# Spectral Shaping of a Superluminescent Diode for Terahertz Cross-Correlation Spectroscopy
## 3 Results and Discussion
### Analysis and Comparison of Structured Spectra to Continuous Spectra
Overall, the influence of the filter period on \(\Delta\)pp can be considered small and detrimental. It should be noted that a better performance is obtained for a feature width of 20 GHz than for 10 GHz in contrast to the calculated power and DR. This effect can be explained if the feature width is understood as the optical line width. The line width is reciprocal to the coherence length. In this case, a high coherence length means a large FWHM of the envelope [cf. Figure 3a)]. This distributes the energy over a larger sampling window and explains the slightly lower amplitude for the 10 GHz feature width measurements and the larger calculated terahertz power. For the limit case of the continuous spectrum, a single pulse in which the entire power is contained is obtained in the time-domain. Since here the power is lower than in the structured case for the reasons described above, the amplitude is larger only for large filter periods. In Figure 6c, the DR for different filter periods is presented. In contrast to \(\Delta\)pp as shown in Figure 6b, the structured spectra outperform the continuous bandpass over the complete filter period range for the dynamic range. The smallest increase of 0.5 dB can be seen for a 20 GHz feature width and a 30 GHz filter period, while the largest increase in DR can be achieved for a filter period of 125 GHz and a feature width of 10 GHz. The DR increases to 71.5 dB compared to the 59.8 dB from the continuous 2 THz BP. This is an impressive enhancement in dynamic range by 11.7 dB. The increase in dynamic range cannot be explained by the increased power alone. The calculated power was only increased by a factor of 4, while an increase in DR of 11.7 dB is associated with an increase in the signal-to-noise ratio by a factor of 14. It follows that structuring the spectrum not only increases the generated power, but also reduces the noise of the system. As mentioned earlier, the discrete spectrum produces many mixing products with low frequencies that do not contribute to the signal but, as these measurements show, to the noise. As a conclusion for maximizing the \(\Delta\)pp, it is better to use a small filter period with larger features. This leads to slightly better results than for the unstructured case. If the dynamic range needs to be improved, small features with large feature periods are more suitable. Compared to the continuous case, a structured optical spectrum will always improve the DR.  
Analyzing the slope m and FWHM of the comb-like structures at three different feature widths (5 GHz, 10 GHz, and 20 GHz) at 15 mW optical power helps to point out the relationship between the spectral shape and the bandwidth. The measurements were done at 15 mW power per antenna because the EDFA was not able to amplify all optical spectra with 5 GHz feature width to 20 mW per antenna. Figure 7a shows the calculated slope m of the terahertz spectra, as indicated in Figures 2c and 3c for different filter periods. A constant behavior for all three features widths can be seen. However, if the mean value of all slopes is considered, the continuous bandpass filtered case shows better results, while the unfiltered spectrum shows the best values for m. This behavior can be explained as follows. Since m corresponds to the bandwidth of the terahertz signal independently of the dynamic range, a high optical bandwidth favors a small slope. However, this positive effect of the unfiltered spectrum is cancelled out by the increased noise, as described above. So far, we have only assumed that the feature width correlates with the FWHM of the envelope in the time-domain. The coherence time as a function of linewidth is calculated as \(t_{c}=1/\Delta\
u\), where \(t_{c}\) is correlated with the FWHM and \(\Delta\
u\) is correlated with the feature width. Hence, the expected coherence time is 50 ps for 20 GHz, 100 ps for 10 GHz, and 200 ps for 5 GHz. Figure 7 shows the measured FWHM for the three feature widths.