Source: http://aoot.osa.org/ome/abstract.cfm?uri=ome-9-3-1015
Timestamp: 2019-04-22 00:41:59+00:00

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In this paper, the implementation of optical elements in the form of Pancharatnam-Berry optics is considered. With respect to 3D bulk and diffractive optics, acting on the dynamic phase of light, Pancharatnam-Berry optical elements transfer a phase that is geometric in nature by locally manipulating the polarization state of the incident beam. They can be realized as space-variant sub-wavelengths gratings that behave like inhomogeneous form-birefringent materials. We present a comprehensive work of simulation, realization, and optical characterization at the telecom wavelength of 1310 nm of the constitutive linear grating cell, whose fabrication has been finely tuned to get a π-phase delay and obtain a maximum in the diffraction efficiency. The optical design in the infrared region allows the use of silicon as candidate material due to its transparency. In order to demonstrate the possibility of assembling the single grating cells for generating more complex phase patterns, the implementation of two Pancharatnam-Berry optical elements is considered: a blazed grating and an optical vortices demultiplexer.
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Fig. 1 Comparison between a diffractive optical element (DOE) on the left and a Pancharatnam-Berry optical element (PBOE) on the right, in the case of 8 phase levels. It is possible to infer the higher flatness and ease of fabrication of 2D with respect to 3D optics.
Fig. 2 TM polarization (in red) has the electric field parallel to the grating vector, whose modulus is given by K = 2π/Λ. The orthogonal TE polarization (in blue) has the electric field parallel to the grating ridges. A qualitative comparison between wavelength and period of the grating is shown, which allows treating the grating as an effective form-birefringent material.
Fig. 3 (a) Comparison of effective indices for TE (blue) and TM (red) polarizations calculated with different numerical methods: zero-order effective medium theory (EMT0), second-order effective medium theory (EMT2), rigorous coupled-wave analysis (RCWA). Incident wavelength 1310 nm and different grating periods from 100 to 350 nm, step 50 nm, were considered at normal incidence. (b) Grating thickness providing π-delay between TE and TM polarizations as a function of the duty-cycle for different grating periods. (c) Optimal configurations of duty-cycle and period providing π-retardation for varying grating thickness from 510 to 560 nm, step 10 nm. (d) Optimal configurations of duty-cycle and period providing π-retardation for fixed grating thickness 540 nm, input wavelength in the telecom O-band from 1260 to 1360 nm, step 10 nm.
Fig. 4 SEM images of a sample at the beginning and at the end of the fabrication process. On the left, it is possible to appreciate the homogeneity of the grating on a wide scale. On the right, detail of the final sample at the end of the pattern transfer process.
Fig. 5 Experimental data of the introduced phase delay as a function of the grating depth. Inset graph: zoom around nearly-optimized Pancharatnam-Berry samples (data shown in Table 1).
Fig. 6 Experimental setup employed to analyze the state of polarization exiting the sample in the transmission analysis measurements.
Fig. 7 (a) Experimental transmission dependence as a function of the analyzer angle for samples fabricated with different etching times, i.e. different grating thickness, fitted by means of Eq. (8). (b) Zoom for the nearly-optimized samples.
Fig. 8 SEM images of the sample labeled PBBG1 (PBBG stands for Pancharatnam-Berry blazed grating). On the left, it is possible to appreciate a wide view of pattern homogeneity and its partition in pixels of different orientation. On the right, the attention is focused on single pixels.
Fig. 9 Scatterometry graphs of samples PBBG1, PBBG2 and PBBG3 illuminated with both left-handed (LH) and right-handed (RH) circular polarization, measured for co-polarized (LH-LH, RH-RH) and cross-polarized output (LH-RH, RH-LH). The three samples have been fabricated with different depths: 493 nm (PBBG1), 542 nm (PBBG2), 582 nm (PBBG3).
Fig. 10 Scheme of the Pancharatnam-Berry optics working principle for OAM-beam sorting with the method of optical beam projection. When a circularly-polarized OAM beam illuminates the optical element, a bright spot appears in the far-field, at a position depending on the carried OAM and on the polarization handedness.
Fig. 11 (a) Numerical phase pattern for the sorting of OAM beams in the range from −3 to + 3. 16 phase levels. Pixel size: 6.125 μm × 6.125 μm. Radius size: 256 pixels. (b) Far-field channel constellation for the given OAM set and circular polarization states.
Fig. 12 SEM inspections of the fabricated PB demultiplexer on silicon substrate. Grating period Λ = 290 nm, duty-cycle 0.5, thickness 535 nm, pixel size 6.125 μm.16 rotation angles.
Fig. 13 Interference patterns of the OAM beams from −3 to + 3 exploited for the sorter characterization. The number and handedness of the spirals denotes the carried OAM. Opposite-handedness far-fields for input right-handed and left-handed circular polarization states. As expected, the bright spot positions are in accordance with the theoretical channel constellation in Fig. 11(b).
Table 1 Phase delay of Pancharatnam-Berry cell (PBC#) samples characterized via ellipsometry (PBC1-PBC5) or transmission analysis (PBC6-PBC8). Comparison between experimental results (δexp) and numerical estimations (δth) calculated with RCWA, assuming the tabulated values of period, duty-cycle and depth.
Phase delay of Pancharatnam-Berry cell (PBC#) samples characterized via ellipsometry (PBC1-PBC5) or transmission analysis (PBC6-PBC8). Comparison between experimental results (δexp) and numerical estimations (δth) calculated with RCWA, assuming the tabulated values of period, duty-cycle and depth.

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