Optical nanoresonators are key building blocks in various nanotechnological applications (e.g., spectroscopy) due to their ability to effectively confine light at the nanoscale. Recently, nanoresonators based on phonon polaritons (PhPs)—light coupled to lattice vibrations—in polar crystals (e.g., SiC, or h-BN) have attracted much attention due to their strong field confinement, high quality factors, and their potential to enhance the photonic density of states at mid-infrared (mid-IR) frequencies, where numerous molecular vibrations reside. Here, we introduce a new class of mid-IR nanoresonators that not only exhibit the extraordinary properties previously reported, but also incorporate a new degree of freedom: twist tuning, i.e., the possibility of controlling their spectral response by simply rotating the constituent material. To achieve this result, we place a pristine slab of the van der Waals (vdW) α-MoO3 crystal, which supports in-plane hyperbolic PhPs, on an array of metallic ribbons. This sample design based on electromagnetic engineering, not only allows the definition of α-MoO3 nanoresonators with low losses (quality factors, Q, up to 200), but also enables a broad spectral tuning of the polaritonic resonances (up to 32 cm−1, i.e., up to ~6 times their full width at half maximum, FWHM ~5 cm−1) by a simple in-plane rotation of the same slab (from 0 to 45°). These results open the door to the development of tunable and low-loss IR nanotechnologies, fundamental requirements for their implementation in molecular sensing, emission or photodetection applications.
Polaritons-hybrid light-mater excitations -are very appealing for the confinement of light at the nanoscale. Recently, different kinds of polaritons have been observed in thin slabs of van der Waals (vdW) materials, with particular interest focused on phonon polaritons (PhPs) -lattice vibrations coupled to electromagnetic fields in the mid-infrared spectral range with -in biaxial crystals, such as e.g. -MoO3. In particular, hyperbolic PhPs -having hyperbola-like shape of their isofrequency curves -in -MoO3 can exhibit ultra-high momenta and strongly directional in-plane propagation, promising novel applications in imaging, sensing or thermal management at the nanoscale and in a planar geometry. However, the excitation and manipulation of in-plane hyperbolic PhPs have not yet been well studied and understood. Here we propose a technological platform for the effective excitation and control of in-plane hyperbolic PhPs based on polaritonic crystals (PCs) -lattices formed by elements separated by distances comparable to the PhPs wavelength -, twisted with respect to the natural vdW crystal axes. In particular, we develop a general analytical theory valid for an arbitrary PC made in a thin biaxial slab. As a practical example, we consider a twisted PC formed by rectangular hole arrays made in MoO3 slab and demonstrate the excitation of Bragg resonances tunable by the twisting angle. Our findings open novel avenues for both fundamental studies of PCs in vdW crystals
Twisted Polaritonic Crystals In article number 2200428, Alexey Y. Nikitin and colleagues introduce a concept of ultracompact polaritonic crystal –deeply subwavelength periodic structure– engineered in an in‐plane anisotropic van der Waals crystal slab. The polaritons inside the crystal can be efficiently controlled by twisting the axes of the periodic structure with respect to the axes of the anisotropic crystal slab. (Image credits: Aitana Tarazaga)
The method for stimulating small businesses (simplification of accounting and taxation systems) is described. The contribution of business entities of the Russian Federation, that applies special tax regimes to the formation of tax revenues of the state budget, is studied. It is revealed that this contribution is different and for different subjects of the Russian Federation it depends on the sectoral structure of the region's economy and natural resource base. The issue of VAT assessment and accounting in the context of the simplified taxation system applied by organizations and individual entrepreneurs is analyzed. Calculations are made and recommendations for improving the simplified tax system at legislative level are provided. Also, the proposals on optimization of accounting and accounting policy in small organizations are given.
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