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MINISTRY OF EDUCATION & TRAINING VINH UNIVERSITY _ Do Thanh Thuy INVESTIGATION OF ULTRASHORT PULSE PROPAGATION IN PHOTONIC CRYSTAL FIBERS Specialization: Optics Code: 44 01 10 ABSTRACT OF DOCTORAL THESIS IN PHYSICS Vinh - 2020 The work is achieved in VINH UNIVERSITY Adviser: Prof Dr Dinh Xuan Khoa 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 available PCF Chapter OPTICAL AND PHOTONIC CRYSTAL FIBERS In this chapter, the development, configuration, classification, main optical properties of photonic crystal fibers used for ultrashort pulse transmission and SC generation are summaried Chapter PROPAGATION OF LASER PULSE IN NONLINEAR FIBER 2.1 Progagation equation in optical fiber 2.1.1 Maxwell equations The propagation of electromagnetic field in optical medium is described by Maxwell equations From which, the wave equation and nonlinear Schrodinger equation are derived to describe the propagation of short and ultrashort pulse in nonlinear medium, generally, and fiber, especially 2.1.2 Propagation of short pulse Using slow-variable envelope approximation, the Schrodinger nonlinear equation decribing the propagation of short pulse is derived as following:  3 (3)  2   i A  z, t   i 1 A  z, t   2 A  z, t   A  z, t  A  z, t   (2.14) z t t 2c where   3 (3) 0 / 8n 0  c  n20 / c is nonlinear coefficient (3) corresponding to third-order nonlinearty, n2  3 n 0  is the 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 following: i A  z, t  z  i 1 A  z, t    A  z, t  i  A  z , t   02  (3)   3  t t t c2  t    n '      1  i     1  f R  A  z, t  A  z, t   f R A  z, t  hR t  t1  A  z , t1  dt1      n   t     (2.20)  Using normalized arguments and function as following: U   ,    t  1 z 0 P0 A  z , t  , LD  ,  02 L , LN  , N2  D , 2  P0 LN 3 z  , 3  , LD 2  (2.27)  T S  s , R  R 0 0 We have:  U U i 2U  3U   sign       i N  U 2U  i S U 2U   R U 3              (2.28) 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:  , ,N = and given as following:  U  3   sign( 3 )  iN | U |2  U     (2.49) Considering β3 = 0.1 ps3/km, the propagation of pulse is simulated and illustrated in Fig.2.1 Fig 2.1 Propagation of hyperbolic secant with β3=0.1 ps3/km through normalized distance of  = 12 From Fig.2.1 we can see the input intensity will be separated to some small pulses in certain delay time It results the begin spectrum will separated to two parts which is blue and red shifted Next, we consider the second-order dispersion plays the main role and the third-oder one is seem as disturbance It means = 0.02, S = and = 0, and substituting into Eq (2.28) we have: U i 2U  3U  sign       i N U 2U    (2.50) The propagation of soliton of N = is presented in Fig 2.2 From this figure we can see a fundamental soliton will be separated at normalized distane of  = 0.38 That means the dispersion wave is blue shifted Fig 2.2 (a) Pulse shaping; (b) Spectral changing Simulated for N = 3, z = 1.2LD , = 0.02, S = 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