Análisis descriptivo

The very small size of an LED, compared to a doubling ciystal, photomultiplier tube and power supply, gives tremendous impetus to the ideal of miniaturising an autocorrelator. To take this further, it is necessary to reduce the size of the interferometer section, which is done most readily be replacing the traditional loud speaker with some other means of providing a temporal delay. Recent research has been reported on the development of a compact Fourier-transform spectrometer in which a Michelson-type of delay-line was replaced by a polarising interferometer

based on a Wollaston prism [28]. It was decided to adopt a similar approach here, and a compact, unidirectional autocorrelator was developed as a result.

A Wollaston prism comprises two wedges of biréfringent material, joined by

their hypotenuses (Fig. 3.14). The wedges are oriented so that their optic axes are perpendicular to each other, and parallel to the entrance and exit faces of the prism. The effect of this on an incident beam of light is that ordinarily and extraodinarily polarised rays experience a different change in refractive index at the interface

between the wedges, and hence are refracted differently, and leave the prism with an angular separation. This behavioui' leads to the use of Wollaston prisms as polarising beam splitters. The angle of separation, or splitting angle, a , is given by [29]

w„)tan0

where no and Ue aie the ordinary and extraordinary refractive indices of the prism material, and 0 is the wedge angle.

<x-

Figure 3.14 Wollaston prism, showing the beam splitting effect at the interface between the wedges, which have orthogonal optic axes.

The orientation of the optic axes in the two wedges is such that a beam which is ordinary in the first wedge becomes extraordinary in the second, and vice versa. Thus there is an optical path difference, A, between two orthogonal beams propagating through the prism, which varies with position along the prism due to the varying relative thickness of the wedges. This can be shown to be [29]

A = 2d{n^ -«o)tan0 _(3.9)

where d is the displacement from the centre of the prism, at which point the wedges aie of equal thickness so there is no path difference. This path difference means that a Wollaston prism introduces a temporal delay between the two polarisation components of an incident ultrashort pulse, and this delay can be varied by scanning

the prism across the incident beam. This is precisely the effect needed for autocorrelation, such that a Wollaston prism can replace the components of a Michelson delay-line in an autocorrelator.

The prism used here was made of quartz, with a wedge angle of 26" and a length of 20 mm. The birefringence («e - «o) of quartz at 800 nm is approximately 0.0089 [30], so using the above dimensions in Equation 3.9 gives a change in path

length across the whole prism of ±87 pm, corresponding to a maximum available delay of approximately ±300 fs. This is perfectly adequate for the measurement of 100 fs pulses. Different amounts of delay may be readily attained by using larger or smaller prisms, and different prism materials, such a calcite or magnesium fluoride.

The autocorrelator was configured as shown in Fig. 3.15. A polariser was used

to polarise the incident beam at 45° to the optic axes of the prism so that ordinary and extraordinary components would be present. The beam was then focussed into the prism with a 30 mm focal length lens to produce a spot size of 40 pm. To obtain full resolution of the fringes of an interferometric autocorrelation, the delay introduced across the beam due to its physical dimension must not exceed one-half of the wavelength. For 800 nm pulses a 40 pm spot size is sufficiently small. On exiting the prism, the two spatially separated and orthogonally polarised components were collimated by a second 30 mm focal length lens, and then passed through a further polariser to select a common 45° polarisation component to allow the necessary interference between the beams. Finally, a 15 mm microscope objective focussed the two beams on to the same place on the LED. The Wollaston prism was mounted on a translation stage driven by an electromagnetic actuator to scan it continuously across the incident beam. An electronic trigger signal was taken from the actuator to

maintain synchronism between the prism motion and the oscilloscope trace

displaying the LED output.

polariser at 45° collimated input beam | LED polarisation' state Wollaston prism on translation stage

Figure 3.15 Configuration of the Wollaston prism and LED autocorrelator.

Note that in Fig. 3.15 the Wollaston prism is portrayed as being angled with respect to the incident beam. This was to compensate for the fact that the

polaiisation components are refracted at both the interface and the exit face of a Wollaston prism. On leaving the prism, the two beams therefore appear to have split at a plane which can be shown to lie halfway between the interface and the exit face, as illustrated in Fig. 3.16. fri the correlator, this plane was set normal to the beam propagation direction so that the two beams could be properly collimated by the second lens for all positions of the prism.

Figure 3.16 Beam-splitting effect in a Wollaston prism, illustrating how the beams appear to trace back to a common plane halfway between the prism exit face and the interface (blue line).

A fringe-resolved interferometric autocorrelation of the pulses from the self-

modelocked femtosecond Ti:sapphire laser is presented as Fig. 3.17. The small level of chirp evident is due to the same cause as that given to explain the autocorrelation of Fig. 3.14b. A pulse duration of 88 fs can be inferred from Fig. 3.17; this is slightly longer than the pulses presented in Fig. 3.13, due to a small amount of pulse

broadening induced by dispersion in the quartz prism. The noise on Fig. 3.17 may be related to the mechanical translation of the prism, or may have been caused by inhomogeneities in the prism material or at the prism interface.

There are several advantages and disadvantages to the Wollaston autocorrelator. It was a compact device, which was simple and straightforward to align. No attempt was made to calibrate it; instead the pulse duration was calculated from the wavelength and the number of interference fringes. However, the precise way in

which the delay relates to the properties of the prism means that an accurate calibration could be done. Improvements to the method of scanning the prism would probably result in reduced noise and a better quality output. The principal

disadvantage lies in the dispersive pulse broadening of the prism glass, which suggests that a Wollaston prism autocorrelator would not be appropriate for

measuring the hypershort pulses now becoming commonplace. However, judicious selection of the prism material can help to reduce this problem; the dispersive properties of various materials vary quite dramatically with wavelength so a material can be chosen to suit a particular application. Some values of pulse broadening in various materials at different wavelengths are given in Table 3.2.

Intensity (arbitrary)

•200 ■100 0

Delay (fs)

100 200

Figure 3.17 Interferometric autocorrelation trace of pulses from the Ti:sapphire laser, recorded with tlie Wollaston autocorrelator. The inferred pulse duration