Kerr-lens modelocking

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Kerr-lens modelocking is a method of modelocking lasers via a nonlinear optical process known as the optical Kerr effect. This method allows the generation of pulses of light with a duration as short as a few femtoseconds.

The optical Kerr effect is a process which results from the nonlinear response of an optical medium to the electric field of an electromagnetic wave. The refractive index the medium is dependent on the field strength .

Because of the non-uniform power density distribution in a Gaussian beam (as found in laser resonators) the refractive index changes across the beam profile; the refractive index experienced by the beam is greater in the centre of the beam than at the edge. Therefore a rod of an active Kerr medium works like a lens for high intensity light. This is called self-focusing and in extreme cases leads to material destruction. In the laser cavity short bursts of light will then be focused differently to continuous waves (cw).

The favor the pulses over cw, the cavity could be made unstable for cw-operation, but more often a low stability is a by-product of a cavity design putting emphasis on aperture effects. Older designs used a hard aperture, that simply cuts off, while modern designs use a soft aperture, that means the overlap between the pumped region of the gain medium and the pulse. While the effect of a lens on a free laser beam is quite obvious, inside a cavity the whole beam tries to adapts to this change. The standard cavity with flat mirrors and a thermal lens in the laser crystal has the smallest beam width on the end-mirrors. With the additional kerr lens the width on the end-mirror gets even smaller. Therefore small end-mirrors (hard aperture) favor pulses. In Ti:Sa oscillators telescopes are inserted around the crystal to increase the intensity. For a soft aperture consider an infinite laser crystal with a thermal lens. A laser beam is guided like in a glass fibre. With an additional kerr lens the beam width gets smaller. In a real laser the crystal is finite, but for a soft aperture laser the cavity mirrors are designed to act as a 1:1 telescope imaging the light, which exits an end-face, back onto the same end-face. So for the beam, the crystal looks infinite.

The length of the medium used for KLM is limited by group velocity dispersion. KLM is used in Carrier envelope offset control.

[edit] Starting a Kerr-lens modelocked laser

Initiation of Kerr-lens modelocking depends on the strength of the nonlinear effect involved. If the laser field builds up in a cavity the laser has to overcome the region of cw operation, which often is favored by the pumping mechanism. This can be achieved by a very strong Kerr-lensing that is strong enough to modelock due to small changes of the laser field strength (laser field build-up or stochastic fluctuations). Modelocking can also be started by shifting the optimum focus from the cw-operation to pulsed operation while changing the power density by kicking the end mirror of the resonator cavity (though a piezo mounted, syncronous oscilating end-mirror would be more 'turn key'). Other principles involve different nonlinear effects like saturable absorbers and saturable Bragg reflectors, which induce pulses short enough to initiate the Kerr-lensing process.

[edit] Modelocking - evolution of the pulse

Intensity changes with lengths of nanoseconds, are amplified by the Kerr-lensing process and the pulselength further shrinks to achieve higher field strengths in the center of the pulse. This sharpening process is only limited by the bandwidth achievable with the laser material and the cavity-mirrors as well as the dispersion of the cavity. The shortest pulse achievable with a given spectrum is called the bandwidth-limited pulse.

Laser media for ultrashort pulses (e.g. Ti:Sapphire) Dispersion management with prism sequences. Chirped mirror technology allows to compensate timing mismatch of different wavelengths inside the cavity due to material dispersion while keeping the stability high and the losses low.

The Kerr effect leads to the Kerr-lens and Self-phase modulation at the same time. To a first approximation it is possible to consider them as independent effects.

[edit] Applications

Since Kerr-lens modelocking is an effect that directly reacts on the electric field, the response time is high enough to produce light pulses in the visible and near infrared with lengths of less than 5 femtoseconds. Due to the high electrical field strength focused ultrashort laser beams can overcome the threshold of 10¹⁴ W cm^-2, which surpasses the field strength of the electron-ion bond in atoms. These short pulses open the new field of ultrafast optics, which is a field of nonlinear optics that gives access to a completely new class of phenomena like measurement of electron movements in an atom (attosecond phenomena), coherent broadband light generation (ultrabroad lasers) and thereby gives rise to many new applications in optical sensing (e.g. coherent laser radar, ultrahigh resolution optical coherence tomography) material processing and other fields like metrology (extremely exact frequency and time measurements).