Design and Tuning of Substrate-Fabricated Dielectric Metasurfaces Supporting Quasi-Trapped Modes in the Infrared Range

Abstract

Optical metasurfaces supporting resonances of trapped modes allow obtaining narrow features in their reflection and transmission spectra and are the technological basis for the fabrication of highly sensitive sensor coatings and near-field pumping systems for two-dimensional lasers. In the present work, we propose and experimentally verify the strategy for tuning the parameters of an all-dielectric metasurface placed on the substrate in order to implement the narrow resonance of a quasi-trapped mode (QTM) at the required wavelength. We use a Si disk with an eccentric hole as a building block irradiated by a linearly polarized plane wave normally incident to the disk’s base. In this case, the normal components of the magnetic dipole moment are excited due to the bianisotropic response in the system. Using the electrostatic approximation for the polarizability of a single disk and solving the equation for the self-consistent dipole response of a lattice composed of such disks, we plot the parametric curve in the plane (wavelength vs geometric size of the disk) that corresponds to the conditions of QTM excitation accounting for the overcoming effect of diffraction into the substrate. Fixing the arbitrary wavelengths from the infrared (IR) range of the spectrum, we use this curve to select the disk’s size and the period of the metasurface, which are the basis for the fabrication of the necessary metasurfaces. Analyzing the reflection spectra of the fabricated metasurfaces, we observe the narrow spectral features at given wavelengths and, using numerical simulation, identify them as QTM resonances. We demonstrate the polarization control of the amplitudes of the QTM, which allows switching of the intensity value of the electric field on the surface of the Si disks.

Lasing Effect in Symmetrical van der Waals Heterostructured Metasurfaces Due to Lattice-Induced Multipole Coupling

“…Note that the considered metasurfaces can be fabricated from a stack assembled from various materials using the electron beam lithography method. A remarkable feature of the considered resonances is the low sensitivity to periodicity inaccuracies and boundary effects for the real metasurface . Moreover, even with a low level of coherence and the absence of the possibility to control the quantum statistics of photons, the proposed metasurfaces allow one to observe the partially coherent radiation from the large area in the direction perpendicular to the surface.…”

“…The choice of the parameters is due to the need to match the octupole resonance with the interband transition for MoTe 2 material in the vicinity of wavelength λ v 53 as well as the possibility to maintain the subdiffraction regime when the metasurface is placed on the SiO 2 substrate. 54 The location of a metasurface on a dielectric substrate is an important distinction with respect to ref 45 and is of fundamental importance for observing lasing in such a system. In particular, the presence of dielectric SiO 2 substrate does not violate the conditions for excitation of the OQTM resonance due to the coupling mechanism but, at the same time, provides the appearance of an additional way of interparticle interaction through the wave reflected from the dielectric boundary.…”

“…Note that in the considered case, the regime of diffraction into the substrate corresponds to the wavelength range λ < 1070 nm that is outside the spectral range in Figure 1 c. The choice of the parameters is due to the need to match the octupole resonance with the interband transition for MoTe 2 material in the vicinity of wavelength λ v 53 as well as the possibility to maintain the subdiffraction regime when the metasurface is placed on the SiO 2 substrate. 54 …”

“…In threshold conditions, the quality factor of the OQTM resonance is Q = 819 with FWHM = 1.4 nm, see Figure 2 b, and the lifetime of the lasing mode is τ p = 4.1 × 10 –13 s. The photoluminescence spectrum for threshold and above-threshold conditions is, in fact, determined by the characteristics of the resonator (metasurface) and slightly changes with increasing pump intensity, which is a peculiarity of the considered system. Note that the octupole quasi-trapped mode can be excited in relatively small metasurfaces; 54 therefore, experimental observation of lasing should also be possible in spatially limited metasurfaces. The multipole analysis in Figure 2 c performed for the photoluminescence spectrum in Figure 2 b was based on the same definitions of the various multipole contributions to the reflection coefficient as in section S3 of Supporting Information but with the replacement of the scattered fields by the fields emitted from the metasurface.…”

“…A remarkable feature of the considered resonances is the low sensitivity to periodicity inaccuracies and boundary effects for the real metasurface. 54 Moreover, even with a low level of coherence and the absence of the possibility to control the quantum statistics of photons, 70 the proposed metasurfaces allow one to observe the partially coherent radiation from the large area in the direction perpendicular to the surface. It is worth noting that wavelength tuning, in this case, can be realized by filling such a system with an electrically controlled optically transparent medium.…”