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J. Eur. Opt. Society-Rapid Publ. 21, 34( 2025)
Fig. 1.( a) Diagram of the designed grating out-coupler.( b, c) Intensity distribution of the fundamental quasi-TE mode showing the confinement in( b) a 2 3 lm 2 Si waveguide( thick SOI platform) waveguide and( c) in a 911 nm thick SiGe layer deposited on top the same Si waveguide.( d) transmission as a function of the thickness of the SiGe layer.
demanding than simply coupling to a few-micrometer single mode fiber, because a part of the signal intensity is already lost during the propagation along the grating [ 11, 16 ]. To obtain a large beam with a controlled intensity cross-section over the surface of the grating out-coupler, it is necessary to increase the strength of the grating gradually along the propagation direction.
This paper is devoted to the theoretical study of an out-coupler grating on thick silicon platform for LiDAR applications. The aim is to create a large Gaussian-shaped beam( around 500 lm) propagating in a vertical direction with respect to the plane of the chip. Although the work is purely based on theoretical considerations and simulations, tolerances, and fabrication constraints as well as material dispersion properties are constantly considered.
2 Design
The overall design is presented in Figure 1a. The hypothesis considered at start is a 3 lm thickand2lm wide silicon strip waveguide supporting quasi-TE( electric field along y-axis) fundamental mode, as well as many other modes. Light is coupled adiabatically from a single-mode( SM) rib waveguide into the strip waveguide, so that only this fundamental TE mode is excited, and the waveguide effectively acts as a SM waveguide [ 17 ]. The modal intensity distribution is given in Figure 1b. The high confinement of the mode inside the large high-refractive index waveguide makes the design of grating out-coupler directly on top of it nearly impossible for high efficiency. The mode needs to be pushed closer to the surface. We propose the inclusion of a top layer of higher refractive index material, namely, SiGe. The fundamental mode establishes in this layer, on which a binary grating can be patterned to extract the field. The modal distribution is presented in Figure 1c.
The refractive index of SiGe depends on the ratio between Si and Ge. In the C-band, germanium absorbs light, and it is important to find a trade-off between the amount of Ge which increases the refractive index of the top layer and the overall absorption of this layer. The refractive index of this layer affects the efficiency of the grating that will be patterned on it as well as the necessary thickness.
SiGe epitaxial growth procedure is a silicon complementary metal-oxide-semiconductor( CMOS) compatible fabrication technologies bringing significant benefits to SiGebased devices [ 18 ]. We chose a stoichiometry corresponding to 80 % of Si and 20 % of Ge. It yields a refractive index n SiGe = 3.606 at k = 1550 nm. According to the transmission through an SiGe layer measured for several thicknesses, we opt for a thickness t SiGe = 911 nm. Deviations from this