Advances in optical parametric devices, in particular those requiring high conversion efficiency, rely on pump laser and gain medium properties. We describe and theoretically model the source of dephasing due to angular deviation from ideal phase matching in optical parametric amplification. Real laser beams have angular content, which is described by their spatial frequency spectrum. Such beams cannot be treated as single plane waves in nonlinear interactions. Our mathematical model is based on a plane wave decomposition of Gaussian and top-hat beams into their components in spatial frequencies. Several popular nonlinear materials (beta-barium borate, lithium borate, and potassium dihydrogen phosphate) are examined for phase matching angles and dephasing is rigorously calculated. The impact of the beam angular content on small signal gain and on conversion efficiency in the strongly depleted regime is evaluated numerically. In addition, a criterion is formulated for beam quality tolerance in optical parametric amplifiers, for critical and noncritical phase matching. The impact of initial conditions in optical parametric amplification is considered. Our calculations are intended primarily for devices pumped with long (nanosecond) pulses.
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