Continuously wavelength-tuneable general transmittance function in first-order fibre multiwavelength filter based on composite combination of wave retarders

The wavelength tunability of a general transmittance function (GTF) is investigated in a first-order fibre multiwavelength filter based on a polarisation-diversified fibre loop, which utilised a composite combination of wave retarders. The filter consists of a polarisation beam splitter, two equal-length high birefringence fibre (HBF) segments, and two different sets of wave retarders with each set positioned before each HBF segment. Specifically, a combination of a set of dual quarter-wave retarders (QWRs) and another set of a QWR and a half-wave retarder is focused upon. By considering the effect of the four wave retarders and two HBF segments on the output polarisation state (OPS) of each element in the filter, the four wave retarder angles (WRAs) are identified that caused all polarisation states on the OPS trace of the second HBF move in the direction of wavelength decrease, resulting in a redshift of the GTF. 360 WRA sets are derived that enabled tuning the GTF by one free spectral range S_R. For eight sets chosen from the WRA sets, inducing a wavelength shift of S_R/8 for each set order, wavelength-shifted spectra are calculated. Finally, this theoretical prediction is experimentally verified, confirming the wavelength tunability of the GTF of the filter.