Raman-like stimulated Brillouin scattering in phononic-crystal-assisted silicon-nitride waveguides

We study theoretically stimulated Brillouin scattering (SBS) in silicon nitride (SiN) waveguides created as a phononic line defect inside a pillar-based phononic-crystal membrane of the same material for efficient confinement of the generated acoustic phonons to the optical waveguides. The phononic defect is carefully designed to confine the transversally resonating breathing acoustic mode inside the phononic band gap of the host phononic crystal. These breathing acoustic modes are well excited by the fundamental optical modes of the waveguides. By optimizing this structure, we show the possibility of achieving high SBS gain in an integrated platform with full complementary metal-oxide-semiconductor (CMOS) compatibility with other photonic and electronic functionalities. The combination of low-loss traveling photons and long-lasting resonating phonons in the proposed SiN waveguide paves the way for the demonstration of efficient on-chip SBS devices.

Figure 1

Phononic dispersion diagram of a free-standing SiN nanowire. (a) Phononic dispersion bands of a nanowire with $(w,h)=(600,400)$ nm and $(E,\nu ,\rho )=(250\text{GPa},0.25,3100\mathrm{kg}/{\mathrm{m}}^3)$. Here $E$, $\nu$, and $\rho$ are Young's modulus, Poisson's ratio, and mass density, respectively. The acoustic wave number is normalized to $a$, which is the length of the simulated portion of the waveguide (i.e., $a=500$ nm). Dispersion bands can be classified as Brillouin-like acoustic phonons and Raman-like acoustic phonons based on the starting frequency at $K_{m}a=0$. (b) Vibration profiles and propagation direction (i.e., along the $y$ direction) of the acoustic modes of the SiN nanowire at $K_{m}a=0.3$ for bands 1–4 and $K_{m}a=0.01$ for band 5 in (a). White arrows depict the dominant vibration direction.

Figure 2

Proposed SiN structure for the SBS interaction. (a) Schematic of the pillar-based SiN waveguide for SBS generation, showing the phononic crystal and the optical ridge waveguide along with the vibration profile of the breathing acoustic mode confined inside the phononic band gap of the PnC. The PnC is formed by a triangular lattice of SiN pillars standing on a thin SiN membrane. The phononic line defect is designed such that the breathing vibration is maximized inside the optical waveguide. The displacement profile in (a) is at normalized wave number $K_{m}a\approx 0$. (b) Phononic dispersion diagram of a primitive unit cell of the PnC [highlighted in (a)] over an irreducible Brillouin zone [shown in the inset of (b)]. The pillars' height, radius, and membrane thickness are $(h/a,r/a,t/a)=(0.64,0.44,0.16)$, respectively.

Figure 3

Forward SBS gain in SiN nanowires and PnC-assisted SiN waveguides. (a) Variation of the FSBS gain in the SiN nanowire for the acoustic mode shown in (b) as a function of its width $w$ for three different heights ($h=0.3$, 0.4, and $0.45\mu \mathrm{m}$). In addition, the FSBS gain for a PnC-assisted waveguide with the total thickness of 400 nm is compared with that of different nanowires. The gain is slightly reduced because of the extension of the acoustic waves to the pedestal. (b) Acoustic breathing vibration mode and the electric field of the fundamental TE optical mode (i.e., ${\mathrm{TE}}_1$ whose electric field lies in the plane of the nanowire) used in the simulation of the FSBS gain of nanowires. In addition, the breathinglike acoustic vibration mode inside the PnC-assisted waveguide is depicted, which is a combination of two primary vibrations: breathing and flexural.

Figure 4

Properties of a SiN nanowire on a membrane without PnC. (a) Cross section of the nanowire (height equal to 400 nm and width equal to 600 nm) on a membrane with the width of $w$ and the height of 80 nm. (b) Breathinglike acoustic modes of the structure shown in (a) at $K_m=0$ for different membrane widths. The color code for the representation of the acoustic resonances is the breathinglike parameter. (c) Zoomed-in version of a resonance mode of the structure in (a) in the region identified by the dashed black square in (b) demonstrating mode splitting (or avoided crossing) due to the coupling between a breathinglike acoustic branch and other acoustic branches of the structure. (d) The FSBS gain calculated for the closest mode of the structure in (a) to the breathing mode of an ideal nanowire [i.e., the mode with the largest breathinglike parameter in (b)] as a function of $w$.