Optimisation of pockels effect in poled amorphous waveguides for efficient electro-optic modulation

The induced second-order optical nonlinearity (SONL) in amorphous materials, such as silica glasses, has been extensively studied but remains significantly weaker compared to crystalline materials. Recent advancements demonstrated a remarkable induced <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>χ</mml:mi> <mml:mrow><mml:mi>xxx</mml:mi></mml:mrow> <mml:mfenced><mml:mn>2</mml:mn></mml:mfenced> </mml:msubsup> </mml:math> value of 29 pm/V in amorphous sodo-niobate thin films (Na₂O:Nb₂O₅) using a patterned thermal poling technique. In contrast to standard electro-optic single-crystalline materials, such as lithium niobate, thermally poled amorphous thin films exhibit a unique spatial distribution of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>χ</mml:mi> <mml:mfenced><mml:mn>2</mml:mn></mml:mfenced> </mml:msup> </mml:math> nonlinearity, due to the structured electrodes poling process. This necessitates an advanced modelling approach tailored to poled amorphous materials. This study presents a theoretical analysis of the sodo-niobate dielectric permittivity tensor, then applies it to the design of electro-optic modulators using numerical simulations, to identify the optimal device geometry, device orientation, fabrication process, and poling configuration. Experimental parameters were included in the simulations to ensure design compatibility with fabrication. The optimized device configuration achieved a voltage-length product (V_πL) of 3.87 V.cm. These designs establish poled sodo-niobate waveguides on SiO₂ as a promising amorphous platform with a significant induced SONL response and practical fabrication potential for future electro-optic modulator applications.