Abstract
Here we theoretically and experimentally demonstrated the arbitrary phase modulation of a general transmittance function (GTF) of the first-order optical comb filter based on a polarization-diversity loop structure, which employed two ordered waveplate sets (OWS’s) of a quarter-wave plate (QWP) and a half-wave plate (HWP). The proposed comb filter is composed of a polarization beam splitter (PBS), two equal-length polarization-maintaining fiber (PMF) segments, and two OWS’s of a QWP and an HWP with each set located before each PMF segment. The second PMF segment is butt-coupled to one port of the PBS so that its principal axis should be 22.5° away from the horizontal axis of the PBS. First, we explained a scheme to find four waveplate orientation angles (WOA’s) allowing the phase of a GTF to be arbitrarily modulated, using the way each component of the filter, such as a waveplate or PMF segment, affects its input or output polarization. Then, with the WOA finding method, we derived WOA sets of the four waveplates, which could give arbitrary phase retardations ϕ’s from 0° to 360° to a GTF chosen here arbitrarily. Finally, we showed phase-modulated GTF’s calculated at eight selected WOA sets allowing ϕ’s to be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, and then the predicted results were verified by experimentally measured results. It is concluded from the theoretical and experimental demonstrations that the GTF of our filter based on the OWS of a QWP and an HWP can be arbitrarily phase-modulated by properly controlling the WOA’s of the four waveplates.
Highlights
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]
Before we begin to address the principle of the phase modulation of a general transmittance function (GTF), let us consider the previous conclusions on the relationship between State of Polarization (SOP) changes and the continuous wavelength tuning of a narrowband transmittance tn given by (3) in the comb filter composed of two polarization-maintaining fiber (PMF) segments, two ordered waveplate sets (OWS’s) of an half-wave plate (HWP) and a quarter-wave plate (QWP), and the third HWP. [23,24]
Linear movement of λpeak,GTF with respect to φ, displayed as red-dotted arrows, directly tells us that the continuous or the desired arbitrary phase modulation of tGTF2 can be realized. These calculation results clearly manifest that tGTF2 can be continuously wavelength-shifted within ∆λ using the WOA sets shown in Figure 4, implying the arbitrary phase modulation capability of tGTF2 within 360◦
Summary
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]. Before we begin to address the principle of the phase modulation of a GTF, let us consider the previous conclusions on the relationship between SOP changes and the continuous wavelength tuning of a narrowband transmittance tn given by (3) in the comb filter composed of two PMF segments, two OWS’s of an HWP and a QWP, and the third HWP. It can be deduced from the aforementioned conclusions of the previous works that a location change of O(λ0 ) along the SEout,GTF trace, accompanied by a shift in λpeak , is responsible for a phase modulation in the GTF, resulting in a wavelength shift in the transmission spectrum.
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