Coherent Control and Enhanced Parametric Gain by Dual-Beam Pumping of 2D Nonlinear Photonic Crystals

Two-dimensional periodically poled LiNbO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> and LiTaO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> lattices afford unique spectral and spatial functionalities, enabling coherent parametric sources and amplifiers for advanced classical and quantum applications [1], [2]. Such capabilities can be further enhanced with structured optical excitations, as highlighted in recent theoretical studies on dual-pump optical parametric generation (OPG) [3]. Here we present results confirming such predictions with experiments in hexagonally poled LiTaO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (HexLT) coherently excited by a dual-beam pump at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda_{\mathrm{P}}=532$</tex> nm (Fig.1a, wavevectors <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{p 1}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{p 2}$</tex>), generating signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k_{s})$</tex> and idler <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k_{i})$</tex> outputs around <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda_s \sim 0.76-0.82 \mu \mathrm{~m}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda_{\mathrm{i}}$</tex> ~ 1.50 - 1.77 μm, respectively. Moreover, we model the OPG process in a semiclassical approximation and 2D beam propagation, extending the results of Ref. [3] beyond plane-wave approximations, to account for realistic experimental conditions. Fig. 1b shows a 2D map of the computed spectral <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\lambda_{\mathrm{s}})$</tex> and angular <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\theta_{s})$</tex> signal emission from a HexLT lattice pumped by two Gaussian beams whose incidence angles realize the special pump-lattice resonance condition whereby the transverse components of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{p1}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{p2}$</tex> match those of reciprocal lattice vectors (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G_{10}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G_{01}$</tex> in Fig. 1a). The OPG simulations exhibited excellent agreement with the measured far-field distributions (Fig. 1c) and supported further quantitative analyses of the gain enhancement and coherent OPG response expected in the spectral region of Fig. 1d, explored in subsequent experiments with the setup of Fig. 1e.