Nghiên cứu tương tác tán xạ raman cưỡng bức trong môi trường phi tuyến chứa trong sợi tinh thể quang tử lõi rỗng TT TIENG ANH

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENCE ACADEMY 0F MILITARY SCIENCE AND TECHNOLOGY THAI DOAN THANH INVESTIGATION OF RAMAN STIMULATED RAMAN SCATTERING IN NONLINEAR MEDIUM CONTAINED BY HOLLOW-CORE PHOTONIC CRYSTAL FIBRES Specialization: Optics Code: 9.44.01.10 A SUMMARY OF PHYSICAL DOCTORAL THESIS HA NOI - 2021 This thesis has been completed at: ACADEMY 0F MILITARY SCIENCE AND TECHNOLOGY Scientific supervisors: Dr Nguyen Manh Thang Assoc Prof Dr Ho Quang Quy Reviewer 1: Prof Dr Tran Cong Phong Reviewer 2: Assoc Prof Dr Trinh Dinh Chien Reviewer 3: Dr Nguyen Minh Hue This thesis is defended at Doctoral Thesis Evaluating Committee held at Academy of Military Science and Technology at…… ….h…………, date…………month………….year 2021 The thesis may be found at: - Library of Academy of Military Science and Technology - Vietnam Nationnal Library INTRODUCTION Fiber lasers are studied via Stimulated Raman scattering in fiber optic media With the property of tunable wavelength and allconducted in optical fiber, fiber Raman laser is used in optical communication for the amplification of transmission signal and expanding transmission spectrum Traditional fiber doped –Raman active centers has been investigated and used in areas, However, there are still existences such as low Raman efficiency, low power, so it is necessary to have large length fibers, and the flexiblit ability to expand differently spectral regions Currently, the researches of solid-core crystal fiber, as well as hollow-core (HC-PCF) crystal optical fiber has been extensively studied for supercontinuous generation with the ultrawide spectrum evenly from a monochrome light pulse Supercontinuous generation phenomena is a combination of nonlinear effects such as high-order group velocity dispersion, phase modulation, four-wave interaction, and stimulated Raman scattering These effects are highly efficient due to the band gap properties, the small cross-section of fundamental mode and the high nonlinear coefficients of optical fibers For HC-PCF, the core can be filled with high nonlinear gases with high concentration, so the nonlinear effect will increase significantly Therefore, Raman lasers using hollow-core optical fibers have been studied extensively in recent years Using a Raman laser configuration with hollow-core optical fibers, the backward and forward-pump methods are used, and for a variety of interesting and varied pulsed properties However, up to now, the results obtained in the experiment of Raman laser generation in hollow-core fiber have not been explained some specific properties of the emitted laser pulse such as the formation of multi-peak generation, the phenomenon of self-similar pulse series, the effect of coherent interaction, and the effects of structural parameters such as length, pressure has not been examined in detail, maximum transmission efficiency… To further clarify the nature of Raman scattering in HC-PCF, The coherent SRS regimes in both the backward and forward stimulated Raman scattering in the nonlinear Raman active gas medium H2 The effects of hollow-core size, Doppler broadening, a collision between H2 gas molecules and between them, and the inner wall of the hollowcore optical fiber HC-PCF on the broadening of the Raman spectral line were also initially studied The results are presented in the thesis: “Investigation of Raman stimulated Raman scattering in nonlinear medium contained by hollow-core Photonic Crystal Fibres” CHAPTER RAMAN SCATTERING AND RAMAN INTERACTION IN HOLLOW-CORE PHOTONIC CRYSTAL FIBERS 1.1 Spontaneous Raman scattering and Stimulated Raman scattering 1.2 Generation, amplification, and Raman laser in fiber optics 1.3 Hollow-core photonic crystal fiber (PCF) 1.4 The coherent SRS in the HC-PCF 1.5 Conclusion of chapter This chapter presents an overview of some physical basics related to Raman lasers, especially Raman lasers in optical fibers in general and photonics optical fibers in particular From the interpretation and analysis, I proposed the problems need to be studied in order to understand the nature of stimulated Raman scattering in gas-filled hollow-core photonics optical fibers that have special nonlinear properties In the next chapters I will present theoretical basics and simulate the processes of Raman laser generation and analyze the physical process mainly affecting the Raman signal generation and its spectrum CHAPTER COHERENT BACKWARD RAMAN SCATTERING INTERACTION IN NONLINEAR MEDIUM FILLED HC-PCF 2.1 Some effects in Raman interactions Presenting some principle effects and their applications in pulse compression, Raman amplification 2.2 The equations for stimalated Raman scattering 2.2.1 The oscillation of synchronous material exitation like as optical phonon While spontaneous Raman scattering only scatters a small amount of incident photon to transform into a Stokes photon and the component phases  of the molecular oscillation are synchronized, in the stimulated Raman scattering, there is a large number of Stokes photon scattered in the scattering fields and the component phases  of the molecular excitation are synchronized This synchronous stimulation in the active medium is considered as the coherent material excitation wave and is called the optical phonon Optical phonons are similar to the show and describe a particular type of motion at the same frequency Each optic photon has energy Ω like the excitation quantum of the oscillator mode A coherent wave of excitation materials has no dispersion and behaves similarly to classical waves with defined wave vectors k and   kz Therefore, the optic phonon field q in (1.4) can be rewritten as follows: q( z, t )   Q  t  exp i  kz - t    c.c  (2.1) where Q  t  is the time-dependent complex envelope of the phonon amplitude The optic phonon can be destroyed during the collision process 2.2.2 Phase-matching diagram for SRS Suppose an optical mode with frequency p passing through the optical medium contained inside the hollow core of HC-PCF is affected by dispersion characterized by a transmission constant    [m-1] We consider the action fields consisting of the pump pulse and the Stokes seed pulse, passing through the active medium contained in the HC-PCF and assuming the dispersion relationship      is represented by the curves in Fig 2.3 Figure 2.3 Optical phase-matching diagram for SRS Phonon generated by the FSRS process (vector 1); Phonon generated for anti-Stokes (Vector 2); Phonon generated during BSRS (vector 3) 2.2.3 Wave propagation equations The system of wave propagation equations for both forward and backward directions are as follows:  E j  z, t  z  n j E j  z, t  t c  i 0 2j 2k j PjN  z, t  exp  ik j z   j E j  z, t  (2.13) 2.2.4 Hamiltonian density formalism Based on the basis of the Hamiltonian density matrix formalism, The equation system of amplitude equations describing the SRS interaction are drived: E p z   n p E p c t  iN  p    p Ep   QEs  4n p c  q 0 Es ns Es iN s    * s     Q E p  Es z c t 4ns c  q 0 Rewrite the equation for the coherent oscillator (2.23) i    Q *   2Q    E p Es t 2m0   q 0 (2.33) (2.34) (2.35) in which the index j  p, s notation for pump  p and Stokes s frequency 2.2.5 The formalism of the density matrix operator Stimulated Raman scattering is described according to the energy level diagram as shown in Figure 2.4, we derive the interactive propagation equations for pump waves and Stokes as follows: E p E p p   pvp  (2.76)   i   QEs  E p z v p t  s vs  E  Es (2.77)  s  i 2Q* E p  s Es z vs t * where,   cN 0s1 , v p , s  c is group velocity n p,s 4n s Figure 2.4 Diagram of energy levels for SRS The system of four equations (2.35), (2.76), and (2.77) describe in detail the progression in space-time, the interaction between the applied fields, and the coherent material oscillation from the point of view of quantum mechanics Next, I will analyze the relationship between the model of quantum mechanics and the classical model by the relationship between oscillate amplitude q and coherent 22  t  2.3 Coherent theoretical model of BSRS and asymptotic solution The backward amplification process can be divided into two modes, linear and nonlinear ones (Figure 2.5) Figure 2.5 Amplification mode of reverse Raman scattering: a) Linear; b) Nonlinearity Using slowly-varying envelope approximation, rapid decay, and the Sine-Gordon approximation method we obtain the differential equation: d 2 d    sin  dZ Z dZ (2.97) where  Z     x, T  , with Z  xT is the self-similar variable The solution of the equation depends on boundary conditions In the context of my research  (0)  , which means that before the interaction between the pump field and the Stokes field (seed) there was no coherence,  '(0)   (very small) suggests that the initial Stokes amplitude is very small Figure 2.6 Normalization spectral density IN changes according to the same variable Z The dynamics of the pump, Stokes, and the coherent field strength under the self-similar variable are described by the normalized energy density as shown in Figure 2.5 Figure 2.6 shows the evolution of the pump, anti-Stokes signal, and coherent field dynamics correspond to the self-similar variable Z It may appear a series of Stokes oscillations caused by a phase shift from a self-similar function   Z  The physical origin of this activity can be understood as the ability to remember ‘coherence’ after the applied field passes in the coherent inverse Raman scattering regime 2.4 Coherent model of BSRS for simulation The principle model of (highly coherent) transient BSRS with a design diagram is shown in Figure 2.7 With this design scheme, the seed Stokes pulse and the pump pulse propagate in opposite directions through the nonlinear medium contained in the HC-PCF Figure 2.7 Basic diagram of BSRS Based on the experimental ability at the Raman Laboratory, Mark Plank Institute for Light Science (Germany), the parameters used for the simulation are selected as follows: - The nonlinear medium H2 is compressed at a pressure of 5bar; the orthogonal-H2 density is 62% and the paragonal-H2 is 38% at room temperature In this condition of the nonlinear medium, the transmission constants of the Stokes and the pump waves are respectively  s  5,5 106 m 1  p  5,9 106 m1 The normalized 11 Figure 2.9 Variation of pulse train as pump energy increases In the limit of pump energy or large interaction lengths (as in HCPCF), Equation (2.97) gives a 2-form pulse solution   arctan(exp( Z )) Substitute for (2.96) and (2.92) we have the solution: Ap  a0 tanh( Z )   P As  2 a0 sec h( Z ) P  sec h( Z ) (2.98) (2.99) (2.100) Equation (2.98) - (2.100) shows the asymptotic state from the evolution of the coherent field and the Stokes field Solution (2.100) shows the asymptotic state of the Stokes envelopes In this state, the speeds of the Stokes and the coherent waves are equal and are shaped asymptotically to the pulse train with a special form, the hyperbolicsecant, or the soliton pulse 12 Figure 2.10 Shifting of a pulse train with increasing pump energy experimentally Soliton train in figure 2.10 is consistent with the results obtained by experiment in the work of N M Thang [92] presented in Figure 1.13 With the support of colleagues at the Gas Raman Laboratory, the Mark-Plank Institute for Light Science performed experiments and obtained a soliton train moved at the superluminous velocity (Figure 2.10) At this point, we can confirm that the theoretical model and the implemented simulation method can be used to explain the process of soliton train appearance in the highly coherent reverse Raman interaction in the backward pump configuration 2.5.3 The self-similar effect in linear and nonlinear regimes The soliton’s movement shown in Figure 2.11 are said to be selfsimilar in nonlinear regime when the pump power is larger than that of threshold In this case, when the pump pulse energy is greater than 14J, a three-soliton trsain appears 13 Figure 2.11 Stokes pulses develop not following the same rule in linear mode BSRS (below pump energy threshold) with different pump energies In contrast, when the pump pulse energy is less than 14µJ, the seed pulse is almost exclusively amplified and the peak is slightly amplified and no successive peaks appear In the low energy range (below the threshold) for the linear interaction regime (0-9µJ), the normalized Stokes intensity shown in Fig 2.11 does not follow the self-similar law at different pumping energies of pulses This can be analyzed as follows, for a defined fiber length and coherent destruction rate, its operating regimes depend on pump power, therefore at such low pump energy values the time range required for trasient BSRS regime is very short and thus the pump pulse width is outside the given range  and  This is also true for FSRS when the pumped energy is below the threshold As the pump energy increases, the pump pulse range required for highly coherent regime expands, so the experimental pump pulse range 14 is within the required range and leads to the interaction system operating in trasient BSRS regime and obeying the self-similar operation Figure 2.12 shows the operating range of the Stokes signal in the energy range 13µJ -18µJ Figure 2.12 Coherent BSRS regime performs the self-similar behavior of Stokes pulse trains, Stokes intensity is normalized according to the 2nd pulse at different pump energies The results in gigure 2.12 show that when the pumped energy (exceeds the threshold) and changes, the 2nd and 3rd pulses are invariant by the self-similar variable Z However, the first peak is changed, it can be explained by the competition effect of the forward Stokes pulse from the pump pulse at the first pulse position over time, the interaction of three wave is violated The second and third pulses are less affected, so it follows the self-similar behavior The appearance of a series of soliton pulses in igure 2.9 and 2.10, and the self-similarity is shown in figure 2.12 15 2.6 Conclusion of chapter This chapter has developed an approximately asymptotic solution in the high pump energy limit for the coupling Raman interaction equation system, describing the highly coherent inverse Raman interaction to explain the observed presence of synchronous soliton train has been observed experimentally in a nonlinear gas medium contained in HC-PCF fibers previously The calculated results are relatively consistent with the experiment, explaining the process of forming a pulse train from a "single" initial signal pulse In the limit of high pump energy, the pulse train can become a soliton train moving at superluminous velocity The results of this study can be considered as the further development of the "single" pulse soliton formalism in time in BSRS which has been previously studied Interestingly, the model also demonstrates and explains how this pulse train action obey the self-similar behavior like as in the transient FSRS This study also demonstrates the Raman amplification in different regimes, is able to descibe the complexity of nonlinear optical interactions based on the HC-PCF potential fiber configuration CHAPTER INTERACTION DYNAMICS IN THE HIGHLY COHERENT FORWARD RAMAN SCATTERING REGIME 3.1 Coherent FSRS in a H2 gas filled HC-PCF 3.1.1 The FSRS equations The set of envelope equations describing the coherent interaction in the coherent Raman scattering has been derived as follows: 16 E p z  p   pvp  E p  i   12 Es  E p v p t  s vs  Es Es    i 12* E p  s  s z vs t  n - n0  n 1  i1E *p Es 12  i1* E p Es* 12*  t 2 T1 12 *   i1 nE p Es*  12 t T2 (3.1) (3.2) (3.3) (3.4) The equations are presented in chapters and 3.1.2 The FSRS model for simulation The calculated model of (highly coherent) transient FSRS with a minimum design diagram is shown in Figure 3.1 Unlike the model for BSRS, Stokes and pump waves propagate in the same direction through a nonlinear medium Figure 3.1 The basic principle diagram of FSRS - Common laser pump source (assuming Nd: YAG 1064 nm) or laser source whose frequency is in the infrared or visible region Pump source laser of 1064nm, HC-PCF has a length of 4m The two Stokes and pump pulses are shown in Figures 3.2a and 3.2b 17 b) a) Figure 3.2 a) Stokes pulse and b) initial pump pulse - Using HC-PCF with tranmission window supporting for frequency (  s ) and pump frequency (  p ), the loss for two waves is  s   p  0.01 dB/m - Gas pressure H2 is bar The relaxation time of the population inversion of molecules H2 is 1000ns; relaxation time of molecular coherence of 5ns; normalized number of molecules N = n0   at gas pressure of bar; The propagation constants of the Stokes and pump waves are respectively  s  5.5 106 m 1 ;  p  5.9 106 m1 ,  Raman coupling strength of 1*  7.4 108 m V2  - The hollow core radius of HC-PCF is r =5µm - Initiall y Stokes pulse amplitude is very small Es  0, 01.E p 3.2 Results and discussion 3.2.1 Evolution of the fields Figure 3.3 shows evolution the time structure and amplitude of three pump - Stokes - coherent pulse fields versus time at different positions along the HC-PCF fiber: z = 0.5 m (figure 3.3a), z = m (figure 3.3b), z = m (figure 3.3c), z = 2.5 m (figure 3.3d), z = 3m (figure 3.3e) and z = m ( figure 3.3f) The evolution and increase in 18 the intensity of the Stokes field coupled with the decrease of the pump field intensity along the fiber are caused by the energy exchange of the pump and Stokes fields a) z = 0,5 m b) z = m c) z = m d) z = 2,5 m e) z = m f) z = 4m Figure 3.3 Evolution and interaction of three the pump (Ip) Stokes (Is) - coherent (Ic) fields versus time in gas H2 at different positions along the HC-PCF optical fiber 3.2.2 Evolution of coherence and population inversion The change of the magnitude of the coherence field |𝜌12 | and the population inversion |𝑛| by space-time (phase time (z, t)) is simulated in Figure 3.4 Figure 3.5 simulates the normalized intensity of the pump pulse and the Stokes signal pulse along the fiber length This process obeys to the conservation law of energy in Raman interactions 19 Figure 3.4 Evolution of the magnitude of the coherent field (upper figure) and population inversion (lower figure) Figure 3.5 Change of pump beam intensity and Stokes versus spacetime 20 3.2.3 The process of exchanging energy between fields In Figure 3.5, the process of exchanging energy between fields obeys the law of energy conservation The evolution of the pump field energy and the Stokes field along the HC-PCF length is calculated and presented in figure 3.6 Figure 3.6 Exchanging of the pump and Stokes signal energy Effect of pulse width: Assume the pump pulse amplitude is constant and the pump pulse width decreases from 22ns to 8ns Other parameters remain as above The energy exchange of the pump fields and the Stokes signal field is simulated as shown in Figure 3.7 Effect of pump pulse width on energy exchange (figure 3.7) and generated efficiency at output 4m (figure 3.8) Effect of gas pressure: Effect of active gas pressure H2 on generation efficiency of Stokes frequency with the pump pulse width parameters 15ns and fixed fiber length z = 4m calculated and presented in Figure 3.9 We see that when reducing the pressure from bar (T 2= 2.5ns) to 0.5 bar (T2= 5.2ns), the Stokes generation efficiency also increases and is asymptotic to the total energy curve En0 The 21 efficiency is calculated at the fibre’s output 4m (3.10) Therefore, the input pulse energy, the pump pulse width, the gas pressure affects the pump energy exchange to Stokes and vice versa, the maximum efficiency, as well as the output efficiency, depends on structural (design) parameters Figure 3.7 Influence of pump pulse width on energy Figure 3.8 Stokes generation efficiency at output 4m exchange Figure 3.9 Effect of gas Figure 3.10 Stokes generation pressure H2 on energy efficiency at output 4m exchange 3.3 Conclusion of chapter In this chapter, the transient FSRS dynamic in the H2 nonlinear gas contained in HC-PCF has been studied and discussed The results 22 clearly show the nature of the interaction process, the energy exchange process among pump - Stokes waves with the presence of coherence one The evolution of fields in the interaction process is shown along with the optical fiber in detail, analyzing coherent field behavior and population inversions to show clearly the picture of nonlinear interactions highly coherent in stimulated Raman scattering Investigate the process of energy exchange between the pump field and the Stokes field, the effect of the pump pulse width, the fiber length, the pressure on the energy conversion efficiency between the pump field and the Stokes field In the case of choosing a fiber length of 4m will give optimum performance and that optimum value depends on pulse width and gas pressure REMARKABLE CONCLUSION The thesis studied the coherent Raman scattering process in the H2 nonlinear medium filled HC-PCF: A The results of the thesis The thesis presents an overview of the Raman scattering in the active nonlinear medium; the relationship between spontaneous scattering and stimulated scattering shows that the forcing process is nonlinear and strongly depends on the length of the interaction; This leads to some applications of stimulated Raman scattering, especially in fiber communication The structure and some special properties of HC-PCF have also been presented for the purpose of showing their role when used to contain nonlinear media in optical research in general and Raman interactions in particular, especially the transient SRS regime Finally, an overview of soliton generation, self-similar effects, the effects of parameters such as fiber length, pressure, 23 during the coherent Raman interaction occuring in a nonlinear medium contained in HC- PCF, from there, draws some problems that need further clarification by theory The set of coupling SRS equations describing from the visual to the quantum The process of stimulated Raman scattering is derived to analyze, explain and support experimental Raman scattering studies Based on this system of coupling SRS equations, we propose an approximate asymptotic solution model for the highly coherent BSRS in the nonlinear medium H2 to account for the soliton train appearance from a single "pulse" initial signal The self-similar effects have been observed experimentally at the first time Research on coherent stimulated Raman scattering (FSRS) in gas H2 contained in HC-PCF The complex dynamic interaction process between pump, Stokes signal, coherence laser fields, and the nonlinear medium molecular inversion density of the highly coherent FSRS regime is numerically described and analyzed in detail The effects of pump pulse width, fiber length, and gas pressure contained in the HCPCF have been investigated to give optimal parameters for Stokes generation efficiency B The main contribution of the thesis From the results obtained in the thesis, the following new contributions are: Successfully proposed an approximatly asymptotic solution for highly coherent BSRS in the H2nonlinear medium filled HC-PCF The simulated results show the soliton train of Stokes wave, which has fluorescent shift into short time region It confirmed the presence of pulse series in transient BSRS regime in nonlinear gas H2 contained in 24 HC-PCF obeystheself-similarity The obtained results explains more clearly the appearance of the soliton train have been experimentally observed Detailed description and analysis of the complex dynamic interactions between pump - Stokes - coherence fields, and the population inversion of nonlinear medium in highly coherent FSRS The results show clearly the role of coherent field in the transient SRS regime Investigating the effects of pump pulse width, fiber length, and gas pressure contained in the HC-PCF to give optimal parameters for Stokes generation efficiency The results give a choice response to the suitble optimation of experimental design C Further directions In the limits of the thesis, the Ph.D student focuses on examining dynamic processes with the main purpose of detecting interesting complex effects that occur during highly coherent Raman interactions without the attention of statistical surveys In the future, the effects of pulse width, pulse energy, gas pressure, fiber length on the propagation threshold, propation efficiency and formation of the soliton train, or broadband frequency (comb) Raman generation in the nonlinear gas mixture, optimal frequency transmission for Stokes in the highly coherent SRS regime will be specifically explored for the purpose of the selection of the optimal parameter set for the experimental design LIST OF PUBLICATIONS Thang Nguyen Manh, Thanh Thai Doan (2016), “A train of backward Raman soliton pulses in hollow-core photon crystal fibres filled with hydrogen gas”, Optik, vol.127, no.21, pp 10259–10265 Thai Doan Thanh and Nguyen Manh Thang (2017), “Selfsimilarity in transient backward stimulated raman scattering by gas filled photon crystal fibres”, Advances in optics photons spectroscopy and applications IX, Publish House for Science and Technology, ISBN: 978 -604-913-578-1, pp.199206 Thai Doan Thanh, Ho Quang Quy, Nguyen Manh Thang (2018), “Coherent Raman scattering interaction in hydrogen gas-filled hollow core photon crystal fibres”, Optik, vol.161, pp 156-160 Thai Doan Thanh, Ho Quang Quy, Nguyen Manh Thang (2020), “Efficiently Coherent Stokes Generation in Hydrogen Gas-Filled Hollow Core Photon Crystal Fibres”, Communications in Physics, vol.30, no.2, pp.143-150 ... CHAPTER RAMAN SCATTERING AND RAMAN INTERACTION IN HOLLOW-CORE PHOTONIC CRYSTAL FIBERS 1.1 Spontaneous Raman scattering and Stimulated Raman scattering 1.2 Generation, amplification, and Raman laser... Thanh, Ho Quang Quy, Nguyen Manh Thang (2018), “Coherent Raman scattering interaction in hydrogen gas-filled hollow core photon crystal fibres”, Optik, vol.161, pp 156-160 Thai Doan Thanh, Ho Quang. .. scattering and stimulated scattering shows that the forcing process is nonlinear and strongly depends on the length of the interaction; This leads to some applications of stimulated Raman scattering,