Manipulating second-harmonic light from semiconductor nanocrystals

Abstract

Among the nonlinear behaviors exhibited by light, secondharmonic generation (SHG)1 is one of the most important. In SHG, the frequency of an incident light beam is doubled inside of a nonlinear crystal: see Figure 1(a) and (b). SHG is nowadays employed in many applications, including laser sources and nonlinear microscopy. SHG usually relies on bulk nonlinear crystals—see Figure 1(b)—such as lithium niobate, potassium titanyl phosphate, or beta barium borate. Unfortunately, these materials are difficult to integrate with other devices (due to the difficulties inherent in their manufacturing and machining) and are not costeffective. Furthermore, special phase-matching conditions are often required in order to obtain useful conversion efficiencies. Although the output beam profile in bulk crystals can be engineered by complex periodic poling,2 this technique is not easily accessible (due to its requirement for a spatially inhomogeneous distribution of high voltages across the crystals). To overcome these issues, it would be useful if we could replace bulk nonlinear crystals with ultrathin surfaces composed of nanocrystals that can generate SHG with high efficiency. Such nonlinear ‘metasurfaces’ could also be used to manipulate the SHG radiation pattern to form complex beams with arbitrary patterns: see Figure 1(c–e). This may sound like science fiction, but optical technology is rapidly advancing toward achieving Figure 1. (a) Schematic of the nonlinear process of second-harmonic generation (SHG), which doubles the frequency of light in a crystal. (b) A conventional SHG process within a bulk nonlinear crystal, generating a blue Gaussian beam in the forward direction. (c) SHG from small objects, such as anisotropic molecules, is emitted in both forward and backward directions, resulting in a dipolar radiation pattern resembling a figure eight. (d) For larger nanocrystals, the emission can differ in forward and backward directions due to the interference of several resonant modes (multipoles) inside the nanocrystal. (e) Our goal of initiating SHG within small nanocrystals to design a radiation pattern that creates a complex beam shape (e.g., a kangaroo) with high conversion efficiency. !: Angular frequency. .2/: Second-order susceptibility.