4.5 Conclusions
5.1.1 A Brief Overview on Temporal Shaping Approaches 72
Several approaches for temporal shaping of laser pulses were developed in the past that might be classified in spectral and non-spectral meth-ods. The first class, that takes advantage of the spectral composition of laser pulses, is best represented by Fourier synthesis pulse shaping of ultrashort pulses [69]. In these methods wavelength components of an ul-trashort pulse are dispersed in space, individually delayed or filtered (by amplitude or phase masks) and recombined to a single beam. Major char-acteristics of this technique are the tight control of the actual temporal pulse shape as well as its reversibility (if no amplitude masks are used).
Another approach exploiting the spectral composition of ultrashort pulses is material dispersion that introduces wavelength-dependent phase terms resulting in a temporal broadening of a previously transform-limited pulse [70, pp. 352-354].
The second class of pulse shaping techniques, the non-spectral class, rather generates various sub-pulses (independent of their spectral compo-sition) and delays them with respect to each other prior to recombining them into a single beam (see e.g. [71, pp. 205-213] for a short summary of such methods). If no active components are applied, this process is irreversible and exhibits a much lower degree of controlling the output waveform as compared to the spectral methods. Thus, it is more often referred to as pulsestretching instead of pulseshaping.
Figure 5.1: Pulse duration over FWHM bandwidth for Gaussian shaped transform-limited ultrashort pulses with center wavelengthλ0.
5.1.2 Temporal Shaping Strategy in This Work
In the present work, transform-limited ultrashort laser pulses of 100 to 200 fs pulse duration emitted at 80 MHz pulse repetition rate (thus, 12.5 ns pulse period) need to be converted into a continuous wave (cw) signal in order to definitely eliminate previously discussed nonlinearities (see Chapter 4). As this requires a temporal overlap of successive pulses, the extreme duty cycle of approximately 10−5 represents the main challenge of this task. In the following, prospects of some approaches for achieving pulse stretching from fs- to ns-scale will be briefly discussed.
Owing to the relation of pulse duration and spectral width of transform-limited pulses (compare Eq. (3.1)) a spectral reduction of the radiation represents one approach for pulse broadening. Moreover, this spectral reduction is, to some degree, anyway required for the development of the measurement facility introduced in Chapter 6. However, considering the desired standard full-width-at-half-maximum (FHWM) bandwidth of approximately 5 nm for the final setup, the achievable increase in pulse duration by this approach is rather limited (see Fig. 5.1). Apart from the fact that the FWHM bandwidths of 100 fs pulses below 580 nm cen-ter wavelength are readily narrower than 5 nm, the maximum achiev-able transform-limited pulse duration for 5 nm equals 1.76 ps (at λ0 = 2500 nm), thus, still four orders of magnitude lower than the pulse period.
In addition to the spectral reduction, the ultrashort pulses could be dis-persed by application of varying group velocities to the respective spectral components (see e.g. Eq. (3.21)). Two approaches might be distinguished in that: firstly, material dispersion can be exploited [70, pp. 352-354]
or, secondly, Fourier synthesis methods might be applied [69]. Regarding Fourier synthesis methods there are no general restrictions in the amount of introduced pulse spreading given that an arbitrary large phase term can be experimentally added to certain frequency components. However, such setups can become quite challenging regarding alignment control and might be practically limited when scaling fs- to ns-pulses. Material dispersion, on the other hand, is more promising as it is experimentally quite conveniently implementable by coupling light into optical fibers. A major drawback of material dispersion is, however, that extensive mate-rial or fiber lengths of more than 1 km are required to convert a 100 fs transform-limited pulse at 870 nm center wavelengths into a ns-pulse.1
Turning the discussion towards non-spectral pulse stretching, most ap-proaches yield difficulties comparable to Fourier synthesis methods re-garding alignment and complexity [71, pp. 205-213]. Especially those setups consisting of various mirror, beam splitter and prism combinations can result in tremendous alignment effort. A significantly more feasible approach is represented by multimode optical fibers. In addition to the previously discussed material dispersion, these fibers exhibit modal dis-persion which enhances pulse stretching capabilities substantially [70, pp.
351-352]. For example, 100 m of a multimode fiber with numerical aper-ture NA = 0.22 is sufficient to achieve impulse responses in the ns-range.
Moreover, physical delay lines can be realized when fibers of different lengths are combined, thereby enhancing the duty cycle of the ultrashort pulse train by several factors [72, 73]. Applying this prior to the actual pulse broadening by modal dispersion results in a significant reduction of the necessary fiber lengths and, hence, a significant reduction of overall material absorption. This argumentation exposes that multimode optical fibers are an excellent choice for a pulse-to-cw-conversion of the ultrashort pulse trains utilized in this work.
1Assuming a silica-glass fiber with a group velocity dispersion parameter ofDλ≈
−80 ps/km/nm [70, p. 353].
Hereafter, the physical concept of pulse stretching in step-index2 mul-timode optical fibers, a new method for characterizing their properties and further effects of the fibers on the radiation properties will be dis-cussed. Finally, a monolithic fiber concept for pulse-to-cw-conversion will be presented that has been developed in the course of this work.