By employing a distinctive “concentric stepped ring” structure, the Fresnel lens decomposes the continuous surface of a conventional lens into multiple “annular micro-lenses,” each functioning as an independent refracting surface. This design dramatically reduces the lens thickness and mass while maintaining focusing or imaging performance comparable to that of a traditional convex lens. Because of this thin and lightweight architecture, Fresnel lenses are widely used in lighthouse illumination, projection systems, solar concentrators, and compact imaging devices—particularly in applications where high focusing efficiency is required under tight volume and cost constraints. In this case, a 2D FDTD simulation is performed for a Fresnel lens derived from a spherical lens profile, demonstrating its wavefront-shaping capability and characteristic phase behavior.
The blazed grating is a specially optimized diffractive structure designed to efficiently direct most of the incident light energy into a designated diffraction order by introducing a blaze angle on the grating surface. This significantly improves diffraction efficiency while suppressing unwanted orders. In this case study, an `FDTD` simulation is performed on a blazed grating to analyze its energy distribution among different diffraction orders.
The tapered-waveguide-type polarization converter achieves efficient polarization conversion by enabling smooth energy coupling between different polarization modes through a gradually varying waveguide cross-section along the propagation direction. This structure offers advantages such as broad bandwidth, low loss, and high tolerance to fabrication errors, making it widely used in optical communications, polarization multiplexing, and polarization control in silicon photonic chips. In this example, the FDE solver is first used to sweep the waveguide width and analyze the variation of the effective refractive index of the TM1 and TE0 modes, identifying the region where the two modes intersect to guide the design range of the tapered waveguide. Subsequently, the FDTD solver is employed to perform a three-dimensional simulation of the entire structure to calculate the light propagation and polarization conversion efficiency within the tapered waveguide.
The bull’s-eye aperture is a metallic subwavelength optical structure characterized by a central circular hole surrounded by periodically distributed concentric grooves. When incident light illuminates the metal surface, the concentric slits excite surface plasmon polaritons (SPPs) at specific wavelengths, which are re-radiated through the central aperture to the opposite side, resulting in strong transmission and significant field enhancement. In this case study, a bull’s-eye aperture fabricated on a silver film is simulated to demonstrate its characteristic field enhancement and directional radiation effects.
In FDTD simulations, obtaining the field distribution at locations far from a device usually requires expanding the simulation domain so that light can fully propagate to the target plane. While this approach is straightforward, it significantly increases computational cost and simulation time. This case presents a Grating Projection(GP)–based approach that can quickly obtain the distribution of fields propagating in homogeneous media at any specified location, and verifies its accuracy through comparison with FDTD simulation results.
In nonlinear optics, four-wave mixing (FWM) is a typical third-order nonlinear effect widely employed in areas such as all-optical signal processing, wavelength conversion, and the generation of new light sources. When light propagates through a material with Kerr nonlinearity, the nonlinear interaction of multi-frequency optical fields can generate new frequency components, achieving frequency mixing and energy transfer. This case demonstrates an FDTD simulation workflow for four-wave mixing based on a third-order nonlinear material.
Subwavelength optical devices hold great potential in light field manipulation and photonic integration. However, at subwavelength scales, light undergoes strong interference and diffraction, making it difficult to achieve efficient focusing. Garcia-Vidal et al proposed a structure consisting of a single subwavelength aperture in a metallic film surrounded by periodic surface grooves. By exciting surface plasmons, this design enables far-field focusing. In this case, we reproduce the structure with FDTD simulations and analyze the focal spot size to demonstrate its focusing capability.
The Diffraction grating is a classic type of periodic optical element, widely used in fields such as spectroscopy, laser beam control, and beam splitting. Their functionality relies on spatially modulating the wavefront of incident light to generate a series of discrete diffraction orders in specific directions. Since a grating's performance is governed by its diffraction-order energy distribution, precise quantification of this distribution becomes critical for design optimization. This case demonstrates how to use the grating projection functions in an FDTD simulation of a two-dimensional periodic grating, allowing for accurate evaluation of the energy distribution among diffraction orders and their corresponding efficiencies.
The Wilkinson power divider is a three-port device used for power distribution. Compared to a conventional T-junction power divider, it can match all ports and achieve arbitrary power distribution. Unlike resistive power dividers, the Wilkinson power divider not only can isolate the output ports but also indicate no loss when the ports are matched, only dissipating reflections from the output ports. This case models and simulates an equal-split (3dB) Wilkinson power divider designed in Example 7.2 from Pozar.
Traditional curved optical lenses rely on phase accumulation along the light path to control light, which is limited by the refractive index of natural materials. To correct various image aberrations, multiple lenses are usually needed. However, combining multiple optical lenses occupies a lot of space, making it difficult to miniaturize optical systems. Metalenses, however, manipulate incident light to bend beams through the arrangement of artificial sub-wavelength units on the dielectric surface. A single metalens can achieve the same performance as a device that requires multiple optical lenses. Compared to traditional optical lenses, metalenses are smaller, lighter, cheaper, have better imaging quality, and are easier to integrate. They provide a new solution for compact integrated optical systems. This case study, based on the research of Xicheng Xia and Zan Yao, introduces how to use FDTD to simulate metalenses, helping readers achieve miniaturization of optical systems.
