Light pulse frequency spectrum

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

If an intense ultrashort light pulse at a given wavelength (or frequency) is focused in a liquid or solid medium (water, glass, etc.), its spectrum broadens considerably while propagating in the medium and the output beam appears as a white light beam. This is mainly due to self phase modulation [36], a non linear process that... 

The equivalent in the frequency domain is to excite the sample by light pulses and to record the complete amplitude and phase spectrum at a large number of frequencies simultaneously (B). Surprisingly, a useful technique for performing this kind of measurement does not exist. 

Fig. 6.77 Information drawn from FROG (a) plot of measured light frequencies versus delay time r in units of pulse length AT (b) frequency spectrum of (a) (c) frequency chirp [777]...

Any pulse can be described both in the time domain and in the frequency domain. In the time domain a signal may be oscillatory. The time domain behaviour is what is seen on an oscilloscope screen, because an oscilloscope is essentially an instrument for displaying a signal as a function of time. But a varying signal may also be described in terms of the components of each frequency present. This is a frequency domain description and is what is displayed by a spectrum analyser, just as an optical spectrum indicates the amount of each frequency (or wavelength) in a source of light. These two descriptions are related by a Fourier transform (Bracewell 1978), which may be written... 

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