Coupling power into accelerating mode of a three-dimensional silicon woodpile photonic band-gap waveguide

Silicon woodpile photonic crystals provide a base structure with which to build a three-dimensional dielectric waveguide system for high-gradient laser-driven acceleration. To realize an on-chip woodpile laser accelerator, a key component is the power coupler to deliver laser power to the fundamental accelerating mode. The woodpile waveguide is periodically loaded in the longitudinal direction; therefore simple cross-sectional mode profile matching is not sufficient to launch the accelerating mode appropriately and will result in significant scattering loss. Several traveling-wave coupler design schemes developed for multicell radio frequency cavity accelerators can be adapted to the woodpile accelerator coupler design. This paper presents design procedures and results using these methods. We present simulations indicating near 100% power transmission between the transverse electric mode of a silicon-guide side coupler and the transverse–magnetic-like accelerating mode of a woodpile waveguide. The coupler launches a full traveling-wave propagation of the accelerating mode, which maintains its propagation quality over long waveguide structures, and provides better tolerance on the structure fabrication uncertainty and material breakdown than standing-wave coupling.

Figure 1

Conceptual schematic of an on-chip woodpile accelerator consisting of multiple accelerator cavities. Inset: layout of a woodpile accelerator waveguide section supporting speed-of-light accelerating mode. Individual silicon rod’s width, height, and spacing within each horizontal layer are denoted as $w$, $h$, and $a$, respectively.

Figure 2

(a) A TE-mode silicon woodpile waveguide excited by back-to-back silicon guide couplers. (b) Calculated $\mathrm{\Sigma }(z)$ and the normalized backward wave amplitude $|R|$ in this woodpile waveguide.

Figure 3

(a) Mode launchers at the front and back of a multicell rf cavity waveguide to achieve traveling-wave match. (b) An equivalent configuration for a woodpile waveguide and back-to-back silicon guide mode launchers.

Figure 4

(a) Multiple-cell simulation to determine the required ${S_{22}}^{\mathrm{m}}$ for a traveling-wave match to a TE-mode woodpile waveguide. (b) The traveling-wave mode launcher design: perturbation in a silicon guide by a piece of perfect conductor, with its dimensions marked in the inset.

Figure 5

(a) TE-to-TM mode coupler layout for a 7-cell woodpile accelerating waveguide, and (b) its multiple-cell simulation results to determine the required ${S_{22}}^{\mathrm{m}}$ for traveling-wave launch.

Figure 6

Two TM-like speed-of-light modes of the original woodpile accelerating waveguide design: (a) the in-phase fundamental accelerating mode, (b) the out-of-phase spurious mode.

Figure 7

(a) Effect on the total transmission $|S_{21}|$ and the normalized backward wave amplitude $|R|$ in the accelerating waveguide as the reflection magnitude $|{S_{22}}^{\mathrm{m}}|$ of the mode launcher varies. (b) The phase advance per cell and the normalized backward wave amplitude as the mode launcher uses the tuning dimensions $l_{\mathrm{x}}=66\mathrm{nm}$ and $z_0=863\mathrm{nm}$.

Figure 8

New TM-like propagating modes of different woodpile waveguide channel dimensions, with their vector electric fields plotted in (a) mode 1, (b) mode 2, and (c) mode 3, and dispersion curves plotted in (d).

Figure 9

(a) TE-to-TM mode power coupler design for the new accelerating mode, and (b) its multiple-cell simulation results to determine the required ${S_{22}}^{\mathrm{m}}$ for traveling-wave match.

Figure 10

Phase advance per cell $\psi$ and normalized backward wave amplitude $|R|$ of an 8-cell power coupler structure, proving it is traveling-wave matched to the new woodpile accelerating mode.

Figure 11

Schematic representation of the silicon membrane transfer method to stack multiple woodpile layers.

Figure 12

(a) Side SEM view of an 18-layer silicon woodpile structure. (b) Top SEM view of the middle layers of a woodpile waveguide structure. Both are fabricated by the silicon membrane method.