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A high-contrast and compact wavelength diplexer is presented for conventional 1550 nm and emerging 2000 nm based on a subwavelength-grating (SWG) coupler. The SWG silicon waveguide thoroughly blocks the light propagation around 1550 nm but fully supports 2000 nm (extinction ratio: 43.11 dB). This grating type anisotropic metamaterial not only efficiently reduces the coupling length but also expands the operational bandwidth. Simulated by 3D finite-difference time-domain method, the proposed diplexer possesses a remarkably low insertion loss and a high contrast of 25.24 (31.7) dB at 1550 (2000) nm. The operational bandwidth of 200 (108) nm is achieved with contrast over 15 dB and insertion loss below 0.22 dB. The footprint of diplexer is only 5.27 μm × 11.85 μm. Moreover, such design has the scalability by simply tuning the geometrical parameters of SWG.

In this letter, we propose ultra-compact TE-polarized even-to-odd mode converter designs by introducing Ge/Si patterns into silicon waveguide-integrated functional region. The Ge areas with continuous boundaries are determined by topology optimization that combines finite element method, geometric projection method, and method of moving asymptotes. Both two-dimensional (2D) and quasi-3D designs are presented. Simultaneous beam splitting and phase shifting are achieved in the functional region with only $1.0 \times 1.55\;{\rm{\mu }}{{\rm{m}}^2}$ area. Based on the 3D finite-difference time-domain simulations, the quasi-3D designs possess satisfactory mode purity (>0.99) at center wavelength 1550 nm, and the mode purity keeps higher than 0.92 within the wavelength range from 1500 to 1600 nm. Meanwhile, the forward transmission efficiency is shown higher than 0.89 within the operational bandwidth. Moreover, the robustness is demonstrated by considering the loss of Ge material and the geometric deviations. The proposed mode-order converters bring together advantages including wavelength footprint, high mode purity, low insertion loss, and large operational bandwidth.

Among other aims, degrowth calls for a deprioritization of economic growth as primary indicator of success. However, deprioritizing economic growth is challenging because it is the antithesis of business as we know it today. Yet, in this study, we find examples of enterprises operating in the renewable energy industry in the Global South, which deprioritize traditional economic growth as their preferred indicator of success. We interviewed 30 renewable energy enterprises (REEs) on the basis of an importance-performance analysis (IPA). Our findings confirm that conventional measures of financial performance are not universally applicable to all enterprises in the Global South. Specifically, we observed that the REEs that are least satisfied with conventional economic performance indicators possess two characteristics in common: (1) they have strong social motivations (e.g., energy access and poverty alleviation) and (2) they are averse to economic growth in the traditional sense. We draw insights from these REEs for the future of post-growth enterprise, including the importance of localness in success and performance appraisal as the Global South transitions toward degrowth. We also introduce 14 alternative performance indicators, suggested by the REEs themselves, which may help bring enterprises closer to post-growth orientation in the Global South.

Thiol compounds have been shown to be important in many fields such as protein chemistry and carbohydrate chemistry. Their pKa's in aqueous solution are important for understanding the properties and reactivities of thiols in complex biochemical systems. To elucidate the structure–activity relationships and substituent effects on pKa's of thiols, pKa's of 58 thiols were calculated using different DFT methods with two types of solvation models including PCM-Bondi and SMDsSAS. It was found that the M06-2X method with the SMDsSAS model can give the optimal precision with the smallest RMSE value of 0.77 pK unit. Based on this model, the pKa's of thiols (R-SH in which R = alkyl, cycloalkyl, aryl, heterocyclyl and fluorinated hydrocarbyl) were systematically investigated. The substituent effects as well as the structure–activity relationships behind these data were also examined. Significant substituent effects were found in heterocyclyl, alkynyl and fluorinated hydrocarbyl thiols with a wide pKa range of over 10.0 pK units. In addition, analyses including the natural bond orbital (NBO) and the energies of frontier orbitals were performed in order to further understand the substituent effects on pKa's. Good linear relationships between the pKa's with substituent constants σp+ and natural charges on S atoms were observed in different types of thiols.

In the dual catalytic Suzuki–Miyaura reactions, the cross-coupling of Csp3-hybridized center organotrifluoroborate salts has been implemented successfully by single-electron transfer (SET), where the redox potentials are important for understanding the reactivities of organotrifluoroborate salts. To this end, the ΔGgas values of 27 organotrifluoroborate anions were calculated by using different composite high-level ab initio and DFT methods. Among different DFT methods, the M05-2X method gave the highest precision with a smallest RMSE of 1.58 kcal mol−1. Then, the 24 E° values of organotrifluoroborate anions were calculated by using the M05-2X method with two types of solvation models including PCM and SMD. It was found that the M05-2X method with a PCM–UAHF model can provide the most accurate results with the lowest RMSE value of 0.16 V. Therefore, the E° values of Csp3-hybridized center organotrifluoroborate anions (R–CH2–BF3−) including R = alkenyl, alkynyl, aryl and heterocyclyl and the Csp2-hybridized center vinyltrifluoroborate anions were systematically investigated with this theoretical protocol. The results indicated that for the Csp3-hybridized center organotrifluoroborate anions, the E° values range from 0.36 V to 1.57 V, and the electron-donating groups (EDG) of –N(CH3)2, –NHCH3etc. can significantly lower the E° values of organotrifluoroborate anions, which are favorable for reactions, whereas the electron-withdrawing groups (EWG) of –NO2, –CN etc. make the organotrifluoroborate anions unfavorable for reactions. For the Csp2-hybridized center organotrifluoroborate anions, the E° values range from 1.38 V to 2.43 V. In addition, the analysis of the natural bond orbital (NBO), the ground-state effect (GE), the radical-state effect (RE) and the energies of frontier orbitals was performed in order to further disclose the essence of the E° value change patterns. The linear relationships between the E° values with substituent constants σ+p and the natural charges of the corresponding C atoms of radicals, etc. were found in different types of organotrifluoroborate anions.

We propose and numerically demonstrate a design of bidirectional transverse electric (TE) polarized mode-order converter based on silicon-on-insulator platform. This converter is realized by introducing high refractive index material inlaid in a silicon slab waveguide. Simulated by three-dimensional finite-difference method time-domain, the forward (TE0 to TE1-like conversion) transmittance reaches approximately 88.2%, while the backward value (TE1 to TE0-like conversion) is about 89.4% at the wavelength of 1550 nm. The footprint of this converter is as small as 0.95 × 1.5 μm2. Fabrication tolerance analysis demonstrates satisfactory robustness. Moreover, we present a polarization-independent converter with slightly modified geometry. The transmittance keeps above 87.2% within the wavelength range from 1500 nm to 1600 nm for both TE and transverse magnetic modes. These devices are expected to contribute to the on-chip mode division multiplexing.

We propose a design of reciprocal optical diode based on asymmetric spatial mode conversion in multimode silicon waveguide on the silicon-on-insulator platform. The design possesses large bandwidth, high contrast ratio and high fabrication tolerance. The forward even-to-odd mode conversion and backward blockade of even mode are achieved by partial depth etching in the functional region. Simulated by three-dimension finite-difference time-domain method, the forward transmission efficiency is about −2.05 dB while the backward transmission efficiency is only −22.68 dB, reaching a highest contrast ratio of 0.983 at the wavelength of 1550 nm. The operational bandwidth is up to 200 nm (from 1450 nm to 1650 nm) with contrast ratio higher than 0.911. The numerical analysis also demonstrates that the proposed optical diode possesses high tolerance for geometry parameter errors which may be introduced in fabrication. The design based on partial depth etching is compatible with CMOS process and is expected to contribute to the silicon-based all-optical circuits.

Metasurfaces, two-dimensional structures composed of nanoantennas in an array configuration, can be used to fully control electromagnetic waves, which requires a 2π phase shift. Herein, we apply the silicon metasurface as an example to interpret the mechanisms of full 2π phase coverage. It is found that the mechanism varies from Fabry-Perot resonance to Mie resonance as the period increases for a metasurface with certain height. Particularly, there is a transition region between these two types of resonance. We present the corresponding periods and wavelength regions of the different mechanisms when considering the phase-gradient metasurface with at most three diffraction orders. Moreover, the transmission enhancement of metasurface is investigated. The transmission efficiency can be effectively improved when the nanoantenna is changed from a uniform structure to a gradient-index one. We expect that the results can simplify the design process and provide a reference for the future design of all-dielectric metasurface with 2π phase control.

We propose a silicon-based asymmetric directional coupler assisted by subwavelength grating anisotropic metamaterial operating at the emerging 2 μm waveband. The effective medium theory is utilized to explain the principle of the proposed structure. Three devices with mode-order conversions are presented. Firstly, TE0-to-TE1, TE0-to-TE2, and TE0-to-TE3 conversions with remarkably high transmittance (>−0.17 dB) and extremely high mode purity (>98.81%) are achieved at the central wavelength of 1985 nm. The fabrication tolerance analyses demonstrate reasonable robustness of the proposed structure. Secondly, such structure can realize a reciprocal optical diode with an exceedingly high contrast ratio (>34 dB) based on spatial symmetry breaking. Finally, we present a symmetric 3 dB mode converter and splitter just by adjusting the length of subwavelength grating and the gap of asymmetric directional coupler. The results reveal that the transmittances of both output ports approach −3 dB around 2 μm and the transmittance difference remains below −10 dB above 40 nm within the waveband from 1.95 μm to 2.05 μm.