## 4 Conclusions  
In summary, we proposed and experimentally demonstrated a narrowband wavelength-tunable fiber comb filter based on the PDLS with composite combination of wave retarders. The demonstrated filter is comprised of a PBS, two HBF segments of the same length, an ordered WRC of a QWR and an HWR before the first HBF segment, and an ordered WRC of an HWR and a QWR before the second HBF segment. The second HBF segment is butt-coupled to one port of the PBS so that its slow axis should be oriented at 22.5\({}^{\circ}\) with respect to the horizontal axis of the PBS. Through this butt-coupling between the second HBF segment and the PBS, one HWR for the spectrum visibility can be eliminated compared with the recent previous works [23; 24]. By comparing the narrowband transmittance function \(t_{narrow}\) with the filter transmittance \(t_{filter}\) obtained by Jones matrix formulation, we found the AOA sets of the four wave retarders, which could give additional phase shifts (\(\psi\)'s) from 0\({}^{\circ}\) to 360\({}^{\circ}\) to \(t_{narrow}\). From comb spectra calculated at the eight selected FAOA sets, which cause \(\psi\) to increase from 0\({}^{\circ}\) to 315\({}^{\circ}\) by a step of 45\({}^{\circ}\), it is confirmed that the first-order narrowband comb spectrum can be continuously tuned by properly adjusting the AOA's, which clearly indicates the continuous wavelength tunability of the proposed filter adopting composite combination of ordered wave retarders. The validity of our calculation results were examined by actually implementing the proposed filter and confirmed by appropriately choosing the AOA of each wave retarder. Then, it is concluded that our filter employing the composite combination of wave retarders can be continuously wavelength-tuned by properly controlling the AOA's of the wave retarders. Primary optical components comprising the proposed filter, including a PBS, four wave retarders, and HBF, can be implemented in an integrated form [27; 28; 29], and thus the filter can be utilized as an integrated optical communication element in fiber-optic networks. Our wavelength-tunable narrowband comb filter is anticipated to be beneficially utilized in microwave photonic signal processing, optical sensor interrogation, and multiwavelength lasing. Some points to be considered for the use of our filter in practical applications are the wavelength dependency of the wave retarders and the temperature dependence of the HBF birefringence. Achromatic wave retarders can resolve this wavelength dependency. In terms of the temperature dependence, hermetical  
Figure 6: (**a**) Variation of the peak wavelength denoted by \(\lambda_{0}\) in Figure 5, measured at the eight FAOA sets and (**b**) two superimposed plots with four narrowband transmission spectra measured at the FAOA sets I, III, V, and VII in upper plot and four narrowband transmission spectra measured at the FAOA sets II, IV, VI, and VIII in lower plot.  
-scaling or packaging of HBF segments can facilitate their temperature insensitivity, and, furthermore, a thermoelectric cooler can also be employed for stabilization of the HBF birefringence.  
Conceptualization, [PERSON] and Y.W.L.; methodology, [PERSON]; software, J.J.; validation, [PERSON] and Y.W.L.; formal analysis, [PERSON]; investigation, [PERSON]; resources, [PERSON] and [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government(MOTIE). (P0012451, The Competency Development Program for Industry Specialist).  
The authors declare no conflict of interest.