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The ability to manipulate the frequency of light is a cornerstone of a wide range of applications in photonics expanding spectral ranges of the light sources. To boost the second harmonic generation efficiency, intense efforts toward exploiting artificial microstructures for frequency doubling were carried out. The sought-after approach of utilizing photonic crystals is inspired by their unusual light dispersion. In such structures, the dynamics of the field of femtosecond laser pulses is of paramount importance for frequency conversion. In this work, we investigate the phase-matched second harmonic generation under the effect of diffraction-induced femtosecond laser pulse splitting in one-dimensional photonic crystals at the Bragg diffraction in the Laue geometry. We demonstrate that the interaction of the two pulses at the fundamental frequency that appears in photonic crystals through the dynamical light diffraction leads to a nonmonotonic dependence of the frequency up-conversion efficiency with respect to the laser pulse duration, thus allowing to increase the second harmonic power by tuning the pulse duration.

Artificial hyperbolic metamaterials (HMM) are perspective for the nonlinear optical applications, their exciting functionality being due to the hyperbolic dispersion induced by a strong shape anisotropy. Here we study the second harmonic generation (SHG) in HMM formed by arrays of silver nanorods in anodic alumina. In the hyperbolic dispersion regime, giant SHG is observed associated with the fulfillment of the phase-matching conditions supported by the epsilon-near-pole resonance at the SHG wavelength, and an increase in the pump field in the epsilon-near-zero (ENZ) spectral range. We predict a strong increase in the SHG efficiency for metamaterials with the ENZ resonance at the second harmonic frequency.

We present experimental and theoretical studies of the anomalous high transmission of light (the Borrmann effect) under the Laue diffraction in a one-dimensional photonic crystal (PhC) characterized by spatial modulation of both refractive index and absorption. We show that a strong modulation of the refractive index along with the large PhC period provide new features of the Borrmann effect as compared to the well-known x-ray Borrmann effect in crystals appearing in PhC wavelength-angular transmission spectra. Namely, the maximal transmission is attained at the Bragg angles of incidence and corresponds alternatively to even or odd orders of the Bragg angles depending on the light wavelength. Second, a dramatic decrease of the angular width of the high transmission areas in the spectrum appear near the diabolic points. According to our description, this effect can be treated as a result of the topological phase transition accompanied by exchange of the parity of spatial distribution of the electromagnetic field of the two eigenmodes experiencing degeneracy. We demonstrate that these peculiarities are inherent to the PhC with the optical losses located in layers with higher refractive index, and disappear if the losses are specific for the PhC layers with lower refractive index. The suggested underlying mechanism involves the contribution of the waveguide PhC modes to the PhC transmission spectra.

Phase-matched second-harmonic generation (SHG) under the Bragg diffraction in the Laue geometry in one-dimensional photonic crystal (PhC) is studied theoretically and experimentally. We demonstrate that the phase-matched SHG can be realized in a PhC by compensation of the material dispersion of the PhC constituent layers of adjustable thickness. The second-order nonlinear susceptibility is introduced in the porous quartz-based PhC by its infiltration by sodium nitrite. We observed that two second-harmonic (SH) beams appear after passing through the PhC under the phase-matched process, which correspond to the transmission and diffraction angular directions. The appearance of the phase-matched SHG is confirmed by a pronounced SH spectral dependence and a narrow SH angular distribution, with the FWHM of the SH peak of approximately 3.5 times smaller as compared to the case of non-phase-matched SHG.