## 2 Principle of Operation  
Figure 1a shows a schematic diagram of the proposed filter composed of a PBS, two HBF segments of the same length, an ordered WRC of a QWR and an HWR (designated as QWR 1 and HWR 1, respectively) before the first HBF segment depicted as HBF 1, and an ordered WRC of an HWR and a QWR (designated as HWR 2 and QWR 2, respectively) in front of the second HBF segment depicted as HBF 2. HBF 2 is butt-coupled to port 3 of the PBS so that its slow axis should be oriented at 22.5\({}^{\circ}\) with respect to the horizontal axis of the PBS. This butt-coupling between HBF 2 and the PBS maximizes the extinction ratio of the narrowband comb spectrum of the filter. Each ordered WRC  
can modify the effective phase delay difference between the fast and slow axes of HBF 1 or HBF 2. A change in this effective phase difference indicates a change in the effective birefringence of the entire polarization-diversity loop, which results in a wavelength shift of the transmission spectrum in the PDLS-based comb filter. In particular, the second WRC composed of HWR 2 and QWR 2 also functions as an effective rotator of HBF 2, which can adjust the effective angular difference between the two principal axes of HBF 1 and HBF 2. Input light incident on port 1 of the PBS is decomposed into linear horizontal polarization (LHP) and linear vertical polarization (LVP) components, which circulate through the polarization-diversity loop of the filter in the clockwise (CW) and counterclockwise (CCW) directions, respectively. If two orthogonally polarized modes propagating along the fast and slow axes of the HBF encounter with each other, having the same state of polarization (SOP) through some polarization conversion components (like wave retarders or polarizers), these orthogonal modes can interfere with the phase delay difference \(\Gamma\) resulting in a periodic interference spectrum. The periodic comb spectrum of our filter is based on this polarization interference defined by \(\Gamma=2\pi BL/\lambda\), where \(B\), \(L\), and \(\lambda\) are the HBF birefringence, HBF length, and wavelength in vacuum, respectively. Engineered selection of the AOA's of the wave retarders located before the HBF can create an additional phase difference \(\psi\), resulting in a total phase difference of \(\Gamma+\psi\). A monotonous change in \(\psi\) gives a monotonous wavelength shift in the interference comb spectrum. As can be found from Figure 1a, the LHP and LVP components emerging from ports 2 and 3 of the PBS are guided in CW and CCW directions, respectively. Here we assume the horizontal and vertical axes of the PBS as \(x\) and \(y\) axes, respectively, and the direction of light propagation as the \(z\) axis for convenience. As seen in Figure 1b, linear horizontally polarized light from port 2 of the PBS goes through a linear horizontal polarizer (i.e., \(x\)-axis polarizer), QWR 1 (with its slow axis oriented at \(\theta_{Q1}\) with respect to the \(x\) axis), HWR 1 (oriented at \(\theta_{H1}\)), HBF 1 (oriented at \(\theta_{B1}\)), HWR 2 (oriented at \(\theta_{H2}\)),  
Figure 1: (**a**) Schematic diagram of the proposed filter, (**b**) propagation paths of light circulating within the filter, and (**c**) equivalent arrangement of high birefringence fiber (HBF) segments for continuous wavelength tuning of narrowband comb spectrum. QWR 2 (oriented at \(\theta_{Q2}\)), HBF 2 (oriented at \(\theta_{B2}\)), and a linear horizontal analyzer (i.e., \(x\)-axis polarizer) in turn along the CW path. In a similar way, linear vertically polarized light from port 3 of the PBS passes through a linear vertical polarizer (i.e., \(y\)-axis polarizer), HBF 2 (\(-\theta_{B2}\) oriented), QWR 2 (\(-\theta_{Q2}\) oriented), HWR 2 (\(-\theta_{H2}\) oriented), HBF 1 (\(-\theta_{B1}\) oriented), HWR 1 (\(-\theta_{H1}\) oriented), QWR 1 (\(-\theta_{Q1}\) oriented), and a linear vertical analyzer (i.e., \(y\)-axis polarizer) in sequence along the CCW path.