## 2 Noise and Noise Equivalent Power Calculations  
In up-conversion detection (or optical detection), the electric field of the MMW/THz radiation causes a slight change in the electrical bias current, which increases the emitted light from the GDD [17]. This increase in the GDD light intensity derives from de-excitation or recombination rather than electron excitation. The DC bias field accelerates positive ions towards the cathode, which produces a secondary electron emission from the cathode. The large densities of these secondary electrons and positive ions yield a large increase in recombination near the cathode, which generates an increase in GDD light intensity at the negative glow region [20,22]. In this sensor system, the input signal to the GDD is an MMW/THz wave, and the output signal from the GDD is an optical wave instead of an electronic current. This upconverted wave was shown to have a much faster response time [19]. Those emitted light changes in the GDD intensity are detected by the LTF component. The output signal of the LTF is an electronic square wave frequency which is proportional to the GDD emitted light changes. The electronic response time then depends on the speed of the opto-electronic components. In the present case, that component is the LTF converter. The noise mechanism of the suggested sensor evolves both from the GDD and from the LTF. The GDD is a plasma device, in which the total noise power evolves from two noise sources. The first is Johnson-Nyquist noise or thermal noise given by:  
\[N_{0}=kT_{e} \tag{2}\]  
where \(N_{0}\) is the noise spectral density [W/Hz], \(k\) is the Boltzmann constant [1.380649 \(\times\) 10 - 23 J/K], and \(T_{e}\) is the electron temperature [K]. The second is shot noise power caused by random fluctuations of the electric DC current in the plasma given by:  
\[S=2 el_{DC} \tag{3}\]  
where \(S\) is the shot noise spectral density, \(e\) is the electron charge [C], and \(I_{DC}\) is the electric current in the plasma. Usually, the dominant noise source in the plasma is the thermal noise due to high \(T_{e}\), which is on the order of \(T_{e}\cong\) 40,000 K.  
Figure 3: Emission spectra of GDD N527 with MMW/THz influence (blue line) and without MMW/THz influence (orange line). One count is equal to 20\(\mu\)W. (Courtesy of Prof. Dr. [PERSON], Electrical and Electronics Engineering Department, Ankara Yildirim Beyazit University, Turkey). While the electronic detection (or electrical detection) is controlled by ionizing collisions and by electron energy or temperature, the up-conversion detection is controlled by positive ion-secondary electron recombination processes and is affected primarily by positive ion energy or temperature. Due to the larger mass of the ion as compared to the electron mass, the positive ion temperature is orders of magnitude less than the electron temperature. Thus, up-conversion detection Johnson noise is significantly less than the electronic detection Johnson noise [14]. Furthermore, according to the literature, the electron temperature in plasma, \(T_{e}\), is on the order of 30,000-40,000 K, while the ion temperature \(T_{i}\) is around 500 K [25]. Therefore, the noise generated in up-conversion detection is composed of both thermal noise (using \(T_{i}\)) and shot noise (due to recombination between secondary electrons and positive ions near the GDD cathode). The influence of those noise sources on the GDD emitted light fluctuations can be measured with a basic optical power meter. For example, measuring the irradiance of the GDD in two successive measurements and subtracting them, yields the total noise in the GDD irradiance. The GDD irradiance is the input signal to the LTF component which is attached to it. Thus, the output frequency noise, \(\Delta f_{n}\), is the subtraction of two successive output frequency measurements.