Frequency Tripling via Sum-Frequency Generation at the Nanoscale

Abstract

High refractive index dielectric nanostructures can be exploited to enhance nonlinear optical processes via the strong light confinement by their resonant modes. The sensitive dependence of these modes on the geometry and material composition offers ample opportunities for tailoring the optical response of the system. Here we report sum-frequency generation (SFG) by individual AlGaAs nanocylinders, pumped by two pulsed beams at a telecommunication frequency, ω, and its duplicate, 2ω. Under such a scheme, the SFG at 3ω = ω + 2ω is degenerate with the thirdharmonic generation (THG) seeded by the input at ω, thereby tripling its frequency via the second-order permittivity χ (2) , rather than via χ (3) as in THG. The concurrent detection of THG and SFG enables us to determine χ (3) = 7 × 10 −20 m 2 /V 2 by comparing experiments to numerical simulations and based on the known value of χ (2) . We observe a rich size-and polarization-dependent behavior that gives appeal to the studied system as a key component of miniaturized photonic devices.

Coherent Control of the Nonlinear Emission of Single Plasmonic Nanoantennas by Dual‐Beam Pumping

“…In fact, in centro‐symmetric structures and axial illumination/collection geometry, one should expect γ = 0, as discussed in Ref. [24], and no interference fringes should be observed. The detection of such fringes goes far beyond being a mere side effect of the frequency degeneracy between SFG and THG.…”

Nonlinear Dielectric Nanoantennas and Metasurfaces: Frequency Conversion and Wavefront Control

“…(3) = 0.6 (1550 nm) 145 [a-Si:H] Ge λ > 1090 146 4.33−4.04 (1090−2000 nm) 146 χ 1111 (3) = 0.4 (2000 nm) 144 a-Ge λ > 1300 147 4.67−4.35 (1300−2000 nm) 147 χ 1111 (3) = 0.57 (1650 nm) 137 Al 0.22 Ga 0.78 As λ > 720 78 3.60−3.27 (720−2000 nm) 78,81 χ eff (3) = 0.07 (1554 nm) 148 ZnO λ > 400 85 2.22−1.92 (400−2000 nm) 84,85 χ 1111 (3) = 0.03 (1500 nm) 149 TiO 2 (thin film) λ > 370 150 2.84−2.26 (370−2000 nm) 150,151 χ 1111 (3) = 0.02 (1550 nm) 152 a Transparency range, refractive index, and primary component or effective value of χ (3) of crystalline and amorphous dielectrics investigated for resonant THG on the nanoscale. χ (3) is relatively low in many ordered crystals, assuming isotropic conditions usually represents a good approximation.…”

“…The increased response is attributed to the better spatial overlap of the pumped modes, both containing electric and magnetic dipole contributions, and the more directional emission toward the collecting lens, as enabled by the particular crystalline cut. Zilli et al 148 investigated a (100)-AlGaAs nanodisk for frequency tripling via SFG, by pumping the resonator at ω and 2ω (3ω = ω + 2ω), so that the SFG signal is degenerate with THG. The nanonantenna was excited at the magnetic dipole or anapole resonance for the lower energy pump, by tuning the disk diameter.…”

“…Zilli et al investigated a (100)-AlGaAs nanodisk for frequency tripling via SFG, by pumping the resonator at ω and 2ω (3ω = ω + 2ω), so that the SFG signal is degenerate with THG. The nanonantenna was excited at the magnetic dipole or anapole resonance for the lower energy pump, by tuning the disk diameter.…”

Cascaded Optical Nonlinearities in Dielectric Metasurfaces

“…Four-wave mixing, one of the hallmarks of third-order nonlinearities, can also be achieved by SHG of one pump beam, followed by difference frequency generation (DFG) with a second pump beam . Traditionally, χ (2) :χ (2) (3ω) is weak in bulk media since phase-matching limits frequency mixing to one process at a time. − In nonlinear metasurfaces, due to the relaxation of phase-matching limitations, several of the frequency mixing products observed experimentally might be explained by cascaded second-order optical nonlinearities. − However, given that both χ (3) :THG and χ (2) :χ (2) (3ω) occur at the same frequencies and are assumed to have the same polarization response in cubic crystal systems, it is difficult to distinguish between the two processes in these types of non-phase-matched systems. Understanding the origin of light conversion in these systems is critical since the efficiencies of cascaded harmonic generation could compete with those of conventional direct frequency mixing processes or even surpass them. , …”