Extraordinary optical transmittance generation on Si3N4 membranes

Abstract

Metamaterials are attracting increasing attention due to their ability to support novel and engineerable electromagnetic functionalities. In this paper, we investigate one of these functionalities, i.e. the extraordinary optical transmittance (EOT) effect based on silicon nitride (Si₃N₄) membranes patterned with a periodic lattice of micrometric holes. Here, the coupling between the incoming electromagnetic wave and a Si₃N₄ optical phonon located around 900 cm^-1 triggers an increase of the transmitted infrared intensity in an otherwise opaque spectral region. Different hole sizes are investigated suggesting that the mediating mechanism responsible for this phenomenon is the excitation of a phonon-polariton mode. The electric field distribution around the holes is further investigated by numerical simulations and nano-IR measurements based on a Scattering-Scanning Near Field Microscope (s-SNOM) technique, confirming the phonon-polariton origin of the EOT effect. Being membrane technologies at the core of a broad range of applications, the confinement of IR radiation at the membrane surface provides this technology platform with a novel light-matter interaction functionality.

Fig. 1. (a) Experimental (light blu line) and fitted (black empty diamond symbols) transmittance of the Si₃N₄ membrane, measured in the THz-UV range. The vertical black dashed line separates the phonon absorption region (low-frequency) to the high-frequency part characterized by Fabry–Pérot fringes. (b) Real (light blue line) and imaginary (black line) parts of the dielectric function, extracted from the fitted transmittance by considering the Fabry–Pérot effect.

Fig. 2. Optical microscope images of the patterned Si₃N₄ samples, with 3 μm (a), 5 μm (b) and 7 μm (c) hole diameters d, and lattice parameter a = 12 μm. (d) Shows the transmittance spectra for unpatterned and patterned samples. (e) Depicts instead the normalized transmittance, defined as the ratio between the transmittance of each patterned sample and the one of the unpatterned. (f) Sketch depicting the self-standing 500 nm thick Si₃N₄ membrane patterned with circular holes, filled with air. The membrane side is 500 μm. This picture schematically describes the EOT phenomenon, in which the incoming light at phonon frequency excites a surface phonon polariton, indicated by black arrows, trapped at the air–membrane interface. The scattering process and the radiative decay of this mode through the holes generate extra light at phonon frequency, giving rise to the EOT phenomenon, as described, for instance, in ref. .

Fig. 3. (a) Experimental (light blue line, already reported in Fig. 2e) and simulated (black dashed line) normalized transmittance for the sample with d = 3 μm. The simulation has been performed under an incident plane wave polarized along y. (b) and (c) |E_z| distribution maps on the Si₃N₄ unit cell surface (xy plane) at a fixed height equal to the membrane thickness, in (900 cm⁻¹) and out of resonance conditions (1650 cm⁻¹), respectively. The electric field values were normalized between 0 and 1. (d) |E_z| value along a line of length 2d (where d is the hole diameter), connecting the hole center (located at 0 μm) and the border of the unit cell, as shown in the corresponding inset. Light blue open circles highlight points obtained with a 200 nm spatial resolution (black dashed line is a guide for the eyes).

Fig. 4. (a)Nano-IR maps of the scattering amplitude and phase variations over the d = 3 μm holes. On the left column, maps were obtained with infrared radiation at 900 cm⁻¹, resonating with the SPhP excitation. On the right column, maps were measured with radiation at 1650 cm⁻¹, out of resonance with the SPhP excitation. Maps were obtained from the same spatial region and, in order to reduce the background noise, were acquired by sampling the signal at the cantilever 3rd harmonic frequency. The black bar indicates a distance of 5 μm as a scale reference. (b) Amplitude and phase signals extracted from the maps in resonance (green line) and out of resonance (red line) of the SPhP excitation as a function of the distance from the hole center compared with the hole depth profile (blu line). The profiles shown were extracted from the hole in the upper right side.