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Maximizing Sum Frequency Generation Efficiency

Yutian Zhang

Published Nov 1, 2022• 0 citations
OpenAlex

Abstract

In this thesis, high-efficiency frequency conversion Sum Frequency Generation (SFG) is theoretically analyzed and experimentally demonstrated. Our approach to SFG consists of two input phase conjugated broadband signal and idler beams undergoing SFG. By using the signal waveform as a gating beam, a specific mode may be recognized and separated out, providing a promising method for mode selection. The signal and idler are produced by a monochromatic pump and a broadband signal through Difference Frequency Generation (DFG). To obtain good mode selectivity, high conversion efficiency of the selected mode is required. We study the factors that influence the conversion efficiency of the selected mode, like the length of the waveguide and the power of the gating beam. The highest conversion efficiency of the mode achieved is over 90%. By breaking the correlation between mode and gating beams, we find around 40% conversion efficiency of the mismatched mode.

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Journal of the Optical Society of America B•Feb 4, 2026•0 citations
In this thesis, high-efficiency frequency conversion Sum Frequency Generation (SFG) is theoretically analyzed and experimentally demonstrated. Our approach to SFG consists of two input phase conjugated broadband signal and idler beams undergoing SFG. By using the signal waveform as a gating beam, a specific mode may be recognized and separated out, providing a promising method for mode selection. The signal and idler are produced by a monochromatic pump and a broadband signal through Difference Frequency Generation (DFG). To obtain good mode selectivity, high conversion efficiency of the selected mode is required. We study the factors that influence the conversion efficiency of the selected mode, like the length of the waveguide and the power of the gating beam. The highest conversion efficiency of the mode achieved is over 90%. By breaking the correlation between mode and gating beams, we find around 40% conversion efficiency of the mismatched mode.
We analyze the dynamics of sum-frequency generation (SFG) and difference-frequency generation (DFG) for broadband input fields. We demonstrate that amplitude modulation of the input fields significantly affects conversion efficiency of SFG and DFG, but frequency modulation does not affect conversion efficiency. Analytic results for SFG and DFG output-field intensities are thereby available for arbitrary fields. Self- and cross-phase modulation can affect the dynamics in the limit of very high field strengths, but these effects are of higher nonlinearity and therefore usually negligible. The quantum efficiency of DFG is shown to be generally higher than SFG, but the energy efficiency is much lower if the difference frequency is significantly less than the input frequencies. Optimal SFG quantum conversion efficiency for such systems approaches that of second-harmonic generation only if the quantum fluence (total number of photons) in the two input beams are equal. Optimal DFG quantum conversion efficiency occurs when the number of photons of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$ is small yet sufficient for significant stimulation. A recently developed method for obtaining efficient SFG for multimode input fields is theoretically analyzed. The method involves using an arrangement with two or more nonlinear mixing crystals with a time-delay line situated between the crystals that delays one of the fundamental fields relative to the other. The efficiency in the second crystal depends on the cross-correlation function of the two fundamental fields upon leaving the first nonlinear crystal. The time-delay method is not effective for multimode DFG.
Cascaded second-order nonlinear interaction (&chi(2));based wavelength conversion technique has attracted much attention due to its unique characteristics such as low noise and broadband, which are critical in fiber communication networks. In this report, wavelength conversions based on the newly proposed SFG-DFG (sum frequency generation - difference frequency generation) and conventional SHG-DFG (second harmonic generation - difference frequency generation) are studied and compared both experimentally and theoretically in a LiNbO3 quasi-phase matched (QPM) waveguide. It is shown that the same conversion efficiency can be achieved by employing two pump sources with only half power each (P1, P2) in the SFG-DFG scheme as compared with the SHG-DFG scheme with a single higher power pump beam (P=P1+P2). It is shown that the cascaded SFG-DFG based wavelength conversion has a larger 3-dB pump tolerance bandwidth. The theoretical results are consistent well with the experimental ones. It is found that the pump wavelength difference can be separated by a span as large as 75 nm, while 3-dB signal conversion efficiency is retained in a 45 mm-long device. It is also exhibited that tolerance of temperature for the cascaded SFG-DFG remains the same as that of the cascaded SHG-DFG based devices. The results show that the SFG-DFG wavelength conversion scheme is very attractive for practical applications.
A novel wavelength conversion scheme based on cascaded sum-frequency generation (SFG) and difference-frequency generation (DFG) is proposed and demonstrated in a MgO-doped LiNbO3 quasi-phase-matched waveguide. In this scheme, two pump wavelengths are set outside the communication band. It is shown that the same conversion efficiency can be achieved by use of two pump sources with lower output power (P1, P2) in this scheme compared with the conventional cascaded wavelength conversion technique based on second-harmonic generation and DFG with a single higher-power pump beam (P = P1 + P2) that is due to the use of a larger SFG nonlinear coefficient. The results significantly influence the selection of a suitable nonlinear interaction scheme for practical applications.
We study sum-frequency generation (SFG) in a multimode PPKTP waveguide. We show that under proper quasi-phasematching, it can support one of the two scenarios. In the first, a single pump mode up-converts several different signal modes to different SFG modes. In the second, several different pairs of signal and pump modes are converted to the same SFG mode. By adjusting the relative phases and magnitudes of the pump modes, any superposition of the corresponding signal modes can be selected for up-conversion without affecting other modes, which can be used for spatial-mode de-multiplexing in both classical and quantum communications.
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.