## 5 Experimental Verification of Phase-Modulated Spectra  
In order to verify the predicted phase modulation capability of \(t_{GTF2}\) through experiments, our filter was manufactured with a fiber-pigtailed PBS (OZ Optics) with four ports, two fiber-pigtailed QWPs (OZ Optics), two fiber-pigtailed HWPs (OZ Optics), and two -7.12 m-long segments of bow-tie PMF (Fibercore) with a birefringence of \(\sim\)4.166 \(\times\) 10\({}^{-4}\), as shown in Figure 1a. Figure 6 shows an actual experimental setup for measuring the transmission spectrum of the constructed filter. As shown in Figure 6, we employed a broadband light source (BLS, Fiberlabs FL7701) covering S, C, and L bands and an optical spectrum analyzer (OSA, Yokogawa AQ6370C) to monitor the transmission spectra of the constructed filter. The input and output ports (ports 1 and 4) of the filter were connected to the BLS and OSA, respectively, with optical fiber patchcords (FC/PC type). For acquisition of high resolution and contrast optical spectra, we set the sensitivity and resolution bandwidth of the OSA as HIGH1 and 0.05 nm, respectively. To avoid unwanted position changes of all the optical components comprising the filter, we taped them up on the optical table so that they were immobilized during the spectrum measurement. The transmission spectra of the GTF \(t_{GTF2}\), shown in Figure 7, were measured at the eight WOA sets (Sets I\({}_{\rm GTF2}\)-VIII\({}_{\rm GTF2}\)) in a wavelength range of 1548-1552 nm. From the measured spectra, the FSR of the constructed filter was evaluated as \(\sim\)0.8 nm around 1550 nm. This FSR is determined by \(L\) (\(\sim\)7.12 m) and \(B\) (\(\sim\)4.166 \(\times\) 10\({}^{-4}\)) of PMF used here and increases with wavelength. As confirmed from the theoretical spectra in Figure 5, while the WOA set is switched from Set I\({}_{\rm GTF2}\) (\(\phi\) = 0\({}^{\circ}\)) to Set VIII\({}_{\rm GTF2}\) (\(\phi\) = 315\({}^{\circ}\)), the comb spectrum of deformed narrow passbands, which seems to be analogous to the comb spectrum shown in Figure 5, shifts towards a longer wavelength region step by step by \(\sim\)0.1 nm, resulting in a total wavelength displacement of \(\sim\)0.7 nm. The inset shows the variation of \(\lambda_{peak,GTF}\) (indicated as a red-dotted arrow) according to relative values of \(\phi\), i.e., 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\), and 315\({}^{\circ}\), which are obtained at Sets I\({}_{\rm GTF2}\), II\({}_{\rm GTF2}\), III\({}_{\rm GTF2}\), IV\({}_{\rm GTF2}\), V\({}_{\rm GTF2}\), VI\({}_{\rm GTF2}\), VII\({}_{\rm GTF2}\), and VIII\({}_{\rm GTF2}\), respectively. Blue squares designated as I\({}_{\rm GTF2}\)-VIII\({}_{\rm GTF2}\) indicate the \(\lambda_{peak,GTF}\) positions of transmission spectra obtained at eight Sets I\({}_{\rm GTF2}\)-VIII\({}_{\rm GTF2}\). It can be figured out from the inset that  
Figure 5: Calculated phase-modulated transmission spectra of GTF (\(t_{GTF2}\)), obtained at eight WOA sets (Sets I\({}_{\rm GTF2}\)–VIII\({}_{\rm GTF2}\)) where \(\phi\) of \(t_{GTF2}\) is chosen as 0\({}^{\circ}\) to 315\({}^{\circ}\) with an increment of 45\({}^{\circ}\). \(\lambda_{peak,GTF}\) very linearly increases with \(\phi\) showing an adjusted \(R^{2}\) value of \(\sim\)0.99946 and the tuning of the spectrum wavelength can be mediated by the phase modulation. In particular, through additional experiments, continuous frequency tuning capability was confirmed with respect to numerous \(\phi\) values arbitrarily selected from 0\({}^{\circ}\) to 360\({}^{\circ}\) except integer multiples of 45\({}^{\circ}\) as well.