C.2 The wiggler

The wiggler (see Fig. C.2a) consists of two concentric brass tubes fixed to a solid block. An optical fiber is located and fixed along the inner tube and remains straight. One side of the fiber is feed by the laser diode and the other one is bare. This side protrudes from the inner and outer tubes and exposes its tip, which delivers the laser light to the optical path. The extreme of the outer tube is glued with the fiber and the inner tube fixes a pivot point. Two perpendicular piezoelectric actuators push the outer tube in a hard spherical enlargement located in the middle of the tube, inducing a tilt at the fiber that changes the direction at which the light emerges from the tip of the optical fiber. In the end, the wiggler has a high frequency response ($ >$2 kHz) and a position range of about 11 $ \mu $m after the displacement is amplified by the microscope objective.

The diverging beam that comes out from the tip of the fiber has a Numerical Aperture (NA) of 0.12 and it is located at the focal plane of a collimating lens of focal length $ f=20.0$ mm that projects the parallel light to the microscope objective, which refocuses the light to form the optical trap (see Fig. C.2b).

Figure C.2: The wiggler. (a) When the piezo (green prism) pushes the spherical enlargement, the outer tube also pushes the optical fiber at the glued point. Since the inner tube remains straight, the optical fiber is bended at the pivot point and the light can be redirected. (b) A different bending of the optical fiber (only represented from the pivot point) translates into a different position of the optical trap. According to the definition of Numerical Aperture (NA) $ \textrm{NA}=n\sin\theta_m$ (where $ n$ is the index of refraction of the medium and $ \theta _m$ is the marginal ray) the half-angle of the cone of light that emerges from an optical fiber with NA=0.12 is $ 6.9\,^{\circ}$. The beam expands until it reaches a diameter of $ \phi =4.83$ mm ( $ \tan\theta_m=(\phi/2)/f$, where $ f=20$ mm is the focal length of the collimating lens) before it enters the collimating lens. The entrance pupil of the objective is about 11 mm, so the laser beam is underfilling the objective.
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JM Huguet 2014-02-12