Light Waves at the Boundary of Nonlinear Media

Abstract

Solutions to Maxwell's equations in nonlinear dielectrics are presented which satisfy the boundary conditions at a plane interface between a linear and nonlinear medium. Harmonic waves emanate from the boundary. Generalizations of the well-known laws of reflection and refraction give the direction of the boundary harmonic waves. Their intensity and polarization conditions are described by generalizations of the Fresnel formulas. The equivalent Brewster angle for harmonic waves is derived. The various conditions for total reflection and transmission of boundary harmonics are discussed. The solution of the nonlinear plane parallel slab is presented which describes the harmonic generation in experimental situations. An integral equation formulation for wave propagation in nonlinear media is sketched. Implications of the nonlinear boundary theory for experimental systems and devices are pointed out.

Resonantly Enhanced Second-Harmonic Generation Using III–V Semiconductor All-Dielectric Metasurfaces

“…However, efficient SHG using GaAs has been 7 challenging due to the difficulty in meeting phase-matching conditions for long crystals in the zinc-blende crystal structure which exhibits isotropic refractive indices. In addition, (100)-GaAs possesses only one non-zero χ (2) tensor element (d 14 ) which restricts the choice of nonlinear optical device geometries. In the following we will show that, due to the subwavelength layer thicknesses, resonantly enhanced SHG can be obtained from our GaAs dielectric metasurfaces without any provision for phase matching.…”

“…where (2) is the material's intrinsic second-order nonlinear susceptibility, V is volume, 2 is the field enhancement at the SH wavelength, and is the field enhancement at the fundamental wavelength. In this case, the SHG power is proportional to (2)eff • 2 , where I p is the incident pump intensity.…”

“…Using full-wave time- 13 dependent simulations including second order nonlinearities we first simulated the SHG emitted from our GaAs metasurfaces assuming only a bulk nonlinearity tensor (see Supporting Information, Section 4 for more details). The bulk second-order susceptibility (2) of GaAs is non-zero only when i≠j≠k due to the zinc-blend crystal structure (4 ̅ 3 ) of GaAs 4 . Therefore, the possible generated nonlinear polarizations at the SH frequencies inside the GaAs nano-resonators are , 2 ∝ 2 (2) , , 2 ∝ 2 (2) and , 2 ∝ 2 (2) .…”

“…The bulk second-order susceptibility (2) of GaAs is non-zero only when i≠j≠k due to the zinc-blend crystal structure (4 ̅ 3 ) of GaAs 4 . Therefore, the possible generated nonlinear polarizations at the SH frequencies inside the GaAs nano-resonators are , 2 ∝ 2 (2) , , 2 ∝ 2 (2) and , 2 ∝ 2 (2) . We performed our nonlinear simulation using a freely available finite difference time-domain software package 39 and the details can be found in Supporting Information (Section 4).…”

“…However, due to the centrosymmetric crystal structure of silicon, secondorder nonlinear optical phenomena were not observed in Si-based metasurfaces. Therefore, dielectric metasurfaces based upon other materials that exhibit an intrinsic second order nonlinear susceptibility ( (2) ) are needed to fully exploit this approach for enhanced harmonic generation and other second-order nonlinear phenomena. Nanoscale resonators made from III-V semiconductors can fulfill these requirements.…”