Composition dependence of second harmonic generation, refractive index, extinction coefficient, and optical bandgap in 20 nm thick crystalline Hf1−xZrxO2 (0 ≤ x ≤ 1) thin films is reported. The refractive index exhibits a general increase with increasing ZrO2 content with all values within the range of 1.98–2.14 from 880 nm to 400 nm wavelengths. A composition dependence of the indirect optical bandgap is observed, decreasing from 5.81 eV for HfO2 to 5.17 eV for Hf0.4Zr0.6O2. The bandgap increases for compositions with x > 0.6, reaching 5.31 eV for Hf0.1Zr0.9O2. Second harmonic signals are measured for 880 nm incident light. The magnitude of the second harmonic signal scales with the magnitude of the remanant polarization in the composition series. Film compositions that display near zero remanent polarizations exhibit minimal second harmonic generation while those with maximum remanent polarization also display the largest second harmonic signal. The results are discussed in the context of ferroelectric phase assemblage in the hafnium zirconium oxide films and demonstrate a path toward a silicon-compatible integrated nonlinear optical material.