A proposal for digital electro-optic switches with free-carrier dispersion effect and Goos-Hanchen shift in silicon-on-insulator waveguide corner mirror

Abstract

In a silicon-on-insulator (SOI) waveguide corner mirror (WCM) structure, with the quantum process of a frustrated total internal reflection (FTIR) phenomenon and the time delay principle in the two-dimensional potential barrier tunneling process of a mass of particles, we derive an accurate physical model for the Goos-Hanchen (GH) shift of optical guided-mode in the FTIR process, and in principle match the GH shift jumping states with the independent guided-modes. Then, we propose and demonstrate a new regime of 1 Â N digital optical switches with a matching state between the free-carrier dispersion (FCD) based refractive index modulation (RIM) of silicon to create a GH shift jumping function of a photonic signal at the reflecting interface and the independent guided-modes in the FTIR process, where a MOS-capacitor type electro-optic modulation regime is proposed and discussed to realize an effective FCD-based RIM. At the critical matching state, i.e., the incident of an optical beam is at the vicinity of Brewster angle in the WCM, a mini-change of refractive index of waveguide material can cause a great jump of GH shift along the FTIR reflecting interface, and further a 1 Â N digital optical switching process could be realized. For a 350-500 nm single-mode rib waveguide made on the 220 nm CMOS-compatible SOI substrate and with the FCD effect based RIM of silicon crystal, a concentration variation of 10 18 -10 19 cm À3 has caused a 0.5-2.5 lm GH shift of reflected beam, which is at 2-5 times of a mode-size and hence radically convinces an optical switching function with a 1 Â 3-1 Â 10 scale.

Experimental Verification of Digital Thermo-Optic Switches with Silicon-on-Insulator Waveguide Corner Mirror

“…CORNER STRUCTURE AND THE 1X3 OPTICAL SWITCH BASED ON GH SHIFT WITH MICROSCALE WAVEGUIDES AND TO-RIM Figure 1 depicts the schematic configuration of a 1×3 scale TO DOS based on SOI platform and it consists of one single-mode input waveguide, three single-mode output waveguides, a waveguide corner mirror (WCM) ,an MMI structure and a heater, where the corner mirror material is SiO 2 . Then, the definition of GH total shift is the spatial shift and the angular shift produces an algebra sum through an MMI reflective waveguide structure as [10]:…”

“…In Ref. [10], for the eigenstate of a reflected mode during a GH spatial shift, the partial derivative meets , so the incident angle θ should correspond to an eigenvalue of wave function  (x, z).…”

“…(2b) is that the GH angular shift  pertains to the Neff that is determined by the input waveguide material. We know that all the guided modes of an MMI waveguide structure are the eigenstates of quantum physical process and the effective indices are the eigenvalues of all the refractive indices of optical beam at the phase velocities [10]. So, if the input waveguide channel is a single-mode, N eff would be only the eigenvalue determining one of the GH angular shifts.…”

“…[3] In 2013, Our research group first theoretically proved the quantum Goos-Hänchen (GH) spatial shift, and then proposed a possible regime of digital optical switches. [10]…”

Goos–Hänchen Shift in Single Crystal Silicon Induced by the Electro‐Optic Effects

“…The Goos–Hänchen shift is a lateral shift in a reflected light beam compared to the theoretical geometrical optics . Researchers have investigated Goos–Hänchen shifts in various structures such as metal‐insulator‐semiconductors, silicon on insulator waveguide corners, metal‐insulator‐metals, symmetrical metal‐cladding waveguides, and prism‐metal‐polymer‐metal multilayer structures . Many applications based on Goos–Hänchen shifts have been proposed for optical sensors and optical switching .…”