Theoretical study of integrated grating structures for Silicon Photonics

My thesis focus on the theoretical study of grating structures for integrated Silicon Photonics. The grating structures proposed are analyzed by using different computational techniques, with the aim of better understanding the Physics involved and optimizing the structures for particular applications. The targeted structures are: grating-couplers for both fiber-to-chip and chip-to-chip light coupling, and grating waveguides for slow light applications. The thesis is structured as follows: The first chapter is an introduction. It provides a brief overview of the current state of Silicon Photonics. Afterwards, a summary of the physics of light propagation in periodically patterned media is given, followed by the numercal method employed: Finite-Difference-Time-Domain (FDTD), Rigorous Coupled Wave Analysis (RCWA) and Aperiodic-Fourier Modal Method (A-FMM). Particular attention is devoted to the A-FMM method, of which I implemented a Python version as part of my PhD work. The second chapter presents a theoretical study of the problem of bandwidth in 1D SOI grating-couplers, with standard silicon thickness of 220 nm and operating a λ=1.55 μm. Through a campaign of numerical simulation, both FDTD and RWCA, the mechanism beyond the bandwidth formation are investigated. In particular, two processes behind the bandwidth formation are found. The first one is a finite size contribution, of Gaussian nature, decreasing in strength as the extension of the exciting mode increase. The second one is coming from the intrinsic width of the photonic mode inside the grating, it has a Lorentzian nature and does not depend on the excitation. In addition, a multi-objective numerical optimization of grating-couplers with various values of MFD has been performed, optimizing width and position of each groove in the grating to explore the better trade-off between Coupling Efficiency and Bandwidth. It is shown that combining suitable optimization with smaller-than-standard MFD, great increase in bandwidth can be achieved. The third chapter provides a feasibility study through FDTD simulations on the application of a grating-to-grating approach to the problem of light coupling (λ=1.55 μm) between Photonic Integrated Circuits of different platforms (SOI and InP). Due to the limited scattering-strength available in the InP platform, the most straightforward solution to decrease insertion loss is to employ longer-than-normal grating-couplers, which also requires the re-thinking of the SOI grating. By combination of a design rule for apodization and numerical optimization trough PSO algorithm, InP and Si grating-couplers of different lengths are co-designed, showing that insertion losses of around 3 dB are possible with usable bandwidth (≈ 30 nm). This study could open the way to the use of flip-chip technology for optical connection between different platforms, allowing for easy and cost-effective hybrid integration. In the forth chapter, the slow light performances of Silicon grating waveguide are theoretically analyzed. These waveduides are simply conventional SOI rib waveguide with periodically modulated width. The Silcion thickness is chosen to be 310 nm and the operational wavelength is λ=1.31 μm. It is shown that, by tuning the geometrical parameters, an almost tenfold increase in the slow-light bandwidth can be obtained with respect to structures known in literature. Moreover, taking advantage of the flexibility of the A-FMM methods, the problem of light couplitg to conventional ridge has been analyzed. Transmission spectra through finite-length deleay lines employing different tapers configurations have been calculated, showning that, in the cases of lower group-index, a simple adiabatic taper is enough to deliver high transmission, while this is not true anymore when the group index increses