Third harmonic generation from multilayer Van der Waals nanophotonic structure
Multilayer transition metal dichalcogenides (TMDCs) are an emerging class of dielectric materials with promising applications in modern nanophotonics. They exhibit a much higher refractive index (~ 4 - 4.5) than traditional semiconducting materials like Silicon (~ 3.5) in the near-infrared and infrared wavelength ranges. This not only enables the further miniaturization of optical elements such as lenses, gratings, and waveplates, but is also useful for building nanophotonic structures that can support high-quality factor resonant photonic modes. These properties facilitate efficient light trapping at the nanoscale, enabling strong light-matter interactions. This is particularly useful for nonlinear optical processes with applications in wave mixing processes, entangled sources for quantum applications, nonlinear up-conversion imaging, optical limiters, etc. Here, we investigated third-harmonic generation (THG) originating from a 110nm thick molybdenum disulphide (MoS2) film and a disk resonator with a diameter of 1.082um designed on top of a 2.4um SiO2-Silicon substrate using COMSOL Multiphysics 6.0. The simulation wavelength range was set in the infrared spectrum, spanning 1400 to 1700 nm. To simulate the third-harmonic generation phenomenon, we employed the wave optics module of COMSOL. Our simulation approach entailed frequency domain simulations with a 2D model for the film and a 3D model for the disk resonator, employing a tightly focused Gaussian wave excitation that was modelled using the plane wave expansion method. The parameters for the beam simulation were derived from the experimental data. To investigate the THG phenomena, first we started with the linear simulation solving the Maxwell equation at the fundamental wavelength. This allowed us to calculate the induced electric field within the film and the disk resonator, essential for determining the third-order nonlinear polarization. Subsequently, a second solver was employed, utilizing the third-order nonlinear polarization as the source term for THG process. Moreover, due to the significant computational time required for nonlinear optical processes, we judiciously applied symmetry (anti-symmetric) boundary conditions as needed to optimize memory usage and simulation time. Furthermore, we leveraged impedance boundary conditions to effectively simulate the infinite Silicon substrate, thereby substantially reducing the computation time. We then compared our simulation wavelength dependent THG data with experimental THG measurements performed on MoS2 film and disk samples on 2.4um SiO2 - Silicon substrate fabricated using electron beam lithography. By adjusting the SiO2 thickness, we observed good agreement between the experimental results and simulation data. The optimum SiO2 thickness is found to be 2.425 µm, indicating local variation in SiO2 thickness and highlighting thickness sensitivity of THG response. The good agreement between experimental results and simulation data not only validates the accuracy of our simulations but also can serve as an initial guideline for the development of even more complex nanophotonic designs in the future.
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