New Developments in Pulse Characterisation

It has been seen that the most commonly used pulse diagnostic for femtosecond sources: the second-order intensity autocorrelation, is very limited in its use for pulse characterisation. This measurement does not accurately reflect the pulse shape nor does it provide information on the phase modulation of the pulse; it can only give an estimate of the pulse duration after a specific pulse shape is assumed. A more refined method of pulse characterisation has been presented which involves the use of iterative fittings of the pulse spectrum, the intensity autocorrelation and the interferometric autocorrelation to provide information on the amplitude and phase of the pulse. Although this technique has proved to have a high degree of accuracy it is not completely unambiguous and its reliance

Chapter 2: Pulse Characterisation

on parametric fitting implies a previous estimate of the functional dependence of the pulse, and therefore is difficult to implement for complex shapes and modulations.

More recently, various methods have been devised to enable an unambiguous determination of the amplitude and the phase of femtosecond pulses that is not limited by the rather contrived parametrisation of the amplitude and phase. Diels et al have demonstrated a method of pulse and chirp measurement which can completely reconstruct a femtosecond signal in amplitude and phase from a single measurement. The basic principle is to cross-correlate a pulse that has been broadened by a known dispersion with the pulse to be measured and to use a numerical decorrelation technique to reconstruct the original laser signal.

This technique can be implemented by using a simple autocorrelator (designed for interferometric resolution) into one of whose arms a dispersive element (usually a block of glass) has been inserted which is sufficient to cause a significant broadening of the pulse. An interferometiic cross-correlation between the original short signal and the broadened pulse is then recorded and stored. This data is decorrelated to provide a complete description in amplitude and phase of the dispersed pulse. The original signal is recovered by applying (numerically) the inverse transformation to its stretched-out version. Although algorithms have been improved to yield a sufficiently accurate reconstruction of the pulse with only one iteration the deconvolution process still requires intensive numerical processing and computers with the capability of dealing with very large data files. Moreover the deconvolution procedure is sensitive to measurement errors.

Chilla and Martinez have proposed a rather different scheme which provides a simpler and more direct approach to pulse characterisation. It requires no complex decorrelation procedure to determine the pulse characteristics and can be performed with relatively little computer time. In contrast to the previous method, the measurement is made in the frequency domain rather than the time domain, the pulse shape being retrieved by a simple Fourier transform. The technique relies on a pulse synthesis scheme to unravel the frequency dependence of the phase, while the amplitude of the spectrum is obtained from the power spectrum. The phase retrieval is based on the principle that different time sections in a chirped pulse have correspondingly different frequency constituents. Therefore by using a tunable spectral filter to synthesise a pulse from each of these various frequency constituents, a corresponding series of time delays can be recorded. For a

Chapter 2: Pulse Characterisation

rectangular slit filter, the time delay of each synthesised pulse is equivalent to the frequency phase derivative of the original pulse at the central frequency of the filter, so allowing the spectral phase to be determined uniquely at discrete steps across the pulse spectrum.

Such a scheme can be implemented in practice by directing part of the laser output to a zero-dispersion pulse compressor which consists of a diffraction grating, a lens and a retrorefiecting mirror. A single-slit mask is placed directly in front of the mirror so that only a narrow portion of the spectrum is transmitted by the compressor. The output from such a device is a broadened pulse with a temporal delay equal to the frequency phase derivative of the original pulse at the central frequency of the spectral segment. This delay can be measured by performing an intensity cross-correlation of the synthesised pulse with a reference pulse from the unfiltered part of the laser output. Hence, by scanning the slit across the spectrum, the phase derivative can be found as a function of frequency. A monochromator and photodiode provide the necessary wavelength and intensity information. In this way, the amplitude and phase of each slice of the pulse spectrum can be determined and the pulse shape retrieved by a Fourier transform of these data.

The most recent development in pulse characterisation is the technique known as frequency-resolved optical gating (FROG) It combines both temporal and spectral data in a single measurement: a two-dimensional spectrogram which can be uniquely inverted to determine the intensity and phase of the pulse. For a second-harmonic generation (SHG) FROG arrangement P 1,32,35-37,39]^ this requires the measurement of the

signal pulse spectrum in a SHG autocorrelation, yielding signal intensity versus delay and fi*equency. This trace can be shown to fully and uniquely characterise the pulse, except for a time-direction ambiguity due to the symmetry in delay, which in practice, can be resolved using a variety of simple techniques The pulse extraction problem is equivalent to a two-dimensional phase retrieval which is performed using a suitable algorithm

Finally, it has recently been shown that other nonlinear optical processes besides SHG can be used for second-order autocorrelation measurements. In particular, two-photon- induced free-carrier generation in semiconductors has been utilised to provide second- order autocorrelation measurements of picosecond and femtosecond pulses A significant advantage of incorporating a semiconductor photodiode into autocorrelation measurements is that the desired two-photon response and the transformation of light into

Chapter 2: Pulse Characterisation

electric current are combined into a single solid-state device. In addition, the photodiode provides ease of alignment, the elimination of phase-matching requirements, an increase in sensitivity and a significant reduction in cost. Furthermore, in the case of broadband ultrashort pulses, it is likely that autocorrelations measured with a photodiode will yield a better estimate of the pulse duration than that obtained with a frequency-doubling crystal, owing to negligible material dispersion and spectral filtering At present, commercially available photodiodes should allow for autocorrelation measurements of pulses with wavelengths ranging from 500nm to 10pm.

2.6 Conclusion

The various pulse diagnostic techniques used in the characterisation of pulses throughout this thesis have been described. As will become clear in later chapters, the generation of short pulses from the CPM laser studied here cannot be adequately described by conventional pulse shapes. Since the standard intensity autocorrelation measurement is too limited to yield any categorical information on pulse shape it has been found necessary to consider alternative ways of obtaining such information. As a result, a method of pulse characterisation which combines the iterative fitting of intensity autocorrelations, interferometric autocorrelations and spectra has been presented, that enables a determination of pulse shape and phase to a first approximation. In order to hilly and unambiguously characterise a pulse with arbitrary shape and phase, more sophisticated methods of pulse characterisation are required which were not available during this work. However, a short review of the most recent techniques of pulse characterisation has been included for completion.

Chapter 2: Pulse Characterisation