## 3 Regimes of Operation of DBQW RTD Photo-Detectors
### Non-Oscillating Regime  
The measurement system used for the characterization of the RTD-PD optical modulation response in the non-oscilating regime consisted of continuous wave light from a tunable single mode laser modulated by an external 10 GHz electro-optic modulator driven by an RF signal generator. A single mode optical fiber was used to guide the modulated light and to illuminate the RTD-PD waveguide by means of a lensed fiber. The RTD-PDs, the electrical GSG probe (with high frequency response up to 40 GHz), and the optical fiber were mounted on the positioners as described previously in the DC characterization setup. The variable DC bias was applied via a wide bandwith bias-T (45 MHz-26.5 GHz) connected to the high-frequency probe SMA cable. The RTD-PD electrical response to optical modulated injected signals was measured using a high-bandwidth spectrum analyzer and oscilloscope.  
\begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Quantity** & **Typical order of magnitude** \\ \hline \(\lambda\) & Operation wavelength & 1.55 \(\upmu\)m \\ \(\kappa\) & Light coupling factor & 0.35 \\ \(R_{ref}\) & Waveguide facet reflectivity & 0.3 \\ \(\alpha\)(\(\lambda\),\(V\)) & Waveguide core absorption coefficient & 400 cm\({}^{-1}\) \\  & (at 1.55 \(\upmu\)m and biased in the valley) & \\ \(\gamma_{ph}\) & Overlap integral of the electric and optical fields & 0.25 \\ \(\Lambda\) & Waveguide contact length & 150 \(\upmu\)m \\ \hline \end{tabular}
\end{table}
Table 1: Description of the typical physical parameters of the waveguide photo-detector.  
Figure 4a presents the RF injection locking capture level as function of the DC bias using light (\(\lambda=\) 1,550 nm) modulated by a sinusoidal RF reference signal at 1.2 GHz, with optical power levels in fiber of 1 mW and 6 mW.  
The figure shows the dependence of 1.2 GHz photodetection signal on bias conditions. The responsitivity increases with the transition from RTD-PD peak to valley voltage, \(V_{p}\) and \(V_{v}\), respectively, with an improvement up to 14 dB. As discussed previously, the higher response in this region occurs because the holes photo-generated in the depletion region accumulate around the collector barrier (see Figure 2b), causing a local enhancement field which leads to higher carrier velocity and hence high current. Figure 4b presents the photo-detected RF power as function of the light wavelength with the DC bias voltage as parameter. Again, the increased responsivity under higher voltage bias has also been observed at the wavelength of 1,530-1,570 nm (C-band).  
Figure 4c presents the measured RTD-PD RF power output when biased in the peak and valley regions as a function of incident optical power, and Figure 4d shows the RF power spectra of the photo-detected optical modulated signals. Up to 14 dB gain is obtained in the transition from the peak  
Figure 4: **(a)** RF injection locking capture level as function of the DC bias using light at \(\lambda=\) 1,550 nm. **(b)** Output power as function of wavelength with DC bias voltage as parameter for 1 mW optical power in fiber. **(c)** Output power as function of optical power level at \(\lambda=\) 1,550 nm. **(d)** Power spectra of photo-detected signal using a 10 mW optical signal \(\lambda=\) 1,550 nm). In figures **(b)**, **(c)**, and **(d)**, the RTD-PD was DC biased in the peak \(V_{p}=\) 1.2 V and valley \(V_{v}=\) 2.0 V regions. In all figures, light was modulated by a RF reference source signal at 1.2 GHz.  
to the valley region. The results demonstrate the RTD-PD works as a high-speed optical-to-electrical converter, taking advantage of the optical waveguide design. In what follows, the optical injection locking operation employing RTD-PDs is investigated when the devices are DC biased in the NDR region, _i.e._, when they generate self-sustained oscillations at frequencies close to the detected microwave signals.