Two-dimensional (2D) materials with giant nonlinear optical (NLO) responses are essential for the development of advanced on-chip NLO devices. Using first-principles calculations, we predict a remarkable strain-induced enhancement of second-harmonic generation (SHG) in the high-performance 2D semiconductors ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$ ($X$ = S, Se, Te). The SHG susceptibilities of ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$ under strain are on the order of 1 nm/V, rivaling the highest values reported among 2D materials. This giant SHG response originates from gauge-invariant geometric quantities, including the quantum metric, the shift vector, and the triple phase product. The strain also induces a band-gap variation in ${\mathrm{Bi}}_2{\mathrm{O}}_{2}X$. Intriguingly, in ${\mathrm{Bi}}_2{\mathrm{O}}_2\mathrm{Te}$, strain-induced band-gap tuning drives a transition from a semiconductor to a half-metal, and ultimately to a polar metal. Our findings present a unique platform that combines strain-tunable band-gap engineering with exceptional NLO properties, while also highlighting the crucial role of quantum geometry in enhancing SHG.

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• Ferroelectricity
• Geometric & topological phases
• Nonlinear optical susceptibility
• Nonlinear optical materials