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Symposium on Photonics and Optoelectronics

Implementing Control for Sum Frequency Generation by Using a Chirped Quasi-Phase-Matched Crystal

Baihong Li, Tao Zhang, Zhengxin Yan, Yamin Wang, Wei Liu, Min Li

Published May 1, 2012• 0 citations
Publisher

Abstract

Based on the dressed state formalism, we obtain the adiabatic criterion of sum frequency generation(SFG).We show that the key points of energy conversion for sum frequency conversion correspond to the diabatic points. The high efficiency and broadband sum frequency conversion that we desired can be obtained by using a chirped quasi-phase-matched(QPM) crystal. Therefore,we can control SFG manually.

DOI
10.1109/sopo.2012.6270940

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Based on the dressed state formalism, we obtain the adiabatic criterion of sum frequency generation(SFG).We show that the key points of energy conversion for sum frequency conversion correspond to the diabatic points. The high efficiency and broadband sum frequency conversion that we desired can be obtained by using a chirped quasi-phase-matched(QPM) crystal. Therefore,we can control SFG manually.
An efficient broadband sum-frequency generation (SFG) technique using the two cascaded optical parametric processes ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ and ${\ensuremath{\omega}}_{4}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{3}$ is proposed. The technique uses chirped quasi-phase-matched gratings, which, in the undepleted pump approximation, make SFG analogous to adiabatic population transfer in three-state systems with crossing energies in quantum physics. If the local modulation period first makes the phase match occur for ${\ensuremath{\omega}}_{3}$ and then for ${\ensuremath{\omega}}_{4}$ SFG processes then the energy is converted adiabatically to the ${\ensuremath{\omega}}_{4}$ field. Efficient SFG of the ${\ensuremath{\omega}}_{4}$ field is also possible by the opposite direction of the local modulation sweep; then transient SFG of the ${\ensuremath{\omega}}_{3}$ field is strongly reduced. Most of these features remain valid in the nonlinear regime of depleted pump.
Based on the dressed state formalism, we obtain the adiabatic criterion of the sum frequency conversion. We show that this constraint restricts the energy conversion between the two dressed fields, which are superpositions of the signal field and the sum frequency field. We also show that the evolution of the populations of the dressed fields, which in turn describes the conversion of light photons from the seed frequency to the sum frequency during propagation through the nonlinear crystal. Take the quasiphased matched (QPM) scheme as an example, we calculate the expected bandwidth of the frequency conversion process, and its dependence on the length of the crystal. We demonstrate that the evolutionary patterns of the sum frequency field's energy are similar to the Fresnel diffraction of a light field. We finally show that the expected bandwidth can be also deduced from the evolution of the adiabaticity of the dressed fileds.
We propose an adiabatic scheme for cascaded fourth-harmonic generation (FHG) in chirped dual-period quasi-phase-matched (QPM) crystals, where adiabatic evolution is introduced into the multi-step frequency conversion process. By engineering two chirped QPM gratings for the fundamental-to-second-harmonic ( FF → SH ) and second-to-fourth-harmonic ( SH → FH ) interactions, efficient harmonic generation is achieved through a continuous adiabatic passage in phase-mismatch space, rather than discrete phase-matching conditions in conventional QPM schemes. This approach enables robust and tunable energy transfer among harmonics, allowing controllable generation of second- and fourth-harmonic signals. Numerical results show a maximum FHG efficiency of 94% and a tunable bandwidth of ∼13 nm under realistic conditions. The tunability originates from the controlled shift of QPM resonances along the propagation direction.
Based on an analogy between the macroscopic phenomena and quantum physics, we study the problem of energy conversion for the sum frequency generation (SFG) process in a linear chirped quasi-phase-matched (QPM) crystal. We show that the process of energy conversion from the signal to the sum frequency field is very similar to the process of Landau-Zener tunneling (LZT) in a two-level system. Therefore, the energy conversion mechanism of SFG process can be explained by the theory of LZT. In addition, we obtain the asymptotic and analytical solution of the sum frequency field by solving the coupled equations with the model of Landau-Zener.
We propose an efficient broadband frequency generation technique for two collinear optical parametric processes ω3=ω1+ω2ω_3=ω_1+ω_2ω3​=ω1​+ω2​ and ω4=ω1−ω2ω_4=ω_1-ω_2ω4​=ω1​−ω2​. It exploits chirped quasi-phase-matched gratings, which in the undepleted pump approximation regime perform population transfer that is analogous to adiabatic population transfer in a three-state ``vee'' quantum system. The energy of the input fields is transferred adiabatically either into ω3ω_3ω3​ or ω4ω_4ω4​ field, depending on which of the two phase matchings occurs first by the local modulation period in the crystal. One can switch the output between ω3ω_3ω3​ and ω4ω_4ω4​ by inverting the direction of the local modulation sweep, which corresponds to a rotation of the crystal by angle πππ
Two frequency-cascaded and spatially simultaneous three-wave-mixing processes, each pumped by a different frequency, are studied in a quasi-phase-matching crystal with chirped poling. Theory, numerical simulation, and experiment all show that efficient two-process adiabatic frequency conversion takes place over a broad range of input wavelengths. Experimentally, up to five process cascades are obtained. Furthermore, it is demonstrated that reversing the chirp sign results in a different conversion for the same input wavelength. This method can be applied to generation of an all-optically tunable frequency comb.