In
nonlinear optics
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in Nonlinearity, nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity ...
, filament propagation is propagation of a beam of
light
Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
through a medium without
diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
. This is possible because the
Kerr effect
The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index chan ...
causes an
index of refraction change in the medium, resulting in
self-focusing of the beam.
Filamentary damage tracks in glass caused by laser pulses were first observed by Michael Hercher in 1964. Filament propagation of laser pulses in the atmosphere was observed in 1994 by
Gérard Mourou and his team at
University of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
. The balance between the self-focusing refraction and self-attenuating
diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
by
ionization
Ionization or ionisation is the process by which an atom or a molecule acquires a negative or positive Electric charge, charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged at ...
and
rarefaction of a laser beam of terawatt intensities, created by
chirped pulse amplification, in the atmosphere creates "filaments" which act as waveguides for the beam thus preventing divergence. Competing theories, that the observed filament was actually an illusion created by an axiconic (bessel) or moving focus instead of a "waveguided" concentration of the optical energy, were put to rest by workers at Los Alamos National Laboratory in 1997.
Though sophisticated models have been developed to describe the filamentation process, a model proposed by Akozbek et al. provides a semi-analytical and easy to understand solution for the propagation of strong laser pulses in the air.
Filament propagation in a
semiconductor
A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
medium can also be observed in large aperture
vertical cavity surface emitting laser
The vertical-cavity surface-emitting laser (VCSEL ) is a type of semiconductor laser diode with laser beam emission perpendicular from the top surface, contrary to conventional edge-emitting semiconductor lasers (also called ''in-plane'' lasers ...
s.
Femtosecond laser filamentation in gaseous media
Self-focusing
A laser beam traversing a medium can modulate the refractive index of medium as
:
where
,
and
are linear refractive index, second order refractive index and intensity of propagating laser field respectively. Self-focusing occurs when the phase shift due to Kerr effect compensates for the phase shift because of
Gaussian beam
In optics, a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or ...
divergence. Phase change due to diffraction for a Gaussian beam after traversing a length of
is
:
and phase change because of Kerr effect is
:
.
where
,
(Rayleigh range) and
is the waist of Gaussian beam. For self-focusing to happen the one have to satisfy the condition of
terms be equal in magnitude for both Kerr and diffraction phases. Hence
:
.
On the other hand, we know that area of a Gaussian beam at its waist is
. Therefore
:
.
Note
:
Self-focusing needs a laser peak power higher than the critical power
(order of gigawatts in air
), however, for infrared (IR) nanosecond pulses with peak powers higher than the critical power self-focusing is not possible. Multiphoton ionization, inverse
Bremsstrahlung and electron avalanche ionization are three major results of gas and laser interaction. The later two processes are collisional-type interactions and take time to accomplish (picosecond to nanosecond). A nanosecond pulse is long enough to develop the air breakdown before the power reaches the GW order required for self-focusing. Breakdown of gas produces plasma that has absorbing and reflecting effect so self-focusing is prohibited.
Re-focusing during the propagation of a focused short laser pulse
An interesting phenomenon related to the filament propagation is the refocusing of focused laser pulses after the geometrical focus.
Gaussian Beam propagation predicts an increasing beam width bidirectionally away from the geometric focus. However, in the situation of laser filamentation, the beam will quickly recollapse. This divergence and refocusing will continue indefinitely.
In photo-reactive systems
Filament formation and propagation may also be observed in photopolymer systems. Such systems display a Kerr-like optical nonlinearity via photoreactive-based increases in the refractive index. The filaments form as a result of the self-trapping of individual beams, or
modulation instability of a wide-area light profile. Filament propagation has been observed in several photo-polymerizable systems, including organo-siloxane,
acrylics, epoxy and copolymers with epoxies, and polymer blends. The locations of filament formation and propagation may be controlled by modulating the spatial profile of the input light field. Such photo-reactive systems are able to produce filaments from spatially and temporally incoherent light, because the slow reaction responds to the time-average intensity of the optical field, whereby femto-second fluctuations wash out.
[ This is similar to photo-refractive media with non-instantaneous responses, which enable filament propagation with incoherent or partially incoherent light.
]
Potential applications
The filaments, having made a plasma, turn the narrowband laser pulse into a broadband pulse having a wholly new set of applications. An interesting aspect of the filamentation induced plasma is the limited density of the electrons, a process which prevents the optical breakdown. This effect provides an excellent source for spectroscopy of high pressure with low level of continuum and also smaller line broadening. Another potential application is the LIDAR
Lidar (, also LIDAR, an acronym of "light detection and ranging" or "laser imaging, detection, and ranging") is a method for determining ranging, ranges by targeting an object or a surface with a laser and measuring the time for the reflected li ...
-monitoring of air.
Flat panel dicing using short laser pulses is an important application due to the fact that as the glass substrates become thinner it becomes more difficult to improve the process yield using conventional diamond blade dicing techniques. Using short pulses dicing speeds of over 400 mm/s has been successfully demonstrated on non-alkali glass and borosilicate glass, using a 50 kHz, 5W high-power femtosecond laser. The working principle developed by Kamata et al. is the following. The short pulse laser beam having a wavelength to which the work is transparent is directed to the front surface of the work toward the back surface and focused. A filament in the light beam traveling direction from the beam waist is formed by the auto-focusing action due to the laser beam propagation in the work is formed. The substance in the filament is decomposed by the laser beam and can be discharged from the back surface, and a cavity is formed in the channel. While forming the cavity, the laser beam is scanned, a machined surface is formed, and thereafter the work can be cut with a weak bending stress.
In July 2014, researchers at the University of Maryland
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the Univ ...
reported using filamenting femtosecond laser pulses in a square arrangement to produce a density gradient in air which acted as an optical waveguide lasting on the order of several milliseconds. Initial testing demonstrated a signal gain of 50% over an unguided signal at a distance of about one meter. A field application was demonstrated in 2021, where kHz-repetition-rate 1030-nm terawatt Yb:YAG laser, installed in the vicinity of the 124-m-tall Säntis telecommunications tower was used to guide lightning strikes towards the tower's Franklin rod, opening up the possibility of future laser lightning rods.
References
External links
Experiments Detail How Powerful Ultrashort Laser Pulses Propagate through Air
Filamentation and Propagation of Ultra-Short, Intense Laser Pulses in Air
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Nonlinear optics