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SOLITON OPTICAL FIBERS SUPERCONTINUUM GENERATION NEAR THE ZERO DISPERSION

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SOLITON OPTICAL FIBERS SUPERCONTINUUM GENERATION NEAR THE ZERO DISPERSION Powered By Docstoc
					 International Journal of Industrial Engineering
                                                 OF INDUSTRIAL(IJIERD), ISSN
                                                          and Development
 INTERNATIONAL JOURNAL ResearchJanuary - April (2013), © IAEME 0976 –
 6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1,
                                                                          ENGINEERING
                RESEARCH AND DEVELOPMENT (IJIERD)
 ISSN 0976 – 6979 (Print)
 ISSN 0976 – 6987 (Online)
 Volume 4, Issue 1, January - April (2013), pp. 52-58
                                                                           IJIERD
 © IAEME: www.iaeme.com/ijierd.asp
 Journal Impact Factor (2013): 5.1283 (Calculated by GISI)               ©IAEME
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     SOLITON OPTICAL FIBERS SUPERCONTINUUM GENERATION
                  NEAR THE ZERO DISPERSION

                       Elham Jasim Mohammad 1, Gaillan H. Abdullah 2
           1
            Physics Department, Collage of Sciences/Al-Mustansiriyah University, Iraq,
       2
           Physics Directorate, Technology Materials Chemistry/Ministry of Science, Iraq,


 ABSTRACT

         During the last decade, the development of supercontinua (SC) sources has emerged
 as an interesting and active research field. This is largely due to new technological
 developments, which have allowed more controlled and accessible generation of
 supercontinua.
         In this paper we study the dynamics of Raman soliton during supercontinuum process
 when the pulse experiences initially normal group velocity dispersion with a negative
 dispersion. In this situation, the blue components of the spectrum form a Raman soliton
 moves faster than the input pulse because of Raman induced frequency downshifting ceases
 to occur as the spectrum of Raman soliton approaches the zero dispersion point.
 From this study one can distinguish that the first order bright soliton pulse depends on two
 important bases: first depends on the contents of the optical fibers and building method,
 where it is accomplished by making a balance between the dispersion effect and the nonlinear
 effect. The second depends on the parameters for mode and the starting point of the pulse
 shape inside the fiber such as the pulse width, normalized propagation distance and the
 existence of any nonlinear external effect.

 Keywords : Group velocity dispersion, Optical fiber, Soliton, Supercontinuum.

I.         INTRODUCTION

        In optics, a supercontinuum (SC) is formed when a collection of nonlinear processes
 act together upon a pump beam in order to cause severe spectral broadening of the original
 pump beam. The result is a smooth spectral continuum (see figure 1 for a typical example)
 [1].

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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME




Figure 1. A typical supercontinuum spectrum. The blue line shows the spectrum of the pump
source launched into a photonic crystal fiber while the red line shows the resulting
supercontinuum spectrum generated after propagating through the fiber [1].

        There is no definitive explanation of how much broadening constitutes a
supercontinuum; however researchers have published work claiming as little as 60 nm of
broadening as a supercontinuum.
        Supercontinuum generation in photonics crystal fibers (PCF) has attracted
considerable attention in recent years because of its wide applications ranging from
spectroscopy and metrology to telecommunications. Extensive studies reveal that several
physical phenomena are involved in the process of SC generation when an ultrashort optical
pulse experiences anomalous dispersion and undergoes enormous spectral broadening during
its propagation inside a PCF. Self-phase modulation (SPM), intra-pulse Raman scattering
(IPRS), four wave mixing, cross-phase modulation (XPM), modulation instability, and
dispersive wave (DW) generation are the major nonlinear processes that take part actively
during SC generation [2].
        The interplay between the dispersion and nonlinearity of the waveguide produces
optical solitons whose dynamics play a pivotal role in the process of SC generation when an
ultrashort optical pulse is launched in the anomalous group velocity dispersion (GVD)
domain. In particular, the ideal periodic evolution of a higher order soliton is perturbed by
third and higher order dispersions (HOD) to the extent that it breaks into its fundamental
components, a phenomenon known as soliton fission. These fundamental solitons experience
induced red shifts, and this shift is largest for the shortest soliton with the highest peak power,
also called the Raman soliton. During the fission process, HOD terms lead to transfer of
energy from the soliton to a narrowband resonant DW, also called non-solitonic radiation.
This DW is emitted on the blue side of the original pulse spectrum for positive values of third
order dispersion and is of considerable practical importance for generating blue shifted
radiation [2-4]. The interaction between the soliton and the DW turns out to be quite
interesting and it has been studied extensively in recent years with an analogy to gravity like
potential.
        Though nonlinear propagation of ultrashort laser pulses in dispersive single mode
optical fibers has steadily been investigated over the last three decades, studies on continuous
wave (CW) partially coherent light have been scarce. It is well known that dispersive
properties of the PCF play a governing role in producing the DW and controlling the SC
generation. Recent developments in PCF technology have made it possible to observe new
regimes of nonlinear pulse propagation because such fibers exhibit fascinating dispersion

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  International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
  6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME

  profiles with enhanced nonlinearities. An appropriate design of a PCF not only shifts the zero
  dispersion wavelengths (ZDW) toward shorter wavelengths but also produces dispersion
  profiles with multiple ZD points, features unattainable with conventional fibers [2]. Unusual
  soliton dynamics are expected when an ultrashort optical pulse is launched in the vicinity of a
  ZD point since the broadened pulse spectrum experiences opposite types of dispersion across
  the ZD point.

II.          WAVE PROPAGATION IN FIBERS

     No presentation of nonlinear phenomena in fibers can be done without considering the
  implications of the polarization, on the propagation. The wave equation for the field is [5]:

                                                     1 ∂2E       ∂ 2 PL      ∂ 2 PNL                                     (1)
                                         ∇ 2E −       2  2
                                                           = −µ0     2
                                                                        − µ0
                                                    c ∂t          ∂t           ∂t 2

  Where: t is the time with the polarization terms from:

      P = ε 0 (χ   (1 )
                          .E + χ   (2)
                                         . EE + χ separated into the linear part, PL and the nonlinear
                                                    (3)
                                                          . EEE + ...)
  part, PNL . Tackling (1) for a general system in the vector form is a formidable task. However,
  we can still express a wealth of phenomena with some simplifying assumptions. Assume the
  polarization remains the same throughout propagation, temporal retarded effects (such as
  stimulated Raman scattering and stimulated Brillouin scattering) represent only a perturbation
  and are introduced to (1). Neglecting polarization changes allows a simple scalar treatment to
  be used. It also simplifies the treatment of the susceptibility χ . The nonlinear polarization
  becomes [5]: PNL = χ ( 3 ) . E . E . E . Assuming the spectrum of the electric field is centered
  around the frequency ω 0 , β ( ω ) can be expanded in a taylor series [5]:

                                                             ω                                1                          (2)
                                         β (ω ) = n (ω )           = β 0 + β 1 (ω − ω 0 ) +     β 2 (ω − ω 0 ) 2 + ...
                                                              c                               2

  where β m represents the mth derivative of the propagation constant with respect to ω [5]:

                                                                            d mβ                                       (3)
                                                                  β (ω ) = 
                                                                            dω   
                                                                                m 
                                                                                 

  The first order term, β 1 , describes the motion of the pulse envelope, and is related to the
  group velocity by β 1 = ν g− 1 . All higher order terms describe the dispersion of the medium.
  The dominant contributions come from the second order term β 2 also called GVD and the
  third order term β 3 , also called simply third order dispersion. For completeness, β 2 is related
  to the dispersion coefficient defined as [5]: D = − 2 π2c β 2 .
                                                                                   λ




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   International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
   6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME

III.      SOLITON FISSION REGIME


            In the soliton fission regime a short, high power, femtosecond pulse is launched into
   the photonic crystal fiber or other highly nonlinear fiber. The femtosecond pulse may be
   considered as a high order soliton, consequently it rapidly broadens and then fissions into
   fundamental solitons. During the fission process excess energy is shed as dispersive waves on
   the short wavelength side. Generally these dispersive waves will undergo no further shifting
   and thus the extension short of the pump is dependent on how broadly the soliton expands as
   it breathes [6,7]. The fundamental solitons then undergo intra-pulse Raman scattering and
   shift to longer wavelengths (also known as the soliton self-frequency shift), generating the
   long wavelength side of the continuum. It is possible for the soliton Raman continuum to
   interact with the dispersive radiation via four wave mixing and cross-phase modulation.
   Under certain circumstances, it is possible for these dispersive waves to be coupled with the
   solitons via the soliton trapping effect. This effect means that as the soliton self-frequency
   shifts to longer wavelengths, the coupled dispersive wave is shifted to shorter wavelengths as
   dictated by the group velocity matching conditions. Generally, this soliton trapping
   mechanism allows for the continuum to extend to shorter wavelengths than is possible via
   any other mechanism [6-9].
            We can define a soliton fission length, L fiss , to estimate the length at which the
   highest soliton compression is achieved, such that [10]: L fiss = L D =      τ 02   .
                                                                      N       β 2 γ P0
   where L D is the characteristic dispersion length , N is the soliton order and τ is the minimum
   pulse width. As fission tends to occur at this length then provided that L fiss is shorter than the
   length of the fiber and other characteristic length scales such as the modulation instability
   length, fission will dominate [10].

IV.       SIMULATION RESULT AND DISCUSSION

           We proceed with the supercontinuum generation near the zero dispersion using
   MATLAB which is a great and easy tool to use to simulate optical electronics.
   Supercontinuum sources based on the extreme broadening of laser pulses in nonlinear
   photonic crystal fibers have been predicted to be a very interesting technology in the
   scientific as well as the industrial communities.The first supercontinuum generated in PCF
   operated in this regime and many of the subsequent experiments also made use of ultrashort
   pulsed femtosecond systems as a pump source. One of the main advantages of this regime is
   that the continuum often exhibits a high degree of temporal coherence; in addition it is
   possible to generate broad supercontinua in very short lengths of PCF.
   All the results below are got after following these steps:
           1- Generalized the Nonlinear SchrÖdinger Equation NLSE.
           2- Calculate the attenuation coefficient.
           3- Applied the Taylor expansion.
           4- Found the time domain field and time domain intensity.
           5- Implementation of group velocity dispersion relation.



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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME

       Figure 2 (a) time and (b) input filed spectra versus the wavelength respectively. In the
case of (a), mean= -3.073E-016, mode= -6.25 and the slandered deviation (STD) = 3.609.
While in (b) mean= 0.7137, mode= 5.317E-094 and the STD= 6.703.
                     8                                                                                                                                       100


                     6                                                                                                                                       90

                                                                                                                                                             80
                     4
                                                                                                                                                             70
                     2
    Time Grid (ps)




                                                                                                                                                             60




                                                                                                                                               Input Field
                     0                                                                                                                                       50

                                                                                                                                                             40
                     -2

                                                                                                                                                             30
                     -4
                                                                                                                                                             20
                     -6
                                                                                                                                                             10

                     -8                                                                                                                                       0
                          0                                1000       2000    3000    4000 5000 6000     7000    8000    9000 10000                                0                    1000       2000    3000    4000 5000 6000     7000    8000    9000 10000
                                                                                       Wavelength (nm)                                                                                                              Wavelength (nm)




Figure 2 (a) Time versus the wavelength. (b) The input filed spectra versus the wavelength.

        Supercontinuum generation is a process in which multiple colors are generated
through the nonlinear interaction of the laser pulse with the material. The longer the
interaction length, the larger amount of nonlinear interaction. We will see that the length
scale over which nonlinear effects are manifested is not typically limited by the fiber length,
but by other effects such as dispersion. Figure 3 (a) time domino intensity versus the
wavelength, (b) the spectral intensity versus the wavelength for deferent soliton order.
                                                            50                                                                                                                          100


                                                             0                                                                                                                           50

                                                                                                                                                                                          0
                                                            -50
                              Time Domain Intensity (ps)




                                                                                                                                                                                         -50
                                                           -100
                                                                                                                                                                   Spectral Intensity




                                                                                                                                                                                        -100
                                                           -150
                                                                                                                                                                                        -150
                                                           -200
                                                                                                                                                                                        -200

                                                           -250
                                                                                                                                                                                        -250

                                                           -300                                                                                                                         -300

                                                           -350                                                                                                                         -350
                                                                  0    1000    2000    3000   4000 5000 6000      7000    8000   9000 10000                                                    0    1000    2000    3000   4000 5000 6000      7000    8000   9000 10000
                                                                                               Wavelength (nm)                                                                                                              Wavelength (nm)



Figure 3 (a) Time domino intensity versus the                                                                                                                                            (b) The spectral intensity versus the
                   wavelength.                                                                                                                                                                      wavelength.

        Figure 4 show the distance versus wavelength. It explains the temporal evolution of
an optical pulse launched in the normal dispersion domain close to the ZD wavelength.
Although SC generation in the case of anomalous GVD has been studied extensively, much
less attention has been paid to the case of normal GVD. In soliton fission fundamental
solitons experience intra-pulse Raman scattering induced red shifts, and this shift is largest
for the shortest soliton with the highest peak power, also called the Raman soliton. During the
fission process, high order dispersion terms lead to transfer of energy from the soliton to a
narrowband resonant DW, also called non-solitonic radiation. This DW is emitted on the blue
side of the original pulse.

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 International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
 6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME




        Figure 4 Distance versus the wavelength for deferent numbers of soliton order.

         Figure 5 explain the relationship between the distance and delay. It show the spectral
 evolution of an optical pulse launched in the normal dispersion domain close to the ZD
 wavelength. Numerical simulations shown in Fig. 6 reveal that bending of the temporal
 trajectory occurs earlier and quicker with increasing values of N soliton order. This is
 expected because IPRS increases with the soliton order, producing larger red shifts. The DW
 on the other hand accelerates rapidly with increasing soliton order. Since DW never overlaps
 with the Raman soliton, it is not trapped by this soliton. These features are clearly seen in Fig.
 6 where we show temporal evolution for deferent values of N.




          Figure 5 Distances versus the Delay for deferent numbers of soliton order.

V.   CONCLUSION

     From the results above, numerical features are revealed when a picosecond pulse is
 launched in the normal GVD region with a monotonous dispersion slope. The nonlinear pulse
 broadening phenomenon of supercontinuum generation in fibers has been the subject of much
 recent research. In this paper we have focused on the supercontinuum process taking place
 when a picosecond pulse is launched close to the ZD wavelength of a fiber. We discuss
 soliton dynamics in the light of group delay curve when input pulse is launched exactly at the
 ZD. For a negative value of third order dispersion (TOD), the Raman soliton is formed by the
 blue components of the pulse falling in the anomalous GVD regime and it exhibits unusual
 dynamics by pulling its counterpart in the red region of the spectrum. In the case of a positive

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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
6979(Print), ISSN 0976 – 6987(Online) Volume 4, Issue 1, January - April (2013), © IAEME

TOD, optical soliton is formed by the red components of the pulse and is found to interact
with its counterpart via cross-phase modulation during propagation inside the PCF, resulting
in a spectral pushing. Unusual dynamics of the Raman soliton is observed when the pulse is
launched in the normal dispersion domain with a negative TOD. In this situation, the blue
components of the pulse form a Raman soliton that moves faster than the signal pulse.
However, as it is red shifted through IPRS, it gradually begins to decelerate. This
deceleration stops when the soliton spectrum approaches the ZD point because of a
cancellation of the Raman induced spectral shift.

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[2] S. Roy, S. K. Bhadra, K. Saitoh,M. Koshiba and G. P. Agrawal, Dynamics of Raman
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[3] A. V. Husakou and J. Herrmann, Supercontinuum generation of higher-order solitons by
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[4] J. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, R. Trebino, S. Coen, and R.
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[5] Rafael R. Gattass, Femtosecond-laser interactions with transparent materials: applications
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[6] J. Dudley, G. Genty, and S. Coen, Supercontinuum generation in photonic crystal fiber,
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[7] Tr. X. Tran and F. Biancalana, Dynamics and control of the early stage of
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[8] I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, Dispersive wave generation by
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    25–27.




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