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Optics Express

Birefringence phase-matched direct third-harmonic generation in a ridge optical waveguide based on a KTiOPO4 single crystal

Augustin Vernay, Véronique Boutou, C. Félix, David Jegouso, Florent Bassignot, Mathieu Chauvet, Benoı̂t Boulanger

Published Jun 18, 2021• 11 citations
Publisher

Abstract

Birefringence phase-matched third-harmonic generation at 1594 nm is performed for the first time in a KTiOPO4 single crystal micrometric ridge waveguide. The energy conversion efficiency reaches 3.4% for a pump energy as low as 2 µJ over a pulse duration of 15 ps at a repetition rate of 10 Hz. Strong agreements between theory and experiments for both phase-matching and conversion efficiency is obtained, which let us envision future triple photon generation quantum experiments.

DOI
10.1364/oe.432636

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The European Physical Journal D•Oct 1, 2022•12 citations
Birefringence phase-matched third-harmonic generation at 1594 nm is performed for the first time in a KTiOPO4 single crystal micrometric ridge waveguide. The energy conversion efficiency reaches 3.4% for a pump energy as low as 2 µJ over a pulse duration of 15 ps at a repetition rate of 10 Hz. Strong agreements between theory and experiments for both phase-matching and conversion efficiency is obtained, which let us envision future triple photon generation quantum experiments.
Ridges waveguides carved in bulk nonlinear crystals such as LiNbO 3 [1] or KTiOPO 4 (KTP) [2] are a good alternative to reach a strong confinement of electromagnetic waves with large second-order or third-order non-linearity. We report here on our most recent experiments where we show the possibility to shape the birefringence phase-matching (BPM) conditions for direct Third-Harmonic Generation (THG: ω + ω + ω → 3ω) in micrometric KTP ridge waveguides by acting on their transverse dimensions. This study is the preliminary step for designing quantum optical experiments based on Triple Photons Generation (TPG: 3ω → ω + ω + ω) that is the reverse process of THG, thus exhibiting the same BPM conditions.
We demonstrate, for the first time to our knowledge, that efficient third-harmonic generation can be achieved with a cubic contribution much larger than the quadratic processes. An energy-conversion efficiency of 2.4% is achieved for cubic third-harmonic generation that is phase matched along the x axis of a KTiOPO(4) crystal by use of a picosecond fundamental laser emitting at 1618 nm. The associated cascading processes are only 10% of the pure cubic interaction, which is very suitable for study of the specific quantum optical correlations. Calculations of the third-harmonic generation conversion efficiency with respect to group-velocity dispersion and to the longitudinal Gaussian beam profile account well for our experimental results.
Triple Photon Generation (TPG) is a third-order nonlinear optical interaction in which a photon of energy ℏωp splits into three photons at ℏω1, ℏω2, and ℏω3, with ℏωp = ℏω1 + ℏω2 + ℏω3. The triplets possess different quantum signatures from those of photon pairs, with strong interest in quantum information. In the present study, we report the first experimental demonstration of TPG stimulated over one mode of the triplet, at ℏω1, whereas previous work on TPG concerned stimulation over two modes, at ℏω2 and ℏxω3. The nonlinear medium is a KTiOPO4 crystal pumped in the picosecond regime (15 ps, 10 Hz) at λp = 532 nm. The stimulation beam is emitted by a tunable optical parametric generator: the phase-matching was found at a stimulation wavelength λ1 = 1491 nm, the other two modes of the triplet being at λ2 = λ3 = 1654 nm in orthogonal polarizations. Using superconducting nanowire single photon detectors, the measurements of the polarizations and wavelength signatures of the two generated modes are in full agreement with calculations. It has been possible to generate a total number of photons per pulse on modes 2 and 3 up to 2 × 104, which corresponds to the generation of 104 triplets per pulse, or 105 triplets per second since the repetition rate is equal to 10 Hz. We interpreted these results in the framework of a model we developed on the basis of the nonlinear momentum operator in the Heisenberg representation under the undepleted pump and stimulation approximation.
We report implementation and modelling of an efficient photon-triplets generation experiment based on a difference-frequency-mixing of two picosecond beams at 532 nm and 1491 nm in a type II phase-matched KTP crystal. The photon-triplets flux was measured as a function of the energy of the two incident beams using a coincidence protocol. A maximal flux of 11.6 photon-triplets per second was achieved. These experimental data were satisfactorily described by a semiclassical model based on the quantum fluctuations of vacuum and the classical equations of nonlinear optics.
Demonstrating quantum properties of triple photons generated by χ3\chi ^3χ3 processes
Abstract Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states. Graphic abstract