**5.1 Data normalization**

After measurements by the angular-resolved measurement system, we transformed the AR μ-PL spectrums to obtain the guided modes dispersion relation (reduced frequency *u*=Λ/λ<sup>0</sup> as y-axis versus in-plane wave vector, *k*//, as x-axis) by the relation *k*//= *k*0\**sinθ*. In addition, each wavelength, *I*PL(*õ*), is normalized relatively to its integrated intensity14. The normalized AR μ-PL diagram reveals the clear dispersion relation of guided modes and detaily figures out the relative excitation and out-coupling efficiency.
