高能雷射脈寬受增益介質的增益帶寬限制所限制，因此直接從放大器產生高能短脈衝具有一定的挑戰性。近來，頻譜展寬被利用來進行脈衝壓縮，從而產生高能超短脈衝。有許多方法可以實現展頻，其中，近期有兩種頻譜展寬的方式在微焦耳到毫焦耳的脈衝能量區間越來越受到關注，分別是氣態多通腔體和多重固態薄片。這兩種方法具有一些相似的概念，也就是將非線性過程分為多個步驟進行。然後就我們所知，這兩種方法之間尚缺乏光束品質的比較。
本論文將討論頻譜展寬的物理機制以及氣態多通腔體的設計規則，並根據討論的規則搭建一套氣態多通腔體。此氣態多通腔體將用來對一台固態摻鐿鎢酸釓鉀脈衝放大器進行頻譜展寬，使轉換極限脈衝從170飛秒壓縮到39 飛秒，並與
多重固態薄片在同樣的實驗條件下進行比較光束品質。光束品質量測是利用自製的雷射射束品質(M2)以及空間頻譜均勻性測量系統進行。氣態多通腔體的雷射射束品質分別為1.15和1.09；而多重固態薄片則是1.12和1.05。充態多通腔體的強度加權空間頻譜均勻性的水平軸和垂直軸分別為98.4％ 和96.9％ ;多重固態薄片則分別為97.2％和96.1％。

Spectral broadening is often used these days to generate intense few-cycle pulses by shortening the pulse duration which is limited by the gain bandwidth of the gain medium. Many approaches could realize the spectral broadening. Among them, two methods, multi-pass cell (MPCell) spectrum broadening and Multiple-plate Continuum (MPC), receive increasing attention recently in pulse energy of μJ to mJ level. These two approaches share some similar ideas that split the nonlinear processes into steps. However, currently, there is a lack of a comparison of beam quality between the two approaches to the best of our knowledge.
This thesis will disuse the mechanism of spectral broadening and the design rules of a gas-filled multi-pass cell. Then, the gas-filled multi-pass cell, built according to the discussion, is used to compare the beam quality with a multiple-plate continuum, which compresses pulse width from transform-limited 170 fs to 39 fs with an identical solid-state Yb:KGW amplifier. The beam quality measurements are carried out by home-built M2 and homogeneity measurement systems. The M2 values of the gas-filled multi-pass cell are 1.15 and 1.09; MPC are 1.12 and 1.05. The intensity-weighted spatial-spectral homogeneities of the gas-filled multi-pass are 98.4% and 96.9% for horizontal and vertical axes respectively; MPC are 97.2% and 96.1%.

摘要 i
Abstract ii
致謝 iii
Table of Contents v
List of Figures vii
List of Tables x
Chapter 1 Introduction 1
1.1 Motivation of pulse temporal compression 1
1.2 Self-phase modulation and self-focusing 2
1.3 Spectral broadening methods 7
Chapter 2 Multiple-plate Continuum 9
2.1 Multiple-plate Continuum at 1030 nm pumped by Yb:YAG thin-disk laser 9
2.2 Multiple-plate Continuum pumped by Yb:KGW laser 11
Chapter 3 Multi-pass Cell Spectral Broadening (MPCell) 13
3.1 Design rules of a gas-filled multi-pass cell spectrum broadening 13
3.1.1 Geometry and design rules of Herriot cells 13
3.1.2 Nonlinear phase-shift and design issue 17
3.1.3 Other design rules 19
3.2 Spectral broadening by multi-pass cell 20
3.2.1 Design of the cell pumped by 170 fs, 1.5 mJ, pulses at 1030 nm 20
3.2.2 Experiment Setup and Spectral Broadening Results 23
Chapter 4 Beam Quality Measurements 26
4.1 M2 and spatial-spectral homogeneity 26
4.2 Beam quality measurements 28
4.2.1 Experiment setup for beam quality measurements 28
4.2.2 M2 Measurement Results 30
4.2.3 Homogeneity Measurement Results 31
Chapter 5 Conclusion and Future Works 35
Reference 37
Appendix A. Characterization of Cavity Mirrors 41
Appendix B. M2 Measurement and Control Program 43
Appendix C. Homogeneity Measurement and Control Program 46
Appendix D. Chamber Design 48
Appendix E. Multiple-plate Continuum at 1550 nm 50

1. F. Shimizu, "Frequency Broadening in Liquids by a Short Light Pulse," Physical Review Letters 19, 1097-1100 (1967).
2. R. R. Alfano and S. L. Shapiro, "Observation of Self-Phase Modulation and Small-Scale Filaments in Crystals and Glasses," Physical Review Letters 24, 592-594 (1970).
3. Q. Luo, S. Hosseini, B. Ferland, and S. Chin, "Backward time-resolved spectroscopy from filament induced by ultrafast intense laser pulses," Optics Communications 233, 411-416 (2004).
4. T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
5. T. R. Schibli, O. Kuzucu, K. Jung-Won, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, "Toward single-cycle laser systems," IEEE Journal of Selected Topics in Quantum Electronics 9, 990-1001 (2003).
6. H. Takara, "Multiple Optical Carrier Generation from a Supercontinuum Source," Optics and Photonics News 13, 48-51 (2002).
7. R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, "Compression of optical pulses to six femtoseconds by using cubic phase compensation," Optics Letters 12, 483-485 (1987).
8. M. Ferray, A. L'Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, "Multiple-harmonic conversion of 1064 nm radiation in rare gases," Journal of Physics B: Atomic, Molecular and Optical Physics 21, L31-L35 (1988).
9. F. Meyer, N. Hekmat, T. Vogel, A. Omar, S. Mansourzadeh, F. Fobbe, M. Hoffmann, Y. Wang, and C. J. Saraceno, "Milliwatt-class broadband THz source driven by a 112 W, sub-100 fs thin-disk laser," Optics Express 27, 30340-30349 (2019).
10. V. Malka, S. Fritzler, E. Lefebvre, M. M. Aleonard, F. Burgy, J. P. Chambaret, J. F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J. P. Rousseau, J. N. Scheurer, B. Walton, and A. E. Dangor, "Electron Acceleration by a Wake Field Forced by an Intense Ultrashort Laser Pulse," Science 298, 1596 (2002).
11. K. W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
12. M. Müller, C. Aleshire, A. Klenke, E. Haddad, F. Légaré, A. Tünnermann, and J. Limpert, "10.4  kW coherently combined ultrafast fiber laser," Optics Letters 45, 3083-3086 (2020).
13. G. Jargot, N. Daher, L. Lavenu, X. Delen, N. Forget, M. Hanna, and P. Georges, "Self-compression in a multipass cell," Optics Letters 43, 5643-5646 (2018).
14. S. Gröbmeyer, K. Fritsch, B. Schneider, M. Poetzlberger, V. Pervak, J. Brons, and O. Pronin, "Self-compression at 1 µm wavelength in all-bulk multi-pass geometry," Applied Physics B 126, 159 (2020).
15. J. C. Travers, T. F. Grigorova, C. Brahms, and F. Belli, "High-energy pulse self-compression and ultraviolet generation through soliton dynamics in hollow capillary fibres," Nature Photonics 13, 547-554 (2019).
16. G. Askaryan, "Effect of the gradient of a strong electromagnetic ray on electrons and atoms," Journal of Experimental and Theoretical Physics 15, 1088–1090 (1962).
17. P. L. Kelley, "Self-Focusing of Optical Beams," Physical Review Letters 15, 1005-1008 (1965).
18. N. Pilipetskii and A. Rustamov, "Observation of self-focusing of light in liquids," Journal of Experimental and Theoretical Physics Letters 2, 55-56 (1965).
19. R. W. Boyd, "Chapter 7 - Processes Resulting from the Intensity-Dependent Refractive Index," in Nonlinear Optics (Third Edition), R. W. Boyd, ed. (Academic Press, Burlington, 2008), pp. 329-390.
20. V. Magni, G. Cerullo, and S. De Silvestri, "ABCD matrix analysis of propagation of gaussian beams through Kerr media," Optics Communications 96, 348-355 (1993).
21. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Applied Physics B 79, 673-677 (2004).
22. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Physics Reports 441, 47-189 (2007).
23. T. Nagy, P. Simon, and L. Veisz, "High-energy few-cycle pulses: post-compression techniques," Advances in Physics: X 6, 1845795 (2021).
24. C. Rolland and P. B. Corkum, "Compression of high-power optical pulses," Journal of the Optical Society of America B 5, 641-647 (1988).
25. N. Milosevic, G. Tempea, and T. Brabec, "Optical pulse compression: bulk media versus hollow waveguides," Optics Letters 25, 672-674 (2000).
26. G. P. Agrawal, "Chapter 5 - Optical Solitons," in Nonlinear Fiber Optics (Fifth Edition), G. Agrawal, ed. (Academic Press, Boston, 2013), pp. 129-191.
27. C.-H. Lu, Y.-J. Tsou, H.-Y. Chen, B.-H. Chen, Y.-C. Cheng, S.-D. Yang, M.-C. Chen, C.-C. Hsu, and A. H. Kung, "Generation of intense supercontinuum in condensed media," Optica 1, 400-406 (2014).
28. C.-L. Tsai, F. Meyer, A. Omar, Y. Wang, A.-Y. Liang, C.-H. Lu, M. Hoffmann, S.-D. Yang, and C. J. Saraceno, "Efficient nonlinear compression of a mode-locked thin-disk oscillator to 27 fs at 98 W average power," Optics Letters 44, 4115-4118 (2019).
29. S. Zhang, Z. Fu, B. Zhu, G. Fan, S. Wang, Y. Chen, Y. Liu, A. Baltuska, C. Tian, and Z. Tao, "Solitary beam propagation in a nonlinear optical resonator enables high-efficiency pulse compression and mode self-cleaning," (2020), p. arXiv:2006.15810.
30. C. Robert, "Simple, stable, and compact multiple-reflection optical cell for very long optical paths," Applied Optics 46, 5408-5418 (2007).
31. D. R. Herriott and H. J. Schulte, "Folded Optical Delay Lines," Applied Optics 4, 883-889 (1965).
32. M. Hanna, X. Délen, L. Lavenu, F. Guichard, Y. Zaouter, F. Druon, and P. Georges, "Nonlinear temporal compression in multipass cells: theory," Journal of the Optical Society of America B 34, 1340-1347 (2017).
33. Á. Börzsönyi, Z. Heiner, A. P. Kovács, M. P. Kalashnikov, and K. Osvay, "Measurement of pressure dependent nonlinear refractive index of inert gases," Optics Express 18, 25847-25854 (2010).
34. E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, "Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses," Journal of the Optical Society of America B 14, 650-660 (1997).
35. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, "Measurement of high order Kerr refractive index of major air components," Optics Express 17, 13429-13434 (2009).
36. J. Bernhardt, P. T. Simard, W. Liu, H. L. Xu, F. Théberge, A. Azarm, J. F. Daigle, and S. L. Chin, "Critical power for self-focussing of a femtosecond laser pulse in helium," Optics Communications 281, 2248-2251 (2008).
37. D. P. Shelton and J. E. Rice, "Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase," Chemical Reviews 94, 3-29 (1994).
38. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, "From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases," Physical Review A 77, 053814 (2008).
39. H. J. Lehmeier, W. Leupacher, and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation," Optics Communications 56, 67-72 (1985).
40. J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, "Nonlinear pulse compression in a multi-pass cell," Opt Lett 41, 4511-4514 (2016).
41. J. Weitenberg, A. Vernaleken, J. Schulte, A. Ozawa, T. Sartorius, V. Pervak, H.-D. Hoffmann, T. Udem, P. Russbüldt, and T. W. Hänsch, "Multi-pass-cell-based nonlinear pulse compression to 115 fs at 7.5 μJ pulse energy and 300 W average power," Optics Express 25, 20502-20510 (2017).
42. M. Kaumanns, V. Pervak, D. Kormin, V. Leshchenko, A. Kessel, M. Ueffing, Y. Chen, and T. Nubbemeyer, "Multipass spectral broadening of 18 mJ pulses compressible from 1.3 ps to 41 fs," Optics Letters 43, 5877-5880 (2018).
43. P. Russbueldt, J. Weitenberg, J. Schulte, R. Meyer, C. Meinhardt, H. D. Hoffmann, and R. Poprawe, "Scalable 30  fs laser source with 530  W average power," Optics Letters 44, 5222-5225 (2019).
44. M. D. Perry, O. L. Landen, A. Szöke, and E. M. Campbell, "Multiphoton ionization of the noble gases by an intense 1014-W/cm2 dye laser," Physical Review A 37, 747-760 (1988).
45. M. V. Ammosov, N. B. Delone, and V. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electric field," Sov. Phys. JETP 64, 1191 (1986).
46. "Lasers and laser-related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios" (ISO, 2005), 11146.
47. A. E. Siegman, "How to (Maybe) Measure Laser Beam Quality," in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, OSA Trends in Optics and Photonics (Optical Society of America, 1998), MQ1.
48. G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, "Short-pulse conical emission and spectral broadening in normally dispersive media," Optics Letters 19, 789-791 (1994).
49. "Ultrafast Nonlinear Optics: Third Order," in Ultrafast Optics (2009), pp. 258-315.
50. C. M. Heyl, C. L. Arnold, A. Couairon, and A. L’Huillier, "Introduction to macroscopic power scaling principles for high-order harmonic generation," Journal of Physics B: Atomic, Molecular and Optical Physics 50, 013001 (2016).
51. C.-L. Tsai, Y.-H. Tseng, A.-Y. Liang, M.-W. Lin, S.-D. Yang, and M.-C. Chen, "Nonlinear Compression of Intense Optical Pulses at 1.55 μm by Multiple Plate Continuum Generation," Journal of Lightwave Technology 37, 5100-5107 (2019).
52. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, "Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator," IEEE Journal of Quantum Electronics 28, 908-920 (1992).