# Spectral Shaping of a Superluminescent Diode for Terahertz Cross-Correlation Spectroscopy
## 3 Results and Discussion
### Analysis and Comparison of Continuous Spectra  
First, measurements with a continuous bandpass filter were done to find out the optimal size \(\Delta\)BP and position as a reference for the comb structured filters. There is a slight positive trend for longer excitation wavelength visible (cf. Figure 11), which can be explained by a better conversion efficiency of the low energy photons [14]. However, since the SLD has the maximum in amplified spontaneous emission around 193 THz, the region around 193 THz was chosen for further experiments. Measurements with different continuous bandpass sizes from 0.2 THz up to 5 THz showed a saturation effect of the generated terahertz bandwidth around 2 THz for a bandpass size larger or equal to 2 THz (cf. Figure 11). This was also observed by [PERSON] et al. [12]. To investigate whether an  
Figure 3: (**a**) Terahertz time-domain trace of a spectrally structured SLD. The envelope (green) has a FWHM = 66.45 ps. (**b**) Frequency-domain representation of the trace with a linear fit (red) through the detected peaks (blue). The roll-off is m = \(-\)32.5 dB/THz with a peak DR of 72 dB and a bandwidth of 1.6 THz. (**c**) Optical spectrum of the SLD after a structured 2 THz bandpass filter with a feature spacing \(\Delta\)f = 115 GHz and a feature width of 10 GHz. optical bandwidth above 2 THz provides benefits away from the terahertz bandwidth, we consider terahertz power in addition to the previously mentioned indicators. The current detected in the receiver module is the cross-correlation of the incident electromagnetic field and the optical signal at the receiver after a delay \(\tau\)[4; 15]. Because of this correlation, the average terahertz power is proportional to the power of the squared photocurrent in the detector and can be used as a qualitative comparison factor derived from the discrete time signal [16]:  
\[P_{THz}\propto\ \frac{1}{NT}\sum_{n=0}^{N}I_{Rx}(nT)^{2} \tag{1}\]  
where \(P_{THz}\) is the calculated detected terahertz power at the receiver (\(Rx\)), \(T\) is the time between each data point, \(N\) is the number of acquired data points, and \(I_{Rx}\) is the current at \(Rx\). It should be noted here that the calculated power refers to the detected signal and is not an approximation for the actual radiated power. Nevertheless, it allows a qualitative comparison between different operating points and correlates with the actual power [16]. Figure 4 shows the parameters DR, \(\Delta\)pp, BW and \(P_{THz}\) for continuous bandpass filters from 2 THz to 3 THz in 0.2 THz steps. It can be seen that \(\Delta\)pp drops by roughly 20%, the calculated power by 50%, and the DR by 3 dB (-50%), while the bandwidth increases just by 5% This small gain in bandwidth does not justify a broader bandpass width. For a bandpass filter width of 2 THz, nearly the entire bandwidth is converted into the terahertz signal. For this reason, a bandpass filter width of 2 THz was chosen for the further experiments. This saturation effect can be explained using a simple picture of photomixing. At a bandwidth of 2 THz, there is more than one possible mixing product for difference frequencies below 1 THz. Above 1 THz, there is only one mixing product. So, if the optical spectrum is increased to 3 THz, there is still exactly 1 mixing product for 2 THz, while otherwise mainly mixing products with low difference frequencies are added. Combined with the frequency characteristics of the antennas used, mixed products larger than 2 THz are lost in the noise. As a next step, we analyzed the behavior of a 2 THz bandpass filter for varying optical power at the antennas. The behavior between dynamic range, slope m and bandwidth  
Figure 4: Different continuous bandpass widths from 2.0 to 3.0 THz in 0.2 THz steps and \(P_{Rx}=20\) mW optical power. The three parameters DR, \(\Delta\)pp and \(P_{THz}\) are linearly decreasing with increasing filter width. The bandwidth parameter BW is marginally increasing for larger bandpass sizes.