On-Chip Laser-Power Delivery System for Dielectric Laser Accelerators

We propose an on-chip optical-power delivery system for dielectric laser accelerators based on a fractal “tree-network” dielectric waveguide geometry. This system replaces experimentally demanding free-space manipulations of the driving laser beam with chip-integrated techniques based on precise nanofabrication, enabling access to orders-of-magnitude increases in the interaction length and total energy gain for these miniature accelerators. Based on computational modeling, in the relativistic regime, our laser delivery system is estimated to provide 21 keV of energy gain over an acceleration length of $192\mu \mathrm{m}$ with a single laser input, corresponding to a 108-MV/m acceleration gradient. The system may achieve 1 MeV of energy gain over a distance of less than 1 cm by sequentially illuminating 49 identical structures. These findings are verified by detailed numerical simulation and modeling of the subcomponents, and we provide a discussion of the main constraints, challenges, and relevant parameters with regard to on-chip laser coupling for dielectric laser accelerators.

Figure 1

Two stages of the DLA laser coupling tree-network structure. The electron beam travels along the $z$ axis through the center of this structure. The laser pulses are side coupled with optical power, shown in red. Black regions define the on-chip waveguide network. Blue circles represent the optical phase shifters used to tune the phase of the laser pulse. This geometry serves to reproduce the pulse-front-tilt laser delivery system outlined in Ref. [27] in an integrated optics platform (Supplemental Material Ref. [30]).

Figure 2

Results from the parameter study. A single stage of the tree-network structure is simulated, with a stage length of $192\mu \mathrm{m}$, corresponding to five power splits and $2^5=32$ output ports. In (a) and (b), silicon-on-insulator (SOI) waveguides are assumed. In (c) and (d), ${\mathrm{Si}}_3{\mathrm{N}}_4/{\mathrm{SiO}}_2$ waveguides are assumed. For each $Q$ factor and pulse duration, we compute the maximum input field achievable before damage or nonlinearity occurs. The different-colored regimes in (a) and (c) correspond to different limiting constraints, as labeled in the plots. The dotted line corresponds to the minimum pulse duration before the pulse bandwidth exceeds the DLA resonator bandwidth. The energy gain from one section is plotted in (b) and (d).

Figure 3

Scaling of optimal parameters as a function of the stage length. The red dotted line corresponds to a stage length of $192\mu \mathrm{m}$, which is the length used in Fig. 2. (a) The optimal energy gains and acceleration gradients as a function of stage length for both SOI and SiN structures. (b) The optimal set of pulse duration and the $Q$ factor corresponding to the highest energy gain and acceleration gradient at each stage length. The curves for the SOI and SiN materials are overlaid. (c) The number of stages required to reach 1 MeV of total energy gain as a function of individual stage length.

Figure 4

Schematic of a hybrid structure for DLA laser coupling. (Center) A SOI tree-network–DLA geometry optimized for tight bends and compact waveguides. This section is fed by a ${\mathrm{Si}}_3{\mathrm{N}}_4/{\mathrm{Si}\mathrm{O}}_2$ waveguide section with a relatively higher damage threshold, and lower nonlinearities. This section is then fed by an all-${\mathrm{Si}\mathrm{O}}_2$ power delivery section, as described in the discussion section. Coarse and fine phase shifters are used in different splitting sections.

Figure 5

Waveguide geometries and corresponding horizontal electric-field components [47]. (a),(b) Strongly confined modes. (c),(d) Weakly confined modes. (a) and (c) are SOI material platforms, whereas (b) and (d) are ${\mathrm{Si}}_3{\mathrm{N}}_4/{\mathrm{Si}\mathrm{O}}_2$ materials. Waveguide core heights in (a)–(d) are given by 220, 400, 60, and 100 nm, respectively. Waveguide core widths are given by 0.78, 1.6, 2, and $4\mu \mathrm{m}$, respectively.

Figure 6

(a) Electric-field amplitude for a strongly guiding SOI waveguide. (b) Electric-field amplitude for a weakly guiding SOI waveguide. (c) Comparison of bending loss as a function of bend radius for the four waveguides from Fig. 5.

Figure 7

Idealized schematic of a feedback system for automatic phase control. A dedicated light extraction section is added to the accelerator. Light is radiated from the electron beam that is transverse to the DLA structures, and the frequency content and/or timing of the light is sent to a controller. The phase shifts of each waveguide are optimized with respect to either the frequency or the delay of the signal.

Figure 8

(a) A schematic of the waveguide to DLA connection. Silicon dual pillars with an optimized radius of 981 nm and a gap size of 400 nm are used. (b) The accelerating electric field during one time step. (c) Absolute value of the transverse magnetic field. (d) Absolute value of the acceleration gradient as a function of frequency, normalized by the peak electric field in the waveguide. A Lorentzian line shape is fit to the square of this plot. The square root of this fit is shown in red. Based on the Lorentzian fit, a $Q$ factor of $152\pm 29$ is determined. As computed following the derivation in Ref. [6], but with the waveguide mode impedance and effective area in place of the plane-wave values, this structure has a shunt impedance, $Z_S$, of $449.1\mathrm{\Omega }$ over three periods and a $Z_S/Q$ value of $2.95\mathrm{\Omega }$.

Figure 9

Diagram of a single bend in the tree-network structure with an optical pulse incident from the left. The bend has radius $R$ and accomplishes a vertical climb of $h$ over a horizontal distance $d$. The total length of the bent section is $L$. The electron travels from bottom to top in this configuration. We wish to find an $R$ such that an optical pulse traveling through the bent section is delayed by the same amount of time for the electron to travel the vertical distance $h$.