Waveguide metacouplers for in-plane polarimetry
Abstract: The state of polarization (SOP) is an inherent property of the vectorial nature of light and a crucial parameter in a wide range of remote sensing applications. Nevertheless, the SOP is rather cumbersome to probe experimentally, as conventional detectors only respond to the intensity of the light, hence loosing the phase information between orthogonal vector components. In this work, we propose a new type of polarimeter that is compact and well-suited for in-plane optical circuitry, while allowing for immediate determination of the SOP through simultaneous retrieval of the associated Stokes parameters. The polarimeter is based on plasmonic phase-gradient birefringent metasurfaces that facilitate normal incident light to launch in-plane photonic waveguide modes propagating in six predefined directions with the coupling efficiencies providing a direct measure of the incident SOP. The functionality and accuracy of the polarimeter, which essentially is an all-polarization sensitive waveguide metacoupler, is confirmed through full-wave simulations at the operation wavelength of 1.55$\mu$m.
Summary (2 min read)
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- The SOP evaluation is typically based on the determination of the so-called Stokes parameters, which are constructed from six intensity measurements with properly arranged polarizers placed in front of the detector, thereby allowing one to uniquely retrieve the SOP .
- Also, the authors note that additional realizations of polarimeters do exist, like using advanced micropolarizers in front of an imaging detector, but those approaches are typically complex and expensive .
- Particularly, the last application inspires us to suggest a type of compact metasurface-based polarimeter that couples incident light into in-plane waveguide modes, with the relative efficiency of excitation between predefined propagation directions being directly related to the SOP.
II. STOKES PARAMETERS
- Before the authors begin discussing the realization of the in-plane polarimeter, it is appropriate to quickly review the connection between the polarization of a plane wave, described by the conventional Jones vector, and the Stokes parameters that are typically measured in experiments.
- The latter parameter is, in contrast, inherently difficult to probe experimentally, which owes to the fact that conventional detectors respond to the intensity of the impinging wave (i.e., I ∝ A2x þ A2y), hence losing information of the crucial phase relation between the two orthogonal components.
- Þðx̂þ iŷ; x̂ − iŷÞ, where the latter two bases correspond to a rotation of the Cartesian coordinate system (x̂, ŷ) by 45° with respect to the x axis and the basis for circularly polarized light, respectively.
- Moreover, and in line with the previous work in Ref. , the metacoupler consists of three metasurfaces that launch the waveguide modes in different directions for the orthogonal sets of polarizations ðjxi; jyiÞ, ðjai; jbiÞ, and ðjri; jliÞ, respectively.
III. DESIGN OF WAVEGUIDE METACOUPLERS
- The waveguide configuration considered here consists of an optically thick gold film overlaid by a 70-nmthick SiO2 (silicon dioxide) layer and a PMMA [poly ] layer [see Fig. 1(a)].
- Figures 1(c) and 1(d) show the numerically calculated effective indexes and propagation lengths of waveguide modes supported by the configuration as a function of the PMMA thickness at the telecommunication wavelength of λ ¼ 1550 nm.
- The linear phase gradient of the metacouplers is in this work achieved by incorporating three unit cells within each grating period, with adjacent unit cells featuring a difference in reflection phase of 120°.
- A top view of the supercell is displayed in Fig. 3(a), where the nanobricks are arranged in such a way that xðyÞ-polarized incident light experiences a phase gradient in the yðxÞ direction, thus ensuring unidirectional excitation of the TE1 mode.
- This fact is evidenced in Figs. 3(e) and 3(f), where approximately 26% of the incident power is coupled to the TE1 mode in the desired direction, hence verifying the unidirectional and birefringent response of this waveguide metacoupler.
IV. PERFORMANCE OF THE IN-PLANE POLARIMETER
- The previous section outlines the design of three waveguide metacouplers that each launch the TE1 modes traveling primarily along two directions, with the maximum contrast occurring for the polarization states ðjxi; jyiÞ, ðjai; jbiÞ, and ðjri; jliÞ, respectively.
- The exact size of the waveguide metacoupler is not a critical parameter, but in order to avoid too-divergent TE1 beams the authors ensure that each side of the hexagon is considerably larger than the wavelength.
- The authors emphasize that, unlike related work , there is no mathematical equivalence between D1–D3 and s1=s0–s3=s0, nor is it even possible to find a linear relation (i.e., device matrix) between those quantities that is valid for all SOPs.
- The authors note that these small errors, 064015-6 corresponding to determining the Stokes parameters with an accuracy of six decimals, are obtained using the numerically calculated coupling efficiencies with full precision [i.e., not the rounded-off data presented in Table I and Eq. (7)], thereby highlighting the perfect linear relationship between coupling efficiencies and the Stokes parameters.
- As a final comment to the above discussion, it should be noted that most polarimeter designs utilize the linear relation C¼BS4, where the four-vector S4¼½s0;s1;s2;s3.
- In summary, the authors design a compact in-plane polarimeter that couples incident light into waveguide modes propagating along six different directions, with the coupling efficiencies being dictated by the SOP.
- This allows one to realize simultaneous detection of the Stokes parameters.
- Regarding the spectral bandwidth of the proposed design, it should be noted that phase matching with the TE1 mode is achieved through grating coupling, which makes the polarimeter inherently narrow band, since the period of the grating must be close to the wavelength of the mode.
- Also, it is worth noting that conventional polarimeters typically measure the SOP in a destructive (i.e., strongly modifying or extinction of the incident beam) or perturbative way.
- Moreover, the authors foresee the possibility of a compact circuitry with built-in plasmonic detectors that are integrated into spatially confined waveguides [33,34].
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In summary, the authors design a compact in-plane polarimeter that couples incident light into waveguide modes propagating along six different directions, with the coupling efficiencies being dictated by the SOP. Finally, the authors stress that the suggested in-plane polarimeter can be realized by only one step of electron-beam lithography, while simple proof-of-concept experiments can be performed by placing outcoupling gratings along the six in-plane propagation directions, with the associated scattered light being a measure of the coupling efficiencies. Moreover, the authors foresee the possibility of a compact circuitry with built-in plasmonic detectors that are integrated into spatially confined waveguides [ 33,34 ]. The authors note that the choice of the design wavelength at 1. 55 μm is merely to illustrate its potential usage in compact integrated optical circuitry, but the design strategy can be transferred to any frequency range of interest, be it either at optical wavelengths [ 30 ] or the microwave regime [ 31 ].