High Brillouin Gain in Silicon Subwavelength Slot Waveguides

Introduction

Stimulated Brillouin scattering (SBS) has found wide applications in fields like lasers with ultra-narrow linewidths, microwave photonics filters, and non-reciprocal devices. SBS is a third-order nonlinear optomechanical process where near-infrared photons coherently couple with acoustic phonons in the gigahertz range. This interaction is often orders of magnitude stronger than Kerr and Raman nonlinearities, allowing for substantially lower optical pumping powers.

While SBS was previously restricted to optical fibers, the last decade has seen advances in nanotechnology enabling its implementation in silicon photonics. However, conventional silicon-on-insulator (SOI) waveguides face challenges like phonon leakage to the buried oxide layer due to silicon's high stiffness compared to silica.

Existing Approaches and Limitations

Various approaches have been explored to overcome this phonon leakage issue, each with its own trade-offs:

1. Hybrid Si-SiN membranes exhibit a simulated Brillouin gain of 2.5×103 W-1m-1, limited by weak photon-phonon overlap and high optical losses.

2. Silicon pedestal waveguides provide strong photon-phonon overlap yielding 3×103 W-1m-1 gain but require narrow silica pedestals, complicating fabrication.

3. Suspended silicon rib waveguides are limited to 103 W-1m-1 gain due to weak mode overlap.

4. Phoxonic crystals with simultaneous photonic and phononic bandgaps theoretically reach 8×103 W-1m-1 but suffer from narrow bandwidths and high losses.

5. Subwavelength grating (SWG) waveguides with lateral cladding confine phonons via impedance mismatch but only achieve 1.75×103 to 3.3×103 W-1m-1 gain.

Figure 1: (a) 3D schematic of the subwavelength slot optomechanical waveguide and (b) 2D top view of the simulated cell.

The Proposed Subwavelength Slot Waveguide

This work proposes a new silicon optomechanical waveguide geometry based on a subwavelength grating (SWG) slot, as shown in Figure 1. The periodic nanostructuration of the silicon layer shapes the optical mode distribution to maximize coupling with the mechanical mode.

The key geometrical parameters are the waveguide width W, pitch Λ, and the length LH and width WH of the air holes. With a 220nm silicon thickness, Λ = 300nm (<λeff/2), W = 460nm for single-mode operation, WH = 150nm, and LH = 230nm, 3D multi-physics simulations predict:

• Mechanical mode frequency fm = 4.68 GHz

• Mechanical quality factor Qm = 1.55×104

• Optimized photon-phonon overlap concentrated on slot waveguide walls (Figures 2c, 2d)

• Remarkable Brillouin gain GB = 1.91×105 W-1m-1

• Strong optomechanical coupling rate g0/2π = 435 kHz

Figure 2: (a) Brillouin gain and (b) mechanical frequency as a function of hole length LH. (c) Normalized electric field and (d) mechanical displacement for the optimized design.

The high Brillouin gain results from the large impedance mismatch between silicon and air that enables phonon confinement, combined with the subwavelength nanostructuring that shapes the optical and mechanical mode distributions for maximum overlap.

Moreover, the mechanical frequency can be tuned between 4-9 GHz simply by changing the air hole length, providing additional flexibility.

Advantages and Fabrication

Compared to previous approaches, the proposed SWG slot waveguide exhibits over an order of magnitude higher Brillouin gain without requiring complex geometries. The minimum feature size of 70nm is compatible with immersion lithography, enabling practical fabrication.

This topology overcomes key limitations of prior designs:

• Phonon leakage is minimized by the large silicon-air impedance mismatch

• Strong photon-phonon overlap is achieved through mode shaping

• Low optical loss and wide bandwidths are inherent to subwavelength gratings

• Simple geometry enables straightforward fabrication

Potential Applications

With its ultra-high Brillouin gain and GHz mechanical frequencies, this SWG slot waveguide is a promising platform for implementing various Brillouin-based functionalities on-chip, including:

• Ultra-narrow linewidth lasers

• High-performance microwave photonic filters

• Non-reciprocal devices and isolators

• Optomechanical sensors and transducers

• Coherent photon-phonon information processing

Conclusion

This work proposes a new subwavelength slot optomechanical waveguide design that harnesses the unique dispersion engineering capabilities of periodic nanostructures. Comprehensive simulations predict an exceptionally high Brillouin gain exceeding 1.9×105 W-1m-1 for a 4.68 GHz mechanical mode. This level of performance, combined with practical nanofabrication requirements, could enable the monolithic integration of advanced Brillouin-based functions on the silicon photonics platform. The proposed geometry highlights the immense potential of subwavelength nanostructures as a powerful tool for tailoring light-matter interactions at the nanoscale.

Reference

[2] D. González-Andrade, P. Nuño Ruano, J. Zhang, E. Cassan, D. Marris-Morini, L. Vivien, N. D. Lanzilloti-Kimura, C. Alonso-Ramos, "High Brillouin Gain in Silicon Subwavelength Slot Waveguides," Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, Palaiseau, France; National Research Council Canada, Ottawa, Canada, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.