We investigate the effect of fabrication tolerances on photonic multimode waveguides operating in the vicinity of a third-order exceptional point degeneracy (EPD), known as a stationary inflection point (SIP). An EPD is a point in the parameter space where two or more Bloch eigenmodes coalesce in an infinite periodic waveguide, and at an SIP three modes coalesce to form the frozen mode. Waveguides operating near an SIP exhibit slow-light behavior in finite-length waveguides with anomalous cubic scaling of the group delay with waveguide length. The frozen mode facilitates stronger light-matter interactions in active media, resulting in a significant increase in the effective gain within the cavity. However, systems operating near an EPD are also exceptionally sensitive to fabrication deviations. In this work, we explore wave propagation and the impact of various fabrication imperfections in analytic models and in fabricated photonic chips for three mirrorless devices operating near an SIP. To advance the concept of the SIP laser, we also analyze how the addition of gain and loss affects the SIP performance. Our results show that while minor deviations from the ideal parameters can prevent perfect mode coalescence at the EPD, the frozen mode remains resilient to small perturbations and a significant degree of mode degeneracy prevails. These findings provide critical insights into the design and fabrication of passive and active photonic devices operating near high-order EPDs, paving the way for their practical implementation in a wide range of applications.
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