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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.
The demand for smaller, faster, and lower power semiconductor devices continuously drives advances in optical lithography technology. As the size of semiconductor devices continues to shrink, it is necessary to use alternating phase shift masks (APSM) to improve resolution. For example, at the node, some features to be imaged are smaller than the diffraction limit of the light source used. APSM modulates the phase so that the light interferes with itself after passing through the mask, making the mask pattern edges sharper and clearer, thereby improving pattern contrast. The proximity effects occurring at sub-wavelength scales need to be understood through lithography simulation, so they can be accounted for in mask design, ensuring a predictable and reliable process. This case demonstrates how to image sub-wavelength features using APSM in FDTD.
Antoniades et al. proposed a new type of negative refractive index(NRI) coplanar waveguide(CPW) transmission line(TL), which can be used after conventional TL for phase compensation, allowing the design frequency to propagate through all TLs to achieve positive, negative, or zero phase shifts. The propagation characteristics of this NRI metamaterial are mainly determined by lumped elements. Therefore this new NRI-TL can change the phase characteristics by simply adjusting the value of the lumped element instead of adjusting the length. Thus, this new NRI-TL offers significant advantages over conventional delay lines.
Coaxial-fed rectangular patch antenna is a fundamental type of microstrip antenna composed of a dielectric substrate, a ground plane, and a conductive patch. Compared to traditional antennas, Coaxial-fed rectangular patch antennas are compact, lightweight, easy to integrate, cost-effective, and suitable for mass production. In this case, a rectangular patch antenna mounted on an infinite metal ground plane is simulated using FDTD, and its return loss and far-field directivity are calculated.
By default, mode source calculates mode at central frequency of the specified frequency range and then injects this mode at all frequencies, which is very effective in single-frequency and narrowband simulations. However, in broadband simulations, mode-mismatch errors increase as frequency range expands. In this example, the multi-frequency field of the mode source will be demonstrated using a copper wire with a thin dielectric coating operating in the broadband terahertz range.
In 2007, Kaliteevski et al. successfully excited Tamm plasmon polaritons (TPPs) between metal and Bragg gratings. The TPPs can be directly excited since the dispersion curves of TPPs lie within the light cone. Additionally, both TE and TM polarized light can be stimulated in TPPs since there is no requirement for the angle of incidence. These characteristics make TPPs popular in the fields such as surface light enhancement, nonlinear optics, and lasers. This case will simulate and study this process.
Arrayed waveguide gratings (AWGs) are essential components in dense wavelength division multiplexed (DWDM) systems. As large-scale photonic integrated devices continue to evolve, the miniaturization design of AWGs has become an important topic. In this example, a 2.5D-FDTD solver in SimWorks Finite Difference Solutions was employed to simulate a saddle-shaped silicon nanowire AWG to investigate its output spectral response and loss.
In this case, the Woodpile-Lattice photonic crystal is constructed, and the FDTD solver is used to explore the energy bandstructure of the photonic crystal.
In this case, the operation process and precautions are stressed by using FDTD solver to simulate microring resonance.
The grating coupler has emerged as crucial components in silicon nanophotonics. Addressing the coupling issue between optical fibers and waveguides has become a prominent research focus in recent years. Polarization splitting grating couplers in this case can simultaneously achieve polarization beam-splitting and light coupling functions, which enables the vertical grating coupling between fibers and Silicon-On-Insulator platform for various polarization states. This approach represents one of the most optimal solutions to tackle this issue.
One important issue of silicon photonic circuit is an interface between integrated waveguide devices and optical fibers or free-space optics. Grating couplers have the advantages of easy fabrication, high flexibility, and large alignment tolerance, which makes them the most important solution to solve the coupling issues. In this example, we simulate a focusing grating coupler to study its coupling capability.
Mie scattering is an effect that occurs when particles have a size comparable to or larger than the wavelength of the incident light. In this case, we use SimWorks Finite Difference Solutions to calculate the scattering field of a nanoparticle excited by a Total-field Scattered-field(TFSF) light source. The built-in analysis group of Far field from a closed box is then employed to compute the far-field scattering distribution of the particle.
Wire grid polarizer (WGP) is a type of polarizer composed of a metallic grating with a sub-wavelength period and typically made of metals such as gold, silver, aluminum. Thanks to their advantages, including compact structure, high brightness, high polarization extinction ratio (PER), wide field of view, and ease of integration, WGPs can be widely applied in various fields such as photoswitches, optical displays, and imaging systems.
Optical microcavities based on optical waveguides typically have a high quality factor and can be applied in various fields such as optical filters, lasers, and modulators. This case aims to analyze the resonance spectrum of a 1D Bragg grating microcavity based on an optical waveguide. Using the FDTD method, the resonant frequencies and quality factor Q are calculated too. In the device shown below, the Bragg grating consists of a periodic toothed structure and six parallel air gaps distributed in the center of the structure. By increasing the dimensions of the central structure, a defect is introduced that enables the occurrence of transmission resonance within the stopband of the Bragg structure.
Graphene, with its excellent electrical, thermal and mechanical properties, has attracted extensive attention from scientific researchers since its discovery. The chemical potential of graphene can be regulated by methods such as voltage or chemical doping. This property makes graphene highly versatile in the field of material-light interactions, particularly in relation to surface plasmons. Surface plasmons are electromagnetic surface waves in which the field energy is predominantly concentrated on the surface of a medium and decays exponentially in the direction perpendicular to the interface. By exciting surface plasmons, graphene significantly enhances its ability to interact with light.
Single-mode fibers feature a smaller core diameter than multimode fibers, enabling the single-mode transmission within the operating wavelength range. This design improves the transmission performance and reliability of single-mode fibers. Single-mode fibers are widely used in communication fields, including long-distance fiber optic communication, data center interconnection, wireless base station backhaul, CATV, fiber optic sensing, etc. This case aims to demonstrate a simple mode calculation by taking Corning® SMF-28 single-mode fiber as an example.
The human eye perceives specific colors in response to specific light spectra. Reflective color filters are used to selectively modulate reflection spectra to provide different color perceptions to the human eye. According to the study conducted by Yang et al., a reflective color filter base on a asymmetric Fabry-Perot (FP) cavity was modeled and simulated. The layer exhibits a near-perfect absorption effect across the solar spectrum. If the appropriate thickness is selected, the layer blocks light transmission. By adjusting the thickness of the intermediate layer, a reflection spectrum is achieved that allows the human eye to perceive vibrant colors with high saturation and brightness. This case demonstrates how to calculate the chromaticity coordinates related to the reflection spectrum, and further analyzes the color adjustment patterns of the color filter.
Negative index metamaterial (NIM) refers to an artificial optical structure whose refractive index is negative for electromagnetic waves within a certain frequency range. The purpose of this article is to simulate and explain the metamaterial structure described in the paper written by J. Zhou.
The interaction between incident light and surface electrons of a metallic nanostructure leads to surface plasmon resonance (SPR), which exhibits unique optical properties, including out-of-limit diffraction and local field enhancement. This case involves building a model of a metal film structure with air-hole array and calculating the transmission and reflection spectra of the film by the FDTD method to analyze the near-field distribution on the film surface and the local field enhancement caused by SPR.
Graphene is a single-layer carbon material that is only one atom thick. It can be used in nanoscale plasma systems due to its unique physical properties. Light can be manipulated and controlled by adjusting the electrostatic doping or Fermi level to excite plasmon waves in single-layer graphene.
Chu et al. studied a type of tunable terahertz metamaterial based on single-layer and multilayer doped graphene. They found that even slight variations in the number of graphene layers and Fermi level may lead to significant changes in the resonant wavelength and modulation intensity. This case aims to simulate this tuning process in 3D FDTD.
The whispering gallery modes of a microdisk use the total internal reflection (TIR) of light to confine the light within the microdisk to achieve light enhancement. Simply put, when light propagates in a medium cavity with a high refractive index, the light will be completely reflected at the boundary of the medium due to the difference in refractive index between the medium cavity and the outside world. When the light travels around the boundary of the medium and returns to its original position, the light that meets the phase matching conditions will be enhanced. The whispering gallery mode of a microdisk has a high quality factor and a small mode volume, so it has important applications in many aspects such as optical detection, nonlinear optics, cavity optomechanics, and quantum optics. It is a frontier and popular field of current optical research. In this case, we hope to find the first- and second-order whispering gallery modes of GaN cylinders, reproducing the results in the paper Room-temperature continuous-wave lasing in GaN/InGaN microdisks written by Tamboli et al.
"Metamaterial" is a man-made material with special properties that is not found in nature. This material can regulate basic physical characteristics such as frequency, amplitude, phase and polarization of electromagnetic waves. THz metamaterials are metamaterials that regulate electromagnetic waves with frequencies in the terahertz range. This case simulates the passive metamaterial described in the paper Chen et al. Active teraherz metamaterial devices and analyzes the surface current density of the metamaterial.
Organic solar cells (OSCs) have gradually become a research hotspot in the field of solar cells due to people's demand for clean energy and their advantages such as light weight, mechanical flexibility, and low manufacturing cost. How to improve its power conversion efficiency (PCE) is an urgent problem to be solved. One of the more commonly used methods is to add micro-nano structures for light trapping into the photoactive layer of OSCs to increase light absorption, thereby improving PCE. The photonic crystal (PC) structure is used in the photoactive layer of OSCs, which can enhance the light absorption of solar cells in specific wavelength bands. This case uses FDTD simulation to analyze the light absorption of an OSC with a 2D hexagonal-lattice PC structure.
A black body is an idealised object that can absorb all external electromagnetic radiation without any reflection or transmission. As the temperature rises, the electromagnetic waves radiated by the black body are called black body radiation. Actual objects cannot completely absorb external electromagnetic radiation, so they are also called "gray bodies". The thermal radiation spectrum of a "gray body" can be altered by changing its geometry or the materials used. The ability to modify or tailor the thermal radiation profile of an object is of great importance in many areas of applied physics and engineering. It has been noted that periodic engineering of devices made of metallic and dielectric materials at the subwavelength scale can change the thermal radiation properties of the device. Based on the work of Chan et al., this case studies the thermal radiation of a photonic crystal obtained by periodically arranging a device made of metallic tungsten and a dielectric material with a refractive index of .
"Metamaterial" is a special type of man-made material with extraordinary physical properties that natural materials do not have, such as regulating the frequency, amplitude, phase, etc. of electromagnetic waves. Metamaterials have a wide range of application prospects due to their exotic properties. For example, perfect absorbers designed based on metamaterials can be used as photodetectors, microbolometers, thermal imaging, etc. Based on the work of et al., this case models and simulates a Metal-Insulator-Metal (MIM) plasma metamaterial infrared absorber to study its reflection/transmission/absorption characteristics in the visible to near-infrared band.
As defined by IEEE, Directivity (formerly known as directive gain) is the ratio of the radiated power in the specified direction to the average radiated power in all directions . Directivity, obtained from further analysis of the far field, is one of the important parameters describing the far field radiation characteristics. You can use the Directivity analysis group to compute directivity.
The quality factor Q value is defined as the ratio of the center resonance wavelength to the full width at half maximum (FWHM) of the resonance peak. The higher the Q value, the better the wavelength selectivity of the device, the steeper the output peak, and the higher the sensitivity of the device. Generally, in the simulation of high-Q resonant cavities, the field amplitude obtained is inaccurate. The reason is that the loss rate in the high-Q resonant cavity is slow. If the simulation time is not long enough, the field in the cavity will not decay to 0 at the end of the simulation. At this time, the amplitude of the mode field in the cavity needs to be corrected to obtain the final actual amplitude. This case constructs a photonic crystal resonant cavity structure to demonstrate how to correct the field amplitude when the simulation time of a high-Q resonant cavity is insufficient.
The FDE solver is used to solve modes for the waveguide whose structure is periodic in the propagation direction. However, for structures composed of anisotropic materials or other nonlinear materials, we can solve the dispersion or bandstructure by the FDTD solver. In this case, the optical waveguide model with periodic structure in the propagation axis is constructed, and the bandstructure of the waveguide composed of isotropic material and diagonal anisotropic material is analyzed respectively.
Body-Center Cubic Lattice (BCC) and Face-Center Cubic Lattice (FCC) are two common types of 3D photonic crystal structures. In this case, BCC and FCC photonic crystals are constructed and their bandstructures are analyzed using FDTD solvers.
3D Cubic Lattice is a special case of 3D Rectangular Lattice. The lattice spacing of this type of photonic crystal is equal in three axes in space. In this case, the 3D cubic-lattice photonic crystal is constructed, and the FDTD solver is used to simulate the bandstructure of the dielectric sphere 3D cubic-lattice photonic crystal.
In 2D photonic crystals, different lattice types possess completely different band structures. The base settings in FDTD simulations vary with the different lattice types. In this case, a 2D triangular-lattice photonic crystal formed by air cylinders arranged in parallel in the medium is constructed, and its bandstructure is calculated. Based on the following example, some special settings and precautions for FDTD simulation of non-rectangular lattice photonic crystals are introduced.
Photonic crystals, as a dielectric structure with periodic changes in dielectric constant, can prevent light of a specific frequency from propagating internally, forming a photonic band gap. In this case, a 2D square-lattice PC model is constructed and its bandstructure is analyzed using FDTD. Through this case, some special settings and precautions in FDTD simulations of PC bandstructure are introduced in detail.
In nonlinear optics, the interaction between light and media produces nonlinear polarization. Second-order nonlinear effects are widely used in optical frequency doubling, frequency mixing, and modulation, which play an important role in lasers, frequency conversion and other devices. This example will simulate the generation of second harmonic using second-order nonlinear materials.
The Multi-mode Interference (MMI) coupler is composed of three parts: input waveguide, output waveguide, and multimode interference region. When the optical field is injected into the multimode interference region through the input waveguide, the interference between multiple modes produces a self-imaging effect. This effect causes periodic generations of one or more images of the input field along the propagation direction of the guided wave. As a result, the MMI can achieve optical wavelength division multiplexing/demultiplexing, power division, polarizing splitter and other functions by this effect.
A Bragg grating is an optical device in which there is a periodic variation in the effective refractive index of the structure. The waveguide Bragg grating is a type of one-dimensional photonic crystal structure that enables wavelength selection through periodic modulation of the refractive index. This property can be used to create various optical filters. The impact of the geometrical parameters of the sidewall corrugation, such as depth or misalignment, on the performance of Bragg gratings can be analyzed in silicon waveguide Bragg gratings, as demonstrated by Wang et al.
Y branch waveguide is a kind of important single component in integrated photonic devices, which has a wide range of applications, such as waveguide interferometer, modulator, optical switch, optical power splitter and so on. The power splitter based on Y branch distributes optical power to two or more output devices in a certain ratio. Structurally, Y-branch splitter can be divided into symmetric and asymmetric types. In this example, we use FDTD to simulate the insertion loss, transmitted power and S-parameters of a symmetric Y-branch splitter.
Solar energy is a clean and renewable energy. Therefore, the photovoltaic application of solar energy has become one of the most dynamic research fields in recent years. Solar cell is a device that converts solar energy into electricity. When sunlight irradiates a semiconductor material with photovoltaic effect, electron-hole pairs (photogenerated carriers) are generated. An electric current can be produced by inducing electrodes at both ends of the solar cell. In this example, we simulate a planar silicon solar cell by FDTD to calculate the absorption of solar energy () and further to compute the photon generation rate and the corresponding photocurrent.
In recent years, the unusual dispersion properties of photonic crystals(PCs), including the superlens , self-collimation(SC), and negative refraction, have attracted more and more interest and become an active research area. The SC achieves collimated radiation with almost no diffraction effect when the incident light propagates along a particular direction of the crystal. Line defects in 2D PCs cause bending and splitting of the SC beam. In this example, the effect of “optical switching” can be achieved by altering the line defects (radius of the dielectric rod) in the photonic crystal.
Bragg fiber is a type of air-core fiber that has received significant attention from researchers. it can allow light to propagate in the air core, which avoids problems caused by intrinsic material limitations such as absorption, dispersion, nonlinearity and low damage threshold. The FDE solver in this software can accurately calculate modes for complex structures, including photonic crystal(PC) Bragg fibers. In this example, we use the FDE solver to calculate the modes of the PC Bragg fiber described by Vienne et al and further compare the results with those from Uranus et al.
