This thesis experimentally investigates ion implantation doping of erbium in silicon nitride optical waveguides as a method of endowing the otherwise passive waveguides with gain in the 1.55 um band, transferring the concept of erbium-doped fiber amplifiers to a low-loss, wafer-scale fabricated photonic integrated circuit platform.

After reviewing the fundamentals of erbium-ion absorption and emission and the implantation process used to incorporate erbium ions into Si3N4 waveguides, I demonstrate an erbium-doped waveguide amplifier with high performance enabled by low background loss and favorable host properties. Beyond its relevance as an individual amplifier for optical communication systems that can benefit from higher integration density, the gain section serves as a foundation for new functionalities in silicon nitride photonics. Building on the same platform, I realize a high-coherence, widely tunable continuous-wave integrated laser based on a linear Fabry-Perot cavity with Vernier mode selection using two ring resonators, illustrating the high flexibility of photonic integration that can enable complex active on-chip devices. To support integration of low-loss implanted waveguides with tuning elements and more complicated functionality, I develop a low-temperature silicon dioxide cladding process that avoids absorption caused by hydrogen impurity, addressing a key material limitation and additionally benefiting lower loss lithium niobate and tantalate on insulator waveguides. Finally, I show that erbium-doped gain can power ultrafast integrated sources by implementing a photonic-integrated mode-locked laser based on the Mamyshev oscillator architecture, which mitigates nonlinear pulse breaking in Si3N4 and enables high pulse energies with good coherence. This integrated source is then demonstrated to directly support octave spanning supercontinuum generation and drive a terahertz time-domain spectroscopy system. For low-phase-noise microwave generation based on stabilized mode-locked lasers, I also present an integrated pulse interleaver on Si3N4 platform that alleviates photodiode saturation and provides a path toward tighter integration with on-chip ultrafast sources.