Brillouin scattering from porous silicon-based optical Bragg mirrors

Abstract

Brillouin light scattering experiments were done on porous silicon-based optical Bragg mirrors with modulation wavelengths of ∼100 nm. By using a combination of pseudo-reflection and backscattering geometries, phonon dispersion curves along the superlattice modulation axis were mapped. Excellent agreement is obtained with the bulk acoustic mode band structure calculated using a one-dimensional elastic continuum model. In addition to zone-folding of the bulk longitudinal mode dispersion curve, the samples are marked by a surface-localized acoustic mode at the superlattice-air interface. The frequency of this mode lies near the upper edge of a phononic band gap centered at ∼16 GHz. These results, along with optical reflectance data showing visible-range photonic band gaps, reveal that these samples are one-dimensional hypersonic phononic-photonic crystals.

Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance

“…8 The porosity and thickness of a given p-Si layer were estimated based on the applied current density and etch time by interpolating from porosity and etch rate results previously obtained for p-Si films made from similarly doped a) wafers. 15 A pair of multilayered films with binary periodicity in the porosity were fabricated by applying a periodic four step current density profile consisting of two etch steps at J 1 ¼ 34 mA/cm 2 and J 2 ¼ 3.4 mA/cm 2 separated by 1 s etchstops.…”

“…For visible-range photons in a mesoporous silicon SL with a binary periodicity in the porosity, propagation may be treated using a well-known electromagnetic continuum model which is mathematically similar to the Kronig-Penney model describing electron propagation in a spatially periodic potential. 8,[21][22][23] Denoting the constituent layers by integer j, photon propagation in the layers is defined by refractive indices n j (obtained here using the two-component Bruggeman effective medium model 19 ) and photon wavevectors K j . Without loss of generality, it may be assumed that n 2 > n 1 .…”

“…Additionally, theoretical and experimental studies of stacked phononic crystal mirrors 6,9 have shown the existence of giant phononic band gaps in the MHz frequency range of these structures. As well, Brillouin light scattering studies on binary periodic porous silicon (p-Si) superlattices (SLs) showed a complex bulk longitudinal acoustic band structure, 3,8 with a second longitudinal mode branch observed for phonons directed along the superlattice modulation axis. Furthermore, these light scattering experiments gave evidence of an additional Brillouin peak which was attributed to a surface-localized mode with a frequency within a one-dimensional hypersonic phononic band gap of the bulk longitudinal band structure centered at $16 GHz.…”

“…Multilayered mesoporous silicon films with a spatial modulation in the porosity, and hence in the elastic impedance, exhibit rich acoustic phonon band structures. [1][2][3][4][5][6][7][8][9][10] The resulting bulk acoustic dispersion curves contain multiple zone-folded branches which may be accompanied by the appearance of forbidden phonon frequency bands, or in analogy to photonic crystals, phononic band gaps. Recent ultrasonic measurements along the modulation direction of films with square-wave, 4,7 sinusoidal, 5 and linearly graded modulation 10 variations in the porosity have reported the existence of one-dimensional phononic band gaps in the bulk longitudinal acoustic phonon band structure; these band gaps were centered at frequencies on the order of 1 GHz.…”

An inverse method to determine the dispersion curves of periodic structures based on wave superposition

“…This type of structure is commonly known as an acoustic of elastic metamaterial. Due to their unique properties, phononic crystals and acoustic metamaterials have huge potential in many applications, including vibration and sound isolation [2,6,[9][10][11], acoustic cloaking [11,12], wave guiding [2,11] and acoustic lensing [13,14]. Hence, phononic crystals and acoustic metamaterials have attracted growing interest in recent years.…”