Phase disorder engineering in aperiodic distributed Bragg reflectors for sidelobe suppression

Vertically stacked RGB micro-LEDs require interlayer distributed Bragg reflectors (DBRs) that reflect one color channel while transmitting the others. Periodic quarter-wave DBRs perform this routing well at the design wavelength but exhibit spectral sidelobes that overlap the neighboring emission bands. The resulting parasitic passband reflection dominates the extraction loss, even though inter-channel optical crosstalk through the DBR is comparatively minor (at most a few percent). With RGB emission band separations of only 70-80 nm, quarter-wave stacks cannot adequately suppress these sidelobes. We show that aperiodic DBRs (aDBRs) with 30 independently varied layer thicknesses suppress sidelobes through controlled phase diversity. The round-trip phase distribution is deliberately broadened across the spectrum, which suppresses the systematic off-band constructive interference of periodic stacks while the high index contrast preserves high stopband reflectance through strong multiple reflections. We identify this mechanism with a kinematic phasor walk and verify it with an exact admittance-locus analysis that includes all multiple reflections. Because it is a property of the aperiodic thickness distribution rather than of any specific search procedure, the mechanism is reproduced by multiple 30-dimensional stochastic optimizers, and is difficult to realize within classical parameterized families (chirped, Gaussian-apodized) that are limited by their few free parameters. For a representative TiO₂/SiO₂ aDBR optimized with proximal policy optimization, Lambertian-weighted angular averaging reduces the BG-aDBR red-band parasitic reflectance from 20.0% to 2.4% (8.3×) and the B-aDBR green-band reflectance from 14.8% to 0.8% (18.5×), giving a 27.6% relative gain in red-channel extraction efficiency. Monte Carlo simulations confirm fabrication robustness (>95% yield at σ = 2 nm).