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Optics Express

Design of quasi-phasematching gratings via convex optimization

Christopher R. Phillips, L. Gallmann, M. M. Fejer

Published Apr 16, 2013• 14 citations

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.

DOI: 10.1364/oe.21.010139

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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.

Three-wave nonlinear interactions in chirped quasi-phase-matched (QPM) gratings are shown to exhibit conversion efficiency approaching 100% with increasing input pump and signal intensities, evading backconversion, as long as the idler vanishes at the input and the QPM grating is sufficiently chirped. The signal phase is described in terms of Kerr-like self- and cross-phase modulations, in the cascade χ((3)) approximation. Achieving high gain and efficiency simultaneously can lead to a large nonlinear phase, and the resulting trade-off is discussed.

We present a theory of ultrashort-pulse difference-frequency generation (DFG) with quasi-phase-matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. In the special case of a cw (or quasi-cw) pump, the spectrum of the generated idler is related to the spectrum of the signal through a transfer-function relation that is valid for arbitrary dispersion in the medium. The engineerability of this QPM-DFG transfer function establishes the basis for arbitrary pulse shaping. Experimentally we demonstrate QPM-DFG devices operating in a frequency-degenerate type II configuration and producing pulse-shaped output at 1550 nm from 220-fs pulses at 1550 nm.

Hybridized parametric amplification (HPA), a recent method to achieve high-efficiency parametric amplification by suppressing back-conversion with idler second harmonic generation, has been demonstrated so far only by birefringent phase matching. In this work, we demonstrate HPA by quasi-phase matching (QPM) in quasiperiodic-poled lithium niobate. QPM greatly expands the tuning range of HPA, while avoiding the limitations imposed by spatial walkoff of noncollinear beams. Since HPA has two concurrent processes, QPM requires a quasiperiodic grating with longitudinal spatial frequency peaks at both the parametric amplification and idler second harmonic generation phase mismatches. We investigate several grating designs for high-efficiency HPA in the near-infrared range. Quantum efficiencies of 70-80% are possible for devices pumped at 1030 nm, for both femtosecond and picosecond duration regimes. Pulse energies over 1 mJ can be accommodated using a chirped pump. However, devices must be designed carefully around the propagation effects of temporal walk-off and self-phase modulation.

We present a theoretical analysis of second-order nonlinear difference frequency generation (DFG) in a generalized mirrorless quasi-phase-matching (QPM) frame, aimed at a comparison of counterpropagating DFG configuration (CDFG) to other DFG schemes, in view of all-optical processing applications. Field nonlinear coupling equations have been numerically solved under the hypothesis of phase-matched interaction. The evolution of propagating fields within the material and the wavelength conversion efficiency have been calculated in dependence of operating parameters. The increased complexity in the evolution of amplitude and phase for fields interacting in CDFG with respect to forward-propagating DFG (FDFG) is at the basis of a dramatic increase in the wavelength conversion efficiency under particular settings of device parameters.

A configuration for wavelength conversion and optical amplification by parametric interaction using a nonlinear optical device is proposed. It enables pump generation through second harmonic generation (SHG), difference frequency generation (DFG), and optical parametric amplification (OPA) using a multiple-quasi-phase-matched (M-QPM) LiNbO3 waveguide in a bidirectional manner. Wavelength conversion for the 1.4–1.6 µm band is experimentally demonstrated. In addition, it is demonstrated that the parametric gain band can be changed using various detunings between the pump and QPM wavelengths used for the DFG/OPA process. The proposed method would be useful for enabling high-capacity optical transmission outside the 1550-nm band.