 2 value of Eq. (5) by using

curve fit method. The obtained values of τ 1 and τ 2 are 38 fs and 220 fs

respectively. Using Eq. 4 with f R=0.35 [16], T R value of chloroform is

found to be 8.8 fs. Numerical simulations are carried out for the input

pulse by settingλ=850 nm and the pulse width (FWHM)= 200 fs. The

dominantfiber parameters are β 2=−0.01048 ps2/m, β 3=3.78×10−5

ps3/m, β 4=1.02×10−6 ps4/m, γ =0.15183 W−1m−1 and loss α =

0.01917 dB/m for SPCF and β 2=−0.04226 ps

2

/m, β 3=1.59×10

−3

ps3/m, β 4=4.94×10−7 ps4/m, γ =27.9912 W− 1m− 1 and loss

α =3.46×10−8 dB/m for CPCF. Figs. 5 and 6 show the temporal

evolution of a fundamental solitonfor4L D in SPCFand thenewly designed

CPCF. Since high spectral broadening can be obtained by using low input

power in CPCF, the pulse energy required to balance the linear length and

nonlinear length to obtain the fundamental soliton must be very low in

comparison to SPCF. This is clearly illustrated through numerical

simulation in Figs.5 and 6, where it could be seen that soliton is obtained

at the pulse energy of 1.21 pJand 0.026 pJ forfiber designSPCF and CPCF,

respectively. It is also shown in Fig. 5 that the femtosecond pulse induces

large asymmetrychangeof group velocity due to which itspeakis shifted,

resulting in the shift of soliton towards the trailing edge during the

propagation. Since the ef ficiency of the soliton supported by a PCF also

depends on theconfinementloss, the ef ficiency of thesolitonpulse can be

increasedby choosing the CPCFwhichhas lowlossin comparisonto SPCF.

It is also calculated that the power loss during the solitonpropagation at 4

soliton period in CPCF is 4.21 % and SPCF is 9.14 % .

5. Pulse parameter equation

To get more insight into the dynamics of thepulse propagation, we

make use of the recently developed POM to derive the pulse

parameter evolution equations. To analyse the evolution of the

parameters one can utilize the generalized POM which could derive

the pulse parameters equations from the bare approximation of the

collective variable theory [19]. Even though the physical parameters

like self steepening, Raman and third order dispersion are affecting

the soliton dynamics, these higher order effects on NLSE are already

studied in detail [22,23]. Hence, the prime focus of the paper is toinvestigate the influence of fourth order dispersion in the pulse

parameters by POM approach. We use the hyperbolic secant ansatz to

derive the pulse parameter evolution equations:

U  = x1secht − x2

 x3

exp

ix4ðt − x2Þ2

2+ ix5ðt − x2Þ + ix6

!ð6Þ

where x1, x2, x3, x4, x5 and x6 represent the pulse amplitude, temporal

position, pulse width, chirp, frequency shift and phase, respectively.

Using the generalized POM on the Eq. (1), the pulse parameter

equations of motion corresponding to the bare approximation of the

collective variable theory can be obtained. The pulse parameter

Eq. (7) are useful in investigating the propagation of the hyperbolic

secant shaped nonlinear pulse propagation in PCF.

d x1

d z =

1

2 x4 β 2 x1−3B3 x4 x5 x1 +

1

10B4 x4 60 x

25 +

π 2 x

24 x

43 + 4

1

 x23

0@

1A x1−Γ x1;

dx2

dz = − x5 β 2 +

B3 x242 x

43 + 60 x

25 x

23 + 28

20 x2

3

−B4 x5 x

242 x

43 + 20 x

25 x

23 + 28

5 x2

3

+6

5γ2 x

21;

dx3

dz = − x3 x4 β 2 + 6B3 x3 x4 x5 + B4 −12 x3 x4 x

25−

 x4 π 2 x2

4 x43 + 4

1

5 x3

0@

1A;

dx4

dz = β 2 x

24−

3

 x43

!+ 6B3 x5

3

 x43

− x24

!

+B4 13π 

6 x

44 x

83 + x

244 x

43 + 84 π 

4 x

43 x

24

−30  x2

5 x23

−840

7π 4 x63

−γ13 x

2

1 x2

3

+x5γ23 x

21

 x23

d x5

d z = −

B3 x4 π 2 x

43 x

24−4

5

2 x23

+2B4 x4 π 

2 x

43 x

24−4

 x55

 x23

+ x4γ26 x21

+4γ3 x

21

π 2 x23

dx6

dz = β 2

7

 x23

− x25

2

!+

B3 x5 5π 2

 x2311 x

24 + 8 x

25

 x

23 + 10

20π 2 x2

3

+ γ18 x21 + x5γ29 x

21

+B4 3 −27π 

6 x

44 x

63− x

24 x

2514 x

43 + 840π 

2 x

24−2 x

45

 x

23 + x

2513

 x

23 + 12

1680π 2 x4

3

ð7Þ

where

Γ = α= 2; B3 = β3 = 6; B4 = β4 = 24;γ1 = γ;γ2 = γ=ω0;γ3 = γT R;

1 =−15 + 7π 2

3 + π 2; 2 = 5 −6 + π 

2

; 3 =30

π 4;

4 = 28π 2 −15 + π 2

; 5 =

15 + π 2

5π 2; 6 =

4 15 + 2π 2

15π 2;

7 =1

6+

5

4π 2; 8 =

15 + 8π 2

12π 2; 9 =

−75 + 32π 2

60π 2;

10 = −150 + 8π 2; 11 = −6 + π 

2; 12 = 112 75 + 7π 

2

;

13 = 336 25−6π 2

; 14 = 560π 

2 −6 + π 2

:

ð8ÞFig. 5. Fundamental soliton propagation for SPCF at 850 nm over four soliton period.

Fig. 6. Fundamental soliton propagation for CPCF at 850 nm over four soliton period.

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Fig. 7. Deviation of pulse parameters amplitude (a), temporal position (b), width (c), chirp (d), frequency (e) and phase (f) for SPCF. The solid and dashed curves indicate pulse

dynamic parameter in the presence and absence of β 4.

Fig. 8. Deviation of pulse parameters amplitude (a), temporal position (b), width (c), chirp (d), frequency (e) and phase (f) for SPCF (dashed line) and CPCF (solid line).

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From the obtained dynamical Eq. (7), one can observe that the

fourth order dispersion cannot be avoidable while the numerical

value of  β 4 is significantly high. The evolution of the pulse parameters

along the propagation distance ‘  z ’  can be carried out by solving Eq. (7)

using Runge–Kutta method with initial conditions of SPCF are x1=2.3162 W1/2, x2=0 ps, x3=200 fs, x4=0 THz/ps, x5=0 THz

and x6=0 rad and CPCF are x1=0.3425 W1/2, x2=0 ps, x3=200 fs,

 x4= 0 THz/ps, x5=0 THz and x6=0 rad. Considering the PCF struc-

ture as in the preceding section, we begin to explore the effect of fourthorder dispersion in solitonpropagation using POM. Thedeviation

of pulse parameters during the pulse propagation is shown in Fig. 7(a),

(b),(c),(d), (e) and (f) for amplitude, temporal position, width, chirp,

frequency and phase respectively for SPCF. The deviation of pulse

parameters can be defined as xnð z Þ− xnð0Þð Þ, where xn(0) is initial pulse

parameter and xn( z ) is pulse parameters at the distance ‘  z ’ . It is quite

interesting to observe from Fig. 7 that the fourth order dispersion is

significant and does play crucial role in the soliton propagation. Quite

interestingly in PCF, the incorporation of fourth order dispersion

encounters chirp during the pulse propagation. Thus the β 4 value is

sensitive to soliton propagation and hence one can observe from Fig. 7

that there is a significant deviation in pulse parameters. Fig. 8 illustrates

the dynamics of pulse propagation for both SPCF and CPCF using POM.

Fig. 8 clearly illustrates one can achieve soliton at relatively short

distance using CPCFwhen compared to the SPCF. It should also be noted

from Fig. 8 (a) thatthe deviation of peakpower ofCPCFis low duringthe

propagation due to low loss in comparison to SPCF.

6. Stability analysis

In addition to the fundamental soliton pulse propagation, we have

also analysed the stability analysis. The stability of the soliton pulse

propagation canbe understood in three ways as (i) considering power

perturbation in the initial pulse i.e. simply increasing its input power,

(ii) white noise perturbation in the input pulse and (iii) chirp

perturbation in the input pulse. In Fig. 9, we have plotted the output

power and energy deviation which can be defined as (P out −P ideal)/

P ideal for the case (i) where, P out  is the output power of the pulse after

propagation length 4LD in the presence of perturbation. P ideal is powerof the output pulse after propagation of length of 4LD when there is no

perturbation as in Figs. 5 and 6. It should be noted that the output

power P ideal is calculated with the effect of loss parameters of PCF.

Figs. 10 and 11 show the deviation of power and energy in SPCF and

CPCF forthe white noise andchirpperturbation in the input pulse. It is

evident from the Fig. 9 that there is only minimum power deviation in

CPCF due to low loss when compared to SPCF. Also it is quite clear

from Fig. 9 that there is no significant variation of energy deviation is

observed during the power perturbation in CPCF at 850 nm. From

Fig. 10, it is also observed that there is an additional instability arises

due to white noise perturbation in both SPCF and CPCF and their

power and energy fluctuations are almost same for a small random

noise. In the case of chirp perturbation, we have observed large

deviation of power and energy in SPCF than CPCF in Fig. 11. It is quite

interesting from the Fig. 11 that theincreasing chirp of the input pulse

crucially affects the soliton propagation in SPCF where as the pulse

remain stable in CPCF. It is noteworthy from Figs. 9 and 11that

although the power and chirp perturbation of the input pulse

increases the instability, the soliton power and energy fluctuation in

case of CPCF is only limited. Even though one can observe low power

deviation in CPCF through Figs 9–11, the difference between power

deviation in SPCF and CPCF is minimum due to the power

perturbation. Also, there is no significant difference in energy

deviation between SPCF and CPCF. In the case of chirp free pulse

propagation, one requires high precision experiment to distinguish

the energy deviation of both fibers. Hence, it is concluded that the

stability of the pulse in our newly designed CPCF is good as that of 

SPCF during the perturbation, which can be of interest for telecom-munication and low-pedestal pulse production.

7. Conclusion

In conclusion, the novel result of this work is that we have

successfully investigated new theoretical design of chloroform filled

PCF to achieve high ef ficient soliton pulse propagation at 850 nm. For

this purpose, we have applied FEM and SSFM to investigate the

dynamical behavior of the soliton pulses numerically in PCF. Before

Fig. 9. Variation of output power and energy deviation of perturbed soliton with

unperturbed soliton as a function of power perturbation for SPCF and CPCF.

Fig. 10. Variation of output power and energy deviation of perturbed soliton with

unperturbed soliton as a function of white noise perturbation for SPCF and CPCF.

Fig. 11. The output power and energy deviation of perturbed soliton with unperturbed

soliton as a function of chirp for SPCF and CPCF.

5005R. Vasantha Jayakantha Raja et al. / Optics Communications 283 (2010) 5000–5006 

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investigating the soliton type pulse propagation, a detailed study has

been carried out for linear and nonlinear length scale to understandthe

influence of these two effects in the newly designed PCF. Based on this

fact, we have successfully demonstrated the generation of fundamental

soliton propagation at very short length with low loss and low input

energy at 850 nm in contrast to soliton generation in silica-core PCF.

We have also performed the POM and derived pulse parameter

equations governing the pulse dynamics in PCF. The resultsdescribethe

effect of fourth order dispersion in the pulse parameters at differentparts of the PCF. Finally we have analysed the stability of newly

designed chloroform filled PCF with power, white noise and chirp

perturbation. Numerical simulations on stability analysis show that

soliton propagation in newly designed PCF with chloroform-core is also

stable as that of silica made PCF.

 Acknowledgments

KP thanksDST-DFG, DST, CSIR, DAE-BRNS andUGC, Government of 

India, for the financial support through major projects.

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