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Self-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation.〔Cumberbatch, E. "Self-focusing in Non-linear optics", ''J. Inst. Maths Applics'' 6, 250 (1970)〕〔Mourou, G. A. et al. "Optics in the relativistic regime", ''Rev. Mod. Phys.'' 78, 309 (2006)〕 A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterised by an initial transverse intensity gradient, as in a laser beam. The peak intensity of the self-focused region keeps increasing as the wave travels through the medium, until defocusing effects or medium damage interrupt this process. Self-focusing of light was discovered by Gurgen Askaryan. Self-focusing is often observed when radiation generated by femtosecond lasers propagates through many solids, liquids and gases. Depending on the type of material and on the intensity of the radiation, several mechanisms produce variations in the refractive index which result in self-focusing: the main cases are Kerr-induced self-focusing and plasma self-focusing. == Kerr-induced self-focusing == Kerr-induced self-focusing was first predicted in the 1960s〔Askar'yan, G. A. "Effects of the Gradient of Strong Electromagnetic Beam on Electrons and Atoms", ''Soviet Phys. JETP'' 15, 1088 (1962)〕〔Chiao, R. Y. et al. "Self-trapping of optical beams", ''Phys. Rev. Lett.'' 13, 479 (1964)〕〔Kelley, P. L. "Self-focusing of optical beams", ''Phys. Rev. Lett.'' 15, 1005 (1965)〕 and experimentally verified by studying the interaction of ruby lasers with glasses and liquids.〔Lallemand, P. and Bloembergen, N. "Self-focusing of laser beams and stimulated Raman gain in liquids", ''Phys. Rev. Lett.'' 15, 1010 (1965)〕〔Garmire, E. et al. "Dynamics and characteristics of the self-trapping of intense light beams", ''Phys. Rev. Lett.'' 16, 347 (1966)〕 Its origin lies in the optical Kerr effect, a non-linear process which arises in media exposed to intense electromagnetic radiation, and which produces a variation of the refractive index as described by the formula , where ''n''0 and ''n''2 are the linear and non-linear components of the refractive index, and ''I'' is the intensity of the radiation. Since ''n''2 is positive in most materials, the refractive index becomes larger in the areas where the intensity is higher, usually at the centre of a beam, creating a focusing density profile which potentially leads to the collapse of a beam on itself.〔Gaeta, A. L. "Catastrophic Collapse of Ultrashort Pulses", ''Phys. Rev. Lett.'' 84, 3582 (2000)〕 Self-focusing beams have been found to naturally evolve into a Townes profile〔 regardless of their initial shape.〔Moll, K. D. et al. "Self-Similar Optical Wave Collapse: Observation of the Townes Profile", ''Phys. Rev. Lett.'' 90, 203902-1 (2003)〕 Self-focusing occurs if the radiation power is greater than the critical power〔Fibich, G. and Gaeta, A. L. "Critical power for self-focusing in bulk media and in hollow waveguides", ''Opt. Lett.'' 25, 335 (2000)〕 :, where λ is the radiation wavelength in vacuum and α is a constant which depends on the initial spatial distribution of the beam. Although there is no general analytical expression for α, its value has been derived numerically for many beam profiles.〔 The lower limit is α ≈ 1.86225, which corresponds to Townes beams, whereas for a Gaussian beam α ≈ 1.8962. For air, n0 ≈ 1, n2 ≈ 4×10−23 m2/W for λ = 800 nm,〔Nibbering, E.T.J. et al. "Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses", ''J. Opt. Soc. Am. B'' 14, 650 (1997)〕 and the critical power is Pcr ≈ 2.4 GW, corresponding to an energy of about 0.3 mJ for a pulse duration of 100 fs. For silica, n0 ≈ 1.453, n2 ≈ 2.4×10−20 m2/W,〔Garcia, H. et al. "New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers", ''Opt. Lett.'' 28 1796 (2003)〕 and the critical power is Pcr ≈ 2.8 MW. Kerr induced self-focusing is crucial for many applications in laser physics, both as a key ingredient and as a limiting factor. For example, the technique of chirped pulse amplification was developed to overcome the nonlinearities and damage of optical components that self-focusing would produce in the amplification of femtosecond laser pulses. On the other hand, self-focusing is a major mechanism behind Kerr-lens modelocking, laser filamentation in transparent media,〔Kasparian, J. et al. "White-light filaments for atmospheric analysis", ''Science'' 301, 61 (2003)〕〔Couairon, A. and Mysyrowicz, A. "Femtosecond filamentation in transparent media", ''Phys. Rep.'' 441, 47 (2007)〕 self-compression of ultrashort laser pulses,〔Stibenz, G. et al. "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament", ''Opt. Lett.'' 31, 274 (2006)〕 parametric generation,〔Cerullo, G. and Silverstri S. "Ultrafast optical parametric amplifiers", ''Rev. Sci. Instrum.'' 74, 1 (2003)〕 and many areas of laser-matter interaction in general. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Self-focusing」の詳細全文を読む スポンサード リンク
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