Everything about Self-focusing totally explained
Self-focusing is a
non-linear optical process induced by the change in
refractive index of materials exposed to intense
electromagnetic radiation. 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 travel through the medium, until defocusing effects or medium damage interrupt this process.
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 and experimentally verified by studying the interaction of
ruby lasers with glasses and liquids. 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
n0 and
n2 are the linear and non-linear components of the refractive index, and
I is the
intensity of the radiation. Since
n2 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. Self-focusing beams have been found to naturally evolve into a Townes profile
Self-focusing occurs if the radiation
power is greater than the critical power
» ,
where
me is the
electron mass,
c the speed of light, ω the radiation angular frequency,
e the electron charge and ω
p the plasma frequency. For an electron density of 10
19 cm
-3 and radiation at the wavelength of 800 nm, the critical power is about 3 TW. Such values are realisable with modern lasers, which can exceed PW powers. For example, a laser delivering 50 fs pulses with an energy of 1 J has a peak power of 20 TW.
Self-focusing in a plasma can balance the natural diffraction and channel a laser beam. Such effect is beneficial for many applications, since it helps increasing the length of the interaction between laser and medium. This is crucial, for example, in laser-driven particle acceleration, laser-fusion schemes and high harmonic generation.
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