## 1 Introduction  
To date, optical comb filters have provided versatile spectrum controllability in the fields of interrogation of optical fiber sensors, wavelength routing in optical communications, and photonic processing of microwave signals [1; 2; 3; 4; 5]. In these comb filters, the capability of continuous wavelength tuning is a crucial function to pass desired spectral components or reject unwanted ones in optical signal processing. By utilizing a Mach-Zehnder interferometer structure [6; 7], Sagnac birefringence loop structure [8; 9], Lyot-type birefringence loop structure [10; 11], and polarization-diversified loop structure (PDLS) [12; 13; 14; 15; 16], much effort has been exerted in implementing this continuous tunability of the absolute wavelength in comb filters. Among these filter configurations, optical comb filters based on a PDLS have superior flexibility in the wavelength switching or tuning of their output spectra [12; 13; 14; 15; 16; 17; 18; 19; 20]. Since 2017, successive works have been done to realize the continuous wavelength tuning of periodic transmission spectra in PDLS-based fiber comb filters [21; 22; 23; 24; 25]. A continuously wavelength-tunable PDLS-based zeroth-order comb filter containing one polarization-maintaining fiber (PMF) segment as a birefringent element (BE) was reported by employing three ordered waveplate sets (OWS's): an OWS of a half-wave plate (HWP) and a quarter-wave plate (QWP), another OWS of a QWP and an HWP, and two QWPs [21]. Apart from the zeroth-order comb filters, there have been several works reporting the implementation of the continuous wavelength tuning of flat-top [22; 23], narrow [23; 24], and arbitrary-shaped [25] passband transmission spectra, which could be obtained in a PDLS-based first-order comb filter having two PMF segments. In these previous studies on the first-order comb filters [22; 23; 24; 25], only the OWS of an HWP and a QWP was adopted and placed before each PMF segment to continuously modulate the extra phase delay \(\phi\) in the filter transmittance function. Another OWS of a QWP and an HWP may also be a candidate to achieve the \(\phi\) modulation. To the best of our knowledge, the flexible wavelength tuning of arbitrary-shaped passband transmission spectra, that is, general transmittance functions (GTF's) in addition to some special transmittance functions such as transmittance functions with flattened and narrowed passbands, was not achieved by using an OWS of a QWP and an HWP. Arbitrary phase modulation of the GTF of the first-order comb filter leading to its flexible wavelength tuning should not be underestimated but rather rigorously explored, because application-specific spectral shapes are demanded in some spectral flattening filters and label erasers and their wavelength tuning capability can provide great efficiency to related optical systems. In particular, the new OWS will bring completely different sets of waveplate orientation angles (WOA's) where the phase \(\phi\) of the filter transmittance function can be arbitrarily modulated. On top of that, the conventional scheme utilized to obtain WOA's theoretically in order to enable continuously tuning the filter wavelength [22; 23; 24], based on direct comparison between the filter transmittance function and the known analytic transmittance effortlessly found in literatures, is not suitable for finding theoretical WOA's for continuous frequency tuning of the GTF, because the exact mathematical expression of a desired GTF needed for specific applications is often difficult to seek. Here, we theoretically and experimentally demonstrated the arbitrary phase modulation of a GTF of the PDLS-based first-order fiber comb filter employing two OWS's of a QWP and an HWP. The proposed comb filter consists of a polarization beam splitter (PBS), two polarization-maintaining fiber (PMF) segments of equal length, and two OWS's of a QWP and an HWP with each OWS positioned before each PMF segment.