Fourier transform transverse responses

Similarly to non-selective experiments, the first operation needed to perform experiments involving selective pulses is the transformation of longitudinal order (Zeeman polarization 1 ) into transverse magnetization or ly). This can be achieved by a selective excitation pulse. The first successful shaped pulse described in the literature is the Gaussian 90° pulse [1]. This analytical function has been chosen because its Fourier transform is also a Gaussian. In a first order approximation, the Fourier transform of a time-domain envelope can be considered to describe the frequency response of the shaped pulse. This amounts to say that the response of the spin system to a radio-frequency (rf) pulse is linear. An exact description of the... 

An important feature that affects the numerical solution strategy is that these equations are written in the spectral space, either in the three dimensional space of wave-vectors (/-propagated UPPE) or in a two-dimensional space of transverse wave-vectors plus a one dimensional angular-frequency space (z-propagated UPPE). At the same time, the nonlinear material response must be calculated in the real-space representation. Consequently, a good implementation of Fast Fourier Transform is essential for a UPPE solver. 

Having obtained experimental data in the form of an instrumental response as a function of time (counts N i) or, as we will describe, asymmetry -4(t)), the experimenter seeks to extract information on physical properties and processes in the sample by analyzing the data. When there are clear oscillations in the data, from either an applied transverse field or from well-defined internal fields in well-ordered magnetic states, it is often useftil to transform the data into frequency space by Fast Fourier Transform (FFT, see e.g.. Press et al. 1986), or some alternate transform algorithm (see Alves et al. 1994, Rainford and Daniell 1994). This is particularly useful if a theory that is being tested predicts response as a function of frequency. In xSR of magnetic systems, however, many of the data... 

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