Abstract
We propose a new approach to quasi-phasematching (QPM) design based on convex optimization. We show that with this approach, globally optimum solutions to several important QPM design problems can be determined. The optimization framework is highly versatile, enabling the user to trade-off different objectives and constraints according to the particular application. The convex problems presented consist of simple objective and constraint functions involving a few thousand variables, and can therefore be solved quite straightforwardly. We consider three examples: (1) synthesis of a target pulse profile via difference frequency generation (DFG) from two ultrashort input pulses, (2) the design of a custom DFG transfer function, and (3) a new approach enabling the suppression of spectral gain narrowing in chirped-QPM-based optical parametric chirped pulse amplification (OPCPA). These examples illustrate the power and versatility of convex optimization in the context of QPM devices.
Highlights
Quasi-phasematching (QPM) gratings have received much attention for numerous applications in photonics
We show that for quite a broad range of configurations, QPM device design can be solved via convex optimization techniques [34], meaning that globally optimum designs can be determined rapidly and reliably
The approach we develop is completely applicable to other QPM processes involving the generation of a wave from one or more waves which are unperturbed by the nonlinear process, including sum frequency generation (SFG), second-harmonic generation (SHG), and optical rectification (OR) with undepleted pump(s)
Summary
Quasi-phasematching (QPM) gratings have received much attention for numerous applications in photonics. The d = ±1 constraint inherent in QPM gratings, combined with the fact that thousands of QPM domains are typically present in a single device, means that optimal QPM design of three-wave mixing interactions is challenging, even if one can assume only one envelope (e.g. a generated idler wave) is changing within the device. To overcome this issue, one can work in the first-order-QPM approximation: the grating is written in terms of an arbitrary but smooth phase function φ (z) and duty cycle function D(z) as d(z) = sgn [cos(φ (z)) − cos(πD(z))]
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