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The photonics technology has revolutionized the telecommunication industry in the past 40 years with the deployment of the undersea fiber-optic network. Nowadays, with the maturity of silicon photonics technology, the integrated photonic platform is enabling more and more cutting-edge technologies, such as optical transceivers for data center connectivity, automotive LiDARs for self-driving vehicles, the next-generation astronomical instrumentation and nearterm photonic quantum computers, to name a few. In recent years, silicon nitride (Si3N4) material has attracted a significant amount of attention mainly due to the ultra-low loss that can be achieved. Compared to silicon, Si3N4 has a much wider transparency window, and does not suffer from two-photon absorption and free-carrier absorption over the telecommunication band. The relatively low refractive index of Si3N4 also means less sensitivity of optical modes to the waveguide sidewall roughness, therefore reducing the scattering loss.

In this dissertation, I will first give an introduction of integrated photonics, and a brief overview of some novel applications and current trends. Next I will graphically show our methods for device fabrication and characterization, and then demonstrate a few integrated photonic devices implemented on the Si3N4 material platform, including Bragg gratings, multimode interferometers, polarization beam splitters, and polarization rotators, with an in-depth discussion of their potentialapplications, principles of operation, simulation and experimental results.

I will then embark on a new chapter on arrayed waveguide gratings (AWGs), with emphasis on its application in integrated astronomical spectrometers. To obtain a continuous two-dimensional spectrum, cleaving at the output focal plane of the AWGis required. I will discuss and demonstrate a three-stigmatic-point AWG, which provides an elegant solution to the non-flat focal plane issue in traditional Rowland AWGs. This work is a critical step towards the development of an efficientand miniaturized astronomical spectrograph for the upcoming extremely-large telescopes.

Next, I will introduce a one-dimensional nanobeam cavity enabled by a slow-light waveguide. A cubic relation between the quality factor and the length of the cavity will be derived and experimental verification will be demonstrated. The current progress towards the investigation of the Purcell effect of this nanobeam cavity will be discussed, including the platform and the loss characterization of the deposited amorphous silicon material.

In the final chapter, I will first summarize the major conclusions from the previous chapters. Then I will briefly discuss some future research directions extending the work in this thesis, including ultra-broadband polarization beam splitter, the development of an on-chip Bell state analyzer, and the design of a polarization-insensitive flat-focal-field spectrometer.