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Journal of the Optical Society of America B

Optimal control of transient sum-frequency mixing processes

Roberto Buffa

Published Jul 1, 2002• 5 citations
Publisher

Abstract

An optimal control technique is applied to design a pair of input laser pulses that control the temporal shape of an optical pulse generated in a process of transient sum-frequency mixing. Specific calculations performed for a model crystal in the case of fifth-harmonic generation are discussed as an example. The efficiency of the generation process is enhanced by the use of temporally tailored laser pulses.

DOI
10.1364/josab.19.001599

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An optimal control technique is applied to design a pair of input laser pulses that control the temporal shape of an optical pulse generated in a process of transient sum-frequency mixing. Specific calculations performed for a model crystal in the case of fifth-harmonic generation are discussed as an example. The efficiency of the generation process is enhanced by the use of temporally tailored laser pulses.
Sum-frequency generation in nonlinear optics is a key technology enabling optical frequency conversion. However, how to most effectively enhance the frequency conversion efficiency in nonlinear crystals remains a fundamental problem; shorter crystal length and lower pump intensity while maintaining high-efficiency frequency conversion are critical for enhancing device integration potential and improving device performance in practical sum-frequency generation (SFG) device design. This study employed the Pontryagin maximum principle to investigate the SFG process. A cost functional was formulated that complies with the minimum constraint during SFG, enabling the derivation of optimal control parameters. A central finding revealed an inverse proportionality between the coupling coefficient and the crystal length: for a given crystal length, the pump intensity in the SFG is minimized, and vice versa. The optimal evolution trajectory follows a geodesic path on the Bloch sphere surface, representing the minimal-length evolutionary path from the signal field to the sum-frequency field. This geodesic behavior also indicates that the loss and absorption of the optical field in the crystal medium vanish during SFG. Furthermore, the crystal modulation period for the SFG is determined using the optimal phase-matching function. These results offer valuable insights for the design of compact optical chips and nonlinear optical devices.
The optimal properties for single photons may vary drastically between different quantum technologies. Along with central frequency conversion, control over photonic temporal waveforms will be paramount to the effective coupling of different quantum systems and efficient distribution of quantum information. Through the application of pulse shaping and the nonlinear optical process of sum-frequency generation, we examine a framework for manipulation of single-photon waveforms. We use a nonperturbative treatment to determine the parameter regime in which both high-efficiency and high-fidelity conversion may be achieved for Gaussian waveforms and study the effect such conversion techniques have on energy-time entanglement. Additionally, we prove that aberrations due to time ordering are negligible when the phase matching is nonrestrictive over the input bandwidths. Our calculations show that ideal quantum optical waveform conversion and quantum time lensing may be fully realized using these techniques.