Definiciones conceptuales

width that can be obtained from a picosecond parametric oscillator, namely, the group velocity walkaway amongst the pump, signal and idler pulses, the group velocity dispersion and the spectral bandwidth. It is important that these properties are investigated before any crystal is considered for use as these effects can increase the threshold and cause output pulse broadening.

3.9.1 Group velocity walkaway

One of the most important crystal properties in an ultrashort OPO is the group velocity walkaway between the pump, signal and idler pulses. This mechanism affects the temporal overlap of the thiee waves which results in gain reduction and pulse broadening in the OPO. It is therefore imperative that the group velocity walkaway for a particular nonlineai* material or crystal orientation is calculated to check that this does not exceed greatly the duration of either signal or pump pulse, so as to maintain as high a conversion efficiency as possible. The group velocity walkaway has been calculated for the materials used in this work, with the results being given in subsequent chapters. The relevance of these results to the maximum useful crystal length is also discussed. 3.9.2 Group velocity dispersion

A further feature that will effect the duration of the resonant signal pulse in the OPO is the group velocity dispersion. This effect will cause an initially transform-limited pulse to broaden in pulse duration due to the fact that different wavelengths components of the pulse will propagate at different group velocities. As discussed in Chapter 2 it is possible to fully compensate for the effects of this dispersion by using an intracavity prism sequence.

3.9.3 Spectral bandwidth

Any nonlinear crystal has a limited phase-matching bandwidth, which if it isn't sufficient to accommodate the spectral component of a pulse will lead to pulse broadening and frequency chirping of the pulse. This can be a problem in femtosecond systems in which pulse bandwidths are of the order of tens of nms. In picosecond systems however, bandwidths are more typically of the order of <

Chapter 3 Picosecond Optical Parametric Oscillators

Inm and so this effect is less of a problem. As such crystals of lengths of the order of tens of mms can be used in picosecond systems.

3.9.4 Predictions of pulse durations in ultrafast OPOs

The prediction of the pulse expected from a synchronously-pumped OPO is a

complex process as many interacting processes occur simultaneously. There have however been several attempts to achieve this goal. Two notable pieces of work are by Becker et al [23] and Cheung and Liu [24]. The similarities and differences in the results produced from these models will now be discussed.

The analysis presented by Becker et al [23] is the less complete of the two as they consider only the degenerate case of type I phase-matching, which results in the signal and idler pulses being treated identically, which is obviously not the full story.

The analysis presented by Cheung and Liu [24] is more complete as in this procedure the general case of non-degenerate signal and idler wavelengths in a singly-resonant oscillator is solved. Both model are, however, not complete as several important features have been neglected for simplicity, namely the effects of self phase modulation were not taken into account.

Although the models have some differences, some common results were found to occur; in both cases the pump pulse duration was found to limit the width of the signal pulse obtainable. It was also found in both analyses that the signal pulse duration was ultimately determined by the degree of pump depletion taking place. It was found that the intensity dependent parametric gain caused the pump pulses to broaden because it depletes the centre of the pulse preferentially over the wings. This has the knock-on effect that the OPO is actually being pumped by a longer pump pulses, which results in a longer signal pulse being produced. It is therefore found that signal pulses become broader as operation further above threshold is obtained. It is of course not desirable to operate close to threshold as this can lead to device instability and so a

compromise position must be achieved. The two models produced different results when an actual prediction of the shortest signal pulses available were made. In the degenerate case Becker et al predicted output pulses as short as 0.25 AXp, where Atp represents the pump pulse duration, whereas in the more

complete, non-degenerate analysis, Cheung and Liu predicted the signal pulse durations to be restricted to around 0.4 AXp. The results of these models are

compared with the experimental results in subsequent chapters.

Chapter 3 Picosecond Optical Parametric Oscillators

3.10 Conclusions

In this chapter all the relevant features required to design a picosecond optical parametric oscillator have been outlined, including the factors affecting the

choice of nonlinear crystal and resonator design. In the subsequent chapters a

complete characterisation of several OPOs systems is given, which will demonstrate that these types of devices are capable of producing high output powers across a wide spectral range from the visible to mid-infrared.

Chapter 3 Picosecond Optical Parametric Oscillators

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Chapter 3 Picosecond Optical Parametric Oscillators

21. S. Singh in, Handbook of Laser Science and Technology (Ed., M. J. Weber) 3, Part 1, Section 1.1 (1986)

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