Modeling and design of integrated optical spectrometers (IOS)

In this PhD work the topic of integrated optical spectrometers has been addressed, with a partic- ular focus on the miniaturization of optical spectrometers. In Chapter 1, a unified overview of the solutions reported in the literature was presented, organized both by operating principle (disper- sive, interferometric/FTS, and reconstructive spectrometers) and by technology platform (silicon photonics, hybrid approaches, reconfigurable materials). This framework was used to place the devices proposed in the following chapters within a consistent context. In addition, a collaborative project to collect performance metrics of integrated spectrometers and detectors was suggested: https://github.com/carlamariacoppola/iPHAOS. The first original contribution of this work is described in Chapter 2, where a Vernier on-chip spectrometer is proposed. Starting from the idea of using two cascaded ring resonators with slightly different free spectral ranges, the device achieves an effective increase in spectral resolution without a proportional increase in footprint. This is obtained with a layout that can be fabricated on standard silicon-photonics platforms (i.e. foundry-compatible). The Vernier algorithm is described in detail and all the relevant equations are derived analytically. The chapter also discusses the sensitivity to fabrication tolerances and thermal drifts, and identifies the conditions under which the Vernier operation remains valid. Chapter 4 presents the second original contribution of the thesis, namely a reconstructive spectrometer in which the spectral response of the chip is intentionally designed to be numerically inverted. Although the architecture is reminiscent of the Vernier spectrometer, the underlying operating principle is different. Simulations show which combinations of integrated building blocks (resonators, paths with different optical path difference, thermally tunable elements) yield a filter matrix that is closer to the ideal one. Moreover, several reconstruction methods have been analysed in order to select the most robust under realistic conditions (noise, drift, need for calibration). This is where the added value of this contribution lies with respect to purely theoretical treatments. A key role is played by Chapter 3, which reports the experimental measurements carried out at the University of Southampton. These measurements were performed on a Fourier-transform spectrometer previously designed by the research group within which this PhD work was conducted. Both passive and active measurements were carried out on several samples. This made it possible to demonstrate that phase-shifted Bragg gratings can be effectively used as tunable elements in on-chip spectrometers, while also showing that a better design of the spiral section is required in order to reduce the experimentally observed losses. Finally, the thesis discusses the more demanding case of an on-chip single-photon spectrometer, for which a short introduction to the main concepts and phenomena of quantum optics is provided in order to clarify the operating principles of these edge-case spectrometers.