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arXiv:2109.11368 · Physical Review A

Grating-induced slow-light enhancement of second-harmonic generation in periodically poled crystals

Thomas E. Maybour, Devin H. Smith, Péter Horák

Published Jan 18, 2022• 2 citations
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Abstract

The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.

DOI
10.1103/physreva.105.013517

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The effect of slow light on second-harmonic generation in a periodically poled \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) nonlinear medium is investigated theoretically. A linear \ensuremathπ\ensuremath{\pi}\ensuremathπ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.
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Abstract We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.
We demonstrate both theoretically and numerically that slow light can enhance the stimulated emission of four-level atomic systems in photonic crystals. By applying the Bloch-Floquet formalism and the semiclassical physical model of harmonic oscillators coupled to electromagnetic fields, we develop a formalism that relates the group velocity of slow light to the conversion rate between the electric field and atomic potential energy. From our numerical study of the stimulated emission in fiber Bragg gratings (FBGs) and nongrating fiber, a ninefold enhancement of stimulated emission is observed in a FBG over the nongrating fiber when pumping at the band edge, while a 20-fold enhancement of is observed when the frequency of the stimulated emission approaches the band edge.
Optical poling is a very simple technique for inducing a quadratic nonlinearity in germanium-doped silica fibers [1] , [2] . By injecting into the fiber fundamental frequency (FF) pulses together with a low power second harmonic (SH) seed, a multi-photon quantum interference process naturally generates a quadratic nonlinearity whose period satisfies the quasi-phase matching (QPM) condition. The nonlinear grating writing process takes a few hours before showing a saturation of the SH conversion efficiency, which is always lower than the best values achievable by resorting to thermal poling [3] . Also, the maximum length of the poled region exhibits saturation, and this hampers the SH generation [4] .
We theoretically demonstrate cascaded fourth and second harmonic generation in a periodically-poled nonlinear crystal with a half-order of phase-matching period. We consider a cascaded process in which four photons of the fundamental harmonic firstly convert into an intermediate photon of the fourth harmonic, which parametrically decays into two photons of the second harmonic at the second stage. Phase-matching for this cascaded nonlinear conversion is provided by using an asymmetric periodical poling. We use the quantum spatial Heisenberg equations to describe light propagation and conversion inside the nonlinear crystal. With this approach, we calculate second and fourth harmonic average number of photons as a function of the nonlinear crystal length.
We demonstrate a high-efficiency green light conversion from an external cavity second harmonic generation with a MgO-doped periodically poled LiNbO 3 crystal. The frequency doubler can reach a conversion efficiency of 64% with a fundamental power of 26 mW. Meanwhile, the generated green light is quadrature-amplitude squeezed and 1.2 dB green light squeezing is experimentally measured. The squeezing at different pump levels is also investigated and is in good agreement with the theoretical prediction.