Khảo sát quá trình lan truyền xung cực ngắn trong sợi quang tinh thể tt tiếng anh

For the ultrashort pulse, the high-order dispersion and nonlinear effects give rising of soliton’s disturbance.. The SC generation appears when the powerful pulse propagates through the

MINISTRY OF EDUCATION & TRAINING

ABSTRACT OF DOCTORAL THESIS IN PHYSICS

Vinh - 2020

The work is achieved in

VINH UNIVERSITY

Adviser:

1 Prof Dr Dinh Xuan Khoa

2 Dr Bui Dinh Thuan

Reviewer 1: Prof Dr Tran Cong Phong

Reviewer 2: Prof Dr Nguyen Huy Cong

Reviewer 3: Prof Dr Luu Tien Hung

The thesis was defensed before the doctoral admission board of Vinh university at …h…, ….……., …, 2020

The thesis can be found at:

- Nguyen Thuc Hao library of Vinh university

- Viet Nam National library

PREFACE

Reason to choice the investigation subject

Because of its applications in many fields of science, technology and life, the propagation of the optical soliton in the optical fiber has been being an interesting and attracting subject of scientifics Normally, the soliton’s propagation is stable when its power is high enough so that the Kerr effect is balanced by the group velocity dispersion in medium Depending on pulse power and specific parameters of medium, the soliton can have own different orders However, the first-order soliton, i.e., the fundamental soliton can only keep its shape and spectrum, meanwhile the shape and spectrum

of the higher-order soliton always periodically change For the ultrashort pulse, the high-order dispersion and nonlinear effects give rising of soliton’s disturbance Since that the frequency shift due to the Raman induced scattering and dispersion waves appear Corresponding to the soliton disturbance, there is the soliton fission which is the main reason of supercontinuum (SC) generation The SC generation appears when the powerful pulse propagates through the high nonlinear medium, in which the nonlinear effects as: soliton fission, Raman induced scattering, high-order group velocity dispersion, four-wave mixing rise up together

Lately, the optical group in Vinh university has paied attention on the SC generation in the photonic crystal fibers (PCF) The obtained results lead to generate SC in the infrared region

Moreover, last years, the theoretical and experimental works in the SC generation have focused on the influence of configurations, ground and infiltrated materials on the SC generation efficiency and its spectrum The explicit analysis of nonlinear processes and their influence of one on other are not cared enough about

In the face of above mentioned questions, we choice investigation

subject with title “Investigation of ultrashort pulse in photonic crystal fibers”

The purpose

- Investigation of the influence of high-order dispersive nonlinear effects on the pulse separation and spectral broadening of ultrashort pulse propagating in photonic crystal fiber

- Propose the optimal model of PCF PBG08-ethanol for SC generation at 1560 nm

- Investigation the influence of pulse parameters on the SC generation

- Design and set-up experiment system using available PCF

to observe the SC spectrum and to verify the influence of some parameters on power and spectrum

The contents

- Derive the equation describing the propagation of ultrashort pulse in PCF Use it to simulate the influence of high-order dispersive and nonlinear effects spectral broadening

- Propose modelPCF and investigate the influence of some parameters on the dispersion, zero-dispersion wavelength, and nonlinear coefficient Since that to find optimal values for SC generation at 1560 nm

- Simulate SC generation and investigation the influence of pump pulse parameters on SC generation in proposed PCF

- Design and set-up experiment system using available PCF

to observe the SC spectrum and to verify the influence of some parameters on power and bandwidth

The methods

Theoretical simulation combining with experiment

The original contributions

i) Has proposed the model of PCF PBG 08 - ethanol with

optimal parameters use to generate SC

ii) Has simulated the nonlinear processes which play the

main role in supercontinuum generation and found out the influence of PCF configuration and laser pulse parameters on supercontinuum spectrum

iii) Has designed the experimental system to generate SC in

Chapter 2 PROPAGATION OF LASER PULSE

2.1.2 Propagation of short pulse

Using slow-variable envelope approximation, the Schrodinger nonlinear equation decribing the propagation of short pulse is derived

nonlinear coefficinet of refractive index

2.1.3 Propagation of ultrashort pulse

The micro process has own specific time of (0.110) fs, meanwhile, the ultrashort pulse has its duration from 10 fs to hundreds fs, so it is not accurately to assume that the optical response

of medium is instantaneous Thus, in the expression of the nonlinear polarization of medium must be the terms of response delay We have Schrodinger nonlinear equation for ultrashort pulse as

1 1 1 0

2.2 Numerical simulation methods

Using methods as split-step Fourier or four-order Runge-Kutta to solve Eq.(2.28) with different limit conditions

2.3 Influence of dispersion and nonlinear effects on propagation

of pulse in optical fiber

2.3.1 Influence of high-order dispersion

To simply, first we consider third-order dispersion, and assume that the Raman induced scattering and pulse shock are ignorable For this case Eq 2.28 is simplified to:



(2.48)

If the centrum wavelength of pulse is close to the zero-dispersion one, the third-order dispersion play the main role, i.e 2=0 and 30 For this case Eq (2.48) will be modified with normalized paramters:

and illustrated in Fig.2.1

Simulated for N = 3, z = 1.2L D , = 0.02, S = 0 and = 0

As we known, dispersion coefficient can have possitive or minus sign So in Fig.2.3 the propagation of pulse in anomous-dispersion medium with <0 The values of other paramters are similar to that used in Fig.2.2 In this case there is a spectral peak in low-frequency region 0 (red shift) as shown in Fig.2.3b Thus, in this case, a portion of pulse energy is separated from centrum region as dispersion wave which propagates more speedly then input pulse It results the input pulse broadens

Fig 2.3 (a) Pulse shaping , (b) Spectral change

Simulated for N = 3 , z = 1.2L D , = - 0.02, S = 0 and = 0

Fig.2.4 is results simulated for the case of N = 3.2, z = 2LD ,

= 0.02, = 0,0005 If we consider to the fourth-order dispersion From Fig.2.4 we can see that if consider to disturbance by the fourth-

order dispersion and odd soliton, the balance between the

second-order dispersion and self-phase modulation appears not, consequenlty, the output shape and spectrum of pulse becomes more complex

Fig.2.4 (a) Pulse shaping , (b) Spectrum change

Simulated for N = 3.2 , z = 2L D , = 0.02, and = 0.0005

2.3.2 Influence of Raman induced scattering

The Raman-induced frequency shift (RIFS) is the fact to make spectrum red shifts (Fig.2.5) The magnitude of RIFS is proportional

to T04, where T0 is the duration of input pulse which is very large for ultrashort pulse If ultrashort pulse with T0 = 50 fs propagates in fiber, the RIFS is priority in comparison to dispersion, consequently,

Eq (2.28) can be simplified as:

 (

) (2.51)

Fig.2.6 presents the propagation of ultrashort hyperbolic secant pulse with power of N = 3 (equivalent to 3 fundamental solitons) through normalized distance of  =0.8 We can see that with increasing of the intensity, the frequency changes not only, but the soliton fission appears too (Fig 2.6b)

Fig 2.5 Raman-induced frequency shift for soliton N=1

Fig 2.6 Raman-induced frequency shift for soliton N = 3

2.3.3 Influence of pulse self-steepening

To clearly understant the nature of the pulse self-steepening, we assume other nonlinear effect are ignorable Let 2 = 0, 3 = 0, the Eq.(2.28) is modified as:

 iN2(

( )) (2.52)

Fig 2.7 Ultrashort pulse self- steepning through different normalized

distance

Fig 2.7 is pulse self-steepening simulated for the case of  = 0,  = 0.6; = 1.2 với S = 0.03 and N = 1 From this figure we can see that after propagating through a distance of fiber, the ultrashort pulse will

be unsymetrically reshaped Its trailing edge is steepened up Continuously, we investigate the influence of the second-oder dispersion on the pulse self-steepening The results in Fig 2.8 are simulated for case of S = 0.03, N = 1 ,  = 0, 25 and 50 This figure shows that group velocity disprersion (GVD) can vanishing the optical shock, and then smooth trailing edge In Fig.2.9 are results simulated for the case of S = 0.03 and N=2 We see that if N = 2, there is the overlap of two pulses

Fig 2.8 Propagation of hyperbolic pulse with N=1

Fig.2.9 Propagation of hyperbol with N = 2

2 4 Conclusion

1 The high-order dispersion effects cause the perturbane process, and then results the phase mismatch and dispertion wave generation The generated pulse propagates with different velocity, consequently, the spectrum broadens

2 The Raman induced frequency shift is the main reason of red shift

of pulse spectrum If pulse with power high enough the soliton fission appears in the nonlinear fiber

3 The pulse self-steepening can appear depending on the pulse intensity It results the optical shock in trailing edge

The mentioned effects investigated above will play the main role in the SC generation in PCF which will be presented in the next chapter

Chapter 3 INVESTIGATION OF ULTRASHORT PULSE PROPAGATION IN PHOTONIC CRYSTAL FIBER 3.1 Supercontinuum generation and investigation model

3.1.1 Supercontinuum generation in PCF

The SC generation can be illustrated by the evolution presented

in Fig.3.1

Fig 3.1 Evolution scheme of supercontinuum generation in PCF

3.1.2 Propose model PCF PBG 08 - ethanol

The model of PCF proposed is presented in Fig.3.2 The PCF PBG 08 is drawed from glass PBG 08 of chemical components as: 40% SiO2, 30% PbO, 10% Bi203, 13%Ga203, 7%CdO, 0,6% Sb2O3 and hexagonal lattice with seven rings of capillaries (holes) The parameters d, d’,  are the diameter of first ring, hole and pitch, respectively The holes are infiltrated by ethanol Next, we investigate the influence of d on the dispersion characteristics, as well as nonlinearity of PCF PBG08-ethanol Let d changes from 0.8 μm to 2.8 μm, and d’ 2 μm,  = 3 μm We simulate to find the optimal configuration for SC generation at wavelength of 1.560 m

Fig 3.2 (a) Cross-section

of proposed PCF

(b) Transverse intensity distribution of fundamental mode at

1.56 m

Using expression describing dispersion, refractive indeces of glass PBG 08 and ethanol, the dispersion characteristics, shift of zero-dispersion wavelength, effective area of fundamental mode, and nonlinear coefficient of PCF PBG 08 - ethanol are simulated and presented in the next sections

3.2 Dispersion and nonlinearity of PCF PBG 08 - ethanol

In Fig 3.3 there are dispersion characteristics of PCF PBG 08 - ethanol with d d’ 2 µm which is infiltrated by ethanol (red curve) and by air (blue)

Fig 3 3

Dispersion characteristics of

ethanol red) and PCF PBG 08 - air (blue) with d =d’=2 µm

We can see the zero-dispersion wavelength of PCF ethanol is shifted ZDW 45 nm from that of PCF PBG 08 - air

PBG08-Fig 3.4 (a) Dispersion characteristics of PCF PBG 08 - ethanol with

different values of d;(b) The ZDW vs d

From Fig.3.4 we can see that if d increasesZDW is red shifted The PCF PBG 08 - ethanol with d changing from 1.7856 µm to 1.4716 µm has ZDW shifting from 1.8413µm to 1.5069 µm With changing of d, ZDW will be 55.7 nm (maximum) for d = 0.8 µm and 35.3 nm ( minimum) for d = 2.8 µm (Fig.3.4b)

To investigate the SC generation of pulse at wavelength 1.560 m,

we have to simulate the effective area of fundamental mode Aeff and nonlinear coefficient of t PCF PBG 08 - ethanol with different d ( Fig 3.5)

Fig 3.5

A eff and  on d at wavelength of 1,560

m

The results form Fig 3.5 show that the effective area of fundamental mode Aeff is investly proportional to d and in opposition, the nonlinear coefficient  is proprtional to d It is clear that if d increases from 0.8 upto 2.8m, Aeff decreases from 16.7933µm2downto 4.90844 µm2, meanwhile  increases from 0.1031W-1m-1 upto 0.3528 W-1m-1

SC spectrum will be appeared more slowly for dispersion of order If nineth- or tenth-order dispersions are concerned, the SC spectrum narrowing is ignorable In Fig 3.7 there are dispersion characteristics obtained by the Taylor fitting method, where the black curve is obtained by the FE mode-solve method If the third- or fourth-order dispersion is concerned only, the curves are splitted one from other but if dispersions are concerned with its order upto tenth the dispersion fitted curve coincides to D() Using the fitted curve to Eq (3.5) we have accurate results

higher-Fig 3.6

SC spectrum at z=10cm concerning dispersion with different order

Fig 3.7

Dispersion curves obtained by

FE method (black) coinsides to that by Taylor fitting upto

β 10

The centrum wavelength of pulse is chosen of 1.56 m, means it lies

on the anomous - dispersion of PCF PBG 08 - ethanol with d = 2.6

μm In this case, the SC generation will be affected by the soliton fission, only This process is illustrated in Fig3.8 The change of the diameter d results the shiftting of zero-dispersion wavelength, at the same time the effective area of fundamental mode and nonlinear coefficient change too As shown in Fig 3.9 the bandwidth of SC spectrums are about of 1150 nm, 1600nm and 2000 nm for PCF PBG08-ethanol with d = 1.2 m, 2.4 m and 2.6 m, respectively The narrowing of SC spectrum is caused by the deviation between the centrum wavelength and zero-dispersion ones This situation is similar to that simulated the SC distribution along distance of PCF PBG 08 - ethanol with different d ( Fig.3.10) However, the nonlinear effects depends not only on nonlinear coefficient inside PCF PBG 08

- ethanol, but also on the power of input pulse This comment will be verified in the next section