The authors report on nondegenerate four-wave mixing in the near infrared using a one-dimensional chalcogenide-glass based photonic crystal. For 76 lattice constants, they find a 3.5-fold enhancement of the mixing signal with respect to the optimum-thickness bulk chalcogenide film. The key is the ability to tailor the dispersion relation of light in the photonic crystal, allowing for phase matching. Numerical calculations agree well with the experiments. Photonic crystals are a class of

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... al tailored materials for optics and photonics. They are usually composed of two different dielectrics, which are periodically arranged along d = 1, 2 or 3 dimensions. The periodicity leads to Bloch waves and a photonic band structure, which allows for tailoring the effective material dispersion relation of light. This aspect immediately suggests applications in nonlinear optics, where phase matching is known to be of crucial importance for efficient frequency conversion. Indeed, photonic crystals enable larger conversion efficiencies compared to the constituent bulk materials-as already pointed out theoretically by Bloembergen and Sievers in 1970 ͑Ref. 1͒ and demonstrated experimentally by van der Ziel and Ilegem in 1976 ͑Ref. 2͒ using a one-dimensional ͑1D͒ photonic crystal. More recent experimental examples are phase-matched direct third-harmonic generation ͑THG͒ in three-dimensional polymer-based opal structures, 3 THG in 1D liquid-crystal structures, 4 and phase-matched second-harmonic generation ͑SHG͒ in 1D II-VI semiconductor-based photonic crystals. 5,6 Surface SHG has been accomplished from two-dimensional III-V semiconductor-based photonic crystals. 7 In all these degenerate experiments, only one wave with a single color impinges onto the sample. In this case, phase matching requires simply matching the effective index at the fundamental frequency to that of the harmonic. Tailoring the dispersion relation of light in 1D photonic crystals also allows for phase matching in nondegenerate processes, i.e., nonlinear mixing with different incident colors. Here, we realize phase matching for a third-order process of the type 3 =2 1 − 2 that has not been published so far, to the best of our knowledge. We employ one-dimensional quarter-wave stacks ͑1D photonic crystals͒ composed of a large number of chalcogenide-glass 8 layer pairs. Chalcogenides are chosen because of their known large nonlinear-optical coefficients 9,10 and the ease of fabrication. The 1D configuration is employed because it conveniently allows for many tens of periods, corresponding to sample thicknesses exceeding the bulk phase-matching coherence length. We consider two different samples, one with 52 periods ͑104 individual layers͒, the other with 76 periods ͑152 individual layers͒. Both samples have been fabricated by thermal evaporation of granular As 2 Se 3 and As 2 S 3 in a high-vacuum chamber at pressures below 10 −5 mbar and temperatures around 470 and 365°C, respectively. The nominal As 2 Se 3 and As 2 S 3 layer thicknesses are 106 and 125 nm, respectively. The lattice constant is the sum, i.e., a = 231 nm ͓see inset in Fig. 1͑a͔͒ . Well below their absorption edge, the dispersion of the chalcogenides can be described by a dielectric function corresponding to a single undamped oscillator ͑without employing the rotating-wave approximation͒, i.e., by The resulting refractive index is n͑͒ = ͱ ⑀͑͒. For the As 2 Se 3 , we use ⑀ b = 4.5, b = 4.441 eV/ ប, and 0 = 2.812 eV/ ប; for the As 2 S 3 , ⑀ b = 3.55, b = 3.873 eV/ ប, and 0 = 3.622 eV/ ប. The refractive index of the thick glass substrate is taken as n SiO 2 = 1.5. Using this material dispersion and employing the "cutting surface method," 11 we calculate the band structure k͑͒ of the 1D photonic crystal and depict it in Fig. 1͑a͒ . The gray area highlights the 1D photonic stop band. The retrieved effective refractive index of the structure, defined by n eff ͑͒ = k͑͒c 0 / , is shown in ͑b͒. c 0 is the vacuum speed of light. The calculated and the measured normal-incidence transmittance of a 52-period stack are shown in ͑c͒ and ͑d͒, respectively. Next, we compute the wave vector mismatch ⌬k =2k 1 − k 2 − k 3 =2k͑ 1 ͒ − k͑ 2 ͒ − k͑ 3 ͒ for the generated frequency component 3 =2 1 − 2 on the basis of the retrieved index and plot it on a gray scale versus the two input frequencies 1 and 2 in Fig. 2 . This plot gives an overview about the parameter space to be explored below. The white regions correspond to ⌬k = 0 hence perfect phase matching, i.e., to large nonlinear signals. In our nonlinear-optical experiments, we employ two optical parametric amplifiers ͑OPAs͒, both pumped by a regeneratively amplified Ti:sapphire femtosecond laser system ͑Spectra Physics Hurricane͒ and independently tunable in the spectral range of interest. Unfortunately, tuning the OPA center wavelength is accompanied by changes in the pulse du-a͒ Electronic