Fitting Spectral Linewidths

An important aspect to the present THz spectroscopy of water vapor is to demonstrate the technical capabili- ties of the instrument. A motivating aspect of the instrument’s construction was the higher spectral resolution it would offer, thus enabling better line center measurements. As an initial real-sample demonstration of the instrument spectral resolution, a water peak (as plotted in Figures 3.13 and 3.14, was isolated and numeri- cally fit to find a measure of its linewidth. A full 10,000 ps scan from the dual-detector configuration of the instrument was used for the fitting analysis (with zero-padding only to the next power of 2), and a peak at 1.153 THz was chosen, as it is of moderate intensity and exhibited minimal issues with frequency-domain ringing and distortion.

At the sample pressure of approximately 2 Torr, the overall linewidth is expected to be just below the instrumental resolution of 100 MHz that is associated with 10,000 ps scans, so an instrument-limited spectral linewidth of about 100 MHz is expected. This pressure was chosen to nearly match the expected linewidth to the instrument resolution, but to not exceed it, while maximizing the optical depth of the sample for strong absorption features. The true linewidth of spectral peak will be the convolution of various homogeneous and inhomogeneous broadening mechanisms [19], notably pressure broadening and Doppler broadening, respec- tively. The HITRAN database provides information on self-broadening; for the transition at 1.153 THz and 296K, the self-broadened half width at half-maximum is 0.538 cm−1/atm, yielding an expected full-width pressure-broadening contribution to the linewidth of about 85 MHz. A calculation of Doppler broadening finds a full-width contribution of about 3 MHz. In cases where the pressure- and Doppler-broadening effects are of similar magnitude, a convolution of their line shapes, Lorentzian and Gaussian, respectively, into a Voigt line-shape function, is required. However, given the present order of magnitude difference in contribu- tions and the approximate nature of the analysis, it is thus appropriate to model the peaks as having Lorentzian line-shapes; this line-shape was also utilized in previous THz-TDS studies of water vapor (e.g., [36], [15]). Such a fitting was made and is plotted over the original data points, as shown in Figure 3.16.

As seen in the figure, there are not many experimental data points over the peak. There are three points on the central portion of the peak and perhaps a few more about the base; this is expected as the peak’s Lorentzian linewidth is close to or less than the size of the frequency bins in the spectrum. The fitting result for the Lorentzian linewidth is∆ν₁/2= 98.8 MHz, with 95% confidence bounds of 88.7 to 108.9 MHz; the

somewhat large bounds are reasonable given the low number of datapoints available. Future efforts should re-visit this test, once better control of the experimental pressure is achieved (see discussion in chapter 5), and measure samples at both of lower and especially higher pressures to further verify the spectral resolution performance. However, the present result is nonetheless an initial verification of the instrument performance.

1.149 1.15 1.151 1.152 1.153 1.154 1.155 1.156 1.157

Frequency (THz)

Relative Absorbance

H2O Spectrum Lorentzian Fit

Figure 3.16: Lorentzian fit to a water vapor peak, obtained from a long (10,000 ps) waveform and zero- padding only to the next power of 2 in the scan record length. The linewidth was fitted as 98.8 MHz; see main text for further details.

For the interested reader, it is noted that the curve-fitting was carried out in MATLAB using non-linear least squares fitting in the ’Curve Fitting Toolbox’ and a custom equation for the fitting, that is, the Lorentzian line-shape function [94]: L(x) =1 π 1 2Γ (x−x0)2+ (1₂Γ)2 (3.49)

whereΓis the full width at half maximum andx0is the peak center (these may also be noted, in the context

of spectroscopy [19], as∆ν1/2andν0, respectively).

The referenced scan data was first prepared using the ‘test background.m’ script (included in the ap- pendix,§A.9). The results from this first script were further processed by a new script ‘peakOne createFit.m’, which isolated the desired peak and called a fitting function based on MATLAB’s curve fitting toolbox; the script and fitting function are discussed further and included in the appendix,§A.11.

Chapter 4

Applications in Materials Science

The ASOPS THz-TDS instrument is versatile in its potential areas of application beyond gas-phase spec- troscopy and we have pursued collaborations in this regard. In this chapter, we discuss two areas in materials science and condensed matter physics where we have applied the present instrumentation. In the first example below, in§4.1, we present the details of an all-optical (i.e., non-THz) use of the instrumentation. Here, the vir- tual delay line capability of our instrument is used in an optical pump-probe experiment to measure ultrafast, time-dependent changes in the reflectance of a sample in response to the heat generated from a pump pulse. These time-domain waveforms can be modeled so as to extract the size-dependent heat conduction properties of the sample. Such data can inform efforts to engineer the thermal properties of a material on a nanoscale so as to create thermal metamaterials for a wide array of practical uses. And in the second example below, in §4.2, we return to THz spectroscopy, but of a very different sample. Specifically, we use our spectrometer’s THz pulse itself as the pump pulse to excite a coherent magnon mode in a candidate spintronics material. As the material’s electrons precess in a coordinated fashion, the sample produces a long-duration THz ringing signal that we record much as we would in a regular THz-TDS experiment.