Femtosecond Optics.White Paper0 pages

Femtosecond
optics
by Tomas Jankauskas

Though the definition sometimes varies, an ultrashort
pulse is an electromagnetic pulse with a time duration
of one picosecond (10-12 second) or less. Since ultrashort
phenomena are too fast to be directly measured with
electronic devices, such events are sometimes referred
to as ultrafast (the meaning, however, is the same).
Pulse length is inversely proportional to the optical
spectrum of the laser beam therefore ultrashort pulses
have a very broad spectrum, e.g. the gain bandwidth of
Ti:Sapphire is 128 THZ; thus, the shortest pulse duration
is 3.4 femtoseconds (3.4 • 10-15 seconds). Technically,
such pulses are no longer the shortest artificially
generated electromagnetic waves, attosecond
(10-18 second)[1] pulses have already been achieved, but
this technology is still far from commercial use.

Chromatic dispersion
Since the optical spectrum of an ultrashort pulse is very
broad, group velocity plays a key role in understanding
how ultrashort optics work. Group velocity of a wave
is the velocity with which the overall shape of waves’
amplitudes propagates through space. It would be
correct to say that group velocity is the velocity with
which the whole broad electromagnetic ultrashort
pulse propagates. For free space, where the refractive
index is equal to one, group velocity is constant for all
components of the pulse.
Optical materials possess a specific quality, the phase
velocity of light inside the material depends on the
frequency (or wavelength), and equivalently the group
velocity depends on the frequency. This is called
chromatic dispersion or group-velocity dispersion (GVD).
This means that for different wavelengths of light
the refractive index inside of the material is different.
Therefore, the group velocity, at which light passes
through the material, is different for each wavelength.
Figure 1 shows how refractive index depends on the
wavelength of light in different glasses.

1.9
Lanthanum dence flint LaSF9
1.8
Refractive index (n)

Since the introduction of the first sub-picosecond
lasers in the 1990s, the market for femtosecond optics
has grown rapidly. However, it still can not compete
with longer pulse or CW laser markets. The problem
of femtosecond application of conventional optics
and coatings is the distortion of the temporal pulse
characteristics or the high peak pulse power damage.
To better understand why this happens, let’s look at the
basics of the ultrashort world.

Dence flint SF10

1.7

Flint F2

1.6

Barium crown BaK4
Borosilicate crown BK7

1.5

Fluorite crown FK51A
1.4
0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Wavelength λ (μm)

Figure 1. Refractive index as a function of wavelength for different
commercially available glasses[2]

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