Femtosecond Optics.White Paper
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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. Barium crown BaK4 Borosilicate crown BK7 Figure 1. Refractive index as a function of wavelength for different commercially available glasses[2]

Following from the previous, we can see that inside the material each frequency component of light travels at a different speed. This results in a spread pulse compared to the initial one emitted from the laser. Group velocity dispersion is sometimes called second order dispersion because it arises from the Taylor expansion of the wavenumber k (change in spectral phase per unit length) as a function of angular frequency ω (around some center frequency ω0, e.g. the mean frequency of a laser pulse)[3]: GDD is usually an unwanted effect because a streched ultrashort pulse will lose its two...

Ultrafast optics – what is out there? As mentioned at the beginning of this article, compared to longer pulse or CW, the market of femtosecond optics is not as large. Nevertheless, there are a few solutions available to help you deal with ultrashort pulses. Altechna has been working with femtosecond optics since the beginning of the company in 1996 and has shown its expertise by helping its customers tame the sub-picosecond pulses. References T. Pfeifer et al, Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field, Opt. Lett., Vol. 31,...