Third harmonic generation at 223 nm in the metallic regime of GaP

Abstract

We demonstrate second and third harmonic generation from a GaP substrate 500 m thick. The second harmonic field is tuned at the absorption resonance at 335 nm, and the third harmonic signal is tuned at 223 nm, in a range where the dielectric function is negative. These results show that a phase locking mechanism that triggers transparency at the harmonic wavelengths persists regardless of the dispersive properties of the medium, and that the fields propagate hundreds of microns without being absorbed even when the harmonics are tuned to portions of the spectrum that display metallic behavior. , that the inhomogeneous component of the second harmonic ͑INH-SH͒ signal travels at the group velocity of the pump pulse. In a recent study phase and group velocity matching were demonstrated in lithium niobate in the range of transparency for all fields. The INH-SH was shown to refract at the same angle, and travel at the same velocity, as the pump.5 At the same time, the homogeneous SH component refracts and travels according to the values one expects from material dispersion at that frequency.The inhomogeneous component is generally difficult to observe because it travels locked under the pump pulse, with relatively low conversion efficiencies. In a recent study the results were generalized to include third harmonic generation ͑THG͒ in both positive and negative index media.6 When a pump signal traverses an interface into a nonlinear medium it generates SH and/or TH fields. Each harmonic has two parts: ͑i͒ a homogeneous portion that walk-off from the pump field; ͑ii͒ an inhomogeneous component phase-and velocitylocked to the pump, with no energy transfer between the fields except at interface crossings. The key observation here is that the INH-SH has a k-vector always double that of the pump, even for large phase mismatches. Theoretical findings thus suggest that the INH-SH signal experiences an effective complex index of refraction given by 2k c / 2 = k c / = n , i.e., the same index of refraction as the pump pulse.In Ref. 7, a pump pulse tuned at 1300 nm was launched into a slab of GaAs 500 m thick. Transmitted SH and TH signals were detected at 650 nm and 433 nm, respectively, far below the absorption band edge ͑ϳ900 nm͒. Simulations showed that only the inhomogeneous components propagate. Further experimental evidence 8 shows that the INH-SH is enhanced by several orders of magnitude compared to bulk 7 in an opaque GaAs cavity environment thanks to pump and INH-SH field localization and overlap. 9 The results of more experiments carried out in a high-Q GaAs cavity 10 hint that the INH-SH signal ͑612 nm͒ can achieve conversion efficiencies of order 10 −3 with pumping intensities as low as 0.15 MW/ cm 2 inside the cavity. We now ask the following question: does this phenomenon hold for harmonic fields tuned at frequencies in the metallic range? In other words, will a harmonic field propagate if it happens to be tuned in a region where sign͑͒ sign͑͒, where one expects no propagating solutions? The short answer to this ...

Singularity-driven second- and third-harmonic generation atε-near-zero crossing points

“…In Refs. [15,18] the technique was extended to include the effects of second-and third-order nonlinearities of materials like GaP and GaAs, which have anisotropic χ (2) and χ (3) tensors. Therefore, the methods are quite general and can handle vector field propagation in two dimensions and time.…”

“…This new theoretical aspect that pertains to the ε ∼ 0 condition is modeled by explicitly including electric and magnetic forces, as outlined in Refs. [15,16,18]. We consider the simple case of a 20-nm-thick layer of uniform, Lorentz-type medium.…”

Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity

“…This effect can be understood as inhibition of absorption at the harmonic wavelength for the INH component. Although one might be tempted to think that the INH SH is constantly being replenished by the pump, our simulations show, and experiments suggest [15,16], that pulses travel very long distances (hundreds of thousands of absorption lengths) May 15, 2011 / Vol. 36, No.…”

Second and third harmonic generation at UV and soft x-ray wavelengths from semiconductor gratings

“…Moreover, we stress that the size of the nanoslits carved in the GaAs layer is well below the cutoff for TE-polarized SH and TH. This means that all the TE generated fields are in fact generated only thanks to the phase locking that takes place between the pump and its harmonics, allowing generation even under extremely high absorption condition [18][19][20].…”

“…We demonstrate that harmonic components undergo band gap effects related to the pump wavelength and its harmonics, showing how phase locking [14][15][16] indeed allows the propagation, generation and transmission of light even below cutoff for the sub-wavelength guide and even under extremely high absorption condition [17][18][19][20].…”