Design criteria for ultrafast optical parametric amplifiers

Optical parametric amplifiers (OPAs) exploit second-order nonlinearity to transfer energy from a fixed frequency pump pulse to a variable frequency signal pulse, and represent an easy way of tuning over a broad range the frequency of an otherwise fixed femtosecond laser system. OPAs can also act as broadband amplifiers, transferring energy from a narrowband pump to a broadband signal and thus considerably shortening the duration of the pump pulse. Due to these unique properties, OPAs are nowadays ubiquitous in ultrafast laser laboratories, and are employed by many users, such as solid state physicists, atomic/molecular physicists, chemists and biologists, who are not experts in ultrafast optics. This tutorial paper aims at providing the non-specialist reader with a self-consistent guide to the physical foundations of OPAs, deriving the main equations describing their performance and discussing how they can be used to understand their most important working parameters (frequency tunability, bandwidth, pulse energy/repetition rate scalability, control over the carrier-envelope phase of the generated pulses). Based on this analysis, we derive practical design criteria for OPAs, showing how their performance depends on the type of the nonlinear interaction (crystal type, phase-matching configuration, crystal length), on the characteristics of the pump pulse (frequency, duration, energy, repetition rate) and on the OPA architecture.