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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]

Compensation of phase mismatch by a spatial modulation of the coupling coefficient. Write $d(z)={\sum }_m{d}_m{e}^{imKz}$. The driven amplitude contains $e^{i(\Delta k+mK)z}$, so the selected Fourier component accumulates coherently when $\Delta k+mK=0$. For first-order compensation the full spatial period is $2\pi /|\Delta k|$, twice the nonlinear optical coherence length.

An ideal equal-duty pattern alternating $+d$ and $-d$ has first Fourier coefficient of magnitude $2d/\pi$. Hence its conversion intensity is $4/{\pi }^2$ of a uniformly phase-matched crystal using that same coefficient, under the same undepleted plane-wave assumptions. The modulation can nevertheless allow a larger tensor coefficient or an otherwise inaccessible wavelength. Periodically poled lithium niobate implements such sign reversals using ferroelectric domains.