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The design of a 637-nm wavelength, photonic-integrated-circuit-based external cavity laser (PIC-based ECL) aimed at quantum technology applications is presented together with first experimental results. The PIC is designed to provide relaxed alignment tolerance for coupling to a reflective semiconductor optical amplifier (RSOA) gain chip. This is achieved by using a multi-mode edge coupler (MMEC) in place of the usually employed single-mode coupling schemes. A 1-dB-penalty misalignment tolerance of up to +/- 2.4 um can be achieved in the plane of the chip, creating a path towards reliable flip-chip integration at short wavelengths. The power coupled to the PIC is fed to a Sagnac-loop reflector, filtered by a pair of ring resonators operated in Vernier configuration for providing the required frequency selective optical feedback. The ring resonators are designed to have different loaded Q-factors and they are asymmetrically coupled to bus and drop waveguides with suitably engineered directional couplers to provide single output waveguide emission. Moreover, requirements for high output power and narrow linewidths are balanced. Finally, preliminary measurements strongly suggest lasing in the fabricated devices, with further performance optimization being currently carried out.

The correct numerical calculation of the resonance characteristics and, principally, the quality factor $Q$ of contemporary photonic and plasmonic resonant systems is of utmost importance, since $Q$ defines the bandwidth and affects nonlinear and spontaneous emission processes. Here, we comparatively assess the commonly used methods for calculating $Q$ using spectral simulations with commercially available, general-purpose software. We study the applicability range of these methods through judiciously selected examples covering different material systems and frequency regimes from the far-infrared to the visible. We care in highlighting the underlying physical and numerical reasons limiting the applicability of each one. Our findings demonstrate that in contemporary systems (plasmonics, 2D materials) $Q$ calculation is not trivial, mainly due to the physical complication of strong material dispersion and light leakage. Our work can act as a reference for the mindful and accurate calculation of the quality factor and can serve as a handbook for its evaluation in guided-wave and free-space photonic and plasmonic resonant systems.