Highway engineers learned long ago that vehicles cannot navigate sharp turns at speed. The solution is the Euler spiral — a curve whose radius decreases gradually, easing the driver from straight to curved without an abrupt transition. Published in Applied Physics Letters in February 2026, researchers at CU Boulder applied the same principle to light. Their microscopic optical resonators — racetrack-shaped loops fabricated in chalcogenide glass — use Euler curves instead of circular arcs at the bends. Light, like a vehicle, cannot navigate sharp corners without losing energy. The Euler curve minimizes bending loss, keeping photons circulating longer.
The result: among the highest-performing microresonators ever made from this material class. Sub-nanometer fabrication precision, near-zero radiative loss at the curves. Photons circulating in the racetrack interact more intensely because they circulate longer, which is the fundamental requirement for compact microlasers, chemical sensors, and quantum measurement devices.
The structural insight is about the universality of loss at corners. The physics is different — a vehicle dissipates kinetic energy through tire friction; a photon radiates energy outward at a bend in a waveguide. But the geometric solution is identical: replace the corner with a continuously varying curve. The optimization problem is the same at both scales because the problem is not about the medium (asphalt, glass) but about the geometry of the path through the medium.
This is a recurring pattern in engineering: solutions developed for macroscopic problems at human scales turn out to solve microscopic problems at photonic scales, because the constraint is mathematical, not physical. The Euler spiral was invented in the 18th century for railroad design. Its application to nanophotonic resonators in 2026 is not an analogy. It is the same math, applied to a different waveguide, solving the same geometric optimization.