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Lithium niobate is $\mathrm{LiNb}{\mathrm{O}}_3$, a crystalline oxide containing lithium, niobium, and oxygen. Its non-centrosymmetric structure supports piezoelectricity and useful optical responses.

An applied electric field can change its optical response, allowing electrical control of light in a modulator. The connection between crystal symmetry and macroscopic response makes lithium niobate a bridge between crystallography and optical engineering.

Niobium is the chemical element with atomic number 41 and symbol $\mathrm{Nb}$. It is a transition metal. Niobium and several niobium alloys are used as superconductors. Its common $+5$ chemistry also appears in oxides, including lithium niobate, whose optical and electrical behavior differs from that of the metal.^[ref]

Periodically poled lithium niobate is lithium niobate whose ferroelectric domain orientation is reversed periodically along an optical interaction path. Reversal changes the sign of the relevant second-order nonlinear optical susceptibility, supplying the spatial modulation needed for quasi-phase-matching.

For a uniform collinear conversion mismatch $\Delta k$, a first-order poling period $\Lambda$ can compensate it through $\Delta k-2\pi /\Lambda \simeq 0$, with signs chosen consistently. The generated contributions then reinforce over many domains instead of repeatedly canceling. The poling period, temperature and input wavelengths determine the useful conversion band; domain defects and finite length affect efficiency. ^[ref]