1. Introduction

Polarization-selective functionality is indispensable in a polarization diversity system, which can be achieved by the utilization of polarizers and polarization beam splitters (PBSs) [1–4]. PBS is an essential photonic device that can separately extract TE and TM polarizations from an unpolarized beam, due to the birefringence of an optical system. It has been widely utilized in optical signal processing such as demultiplexing [5], optical routing [6] and logic operations [7,8]. To date, various schemes for PBSs have been reported. PBSs based on the form-birefringent multilayer and diffraction gratings were separately proved workable by Tyan et al. [9] and Davis et al. [10], where they were of high fabrication complexity. A Mach-Zehnder interferometer (MZI) was proposed to function as a PBS with an extinction ratio (ER) around 13 dB by Liang et al [11]. Multimode interference (MMI) was also used as a PBS with an ER under 15 dB by Hong et al. [12], but the length of this structure is relatively long. In order to achieve smaller PBSs, higher birefringence is required. Photonic crystal (PhC) structures were exploited to perform ultra-compact PBSs with an ER around 20 dB, such as PhC fibers [13], the planar PhC based on anisotropy [14] and negative refractive [15,16], the PhC directional coupler (DC) [17], and the PhC-MMI [18], but the design and fabrication of a PBS based on the PhC are still relatively complex. Alternatively, the particular coupling system opens a promising way to realizing ultra-small PBSs with an ER of about 20 dB which has been put forward by Fukuda et al. [19] and Komatsu et al [20]. A series of work have been done by Dai et al. to further reduce the length of PBSs by birefringence enhancement, using the bent DC [21], the asymmetrical DC [22] and the hybrid plasmonic waveguide [23,24]. In contrast to these through-type PBSs, resonance-based PBSs were also proposed, such as the microresonator [25,26], and the PhC ring resonator [27].

However, a PBS based on an optofluidic ring resonator (OFRR) which is one kind of optical microcavity [28–32] has never been reported, which is compact and efficient, and can further reduce the fabrication and structure complexity. An OFRR integrates an optical ring resonator with microfluidics [33–35]. One particular type of the OFRR is based on microcapillaries [36,37], which consists of a fluidic channel along its axial direction and an inherent ring resonator that can support whispering gallery modes (WGMs). These promising features pave the way for designing versatile photonic devices. Thus, it has attracted intense attention due to their important applications as functional devices including sensors [38,39], lasers [40,41], biochemical analysis and detection [34,42], and research on nonlinear optics [36,37] and optomechanics [43,44].

In this paper, we propose a tunable PBS based on the OFRR by utilizing a fused silica microcapillary. As schematically illustrated in Fig. 1, both the microfiber [45] and the fiber tip are perpendicularly deposited in contact with the microcapillary, and separately act as a through port and a drop port. The fiber tip is kept an appropriate gap to the microfiber to download the circulating light via evanescent coupling. The device operation relies on the birefringence introduced by the cross section which the circulating light travels through, as shown in Fig. 2. This birefringence can be identified by the resonance scheme which provides accumulated interaction. Therefore, at a resonance wavelength, only one polarization can travel as a whispering gallery mode (WGM) within the OFRR while another not. Hence, the light with TE and TM polarizations will be extracted with the help of the microfiber and the fiber tip, respectively. Besides, since there is a fluidic channel in the OFRR, the resonance wavelength with TE and TM polarizations can be tuned by taking advantage of this structure [46,47]. Water and ethanol are pumped into the core of the silica microcapillary respectively to tune the resonance wavelength of both polarizations. Experimental results show that this OFRR-PBS is able to achieve a polarization splitting ratio as large as 30 dB, and realize a large tuning range of 7.02 nm by pumping ethanol into the core of the silica microcapillary.

 

Fig. 1 A schematic illustration of an OFRR-PBS.

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Fig. 2 The illustration of enchanced birefringence in the OFRR. T and R represent the wall thickness and the outer radius, respectively.

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2. Device fabrication and principle

The schematic illustration of the OFRR-PBS is shown in Fig. 1. It consists of a microfiber, a fiber tip, and a silica microcapillary. To fabricate the optical microfiber, a standard single-mode fiber (SMF) was drawn to a microfiber using the flame-heated technique [47,48]. By setting appropriate control parameters of the fiber tapering platform, a microfiber with a diameter of around 1 μm was obtained, which has a strong evanescent field for light coupling [45]. As to the fiber tip, it was acquired by cutting a pre-fabricated microfiber in half. A silica microcapillary with an outer diameter of about 72 μm was drawn from an initial outer diameter of 140 μm, after its polyimide coating was stripped by a hydrogen flame heating technology.

As illustrated in Fig. 2, the silica microcapillary can be regarded as a curvier slab waveguide. It is obvious that the refractive index (RI) distribution for the light is a step profile along the TM direction while that along TE orientation is homogeneous. As a result, this leads to a natural birefringence for TE polarization and TM polarization of the fundamental mode. The mode field distributions with TE and TM polarizations were numerically calculated by the finite element method (COMSOL Multiphysics). The capillary was considered as a rotationally axisymmetric dielectric resonator, and the 2-D axisymmetric simulation [49] was carried out. Figures 3 (a) and 3 (b) show the mode field distributions for the silica microcapillary resonator with the diameter of 72 µm and the wall thickness of 2 µm. According to the simulation, the natural birefringence for TE polarization and TM polarization of the fundamental mode is verified by simulation numerical calculation in a wide wavelength range, as predicted in Fig. 3(c). Meanwhile, the effective RI difference increases as the wall thickness descends, as shown in Fig. 3(d). Hence, in comparison with a solid silica cylinder, a hollow-core silica tube with a thin wall can provide a larger effective RI difference. In this work, to achieve the thinner wall, a microcapillary with a wall thickness of around 2 µm was fabricated. Moreover, to reduce the wall thickness is conducive to suppress higher-order WGMs which are not desirable in some cases.

 

Fig. 3 (a) TE mode field distribution, and (b) TM mode field distribution. The white arrows show the direction of electric fields. (c) The effective RI of two orthogonal modes as a function of the wavelength ranging from 1535 nm to 1565 nm. (d) The effective RI difference of fundamental TM mode and TE mode as a function of the wall thickness of the silica microcapillary at 1550 nm. The outer diameter of the silica microcapillary is 72 μm. The case of the thickness of 36 μm corresponds to a solid rod while that of less than 36 μm indicates a hollow-core capillary.

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After finishing fabricating the microfiber, the fiber tip and the silica microcapillary, the OFRR-PBS was assembled. The tapered silica microcapillary was deposited and fixed on to a holder made of polymethyl methacrylate (PMMA), so that it can be treated as a flexible and robust packaged device. The whole device structure is revealed in Fig. 4. The microfiber in touch with the microcapillary acted as both a WGMs launcher and a through port of the PBS. And a fiber tip parallel to the microfiber can be treated as a drop port. Because of the evanescent coupling, the resonance light can be efficiently extracted by the fiber tip. The resonance conditions for TM and TE modes of WGMs in a microcapillary are described by $2\pi R\cdot n_{eff}^{TM}=m{\lambda }_{TM}$ and $2\pi R\cdot n_{neff}^{TE}=m{\lambda }_{TE}$, respectively, where $\lambda$ is the resonance wavelength in vacuum, m is the angular number as an integer, R is the radius of the ring resonator, and $n_{eff}$ is the effective index. Hence, the resonance wavelength separation between TM mode and TE mode is derived as $\Delta \lambda ={\lambda }_{TM}\cdot \Delta n_{eff}/n_{TM}$, where $\Delta \lambda$ indicates $\left({\lambda }_{TE}-{\lambda }_{TM}\right)$ while $\Delta n_{eff}$ describes $\left(n_{eff}^{TE}-n_{eff}^{TM}\right)$. Therefore, due to the birefringence between TM mode and TE mode, at the same wavelength, only can one polarization which meet the resonance condition couple into and circulate within the ring resonator, and then is extracted by the drop port. However, another polarization which deviates from the resonance condition just directly passes through the microfiber and output from the through port.

 

Fig. 4 An optical micrograph of the OFRR-PBS.

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To verify the feasibility of the OFRR-PBS, experiments were carried out in a chamber to avoid air convection at a constant room temperature. A broadband light with chaotic polarization stems from two cascaded erbium-doped fiber amplifiers. A light beam with a certain polarization is obtained after the light passes through the in-line polarizer. A polarization controller is used to tune the polarization state of the polarized light before it is fed to the OFRR-PBS. Eventually, the transmission light from the through port and the drop port can be separately detected by an optical spectrum analyzer. In order to test the splitting ability for two orthogonal polarizations, the light is fed to the device with either TM or TE polarization by controlling the PC. Furthermore, the resonance wavelength with TM and TE polarizations can be tuned by pumping water and ethanol with the help of a syringe pump.

The precise control of the position of the microfiber and the fiber tip was performed under in situ observation using an optical microscope. During the experiment, they were fastened onto a high-precision manual positioner, and kept in touch with the silica microcapillary. It is worth emphasizing that the three-dimensional positioner is only utilized to make sure that the microfiber and the microcapillary are in alignment and it is not necessary to adjust the device again after that. Thus, the OFRR-PBS remained stable and robust. By tuning the positioner, we could find a good state that the transmission spectra of both polarizations showed relatively high ERs. It is worth mentioning that the gap between the microfiber and the fiber tip needed to be controlled to an appropriate value of around 5 μm to avoid the coupling between them and enable more power of the WGMs to couple into the fiber tip, so that the fiber tip can only fetch the light of WGMs with relatively large mode area, due to the weak confinement along the axial direction of the microcapillary. Furthermore, in order to realize the stability and wide applications, a packaged couplig scheme can be achieved [50–52].

3. Results and discussion

Figure 5(a) shows the transmission spectra out of the through port with air in the core. The dips in the spectra indicate resonance wavelengths of two orthogonal polarizations. There are three evident dips in the transmission spectra of TM polarization while only one dip in that of TE polarization within a free spectral range (FSR), and dip 1 and dip 2 denote the fundamental mode of two orthogonal polarizations respectively. Besides, the maximum ER of TE polarization is about 38 dB and the ER of TM polarization is about 20 dB. It is obvious that the resonance wavelengths of the WGMs with TM polarization differ from those with TE polarization, even if they have the same angular number. Such a resonance wavelength separation is caused by the large polarization dependence induced by the birefringence. From Fig. 5(a), the separation $\Delta \lambda$ is about 8.68 nm, which is larger than the FSR and closed to the value calculated by $\Delta \lambda ={\lambda }_{TM}\cdot \Delta n_{eff}/n_{TM}$ and the effective RI shown in Fig. 3. $\Delta \lambda$ is large enough to guarantee that fundamental modes with TM and TE polarizations cannot simultaneously form WGMs. Apart from that, there is geometric uniformity without any RI change along the axial direction of the silica microcapillary, thus spiral modes [53] which result in the ripples and slight asymmetries in the transmission spectra will be excited. In addition, there exist higher-order WGMs in the transmission spectra of TM polarization, which possess relatively large transmission and coupling loss leading to lower Q factors, because the wall is not thin enough to only support fundamental WGMs. This is predicted to be suppressed by further reducing the wall thickness. Figure 5(b) shows the resonance wavelength tuning with TE polarization as water and ethanol are pumped into the core respectively. The resonance wavelength shifts of about 3.43 nm and 4.72 nm are achieved when there is water and ethanol within the core, respectively. Besides, it can be seen that Q factor decreases a lot when the liquid is pumped into the core and the ripples also decrease in the transmission spectra, because there is large absorption loss when the evanescent field of the WGMs interacts with water and ethanol. Figure 5(c) shows the tuning of the resonance wavelength with TM polarization. When water and ethanol are pumped into the core respectively, the resonance wavelength shifts of about 5.58 nm and 7.02 nm are realized. It is worth noting that the tuning range of the resonance wavelength with TM polarization is larger than that with TE polarization. According to the total internal reflection theory, the penetration depth into the core, which is induced by the phase shift on reflection, is larger in the resonance with TM polarization [54]. Thus the sensitivity of TM polarization is larger than that of TE polarization when the RI within the core changes, which is illustrated in [55]. Based on this scheme, the TM and TE polarized light with tunable operation wavelength can be separated by the ring resonator and extracted by different output ports. In addition, when water is pumped into the core to replace air, the extinction ratio increases. It can be explained in the following way: the effective refractive index increases when water is pumped into the core, and it may induce the enhancement of the phase match condition between the microfiber and the microcapillary resonator, leading to the increase of the coupling efficiency.

 

Fig. 5 (a) The transmission spectra out of the through port with air in the core of the silica microcapillary. (b) The resonance tuning with TE polarization. (c) The resonance tuning with TM polarization.

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In order to demonstrate the availability of the drop port, the transmission spectra of both polarizations picked up by the drop port were also analyzed, as displayed in Fig. 6. Figures 6(a) and 6(b) show the transmission spectra of both polarizations picked up by the drop port when there is air in the core. Evident resonance peaks are observed from the drop port, which exactly align to the resonance dips of fundamental WGMs detected from the through port. In Fig. 6(a), there are several broad peaks between the resonance peaks aligning to the resonance dips in the transmission spectra extracted by the drop port, and it could be caused by intermodal interference in the fiber tip. From Fig. 6(b), there also exist some peaks with lower ERs within a FSR in the spectra extracted by the drop port, which exactly align to the resonance dips of the higher-order WGMs detected from the through port. The maximum polarization splitting ratio of TE and TM polarizations are about 30 dB and 13 dB, respectively, and the ERs of the transmission spectra extracted by the drop port are both up to 20 dB. This proves that both orthogonal polarizations at a certain resonance wavelength can be distinguished by the OFRR-PBS, and separated to different output ports. However, in terms of experimental results, the ER of the drop port is lower than that of the through port. It is perhaps because the coupling efficiency between the fiber tip and the microcapillary is not very high, so that just a fraction of power of WGMs is able to be coupled to the fiber tip. Also, the loss induced by scattering and the non-adiabatic fiber taper could contribute to the lower ER.

 

Fig. 6 Two orthogonal polarizations extracted by the through port and the drop port when there is (a-b) air, (c-d) water and (e-f) ethanol in the core.

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In order to take advantage of the tunability of the OFRR, water and ethanol were pumped into the core to tune the resonance wavelength with TE and TM polarizations, respectively, and were in a fixed flow rate to avoid affecting the performance of the device. Figures 6(c) and 6(d) show the transmission spectra of both polarizations picked up by the drop port as there is water in the core. It can be seen that the polarization splitting ratio of TE and TM polarizations are about 10 dB and 28 dB while the ERs of both polarizations extracted by the drop port are about 8 dB and 5 dB respectively. In Fig. 6(c), there is a relatively higher ER peak adjacent to the peak aligning to the resonance dips of fundamental WGMs detected from the through port, because higher-order modes are excited in the fiber tip when the power of the WGMs is coupled to the guided modes in the fiber tip. The ER of TM polarization is lower because coupling efficiency between the fiber tip and the microcapillary decreases when air is replaced by water within the core, which results in a smaller fraction of power of the WGMs coupled to the fiber tip. Figures 6(e) and 6(f) show the transmission spectra of both polarizations picked up by the drop port when ethanol is in the core. The polarization splitting ratio of TE and TM polarizations are about 7 dB and 8 dB respectively while the ERs extracted by the drop port are about 17 dB and 5 dB respectively. In Fig. 6(e), there are some ripples in the transmission spectra extracted by the drop port, because the higher-order modes are excited when the light is coupled to the fiber tip from the WGMs of the silica microcapillary. In addition, from Fig. 6(f), it can be deduced that the lower-ER peaks are aligned to the higher-order WGMs detected from the through port. Besides, according to Fig. 5 and Fig. 6, it can be seen that the insertion loss is larger than 10 dB, which is relatively high, because it mainly results from the inherent loss of the microcapillary resonator, the dust induced scattering loss, and the fluid absorption induced loss. However, the insertion loss can also be decreased by selecting fluid without O-H bonds like acetone, carrying out the packaging process [50–52], and optimizing the geometry of the microcapillary resonator, such as using microbubble resonators [36,37,39]. In addition, from Fig. 6 (a), the resonance with the TE polarization possesses the highest polarization splitting ratio of 30 dB, and the −3 dB bandwidth of this resonance is about 184 GHz. The PBS based on this resonance structure inherently possesses a relatively narrow operation bandwidth, and it is suitable for some situations such as narrow-band optical signal processing and wavelength demultiplexing. In these cases, this OFRR-PBS can be regarded as a combination of a narrow-band filter and a PBS. However, in some other cases, a large wavelength operation range is needed. Then the tuning of the resonance wavelength can provide an alternative solution to address this problem. Based on the tunability demonstrated in Fig. 5, the OFRR-PBS with continuous resonance tuning in a relatively large range can be realized by further parameter optimization, such as decreasing the wall thickness, appropriate selection of fluids with relatively large refractive index differences.

4. Conclusion

To summarize, we demonstrated an efficient PBS based on the OFRR and demonstrated its feasibility. Two orthogonal polarizations can be separated by the microcapillary-based OFRR that introduces the birefringence and the resonance scheme. Each polarization is extracted by tapered fibers, which is naturally compatible with the optical fiber system. The maximum polarization splitting ratio of up to 30 dB was achieved, while the maximum ER of up to 20 dB was obtained at the drop port. In order to demonstrated the tunability in principle, the maximum resonance wavelength shifts of 7.02 nm for TM polarization and 4.72 nm for TE polarization were realized, which can be used to realize the tunable PBS based on the OFRR. This device first offers an alternative way to realize an efficiently tunable PBS, and is potential for applications such as tunable optical filtering, routing, and demultiplexing.