Kerr-lens Mode Locking Without Nonlinear Astigmatism

Shai Yefet, Valery Jouravsky and Avi Pe’er Physics Department and the Institute of Nanotechnology and Advanced Materials,

Bar-Ilan University, Ramat-Gan 52900, Israel.

Introduction:Introduction:We demonstrate a Kerr-lens mode locked folded cavity using a planar (non-Brewster) Ti:sapphire crystal as a gain and Kerr medium, thus cancelling the nonlinear astigmatism caused by a Brewster cut Kerr medium. Our method uses a novel cavity folding in which the intra-cavity laser beam propagates in two perpendicular planes such that the astigmatism of one mirror is compensated by the other mirror, enabling the introduction of an astigmatic free, planar-cut gain medium. We demonstrate that this configuration is inherently free of nonlinear astigmatism, which in standard cavity folding needs a special power specific compensation.

Theory:Theory:

Astigmatism is a well known aberration in folded optical cavities that include Brewster-cut crystals and/or off-axis focusing elements, as in a standard X-fold Ti:sapphire (TiS) cavity, illustrated here:

For continuous-wave (CW) operation, the astigmatism is linear and can be fully compensated by correctly choosing the folding angles of the focusing elements. For mode-locked (ML) operation induced by the nonlinear Kerr effect, an additional nonlinear astigmatism from the Kerr lens is added that is power-dependent and needs to be taken into account. The nonlinear astigmatism can be visualized by calculating the strength of the Kerr effect at the output-coupler (OC) for a given mode-locking point, defined as:

The Kerr strength can be calculated for the sagital and tangential planes separately as a function of the crystal position:

Since the mode size of the laser beam changes as it refracts into the crystal, the Kerr strength is different in each plane, therefore it is clear that a linearly compensated CW beam will not remain circular after mode locking.

TiS crystal

M1 M2

OCHR

Pump source @ 532 nm2

2

0

P

c

dP

dP

SagittalTangential

0

1

0 2 4-2

Z (mm)

Experimental setup:Experimental setup:

The standard technique to compensate for nonlinear astigmatism, is to deliberately introduce linear astigmatism in the "opposite" direction, which results in compensation of the overall astigmatism only for a specific intra-cavity intensity. Illustrated bellow is a novel type of cavity folding that eliminates from the source nonlinear astigmatism in Kerr-lens mode locked lasers. This configuration allows the introduction of a planar-cut crystal in which the laser beam enters the crystal at normal incidence. Thus, the spatial mode of the beam in both planes does not change as it enters the crystal, cancelling the nonlinear Kerr-lens astigmatism from the source, as can be seen from the Kerr strength of each plane.

TiS

M1 M2OC

HR

Pump source@ 532 nm

Top view

2

3D view

OC

M1 TiSM2 P1

P1 P2

P2 HR

SagittalTangential

0

0 2 4-2

Z (mm)

1

Results:Results:

The theoretical predictions are verified by experimental results. The laser mode intensity profile is measured by a CCD camera for CW and mode locked operations in the near-field and also for the mode locked operation in the far-field. For the near field, the CW astigmatism was fitted to be: 0.98, in good agreement to our prediction while the mode locked astigmatism remains exactly the same. The focusing quality of the ML mode was measured in the far field showing a gaussian beam with a quality factor of M2=1.6.

1.56 mm 0.78 mm

CW near-field ML far-field

3.64 mm

ML near-field