## 1 Introduction  
Up to the present, much attention has been given to fiber comb filters, which manipulate optical signals routed in optical systems, due to their structural simplicity, good fiber compatibility, and great facility to fabricate. They have been utilized for the implementation of optical pulse train generation [1], multiwavelength switching or lasing [2; 3; 4; 5], optical label switching [6; 7], and microwave signal processing [8; 9; 10]. Flexible adjustment of the wavelength (or frequency) location of the transmission bands of a comb filter is a crucial function to pass or reject the desired wavelength component in wavelength-division-multiplexing-based optical communication systems. While continuous wavelength tunability has been realized in numerous comb filters based on a Sagnac birefringence loop [11; 12], a Lyot-type birefringence interferometer [13; 14], and a Mach-Zehnder interferometer (MZI) [15; 16], a comb filter incorporating a polarization-diversity loop structure (PDLS) [17; 18; 19; 20] offers the most effective and diverse wavelength controllability (including wavelength switching and tuning) in comparison with conventional comb filters. PDLS-based comb filters are also more robust to external physical perturbations, such as ambient temperature and pressure changes, than MZI-based comb filters [15; 16]. Over the last three years, several studies have been conducted for realization of continuous wavelength tunability in periodic comb spectra of PDLS-based fiber comb filters [21; 22; 23; 24]. A continuously wavelength-tunable PDLS-based zeroth-order comb filter employing one birefringent component, i.e., a high-birefringence fiber (HBF) segment, was proposed by using three ordered wave retarder combinations (WRC's): Two quarter-wave retarders (QWR's), an ordered WRC of a QWR and a half-wave retarder (HWR), and another ordered WRC of an HWR and a QWR [21]. In addition to the zeroth-order comb filters, there have been series of reports on the continuous control of the wavelength location of passband-flattened and -narrowed transmission spectra, which could be obtained in a PDLS-based first-order comb filter with two HBF segments [22; 23; 24]. In terms of these first-order wavelength-tunable comb filters, an ordered WRC of an HWR and a QWR was positioned before each of two HBF segments. By controlling the azimuth orientation angles (AOA's) of the wave retarders comprising the above comb filters, an incremental phase delay (\(\psi\)) of 0\({}^{\circ}\)-360\({}^{\circ}\) can be introduced into the transmittance function of each filter. In these previous works on the first-order comb filters [22; 23; 24], only the ordered WRC of an HWR and a QWR was employed and placed before each HBF segment for implementation of the continuous modulation of the extra phase delay \(\psi\) in the filter transmittance function. Another ordered WRC of a QWR and an HWR may also be a candidate to achieve the continuous \(\psi\) modulation. To the best of our knowledge, the continuous wavelength tuning of passband-narrowed transmission spectra was not accomplished by using an ordered WRC of a QWR and an HWR in the PDLS-based first-order comb filter. The introduction of the new ordered WRC will lead to completely different AOA sets of the wave retarders, required for the continuous frequency tuning of the filter spectrum. In particular, recent previous works failed to implement the continuous wavelength tuning of passband-narrowed transmission spectra [22] or utilized an additional HWR to increase the visibility of passband-narrowed transmission spectra leading to the use of five wave retarders for the desired wavelength-tuning operation [23; 24]. Here, we theoretically and experimentally demonstrate a narrowband fiber comb filter capable of continuously tuning its wavelength position with a composite combination of wave retarders in the PDLS.