###### Abstract  
Hollow core microstructures powered by infrared lasers represent a new and promising area of accelerator research, where advanced concepts of electromagnetism must be used to satisfy multiple requirements. Here, we present the design of a dielectric electromagnetic band gap (EBG) mode launcher-converter for high-power coupling in dielectric laser accelerators (DLAs). The device is based on a silicon woodpile structure, and it is composed of two perpendicularly coupled hollow-core waveguides--a transverse electric (TE)-like mode waveguide (excited from laser power) and a transverse magnetic (TM)-like mode (accelerating) waveguide--in analogy with the TE\({}_{10}\)-to-TM\({}_{01}\) waveguide mode converters of radio frequency (RF) linear accelerators (LINACs). The structure is numerically designed and optimized, showing insertion losses (\(IL\)) \(<\) 0.5 dB and efficient mode conversion in the operating bandwidth. The operating wavelength is 5 \(\upmu\)m, corresponding to a frequency of \(\approx\)60 THz, in With the aim to obtain a hollow-core dielectric waveguide with an electric field profile suitable for the acceleration of charged particles, 3D photonic crystal (PhC)-based structures [6] represent a suitable choice for DLAs. Among these structures, the _woodpile_ one is chosen, thanks to the capacity to obtain a fully 3D frequency band gap. The 3D PhC represents a solution with a flexible design that allows to optimize the e. m. performance, and it is well suited to be manufactured with lithographic procedures [7,8].  
An example of an accelerating structure based on a woodpile PhC was proposed in [9]. However, the design that we illustrate here is original and quite different from the one reported by [PERSON] et al. since the accelerating channel is smaller (the defect is created by removing just one rod and not three rods), resulting in a larger interaction impedance, and, more importantly, the employed waveguides, both coupling and accelerating, are hollow core for better power handling.  
Hereinafter, we present an electromagnetic band gap (EBG) woodpile hollow-core waveguide with an appropriate hollow-core side coupler (or mode launcher-converter) [10]. The design is visible in Figures 1 and 2. The two side-coupling hollow core input waveguides support a TE\({}_{10}\)-like mode with an even transverse profile that can be easily coupled by a Gaussian beam, an optical waveguide or a metallic waveguide. The input power, coming from a laser source, is injected into the two hollow-core TE\({}_{10}\)-like mode waveguides (1 and 2) that arrive to the mode converter section. Here, the waves are converted into the fundamental accelerating TM\({}_{01}\)-like mode, which propagates along the hollow-core central accelerating waveguide (beam channel) [11]. When the wave reaches the end of the accelerating channel (that can be arbitrarily long), it is back-converted into two waves, which are picked up by a second mode converter (3 and 4) and driven out of the structure.  
This mode launcher design finds strong analogies with the traveling wave (TW) ones used for metallic RF LINACs, where the input coupler is realized by a slot that connects the launch waveguide and the first accelerating cell. These structures can be used for relativistic electron acceleration. Examples are disc-loaded waveguides fed by an input coupler and terminating with an output coupler [12]. The iris-loaded section can also be seen as several coupled accelerating cavity/cells.  
These structures can be used for relativistic electron acceleration following exactly the same principle today used for S-C-X band TW metallic acceleration cavities [12], clearly dealing with the strong re-scaled dimensions of electron beams; it is an issue deeply under study in the accelerators community, e.g., for applications in particle plasma waves acceleration.  
Figure 1: 3D model of the presented EBG woodpile coupler. One input (1) and one output (3) TE\({}_{10}\)-like mode hollow-core waveguides are highlighted with red dashed lines.