1 Femtosecond Laser Filamentation Induced Phenomena and Applications
3
of the pulse will self-focus at a different position along the propagation axis resulting
in a continuous ‘series’ of self-focal spots. At each spot, the defocusing effect of the
plasma balances the self-focusing effect. The consequence is a continuous series of
self-focal spots that become a linear narrow nearly cylindrical zone, hence, a filament
along the propagation direction. Inside the continuous series of spots or the filament
core, the intensity is constant or clamped [11]. This clamped intensity is independent
of pressure [13]. This is a surprising result. Note that only the lowest fundamental
spatial mode of the laser undergoes filamentation [7, 14] while the pulse along the
filament core is a continuous propagating series of plane waves [7].
Since the defocusing effect of a plasma is much stronger than the self-focusing
effect, it doesn’t take a high density plasma to balance the self-focusing effect. In
fact, according to our experimental measurement [12], depending on the strength of
external focusing, the plasma density is two to three orders of magnitude lower than
the density of atmospheric pressure air; i.e. most of the molecules inside the filament
are neutrals. These neutral air molecules ‘bathe’ in the high clamped intensity zone.
This is a very special environment in which a large number of neutral molecules
could interact with a high laser intensity for a short time. In this environment, each
molecule would undergo uni-molecular interaction with the high laser intensity as if
it were in a vacuum system because the laser pulse duration (fs time scale) is much
shorter than the mean-free-time of an electron undergoing inverse Bremsstrahlung
process (picosecond time scale) [7]. This would avoid laser induced breakdown. That
is to say, the plasma inside the filament comes from uni-molecular interaction with
the laser. Such an environment is unique and cannot be found elsewhere. We shall
look at some consequences of such interactions. But before we do so, let us look at
the temporal development of the filament core.
At the beginning, we can imagine the filament core along the filament axis as
an imaginary cylindrical zone filled with neutrals. When the laser pulse arrives, the
slice-by-slice self-focusing mechanism essentially means that each slice successively
self-focuses into the imaginary cylinder. Each slice injects a flux of electromagnetic
(EM) field from the side into the cylinder resulting in a high intensity zone in the
form of a thin cylindrical slab. We idealize that the thin slab of high intensity EM flux
fits nicely in the imaginary cylindrical zone. This slab is at least one wavelength thick
and the diameter is the same as that of the filament zone (the imaginary cylindrical
zone); the diameter is about 50–100 µm. Inside this slab, ionization takes place
‘instantaneously’ and the EM flux is then forced out (diverges out) of the zone by the
self-generated plasma. Each successive slice will ‘inject’ a flux of EM field becoming
a ‘slab’ with the same intensity into successive new positions in the cylinder in the
forward propagation direction and diverges out. It is as if a dot of high intensity
light ‘bullet’ (slab of light) propagates through the imaginary filament zone. The
propagation speed of the slab of EM field is the speed of light in the neutral medium;
i.e. c/n 0 where c is the speed of light in vacuum and n 0 is the linear index of refraction
of neutral air [7]. This is because each slab represents the zone in which intensity
clamping takes place. When intensity clamping occurs, the nonlinear index in the
neutrals and the plasma index of refraction cancel each other [7]. It takes a finite time
for the successive slabs to sweep through the filament zone.
3
of the pulse will self-focus at a different position along the propagation axis resulting
in a continuous ‘series’ of self-focal spots. At each spot, the defocusing effect of the
plasma balances the self-focusing effect. The consequence is a continuous series of
self-focal spots that become a linear narrow nearly cylindrical zone, hence, a filament
along the propagation direction. Inside the continuous series of spots or the filament
core, the intensity is constant or clamped [11]. This clamped intensity is independent
of pressure [13]. This is a surprising result. Note that only the lowest fundamental
spatial mode of the laser undergoes filamentation [7, 14] while the pulse along the
filament core is a continuous propagating series of plane waves [7].
Since the defocusing effect of a plasma is much stronger than the self-focusing
effect, it doesn’t take a high density plasma to balance the self-focusing effect. In
fact, according to our experimental measurement [12], depending on the strength of
external focusing, the plasma density is two to three orders of magnitude lower than
the density of atmospheric pressure air; i.e. most of the molecules inside the filament
are neutrals. These neutral air molecules ‘bathe’ in the high clamped intensity zone.
This is a very special environment in which a large number of neutral molecules
could interact with a high laser intensity for a short time. In this environment, each
molecule would undergo uni-molecular interaction with the high laser intensity as if
it were in a vacuum system because the laser pulse duration (fs time scale) is much
shorter than the mean-free-time of an electron undergoing inverse Bremsstrahlung
process (picosecond time scale) [7]. This would avoid laser induced breakdown. That
is to say, the plasma inside the filament comes from uni-molecular interaction with
the laser. Such an environment is unique and cannot be found elsewhere. We shall
look at some consequences of such interactions. But before we do so, let us look at
the temporal development of the filament core.
At the beginning, we can imagine the filament core along the filament axis as
an imaginary cylindrical zone filled with neutrals. When the laser pulse arrives, the
slice-by-slice self-focusing mechanism essentially means that each slice successively
self-focuses into the imaginary cylinder. Each slice injects a flux of electromagnetic
(EM) field from the side into the cylinder resulting in a high intensity zone in the
form of a thin cylindrical slab. We idealize that the thin slab of high intensity EM flux
fits nicely in the imaginary cylindrical zone. This slab is at least one wavelength thick
and the diameter is the same as that of the filament zone (the imaginary cylindrical
zone); the diameter is about 50–100 µm. Inside this slab, ionization takes place
‘instantaneously’ and the EM flux is then forced out (diverges out) of the zone by the
self-generated plasma. Each successive slice will ‘inject’ a flux of EM field becoming
a ‘slab’ with the same intensity into successive new positions in the cylinder in the
forward propagation direction and diverges out. It is as if a dot of high intensity
light ‘bullet’ (slab of light) propagates through the imaginary filament zone. The
propagation speed of the slab of EM field is the speed of light in the neutral medium;
i.e. c/n 0 where c is the speed of light in vacuum and n 0 is the linear index of refraction
of neutral air [7]. This is because each slab represents the zone in which intensity
clamping takes place. When intensity clamping occurs, the nonlinear index in the
neutrals and the plasma index of refraction cancel each other [7]. It takes a finite time
for the successive slabs to sweep through the filament zone.