Optimization of sawtooth surface-relief gratings: effects of substrate refractive index and polarization

Abstract

The effect of the refractive index of the substrate together with the incident polarization on the optimization of sawtooth surface-relief gratings (SRGs) is investigated. The global optimum diffraction efficiencies of the −1st forward-diffracted order of sawtooth SRGs are 63 .3% occurring at n ₂ =1.47 for TE polarization and 73.8% occurring at n ₂ =2.88 for TM polarization. Incident TE polarization has higher optimum diffraction efficiency than TM polarization for all n ₂ <1.85 . In contrast, TM polarization has higher optimum diffraction efficiency than TE polarization for all n ₂ >1.85 . A polymer (n ₂ =1.5) optimum sawtooth SRG exhibits 62.6% efficiency for TE polarization. A silicon (n ₂ =3.475) optimum sawtooth SRG exhibits 68.6% efficiency for TM polarization. These sawtooth SRGs are compared to right-angle-face trapezoidal SRGs. It is found that the optimum profiles of right-angle-face trapezoidal SRGs have only very slightly increased efficiencies over sawtooth SRGs (0.04% for TE and 0.55% for TM).