本研究旨在探討厚非線性晶體中嚴重的群速色散以及其對二倍頻頻率解析光柵Second-Harmonic-Generation Frequency-resolved Optical Gating (SHG FROG)圖形的扭曲，並提出應用粒子群演算法之最佳化方法，以迭代演算重建基頻脈衝之頻域相位以及時域波形，讓擁有高非線性轉換效率之厚非線性晶體得以被應用在準確的飛秒脈衝量測上。實驗上應用25-fs Ti:S laser、Aperiodically Poled Lithium Niobate (APPLN)厚晶體(15mm)以及穿透式脈衝塑型器干涉儀之架構以取得頻率解析光柵圖形。本研究在電腦模擬以及實驗上均成功重建特殊脈衝相位及波型。

Crystal nonlinearity is a widely employed technique in measurements and analyses of femtosecond pulse lasers. To solve the Group Delay Dispersion (GDD) problem and enable the proper usage of thick crystal, which possess excessively high conversion efficiency, in pulse measurements, we thoroughly examine the Second-Harmonic-Generation Frequency-resolved Optical Gating (SHG FROG) traces strongly distorted by excessive GDD. The SHG FROG traces from fundamental pulse with short pulse duration (25fs) in thick Aperiodically Poled Lithium Niobate (APPLN) crystal (~15mm) are considerably different from the standard SHG FROG traces, indicating that GDD severely influences the FROG traces and the standard retrieving method of phases of fundamental fields in SHG FROG is no longer applicable. Here we introduce a new retrieving method making use of the GDD-distorted FROG traces and applying the iterative optimization algorithm: Particle Swarm Optimization (PSO), which allows us to successfully retrieve the spectral phase of the fundamental pulse. In the experiment, we apply a 15mm APPLN as the nonlinear crystal to demonstrate serious GDD effect and meanwhile obtain a PM spectrum that is sufficient for 25-fs Ti:S laser as fundamental pulse. A shaper-assisted interferometer with collinear output beam duplicates is set to scan the GDD-distorted FROG traces with APPLN. The experimental results prove the strength and usefulness of this retrieving algorithm and unprecedentedly demonstrate pulse retrieval using thick crystal and under severe GDD.

ABSTRACT i
ACKNOWLEDGEMENTS ii
TABLE OF CONTENTS iv
TABLE OF CONTENTS OF FIGURES vi
CHAPTER1 INTRODUCTION 1
CHAPTER2 THEORIES 4
2.1 GDD-distorted FROG traces 4
2.2 Method of retrieval: applying GCPSO 9
2.3 Quasi Phase Matching (QPM) and APPLN 13
2.4 Shaper-assisted interferometer 18
2.5 Collinear FROG traces 25
CHAPTER3 SIMULATIONS 32
3.1 GDD-distorted FROG traces 32
3.2 Results of retrieval applying GCPSO 37
3.3 Influence of noise on the retrieved results 43
3.4 Influence of fabrication error of APPLN on the retrieved results 46
CHAPTER4 EXPERIMENTS 49
4.1 Experimental setup 49
4.2 Field Autocorrelation 52
4.3 Compensation of residual spectral phase 54
4.4 Issues of fabrication error of APPLN 56
4.5 Phase retrieval via GDD-distorted FROG traces 59
CHAPTER5 CONCLUSION AND PERSPECTIVES 66
REFERENCE 69

[1] A. M. Weiner, ULTRAFAST OPTICS: John Wiley & Sons, Inc., 2009.
[2] R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses: Springer, 2002.
[3] C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Optics Letters, vol. 23, no. 10, pp. 792-794, 1998.
[4] C.-S. Hsu, H.-C. Chiang, H.-P. Chuang, C.-B. Huang, and S.-D. Yang, "Forty-photon-per-pulse spectral phase retrieval by shaper-assisted modified interferometric field autocorrelation," Optics Letters, vol. 36, no. 14, pp. 2611-2613, 2011.
[5] A. M. Weiner, "Effect of Group Velocity Mismatch on the Measurement of Ultrashort Optical Pulses via Second Harmonic Generation " IEEE JOURNAL OF QUANTUM ELECTRONICS, vol. QE-19, no. 8, pp. 1276-1283, 1983.
[6] E. G. Sauter, Nonlinear Optics: John Wiley & Sons, Inc., 1996.
[7] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics: John Wiley & Sons, Inc. , 2007.
[8] S.-D. Yang and A. M. Weiner, "Ultrasensitive second-harmonic generation frequency-resolved optical gating by aperiodically poled LiNbO3 waveguides at 1.5 µm," Optics Letters, vol. 30, no. 16, pp. 2164-2166, 2005.
[9] C.-S. Hsu, "Ultrashort Optical Pulses Measurements by Modified Interferometric Field Autocorrelation," Ph.D, IPT NTHU, 2011.
[10] M. Clerc and J. Kennedy, "The Particle Swarm—Explosion, Stability, and Convergence in a Multidimensional Complex Space," IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, vol. 6, no. 1, pp. 58-73, 2002.
[11] M. M. Farsangi, H. Nezamabadi-pour, and K. Y. Lee, "Implementation of GCPSO for Multi-objective VAr Planning with SVC and Its Comparison with GA and PSO," presented at the The 14th International Conference on Intelligent System Applications to Power Systems, 2007.
[12] G. S. L. Gallmann, U. Keller, G. Imeshev, M. M. Fejer, and J.-P. Meyn, "Generation of sub-6-fs blue pulses by frequency doubling with quasi-phase-matching gratings," Optics Letters, vol. 26, pp. 614-616, 2001.
[13] A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum., vol. 71, no. 5, pp. 1929-1960, 2000.
[14] R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum, vol. 68, no. 9, pp. 3277-3295, 1997.
[15] D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses," Journal of the Optical Society of America B - Optical Physics, vol. 12, no. 10, pp. 1955-1967, 1995.
[16] Y.-X. Yuan, "Step-Sizes for the Gradient Method," presented at the AMS IP Studies in Advanced Mathematics, 2008.
[17] D. Teodorovic, P. Lucic, G. Markovic, and M. D. Orco, "Bee Colony Optimization: Principles and Applications," presented at the 8th Seminar on Neural Network Applications in Electrical Engineering 2006
[18] D. Bratton and J. Kennedy, "Defining a Standard for Particle Swarm Optimization," presented at the IEEE Swarm Intelligence Symposium, 2007.
[19] Y. Shi and R. C. Eberhart, "Parameter selection in particle swarm optimization " presented at the EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII, 1998.
[20] M. E. H. Pedersen, "Good Parameters for Particle Swarm Optimization," Hvass Laboratories Technical Report no. HL1001, 2010.
[21] S. Kiranyaz, J. Pulkkinen, and M. Gabbouj, "Multi-dimensional particle swarm optimization in dynamic environments," Expert Systems with Applications 38, pp. 2212-2223, 2011.
[22] D. S. Hum and M. M. Fejer, "Quasi-phasematching," Comptes Rendus Physique 8, vol. 8, pp. 180-198, 2007.
[23] A. Galler and T. Feurer, "Pulse shaper assisted short laser pulse characterization," Applied Physics B - Lasers and Optics, vol. 90, issue 3-4, pp. 427-430, 2008.
[24] I. Amat-Roldán, I. G. Cormack, and P. Loza-Alvarez, "Ultrashort pulse characterisation with SHG collinear-FROG," Optics Express, vol. 12, no.6, pp. 1169-1178, 2004.
[25] M. A. Arbore, O. Marco, and M. M. Fejer, "Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings," Optics Letters, vol. 22, no. 12, pp. 865-867, 1997.
[26] M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances," IEEE JOURNAL OF QUANTUM ELECTRONICS, vol. 28. no. 11, pp. 2631-2654, 1992.
[27] R. Oshige, Y. Osawa, and Y. Fukuchi, "All-Optical Gate Switches Employing the Quasi-Phase Matched Cascaded Second-Order Nonlinear Effect: Effect of Fabrication Errors," presented at the Numerical Simulation of Optoelectronic Devices, 2012.
[28] J. S. Pelc, C. Langrock, Q. Zhang, and M. M. Fejer, "Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters," Optics Letters, vol. 35, no. 16, pp. 2804-2806, 2010.
[29] Z. S. O. Gayer, E. Galun, A. Arie, "Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3," Applied Physics B - Lasers and Optics, vol. 91 pp. 343-348, 2008.
[30] P. Brand, B. Boulanger, P. Segonds, Y. Petit, C. Félix, B. Ménaert, et al., "Angular quasi-phase-matching experiments and determination of accurate Sellmeier equations for 5%MgO:PPLN," Optics Letters, vol. 34, no. 17, pp. 2578-2580, 2009.
[31] A. Galler and T. Feurer, "Vector Pulse Shaper Assisted Short Pulse Characterization," Springer Series in Chemical Physics, vol. 92, pp. 902-904, 2009.