Utilizing polarization-selective mode shaping by chalcogenide thin film to enhance the performance of graphene-based integrated optical devices

High refractive index (RI) thin films are capable of pulling waveguide mode profiles towards themselves. In this study, it is shown that by applying high RI coatings with specific thicknesses on the side of optical waveguides, significantly different mode profiles for orthogonal polarizations can be achieved. This phenomenon, that we call it polarization-selective mode shaping, can be extensively used in the enhancement of polarization-dependent integrated optical devices. As an illustrating application, a tri-layer structure consisting of poly(methyl methacrylate)/graphene/chalcogenide on a side-polished fiber is designed to realize an extremely high extinction ratio polarizer. This structure changes the mode profiles in a way that the attenuation of TE mode is maximized, while the power carried by the TM mode remains relatively constant. Simulations and experimental characterizations confirm that polarization-selective mode shaping coordinates four loss mechanisms to maximize the extinction ratio and minimize the insertion loss of the polarizer. The fabricated polarizer is examined in the O, C, and L telecommunication frequency bands. This configuration achieves the high extinction ratio of 51.3 dB and its maximum insertion loss in the tested wavelengths is 1.79 dB. The proposed polarizer has been compared with other state-of-the-art polarizers in the conclusion section which shows its superiority.

Substituting equation 2 into equation 1 leads to the following equations: In the slab waveguide of Figure S1 the fields are independent of y coordinate. Then, two sets of independent equations are obtained.
The first set describes TE modes and the latter describes TM modes. Therefore, TE mode must satisfy ∂ 2 E y ∂z 2 + (k 2 n 2 − β 2 )E y = 0 According to Maxwell's boundary conditions E y and H x components of the fields must be continuous at the boundaries. Also, TM mode must satisfy where, H y and E x should be continuous at the boundaries. 1 For TE mode E y in layers 1-5 we will be Also for TM mode H y in different layers will be where achieved. In these calculations the refractive index (RI) of the core, cladding, and As 2 S 3 are considered to be 1.4711, 1.4660, and 2.43, respectively. The dimensions of these layers are determined in Figure S1. Figure S2 shows that formation of different mode profiles for different polarizations is a direct consequence of Maxwell's equations and by adjusting the thickness of layers, polarization selective mode shaping can be achieved.

Polarization Selective Mode Shaping with Different Coatings
Polarization selective mode shaping can be achieved with different high RI materials such as PMMA, Silicon, chalcogenide and so on. For example, Figure S3 shows mode profiles for side polished fiber with different coatings. The thicknesses are approximately at the optimum value. It means that by increasing coatings thicknesses by a small amount (fewer than 5 nm for PMMA and fewer than 1 nm for As 2 S 3 and Silicon) the structure becomes multimode. This simulation shows that PMMA alone is not strong enough to produce significantly Figure S 3: TE and TM mode profiles for different coatings on the SPF, just before the structure becomes multi-mode. different mode profiles. It also can be observe that, the interaction at the boundary is lower with silicon coating than chalcogenide. Since it is hard to control chalcogenide thickness in the optimum value, a combination of PMMA and chalcogenide layers is used to fabricate the polarizer.

Liquid Drop Test
The polished depth is required to be determined for the optimization of the coating thicknesses. This parameter was approximated by using the liquid drop experiment. In this experiment, different liquids with refractive indices were poured around the bare SPF and the corresponding transmitted powers were measured. To calculate the polished depth, these data were fitted to the expected transmitted power (e −αlp ). Where, l p is the polished length of the fiber and α is the extinction coefficient, which can be calculated by Leminger and Zengerle formula, 2,3 which describes the attenuation of the light in SPFs. In this formula, n cl , k 0 , β 0 , a, V, w, u  The fitting determines the polished depth to be about 5.2 ± 0.2 µm. However, the quality of fitting was not satisfying, and this value was not determined accurately. Therefore, care should be taken in choosing coating thicknesses so that this error can be compensated later in the experiment. The using of PMMA overlay enables the thickness adjustment of this layer throughout the experiment. To adjust the thickness of PMMA layer accurately, the extinction ratio (ER) of the fabricated GILFP was monitored and it was used as a feedback for determining optimum PMMA thickness. To increase this thickness by one step, the GILFP was spin coated by 2% PMMA in anisole solution at the speed of 4000 rpm.
To reduce the PMMA thickness, the GILFP was fixed with the slope of 30 o and, a drop of anisole was dropped on it. After each step, the GILFP was left for one hour for the anisole to be vaporized, then the ER was measured. By following this procedure, the optimum PMMA thickness was achieved.

TM-Pass Confirmation Test
To determine which polarization passes through the polarizer, the fiber was detached from the slide and then it was cleaved from a point 2 cm away from the polished section of the GILFP. Then, it was fixed again to the microscope slide. The transmitted power from the cleaved end was parallelized by a lens and passed through a free-space polarizer (FSP) and the transmitted powers at different FSP orientations were measured by a free-space power meter (FSPM). Due to the short length of the fiber after the polished section, the polarization rotation in the fiber is virtually eliminated, and it is expected to measure the maximum transmitted power when the transmission if the FSP is perpendicular to the polished surface of the GILFP (TM polarization). The results of this test is presented in Figure 5a, and the angles in this graph is the angle of the FSP transmission axis relative to the microscope slide surface. The maximum power is observed at 55 o .
In the cleaving procedure the fiber was rotated relative to the slide, and its polished surface was no longer parallel with the slide. To determine the angle between these two surfaces, SEM image of the GILFP without any tilt was acquired (Figure 5b). The image confirms the rotation of the fiber relative to the slide. The width of the polished surface in this image was measured through the SEM image to be 66 µm. This value is the projected width of polished surface to a plane parallel to the slide surface. Considering the polished depth of 5.2 µm the real polished surface width would be 124.5 µm. Therefore, the fiber's rotation angle is calculated to be θ = ArcCos(66/124.5) = 58 deg, which is approximately equal to the value obtained for the angle at which the maximum power is transmitted.