Dynamic computer-generated nonlinear-optical holograms

We propose and experimentally demonstrate dynamic nonlinear optical holograms by introducing the concept of computer-generated holograms for second-harmonic generation of a structured fundamental wave with a specially designed wave front. The generation of Laguerre-Gaussian second-harmonic beams is investigated in our experiment. Such a method, which only dynamically controls the wave front of the fundamental wave by a spatial light modulator, does not need domain inversion in nonlinear crystals and hence is a more flexible way to achieve the off-axis nonlinear second-harmonic beams. It can also be adopted in other schemes and has potential applications in nonlinear frequency conversion, optical signal processing, and real-time hologram, etc.

Figure 1

(a) Relation between $A(x,y)$ and $b(x,y)$. (b) Schematic of the experimental setup to realize dynamic computer-generated nonlinear optical holograms. The following denotations are used: HWP, half-wave plate; PBS, polarization BS; ${\mathrm{L}}_{1,...,4}$, lens; ${\mathrm{f}}_{1,...,4}=50,100,200$, and 50 mm, respectively; BS, beam splitter; SLM, spatial light modulator; Sample: 5 mol% MgO:$\mathrm{LiNb}{\mathrm{O}}_3$; F, filter; and SF, spatial filter.

Figure 2

Phase structures of the FW with 0-$\pi$ phase modulation corresponding to (a) ${\mathrm{LG}}_{10}$, (b) ${\mathrm{LG}}_{20}$, and (c) ${\mathrm{LG}}_{11}$ and profiles of calculated SH beams corresponding to (d) ${\mathrm{LG}}_{10}$, (e) ${\mathrm{LG}}_{20}$, and (f) ${\mathrm{LG}}_{11}$.

Figure 3

Generated SH beams in experiment corresponding to (a) ${\mathrm{LG}}_{10}$, (b) ${\mathrm{LG}}_{20}$, and (c) ${\mathrm{LG}}_{11}$ and cross section of the simulated (solid red curve) and measured (dashed blue curve) intensities corresponding to (d) ${\mathrm{LG}}_{10}$, (e) ${\mathrm{LG}}_{20}$, and (f) ${\mathrm{LG}}_{11}$.