Reconfigurable Photonic Circuit for Controlled Power Delivery to Laser-Driven Accelerators on a Chip

Dielectric laser acceleration (DLA) represents a promising approach to building miniature particle accelerators on a chip. However, similar to conventional rf accelerators, an automatic and reconfigurable control mechanism is needed to scale DLA technology towards high-energy gains and practical applications. We propose a system providing control of the laser coupling to DLA using integrated optics and introduce a component for power distribution using a reconfigurable mesh of Mach-Zehnder interferometers. Using numerical simulations, we show how such a mesh may be sequentially and efficiently tuned to optimize power distribution in the circuit and find that this strategy has favorable scaling properties with respect to size of the mesh.

Figure 1

Schematic of the proposed DLA laser-delivery control system. Comparison of setup from Ref. [13] (a) and this work (b). (a) In the splitting structure of Ref. [13], an input pulse (large red arrow) is focused to a single grating coupler on the chip surface. The pulse is split a series of times and bends in the waveguide to create group-velocity delay. The phase of the pulses are corrected before injection into the accelerator. (b) In the schematic proposed in this work, the pulse is directly coupled into several waveguides through a grating-coupler array. To mitigate the large variance in coupled powers, the pulses next enter a mesh of MZIs, which is sequentially adjusted, using the protocol from this paper, to provide uniform powers in each waveguide. As before, phase control and group delay are performed using integrated phase shifters and lithographically defined bends before coupling to the accelerator channel. The second scheme eliminates the damage and nonlinearity bottleneck present in (a) directly after the input coupler.

Figure 2

Diagram of MZI mesh for power distribution. (a) Diagram of a single MZI consisting of two input ports and two output ports. Where the two arms come together, a 50:50 beam-splitter operation is performed. Blue regions indicate tunable optical phase shifters with added phases marked as $\theta$ and $\varphi$. (b) The MZI represents a tunable unitary transformation on its inputs $[u_1,u_2{]}^{\mathrm{T}}$ to give outputs $[v_1,v_2{]}^{\mathrm{T}}$. (c) Simplified diagram representing an MZI in the following figures. One may think of this element as a tunable power switch. (d) Individual MZIs are combined into meshes, which may implement tunable unitary operations on several inputs. Shown is a “Clements” mesh geometry, which is used in this work. (e) Schematic of the Clements mesh in (d) using the simple MZI diagram in (c).

Figure 3

Sequential algorithm for tuning single MZI. The red square outlines the MZI being tuned. Black arrows on the left indicate input power to the current layer, black arrows on the right indicate desired output powers (uniform in this case). The dotted line separates the mesh into powers above and below the MZI. (a) When there is more power needed in the ports above the MZI than are supplied in the ports leading into the MZI and above, the MZI should output all of its power to its top output port. (b) When there is more power needed in the ports below the MZI than are supplied in the ports leading into the MZI and below, the MZI should send all of its power to the bottom output port. (c) In the intermediate case, the MZI should output just enough power to its top and bottom output ports to match the target power requirements.

Figure 4

Demonstration of mesh optimization for equal power distribution. (a)–(f) Powers in each port after optimizing the mesh for uniform output power given several random input powers. The colorbar represents the fractional power in each port, where the total power is normalized to 1. The vertical axis represents the input port index and the horizontal axis represents the layer index. Power flows from left to right. Equalization is achieved, on average, after only around five layers given this network with 30 ports.

Figure 5

Analysis of mesh performance vs number of input ports. We plot the mean-squared error between the power in each layer and the target power after the mesh has been optimized. These are averaged over five random input values. We see that the number of layers ($M$) needed to equalize the power in the mesh increases slowly with respect to the number of ports ($N$).

Figure 6

Figure-of-merit scaling for different laser-coupling architectures. Solid blue lines refer to the results using the system of Ref. [13], in which all optical power is initially coupled at a single input facet. Red dotted lines refer to the structure from this work. (a) The acceleration gradient as a function of electron energy gain. For the splitting structure, the acceleration gradient diminishes rapidly as the length of acceleration is increased to match the desired energy gain. However, the structure from this work achieves uniform gradient in principle. (b) Number of output waveguides ($N$) required to achieve a given energy gain of ${\mathrm{\Delta }}_E$. (c)Acceleration length ($L$) required to achieve a given energy gain of ${\mathrm{\Delta }}_E$.