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Femtosecond Filamentation in Transparent Media Physics Reports 441 (2007) 47–189 www.elsevier.com/locate/physrep Femtosecond filamentation in transparent media A. Couairona,∗, A. Mysyrowiczb aCentre de Physique Théorique, École Polytechnique, CNRS, F-91128 Palaiseau, France bLaboratoire d’Optique Appliquée, École Nationale Supérieure des Techniques Avancées–École Polytechnique, CNRS, F-91761 Palaiseau, France Received 5 May 2006; accepted 15 December 2006 Available online 6 February 2007 editor: G.I. Stegeman Abstract This paper introduces and discusses the main aspects of ultrashort laser pulse filamentation in various transparent media such as air (gases), transparent solids and liquids. The properties of femtosecond filaments and their applications are presented. Theoretical models developed to explain filaments and the main predictions inferred from these models are reviewed. The various techniques to observe filaments and to measure their characteristics are described. The main measurements of filament features performed so far are reviewed. © 2007 Elsevier B.V. All rights reserved. PACS: 42.25.Bs; 42.65.Jx; 42.65.Re; 42.65.Sf; 45.65.−k; 52.38.Hb; 05.45.−a; 42.65.Tg; 42.68.Ay Keywords: Filamentation; Ultrashort laser pulses; Optical Kerr effect; Multiphoton ionization; Nonlinear propagation Contents 1. Introduction .......................................................................................................... 50 1.1. Scope of the paper ............................................................................................... 50 1.2. Properties of ultrashort pulse nonlinear propagation .................................................................... 50 1.2.1. Diffraction ................................................................................................ 51 1.2.2. Space–time defocusing ..................................................................................... 52 1.2.3. Group velocity dispersion and higher order dispersive effects ..................................................... 52 1.2.4. Self-focusing .............................................................................................. 52 1.2.5. Self-phase modulation ...................................................................................... 54 1.2.6. Raman contribution to the Kerr effect ......................................................................... 54 1.2.7. Self-steepening ............................................................................................ 54 1.2.8. Photo-ionization ........................................................................................... 54 1.2.9. Plasma defocusing ......................................................................................... 55 1.2.10. Losses due to plasma absorption ............................................................................. 56 1.2.11. Losses due to multiphoton absorption ......................................................................... 57 1.2.12. Refocusing cycles.......................................................................................... 57 1.2.13. Modulational instability ..................................................................................... 58 ∗ Corresponding author. E-mail addresses: [email protected] (A. Couairon), [email protected] (A. Mysyrowicz). 0370-1573/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2006.12.005 48 A. Couairon, A. Mysyrowicz / Physics Reports 441 (2007) 47–189 1.2.14. Filaments in condensed media ............................................................................... 58 1.2.15. Arrest of collapse .......................................................................................... 58 1.3. Properties of light filaments ........................................................................................ 59 1.3.1. Robustness of filaments ..................................................................................... 59 1.3.2. Long range propagation ..................................................................................... 60 1.3.3. Spectral broadening ........................................................................................ 60 1.3.4. Intensity clamping ......................................................................................... 60 1.3.5. Conical emission of white light and colored rings ............................................................... 61 1.3.6. Pulse self-compression ..................................................................................... 61 1.3.7. Pulse mode self-cleaning .................................................................................... 62 1.3.8. Filaments in optical parametric amplifiers ...................................................................... 62 1.3.9. Superluminal velocity ...................................................................................... 63 1.3.10. Generation of THz radiation ................................................................................. 63 1.3.11. Two-colored filamentation and third harmonic generation ........................................................ 63 1.3.12. Multiple filamentation ...................................................................................... 64 1.3.13. Energy reservoir ........................................................................................... 65 2. Modeling filamentation ................................................................................................ 65 2.1. Model scenarii ................................................................................................... 65 2.1.1. Moving focus model ....................................................................................... 65 2.1.2. Self-guiding model ......................................................................................... 66 2.1.3. Dynamic spatial replenishment ............................................................................... 67 2.1.4. Spatial soliton and light bullets ............................................................................... 67 2.1.5. Conical X-waves .......................................................................................... 69 2.1.6. Conical unbalanced Bessel beams ............................................................................ 70 2.1.7. Interpretations of the conical emission......................................................................... 71 2.2. Model equations governing the nonlinear propagation of laser pulses and filamentation ...................................... 72 2.2.1. Reduced model ............................................................................................ 73 2.2.2. Initial pulse ............................................................................................... 74 2.2.3. Raman–Kerr effect ......................................................................................... 74 2.2.4. Model including group velocity dispersion, Raman contribution, plasma and multiphoton absorption, avalanche and recombination ............................................................................................. 75 2.2.5. Model including shock terms, photoionization .................................................................. 76 2.2.6. Plasma generation by optical field ionization ................................................................... 77 2.2.7. Multispecies, multilevel ionization ............................................................................ 77 2.2.8. Model including cross phase modulation for elliptically polarized laser pulses ....................................... 78 2.2.9. Model including nonparaxial terms and vectorial effects.......................................................... 79 2.2.10. Model including third harmonic generation .................................................................... 79 2.2.11. Unidirectional pulse propagation equation ..................................................................... 80 2.3. Numerical techniques for the integration of these models ............................................................... 81 2.4. Semi-analytical approach .......................................................................................... 85 2.4.1. Moment formalism ......................................................................................... 86 2.4.2. Variational method ......................................................................................... 88 2.4.3. Paraxial ray approximation .................................................................................. 91 3. Theoretical results .................................................................................................... 91 3.1. Main results obtained by the analytical approaches (beam–particle analogy) ............................................... 91 3.2. Main results obtained by numerical simulations ....................................................................... 93 3.2.1. Numerical simulations of filamentation in air ................................................................... 93 3.2.2. Numerical simulations of UV filaments in air ................................................................... 96 3.2.3. Infrared filamentation in argon ............................................................................... 97 3.2.4. Pulse self-compression by filamentation ....................................................................... 99 3.2.5. Simulations
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