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Abstract
All-fiber polarization filters have important applications in optical communication, sensing, and fiber lasing. However, the incompatibility between high extinction ratio and short interaction length is a problem for miniaturization. In addition, current passive designs make polarization filters work in a fixed wavelength band, which limits the dynamic polarization control. Here, we integrate subwavelength metal gratings on graphene-covered D-shaped single-mode fibers to achieve tunable polarization filters, whose operating bandwidth has a significant improvement over previous works. In the simulation, the $x$-polarized mode couples effectively with the surface plasmon polariton mode and suffers extremely high transmission loss (up to ${\sim}{38}\;{\rm dB/mm}$). At the same time, the $y$-polarized mode remains low insertion loss of ${\sim}{0.58}\;{\rm dB/mm}$. By changing the chemical potential of graphene, the loss peak of the $x $-polarized mode can be adjusted in the range covering the wavelength bands from 1.272 to 1.353 µm or from 1.54 to 1.612 µm, which results in an adjustable broadband filter with a high extinction ratio over 20 dB. The proposed filter provides a promising polarization control scheme for integrated devices in the fields of communication, sensing, and lasing.
© 2023 Optica Publishing Group
1. INTRODUCTION
Polarization filters play a crucial role in the fields of optical communication, laser generation, and optical sensing. Conventional polarizers such as anisotropic absorbers and polarizing prisms cannot be miniaturized because of their large size. Therefore, polarizers that can be integrated with optical waveguides have attracted much attention [1–5]. The mechanisms of waveguide-integrated polarization filters can be summarized into two categories. One is to use the coupling effect of waveguide modes to import the unwanted polarization mode into another adjacent waveguide, so as to achieve single polarization mode transmission in the original waveguide [1,2]. The other is to adjust the interaction between the guided modes and the surrounding environment to achieve polarization-selective attenuation [3–5]. Compared with the former mode-splitting polarization filter, the lossy polarization filter can achieve a higher extinction ratio at a shorter propagation distance, which will be more beneficial to device integration.
Surface plasmon polaritons (SPPs) are electromagnetic excitations propagating at the interface between a dielectric and a conductor, evanescently confined in the perpendicular direction [6]. The characteristics of small mode volume and high polarization selectivity make SPPs suitable for creating miniaturized waveguide-integrated polarization filters. Specifically, the evanescent field of waveguide mode can excite surface plasmon resonance (SPR) and then form a forward-propagating SPP. When the phase-matching condition is met, the waveguide modes become strongly coupled with SPP modes, resulting in a significant loss of specific polarization at the resonant wavelength. This method has immense potential for creating high-performance polarization filters. For example, a metal-clad polarization filter based on a slab waveguide, which can selectively reduce the transmission of the transverse electric (TE) modes or the transverse magnetic (TM) modes [7], has been proposed. In addition, gold gratings can be deposited onto a D-shaped single-mode fiber (SMF) to generate effective coupling between core modes and SPP modes, it was utilized to achieve high-performance refractive index sensors [8,9]. Combined with SPR, lots of photonic crystal fiber (PCF) polarization filters were designed because of the inherent flexibility and birefringence of PCFs [10], such as Sierpinski–Like SPR-PCF for filters and sensing applications [11], SPR-based dual D-shaped PCF polarization filter [12], and other different types of SPR-based D-shaped PCF polarization filters [13–18]. Even though the designed PCF filters have a high polarization-dependent loss and broad filtering wavelength band, their working wavelength range remains fixed after fabrication. Additionally, the complex structure of PCFs increases the manufacturing cost of relative devices, which limits the application of SPR-PCF polarization filters.
Graphene, as a 2D material, displays a wide range of extraordinary electro-optical properties and has been widely used in optical systems [19]. In 2011, graphene was first used for broadband polarization filtering based on a D-shaped SMF [20]. To further improve the light–graphene interaction, a double D-shaped hole optical fiber coated with graphene was proposed [21]. By simulation, it was proven to achieve more efficient polarization filtering. Further, different polymer-coated D-shaped-fiber graphene polarizers were proposed to enhance the light–matter interaction and applied to ultrashort pulse lasers and optical modulators [22,23]. Although these filters are effective and have low insertion loss, the graphene-caused attenuation is limited (${\lt}\;{18}\;{\rm dB/mm}$) and requires a relatively large light–graphene interaction length for a high extinction ratio. Moreover, the design is challenging to fabricate because the performance is closely tied to the core-graphene distances and the thickness of the polymer [22]. A recent work combined the polarization-dependent losses introduced by SPP modes with the electrically adjustable properties possessed by graphene to achieve tunable refractive index sensors based on PCFs [24]. However, the loss difference between the two orthogonal polarization states is not large enough to achieve a miniaturized and efficient tunable polarization filter.
In this paper, we propose an approach by utilizing graphene to create an adjustable polarization filter. The wavelength at the SPR loss peak of the proposed filter can be adjusted by changing the chemical potential of graphene. This allows the optimum operating wavelength of the filter (which has the maximum extinction ratio) to be dynamically tuned in the C-band or O-band. A single-layer graphene is placed on the polished plane of a D-shaped SMF. Then, an array of subwavelength metal grating is deposited onto the graphene to support $x$-polarized SPP modes. A layer of CYTOP (a kind of amorphous fluoropolymer) is coated on the grating to meet the phase-matching condition. The strong mode coupling between the $x$-polarized core mode (Px core mode) and the SPP mode can cause large transmission loss (up to ${\sim}{38}\;{\rm dB/mm}$). In the meantime, the $y$-polarized core mode (Py core mode) has a low insertion loss (${\sim}{0.58}\;{\rm dB/mm}$) without the influence of SPP mode. By tuning the period of grating, the working wavelength range of the filter can be set in the O-band or C-band. Then, by changing the chemical potential of graphene, the peak of polarization-dependent loss can vary from 1.272 to 1.353 µm or from 1.54 to 1.612 µm, which makes this design a broader working wavelength band and have higher flexibility than the former works. For a 1 mm long filter, the peak extinction ratio can keep higher than 30 dB in the O-band. This design will be used in miniaturized optical systems compatible with fiber optics.
2. STRUCTURE DESIGN AND NUMERICAL SIMULATION
Figure 1 shows the structure of the proposed polarization filter. The single-mode fiber has been polished on one side with a distance ${{\rm t}_{\rm d}}$ of 1 µm between the polished plane and the core. A single-layer graphene is coated on the plane, and then a series of gold grating is deposited on it. The grating has a period ${{\rm p}_{\rm{au}}}$ of 500 nm, a width ${{\rm w}_{\rm{au}}}$ of 225 nm, a thickness ${{\rm t}_{\rm{au}}}$ of 100 nm, and a period number of 20. A layer of 3 µm thickness CYTOP is coated on the gold grating. Its refractive indexes are 1.3348 and 1.3335 at the wavelengths of 1.3 and 1.55 µm, respectively, to help achieve the phase-matching condition between SPP modes and fiber core modes. Additionally, because the SPP modes are sensitive to the refractive index [24], the polymer can avoid the influence of the environment.
Fig. 1. Cross-section view of the D-shaped SMF polarization filter. The SMF is side-polished and coated with a single layer of graphene, a set of gold grating, and a 3 µm thickness CYTOP. ${{\rm t}_{\rm d}}$ is the distance between the polished plane and the core, and ${{\rm p}_{\rm{au}}}$, ${{\rm w}_{\rm{au}}}$, and ${{\rm t}_{\rm{au}}}$ are the period, width, and thickness of the gold grating, respectively.
The proposed filter is analyzed using an eigenmode solver based on the finite element analysis software COMSOL. A perfectly matched layer (PML) is added surrounding the SMF to absorb radiant energy. The mesh size is predefined as “finer” for the main simulation region, while the PML layer and scattering boundary condition are individually designed. The SMF is simulated with a core radius of 4.1 µm, the refractive index of fused silica is modeled using the Sellmeier equation [25]
Fig. 3. Results at the chemical potential of 0.6 eV. (a) Loss spectra of $x$- and $y$-polarized core modes. (b), (c) Normalized electric field distributions of SPP and Px core modes at the uncoupled wavelength (1.22 µm) respectively. (d), (e) Electric field distributions of Px and Py core modes at the resonant wavelength (1.326 µm), respectively.
The surface conductivity of graphene can be described by the Kubo formula, which has a complex value and consists of interband and intraband conductivities [27]
3. NUMERICAL RESULTS
The proposed filter can achieve a high loss of Px core mode while maintaining a low loss of Py core mode. An example is shown in Fig. 3, with the chemical potential of graphene set at 0.6 eV. Figure 3(a) illustrates the losses of Px and Py core modes. The Px mode experiences maximum loss at the resonant wavelength of 1.326 µm, with a maximum value of up to 32.5 dB/mm. In contrast, the loss of Py mode remains around 0.58 dB/mm. To better analyze the resonance condition, Figs. 3(b)–3(e) show the normalized electric field distributions at different wavelengths. Based on the electric field analysis, it is apparent that the SPP mode is exclusively present in the $x$ polarization and couples with the Px core mode. The coupling is at its maximum at 1.326 µm, which results in a significant loss of the Px core mode. On the other hand, the Py core mode remains low loss, as it is not coupled with the SPP mode. To calculate the loss spectra, we use the imaginary part of the core mode’s effective refractive index (${{n}_{\rm{eff}}}$). The formula is shown below with wavelength in the unit of µm:
The loss spectra and dispersion relations of SPP mode and Px core mode when the chemical potential is 0.6 eV are shown in Fig. 4. Pink curves represent SPP mode while blue curves represent Px core mode. The corresponding electric fields are shown by the insets. The solid curves are loss spectra, and the dotted curves are the real part of effective refractive index (${{\rm Re}\_{n}}_{\rm{eff}}$). The loss of the Px core mode occurs due to the coupling between the SPP mode and the Px core mode. This coupling leads to energy transfer from core mode to SPP mode and eventually causes the loss of the core mode [30]. The maximum loss of the core mode happens at 1.326 µm in Fig. 4, which is known as complete coupling. To achieve complete coupling, phase matching is necessary, which requires the propagation constants of SPP mode and core mode to be equal [6]. At the same time, the losses of the Px core mode and SPP mode are also matched. At other wavelengths, incomplete coupling occurs when the phase-matching condition is not met. The inserts of electric fields in Fig. 4 illustrates the coupling of two modes.
Fig. 4. Loss spectra, dispersion relation, and electric mode field distributions of SPP and Px core modes at 0.6 eV chemical potential.
Fig. 5. Results with the period of gold grating ${{\rm p}_{\rm{au}}} = {500}\;{\rm nm}$ and chemical potential changes from 0.5 to 1 eV. (a) Loss spectrum of Px and Py core modes. (b) The real part of the effective refractive index of Px core mode and SPP mode. (c) Extinction ratio and resonant wavelength versus chemical potential.
The filter can achieve high attenuation of the Px core mode while maintaining a low transmission loss of the Py core mode because the SPP mode only couples with the Px core mode. By adjusting the chemical potential of the graphene, the resonant wavelength can be changed, resulting in a tunable $y$-polarization-pass filter. Through simulation, it has been demonstrated that the loss caused by the SPP mode of the proposed filter is almost unaffected by changing the chemical potential from 0.5 to 1 eV. Figures 5(a) and 5(b) show the loss spectra and the dispersion relations at different chemical potentials. Figure 5(c) shows the extinction ratio and resonant wavelength versus chemical potential. Extinction ratio (ER) represents the output power ratio of the desired polarization state to the unwanted polarization state obtained at the receiving end [18,31]. It is also known as crosstalk in related works [1,30,32]. Here, the ER between the $x$- and $y$-polarized modes is expressed as
The filter can operate within the C-band wavelength range by adjusting the period of the gold grating to 440 µm. Meanwhile, the number of periods is increased to 30 for enough light–matter interaction area. The results are displayed in Fig. 6, which presents the loss spectra and dispersion relations at varying chemical potentials between 0.6 and 1 eV. It is evident from the figures that the coupling of SPP mode and Px core mode continues to exist, with the ${{\rm Re}\_{n}}_{\rm{eff}}$ of SPP mode matching that of the Px core mode. The Px core mode has a high loss, while the Py core mode remains at low insertion loss. The resonant wavelength and extinction ratio versus wavelength are shown in Fig. 6(c). The resonant wavelength ranges from 1.54 to 1.612 µm, and the extinction ratio remains greater than 20 dB.
Taking the O-band design as an example, we show the extinction ratio at different lengths of fiber under different chemical potentials in Fig. 7. The wavelengths with extinction ratio greater than 20 dB are defined as the operating wavelengths of the filter. Based on the tunable characteristics of the designed device, its operating bandwidth is represented by the maximum operating wavelength at a chemical potential of 0.5 eV minus the minimum operating wavelength at a chemical potential of 1 eV. The highest extinction ratio reaches 37.4, 74.9, and 112.3 dB, and corresponding bandwidths are 125, 192, and 236 nm, when the lengths are 1, 2, and 3 mm, respectively. Our design uses a 1 mm length, which provides enough bandwidth to cover the entire O-band wavelength and has a low insertion loss of ${\sim}{0.6}\;{\rm dB}$ for $y$-polarized light. To consider the D-shaped fiber’s polished depth and fabrication difficulty, Table 1 shows the results with core-graphene distance settings at 0.5, 1, and 1.5 µm. The loss of Px core mode remains consistently high, at over 20 dB/mm, with the highest loss occurring at 1 µm. On the other hand, the loss of Py core mode does not exceed 1 dB/mm and decreases as the core-graphene distance increases. The resonant wavelength undergoes only a small fluctuation with the change in distance. In conclusion, the performance of the filter is insensitive to changes in core-graphene distances, reducing the complexity of its fabrication.
We have compared the performance of the proposed polarization filter with that of other existing works, as shown in Table 2. The method of waveguide mode coupling can realize polarization filtering in the 1310 and 1550 nm bands simultaneously with a single device [1,2]. However, this method requires a long coupling distance and is difficult to achieve miniaturization. A groundbreaking work using graphene to achieve broadband polarization filtering was reported in 2011 [20]. When using a relatively short length of fiber, polarization filtering with a bandwidth greater than 100 nm can be realized in the near-infrared band. However, the insertion loss is large, which is not conducive to achieving a high extinction ratio. For the SPR-assisted lossy filtering method, a higher extinction ratio can be achieved over a shorter transmission distance [15,32]. For example, a 1 mm long bimetal-coated PCF fiber can achieve an extinction ratio of 53.2 dB at 1310 wavelengths [32]. However, nonadjustable features limit its operating bandwidth. An electrically adjustable polarization filter by injecting liquid crystals into PCF was reported in 2016 [33], which achieves a high extinction ratio (${\sim}{44.52}\;{\rm dB}$) at 1550 wavelengths; however, the liquid crystal orientation angle has a small modulation range for resonant wavelengths. Our work combines graphene with metal gratings to enable a wide range of electrical regulation of resonant wavelengths while achieving a high extinction ratio, thus enabling a miniaturized polarization filter in the O-band or C-band.
Fig. 6. Results with the period of gold grating ${{\rm p}_{\rm{au}}} = {440}\;{\rm nm}$ and with chemical potential changes from 0.6 to 1 eV. (a) Loss spectrum of Px and Py core modes. (b) Real part of the effective refractive index of Px core mode and SPP mode. (c) Extinction ratio and resonant wavelength versus chemical potential.
Fig. 7. Extinction ratio versus wavelength of different lengths, at 0.5 and 1 eV chemical potentials.
Table 1. Results of Chemical ${\rm Potential} = {1}\;{\rm eV}$ at Different Core-Graphene Distances
The fabrication of the proposed polarization filter consists of three main steps. First, a standard SMF is fixed in a groove with a depth of ${\sim}{68}\;\unicode{x00B5}{\rm m}$, and the protruding part of fiber is polished off to form a D-shaped fiber. The roughness of the polished section can reach 1 nm [23]. Second, single-layer graphene can grow on copper foil by chemical vapor deposition process. Then, the gold grating can be fabricated on the graphene using electron beam lithography and electron beam deposition systems. Next, a layer of CYTOP is deposited on top of the graphene and gold grating. After that, the graphene and gold grating can be transferred to the D-shaped fiber following the process in [23]. Third, metal electrodes need to be integrated on the D-shaped fiber to achieve the electrical adjustability of the graphene chemical potential [34]. The fabrication and measurement of the designed polarization filter will be carried out in the future.
4. CONCLUSION
In this work, we propose a high-performance graphene-assisted tunable D-shaped SMF polarization filter that can be adjusted to cover a broad wavelength band. The D-shaped fiber is coated with single-layer graphene and a series of gold gratings. By tuning the chemical potential of graphene, the filter can cover the O-band communication wavelength from 1.272 to 1.353 µm as well as the C-band communication wavelength from 1.54 to 1.612 µm. The gold gratings can support strong SPR. Using the phase-matching condition, the coupling of SPP mode and $x$-polarized fundamental core mode causes an ultrahigh loss of $x$-polarized light up to 35 dB/mm, and the $y$-polarized light remains low loss. With 1 mm length, the extinction ratio of the proposed filter remains larger than 20 dB, while the insertion loss remains at ${\sim}{0.6}\;{\rm dB}$ at the O-band and ${\sim}{1.2}\;{\rm dB}$ at the C-band. The achievable bandwidth at the O-band is 125 nm. Further, numerical results verify that the core-graphene distance has little influence on the performance of the filter, and the single-mode fiber is easier to be obtained than other complex-designed PCF filters, which largely reduces the fabrication difficulty. The proposed design can realize the tunable polarization filtering with high extinction ratio and large bandwidth, which will have a wide application prospect in the fields of communication, sensing, and lasing.
Table 2. Performance Comparison with Other Existing Works
Funding
Natural Science Foundation of Shenzhen Municipality (JCYJ20200109142010888); Hong Kong Research Grants Council (15209321); Innovation and Technology Fund (ITS/107/21FP).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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