Re[f(t)] t -3 -1 2. 3 Exercise 3 Fourier-transform spectroscopy (FTS) is a type of spectroscopy where spectra are genera

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Re F T T 3 1 2 3 Exercise 3 Fourier Transform Spectroscopy Fts Is A Type Of Spectroscopy Where Spectra Are Genera 1 (424.87 KiB) Viewed 99 times

Re[f(t)] t -3 -1 2. 3 Exercise 3 Fourier-transform spectroscopy (FTS) is a type of spectroscopy where spectra are generated by (discrete)-Fourier transforming measurements of electromagnetic radiation from a sample source. FT-spectroscopy can be used in (i) the time-domain or space-domain, (ii) used in nearly all fre- quency ranges of electromagnetic radiation (and hence includes infrared spectroscopy, optical, and nuclear magnetic resonance spectroscopies), (iii) used to measure absorption or emission spectra, and (iv) can be continuous wave or pulsed. In pulsed FTS, a sample is exposed to a short pulse of radiation, the shortness of which determines the resolution in the frequency domain. Consider a pulse for three units of time illustrated above and described by i2nt f(t) Se-1276, 05753 else = (13) (a) Use Eq.12 to compute the pulse's representation in the frequency domain. (b) Sketch a graph of the pulse's power spectrum, |F(w)]. You may use Mathematica to help guide your sketch or generate the plot. Exercise 4 BONUS. Pump probe spectroscopy is an experimental technique used to study ultrafast elec- tronic dynamics. The method employs two pulses: a pump and a probe. The pump pulse is used to excite the sample (“pump” denoting the pumping the populations of the sample from ground to excited). The probe pulse is used to measure changes in optical properties of the sample. By varying the delay between the pump and pulse, one can sequentially observe different vibrionic configurations of the sample (viz. the relaxation dynamics). The process is explained in this video. When the delay is fixed, the pulses can be modelled by a periodic square wave described by, f(t) = -2<< -1 k, -1<t<1 0,1<t<2 (14) where k is the amplitude of the pulse, the period is p = 2L, and L = 2 is the duration of the pulse. Determine Fourier coefficients for the appropriate parity (even or odd) expansion. Expressed f(t) in terms of its Fourier series.