# A DFB-SOA Based Optical Vector Network Analyzer for Characterization of Bandpass Optical Devices
## 2 Operating Principle  
The schematic of the proposed DFB-SOA based OVNA is presented in Figures 1 and 2. An optical carrier, produced via a tunable laser source (TLS), is transmitted to a phase modulator (PM). An electrical signal, produced by an EVNA through frequency scanning, is introduced into the PM. Subsequently, the phase modulated signal output from the PM is then directed to an ODUT with a bandpass filter response. The optical carrier power and the upper sideband power are significantly attenuated outside the passband of the ODUT. The sideband situated at a lower frequency will remain unaffected, as it resides within the frequency range designated for passage. Subsequently, the lower sideband linked to the diminished optical carrier is directed to the DFB-SOA. The DFB-SOA functions as an active optical filter characterized by a tightly confined passband, thereby selectively amplifying a specific wavelength. The optical carrier, aligned with the gain peak of the DFB-SOA, undergoes amplification solely for its power, while the lower sideband remains unaltered. Following the modulation of the optical carrier and the associated sidebands within the photodetector during the photoelectric conversion process, a microwave signal is generated and subsequently routed back to the EVNA for comprehensive transmission spectrum evaluation. In the experimental setup, the microwave signal output is contingent on the lower sideband's traversal across the ODUT's passband. Consequently, the ODUT's transmission spectrum, featuring a bandpass response, is measured via electrical domain analysis. It is worth noting that, the passband of the ODUT should be outside of the gain peak of the DFB-SOA and the wavelength difference between the passband of the ODUT and the gain peak of DFB-SOA should be within the bandwidth of the employed optoelectronic devices and the EVNA. The key device of the OVNA we have proposed is the DFB-SOA. Refer to Figure 3 for the diagram of the DFB-SOA, observing it reveals the placement of two identical fiber Bragg gratings (FBGs) side by side, each with a \(\pi\)-phase-shift in the center, encircling the DFB-SOA's active layer. Both ends of this phase-shifted structure feature anti-reflection (AR) coatings, allowing the input light signal to traverse the component unimpeded. An additional current is directed through this phase-shifted DFB-SOA, enabling the manipulation of the active layer's gain. Figure 1: Diagrammatic representation of our proposed DFB-SOA based OVNA. Figure 3: Schematic diagram of the DFB-SOA. Figure 2: Operation mechanism of the proposed DFB-SOA based OVNA. The \(\pi\)-phase-shifted fiber Bragg grating is segmented into three grating segments, which may be viewed as a cascade of two equivalent cavities with coupling effects among them. By employing the coupled-mode equations and the transfer-matrix approach [21], the amplitude response of the \(\pi\)-phase-shifted FBG may be represented as  
\[\left[ \begin{array}{c}A_{f}(0)\\ A_{b}(0)\end{array} \right]=\left[ \begin{array}{cc}F_{11}^{1}&F_{12}^{1}\\ F_{21}^{1}&F_{22}^{1}\end{array} \right]\cdot\left[ \begin{array}{cc}\exp(j\pi/2 )&0\\ 0&\exp(-j\pi/2)\end{array} \right]\cdot\left[ \begin{array}{cc}F_{12}^{2}&F_{12 }^{2}\\ F_{21}^{2}&F_{22}^{2}\end{array} \right]\cdot\left[ \begin{array}{cc}A_{f}(L)\\ A_{b}(L)\end{array} \right] \tag{1}\]  
where \(A_{f}(z)\) and \(A_{b}(z)\) are the amplitude of the optical signal propagating forward and backward along the grating fiber, \(L\) is the length of the \(\pi\)-phase-shifted FBG. The \(2~{}\times~{}2\) matrix \(F^{i}\) represents the amplitude response related to the \(i\)th grating section.