TM Incident Research Articles

Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure

Nanostructures with steep side wall angles (swa) play a pivotal role in various technological applications. Accurate characterization of these nanostructures is crucial for optimizing their performance. In this study, we propose a far-field detection method based on coherent Fourier scatterometry (CFS) for accurate quantification of steep swa and heights in cliff-like nanostructures. Our approach introduces a parameter termed ‘visibility’, derived from the unique far-field signatures of cliff-like nanostructures. This parameter serves as a quantitative metric for the calibration of swa and heights. The heightened sensitivity of our method is demonstrated, particularly when the incident polarization is perpendicular to the invariant direction of the nanostructure for swa calibration, while both polarization states exhibit sensitivity to height calibration. Furthermore, a comprehensive sensitivity analysis reveals the stable nature of our method, showcasing that even with fluctuations of ±10 nm in the position of the nanostructure, the resulting swa remains stable within a range of ±0.5∘ . The exponential variation of the visibility parameter with edge roundness is observed, with fluctuations in edge roundness within 10 nm resulting in swa variations within 1.7∘ for both polarization states. In experimental validations, our results demonstrate reasonable agreement between CFS-derived and AFM measurements. The AFM data for swa ( 77.99∘±1.37∘ ) and height (148.35 nm ±2.11 nm) are corroborated with CFS-derived value of swa ( 77.75∘±3.61∘ , 78.36∘±3.89∘ ) and height (149.42 nm ±1.66 nm, 150.05 nm ±1.04 nm) obtained from calibration curves for TM and TE incident beams, respectively. Overall, our findings underscore CFS as a potential and reliable tool for nanostructure characterization, offering precise measurements that are pivotal for advancing nanotechnology.

Design and analysis of a highly uniform five-band terahertz filter based on frequency selective surface

In this paper, a highly uniform five-band terahertz filter is presented, achieved by deforming two nested square ring structures. The metal pattern layer of the filter comprises a nested square ring structure with an inner and outer opening, and a metal strip connecting the inner and outer rings. Symmetrical openings divide nested square rings, breaking the current path and generating multiple metal bars of different lengths to excite dipole oscillations. Using metal strips to connect the inner and outer rings, the inner and outer resonant structures are integrated. Compared to a single resonant particle, the coupling of different single resonant particles amplifies the resonance of the combined structure, resulting in a wider stopband width and enhanced isolation between multiple passbands. A metal strip is also added to both ends of the outer ring opening to increase the equivalent capacitance of the outer ring, enhance the resonance, and improve out-of-band suppression. The transmission spectrum has five uniform passbands in the range of 1.3807–1.9917 THz, and the maximum passband ratio (MPR) of 3 dB bandwidth is about 1.16, and the ratio of 10 dB is about 1.17. The transmission coefficient of transmission zero is about 0.1, and the peak transmission coefficient of transmission peak is close to 1. The polarization of TE and TM incident waves is stable, and the filtering characteristics are good. Besides, the rectangular coefficients of the five passbands are all less than 1.33, showing excellent band selectivity. The resonance mechanism is explained by the Q value and electric field current distribution. The influence of structural parameter changes on filtering characteristics is also analyzed, and the main control parameters are found by using correlation analysis tools. From the changes in the MPR curve, it is verified that the structure parameters of the designed filter are in good condition. The multi-passband filter designed in this paper has uniform filtering characteristics, which is helpful to the development of terahertz multi-channel communication.

Graphene-embedded planar and cylindrical Oldenburger–Kolakoski aperiodic photonic crystals

In this paper, we examine the transmission and absorption spectra of light waves in both planar and cylindrical quasiperiodic structures known as Photonic Crystals. In these quasiperiodic multilayers, graphene sheets are inserted between planar and concentric layers of two different dielectric materials (namely TiO2 and SiO2). These structures are called Planar Photonic Crystals (PPCs) and Cylindrical Photonic Crystals (CPCs), respectively. The spatial arrangement of the dielectric layers follows the aperiodic Oldenburger–Kolakoski (O–K) sequence. The transfer matrix method is used to calculate the transmission and absorption spectra of obliquely incident TE and TM waves to investigate the effects of graphene, aperiodic disorder, and incidence angle on the physical behavior of the system. The numerical results reveal that the transmission spectra for cylindrical geometry differ significantly from those for planar geometry, even in the case of a normal incidence angle. Furthermore, the transmission of TM modes is higher than that of TE modes for incidence angles greater than 30°. Finally, we have demonstrated that a substantial number of peaks in the absorption spectra for the CPC case are higher than those for the PPC case, which is a result that may be useful for enhancing the efficiency of optical sensors.

An Ultrathin Multiband Chiral Metasurface for Transmission and Asymmetric Absorption of Electromagnetic Waves

This article presents an ultrathin chiral metasurface which can exhibit multiband asymmetric absorption as well as symmetric transmission in a specific frequency band outside the absorption regions. Unlike most electromagnetic metasurface absorbers, the proposed structure does not have a continuous conducting sheet at the bottom which also allows it to act as a bandpass spatial filter. The metasurface has a substrate thickness of only λhigh/62.5 and λlow/34 at the highest and lowest operational free‐space wavelengths, respectively. The transmission band is centered at 5.5 GHz, and the asymmetric absorption bands are centered at 3, 3.33, and 4.5 GHz, respectively. The operational bands can be tuned as per user requirements. The metasurface has an angular stability of 45° for both TE and TM incidence. It can be used for radar cross‐section (RCS) reduction, electromagnetic shielding, and as a spatial bandpass filter.

DUAL-BAND BANDSTOP FILTERS BASED ON ULTRA THIN FREQUENCY SELECTIVE SURFACES

In this paper, we present designs for terahertz filters with two independent stopbands based on periodic metallic resonant structures patterned on the dielectric substrate. Two simple and thin structures are proposed to realize required characteristics for single-polarized and dual polarized filter designs. To realize single polarized one, a unit cell of the proposed periodic structure consists of two sets rectangular shape conducting metal patches patterned on the top of the dielectric substrate, and the dual-band response is due the lattice resonances observed in the unit cell. To realize dual polarized filter design, a modified unit cell is considered with additional patches on the bottom of the dielectric substrate. The patches on the bottom layer are the same ones as on the top layer but orthogonally oriented. For this case, polarization-independent frequency response can be obtained after geometric optimization of the unit cell because the top and the bottom layers resonantly interact with only the TE or TM incident plane wave to minimize cross coupling effects between the layers. In order to intensively understand the transmission performance of the proposed filters, a large number of simulations using integral equation method are performed based on the different values for permittivity, period of the unit cell, dielectric thickness, and geometric dimensions. The electric field distributions are analyzed to understand the mechanism of the resonance behavior.

Transformation one-dimensional photonic crystal omnidirectional reflector

In this paper, a concept of transformation one-dimensional photonic crystal is proposed to design omnidirectional reflector, which has a reduced thickness compared with that of the omnidirectional reflector using conventional one-dimensional photonic crystal structure. At first, the omnidirectional reflection band of an original one-dimensional photonic crystal is simulated using the transfer matrix method for comparison. Next, the transformation one-dimensional photonic crystal is designed based on transformation optics. Simulation results indicate that the transformation one-dimensional photonic crystal structures with arbitrary shrunken thickness can omnidirectionally reflect the incident TM waves that operates in the same omnidirectional reflection band of the original one-dimensional photonic crystal structure. Such a concept of transformation one-dimensional photonic crystal also can be expanded to any omnidirectional reflector designed by using other multilayer dielectric systems.

T-shaped tunable infrared optical switch based on vanadium dioxide with dual-wavelength channels

A T-shaped tunable infrared optical switch based on a plasmonic structure composed of metal nanorods and vanadium dioxide film is proposed. The dynamic adjustment strategy based on the insulator–metal transition of vanadium dioxide and polarization-sensitive properties of the switch is thoroughly investigated to achieve the modulation of the wavelength and spectral reflectance intensity. Benefiting from the phase transition of vanadium dioxide, the optical switch can achieve two switching modes of ON and OFF states for both TE and TM polarizations of the incident light. Simulation results performed by finite-difference time-domain software show that the modulation depth of the switch can reach up to 85% at the resonance wavelength of 4270 nm under TM incident light. While the switch is illuminated with TE incident light, the modulation depth of the switch can reach 73% at the resonance wavelength of 2643 nm. In addition, when the polarizing angle of the incident light varies from 0 to 90°, the intensity of the spectral reflectance of the switch monotonically decreases at the wavelength of 4270 nm. Meanwhile, the spectral reflectance monotonically increases at the wavelength of 2643 nm. Moreover, the resonance wavelength of the optical switch can be tuned by altering the length of the metal nanorods. Those dynamic adjustment approaches will provide potential applications in optical modulation and solar photovoltaic fields.

A Semi-Explicit Solution of Scattering From Dielectric Bodies Using the Method of Moments

This work presents a novel closed-form expression based on the Method of Moments (MoM) for solving the scattering problem in piecewise homogeneous media. Using point-matching with pulse basis functions in MoM, we derive an expression represents the scattered field as an explicit function of the permittivity value of each homogeneous part. The coefficient matrix depends on the permittivity values in the MoM solution to the scattering problem. Therefore, it requires matrix inversion whenever these values change slightly. Here, we propose a new expression where the matrix coefficients are independent of the permittivity values of each homogeneous part. Accordingly, when the geometry does not change, we propose a semi-explicit procedure for updating the solution with less computational complexity. Although the proposed method can be used for all 2D and 3D problems, the formulation details are implemented for 2D problems, TM incidence. Based on this explicit form, we derive some simple approximate expressions for three specific cases of permittivity perturbations. Our proposed solution is appropriate for microwave imaging, particularly when a priori information is utilized.

The Ultra-Large-Bandwidth Cascade Full-Stokes-Imaging Metasurface Based on the Dual-Major-Axis Circular Dichroism Grating.

A dual-major-axis grating composed of two metal-insulator-metal (MIM) waveguides with different dielectric layer thicknesses is numerically proposed to achieve the function of the quarter-wave plate with an extremely large bandwidth (1.0-2.2 μm), whose optical properties can be controlled by the Fabry-Pérot (FP) resonance. For the TE incident mode wave, MIM waveguides with large (small) dielectric layer thicknesses control the guided-mode resonant channels of long (short) waves, respectively, in this miniaturized optical element. Meanwhile, for the TM incident mode wave, the propagation wave vector of this structure is controlled by the hybrid mode of two gap-SPPs (gap-surface plasmon polaritons) with different gap thicknesses. We combine this structure with a thick silver grating to propose a circularly polarizing dichroism device, whose effective bandwidth can reach an astonishing 1.65 μm with a circular polarization extinction ratio greater than 10 dB. The full Stokes pixel based on the six-image element technique can almost accurately measure arbitrary polarization states at 1.2-2.8 μm (including elliptically polarized light), which is the largest bandwidth (1600 nm) of the full Stokes large-image element to date in the near-infrared band. In addition, the average errors of the degree of linear polarizations (Dolp) and degree of circular polarizations (Docp) are less than -25 dB and -10 dB, respectively.

All-dielectric carpet cloaks with three-dimensional anisotropy control

Abstract In this article, we propose all-dielectric carpet cloaks composed of jungle gym shaped dielectric unit cells and present a design strategy for three-dimensional (3-D) anisotropy control based on the transformation optics. The carpet cloaks are 3-D printable and operate with polarization independent incident waves in arbitrary incident angles due to the 3-D anisotropy control. Realizable anisotropic permittivities of cubic and rectangular unit cells are numerically studied based on the relative permittivity and loss tangent of ɛ r = 2.9 and tan δ = 0.02 of ultra-violet curing resin measured at the microwave frequency. It is shown that the unit cell has little frequency dependence even with the anisotropy in the low frequency range where the effective medium approximation is valid. A carpet cloak is designed based on the design method with a quasi-conformal coordinate transformation and implemented with the unit cells taking into account its realizable anisotropy. Polarization independent 3-D cloaking operations of the designed cloak are confirmed numerically. The designed cloak is fabricated by stereolithography 3-D printing technology and its cloaking performances are evaluated experimentally at 10 GHz. It is shown that non-specular reflections are well suppressed by the carpet cloak for both TE and TM incident waves with different incident angles of 30, 45, and 60°. Frequency independent cloaking operations are also shown experimentally in the X-band. The measured near-field distributions and bistatic radar cross sections are in good agreement with simulated predictions and the validity of the design method is confirmed.

Dual-band and dual-polarized reflective Fresnel zone plate design based on Fractal shape

In this study, a dual-polarized and dual band reflective Fresnel zone plate with reconfigurable beam is proposed on the basis of fractal frequency selective surface (FSS) unit with nearly 360° phase tunability. Firstly, a new phase distribution calculation strategy based on Fresnel diffraction theory is proposed to improve the performance under certain scenarios like sparse arrays. Then, a novel fractal shape is put forward and applied to the design of the Fresnel zone plate. The introduction of the fractal structure makes the unit cell perform dual band, dual polarization and 309° phase tunability characteristics. Due to the self-symmetry of the unit cell, the proposed fractal Fresnel zone plate (FFZP) is capable of beam steering in ± 45° in both TE and TM incident waves. Besides, the proposed structure shows small performance degradation when it comes to oblique incidence up to 45°, which decreases the focal diameter ratio and profile of the proposed FFZP. The operating bandwidth of the FFZP can reach up to 700 MHz at X and Ku bands. It is applicable in a wide range of RF and microwave settings such as satellite and base station.

Stretchable Broadband Absorbers Based on the Hauberk Structure

One of the major challenges in the design of flexible microwave absorbers is to achieve flexibility, particularly the stretchability of the overall structure while ensuring broadband absorption. In general, the comprehensive properties of flexible dielectric materials are good enough, whereas those of flexible conductive materials are relatively poor. Materials with both good conductivity and stretchability are rarely reported. In this letter, a stretchable absorber was designed with the conductive material made into the hauberk structure, utilizing the relative movement of the rings of the hauberk to realize the stretchability. At the same time, this structure can achieve extra-broad-band absorption at large incident angles. Approximately 80% absorption under vertically incident TE and TM waves was measured in (10–40) GHz, showing good agreement with the simulation results. When the overall structure was stretched uniaxially by 10%, experiment results showed that the absorption decreased slightly but was still broadband, which agreed well with the simulation results. What is more, the structure maintained broadband absorption under 0°, 45°, and 75° incident angles.

High Extinction Ratio 4 × 2 Encoder Based on Electro-Optical Graphene Plasma Structure

In this paper, a plasmonic electro-optical encoder based on graphene at THz frequency is proposed. The surface plasmon polaritons (SPPs) in the graphene–insulator–metal structure are excited by an incident TM wave with a wavelength of 9.3 μm. Graphene plasma waveguides have extremely high confinement, relatively low losses, and high tunability. The switching mechanism is based on the application of an external voltage to locally change the chemical potential of the graphene for encoding. Setting the chemical potential to 1 eV allows SPPs to propagate while lowering the chemical potential to 0.1 eV prevents the SPPs from propagating. A 4 × 2 encoder with a minimum encoding extinction ratio (ER) of 37 dB, a maximum modulation depth (MD) of 99.99%, and a structure area of 0.8 μm2 is proposed based on the design rules and simulations using the finite-difference time-domain (FDTD) method. In terms of the obtained results, the proposed structure can be used in optical integrated circuits.

Terahertz plasmonic frequency selection metasurface based on Na-GaAs complementary symmetrical split-rings for refractive index sensing

A Terahertz (THz) plasmonic frequency selection metasurface based on Na-GaAs complementary symmetrical split-ring (PFSM-NCSS) is demonstrated for bulk refractive index (RI) sensing. The sensing performances of the PFSM-NCSS is studied by finite element method (FEM). The results show that the PFSM-NCSS has reflection peaks at 9.25 and 4.4 THz for the TM and TE incident lights, respectively. The parameter optimizations indicate that the reflection peak moves towards lower frequency when P decreases or r increases, and shifts to higher frequency when w1 or w2 increases. The PFSM-NCSS with two loaded dielectrics has minimum relative frequency offset with various θ, which means it has good angular stability. The sensing structure based on the PFSM-NCSS has RI sensitivities of −969.8 and −651.1 GHz/RIU for the TM and TE incident lights, meanwhile DLs of 9.8 × 10−4 and 3.2 × 10−4RIU can be achieved. The PFSM-NCSS provides a feasible THz RI sensing scheme for the cost-effective, real-time biosensors and immunosensors, along with strong light–matter​ interaction, good electromagnetically induced transparency characteristics, and compatibility with the CMOS technology.

Gain-Assisted Giant Third-Order Nonlinearity of Epsilon-Near-Zero Multilayered Metamaterials.

We investigate the third-order nonlinear optical properties of epsilon-near-zero (ENZ) Au/dye-doped fused silica multilayered metamaterials in the visible spectral range for TM incident by using nonlocal effective medium theory at different incidence angles. The nonlocal response affects the permittivity of anisotropic metamaterials when the thickness of the layer cannot be much smaller than the incident wavelength. By doping pump dye gain material within the dielectric layer to compensate for the metal loss, the imaginary part of the effective permittivity is reduced to 10−4, and the optical nonlinear refractive index and nonlinear absorption coefficient are enhanced. The real and imaginary parts of the permittivity are simultaneously minimized when the central emission wavelength of the gain material is close to the ENZ wavelength, and the nonlinear refraction coefficient reaches the order of 10−5 cm2/W, which is five orders of magnitude larger than that of the nonlinear response of the metamaterial without the gain medium. Our results demonstrate that a smaller imaginary part of the permittivity can be obtained by doping gain materials within the dielectric layer; it offers the promise of designing metamaterials with large nonlinearity at arbitrary wavelengths.

Polarization properties in grating-gated AlN/GaN HEMTs at mid-infrared frequencies.

The plasmon resonances of grating-gated AlN/GaN HEMTs can occur in wide frequency regions at mid-infrared frequencies. However, the lack of polarization properties research in grating-gated AlN/GaN HEMTs prevents the application potential. In order to solve the problem, the polarization properties in grating-gated AlN/GaN HEMTs at mid-infrared frequencies were studied in the paper. After using the optical transfer matrix method to calculate the dispersion curves in grating-gated AlN/GaN HEMTs, the plasmon polaritons in conductive channel and phonon polaritons in GaN layer occur under TM incident waves rather than TE incident waves. The phenomenon illustrates the potential of polarization-selectivity has existed in grating-gated AlN/GaN HEMTs. To study the polarization properties of grating-gated AlN/GaN HEMTs in detail, the electric field distribution and transmission properties of the structure were simulated in COMSOL. The results show the excellent polarization-selectivity at mid-infrared frequencies in grating-gated AlN/GaN HEMTs. The studies of these characteristics indicate the vast potential for using grating-gated AlN/GaN HEMTs to design mid-infrared polarizers, mid-infrared polarization state modulators and other devices in the future.

Smile face array: Generating oblique incident and front output vortex beam for both TE and TM waves

A single layer reflective array is designed to generate orbital angular momentum (OAM) beam at microwave frequency. The unit cell of this design is smile face shape distributed over a planar surface. Phase modulation can be realised by changing the size of each unit cell, with very low variation in reflection amplitude. By careful design, oblique incident can be obtained, reducing feed blockage to the output beam. The direction of the output beam can also be intendedly designed. In this work, the front output is chosen as a demonstrative example. In addition, the input beam can be either TE or TM wave, enable dual-mode operation. Furthermore, it is flexible to design the topological mode of the output OAM. The smile array is developed by cutting slots on circular patch array to produce perturbation on TE and TM waves, so that the difference in TE and TM incidence is reduced. As an instance, the topological modes of l = (−2, −1, 1, 2) are simulated, and the mode l = 1 is fabricated and measured. Measurements are conducted for both near field and far field. The measured results show good agreement with the simulated ones, indicating that this dual mode design works satisfactorily when oblique feed is used.

Actively tunable terahertz metasurface absorber due to surface phonon polaritons

A tunable terahertz (THz) metasurface (MS) absorber based on the surface phonon polariton (SPhP) is proposed based on a layered structure that consists of a split-silver-ring array followed by a graphene layer, polar crystal layer, and silver layer. A dynamically tunable, polarization-independent, and angle-insensitive MS absorber is numerically investigated at THz frequencies. By changing the Fermi energy of graphene from 0 to 1.0 eV, the state of the absorber can switch between the OFF state (with an absorptivity above 90%) and ON state (with an absorptance below 3%). The switching intensity (SI) of the absorber remains greater than 80% for TE incidence wave with incident angles from 0° to 70° and for TM incidence wave incident angles from 0° to 40° in the frequency range from 2.74 to 3.51 THz. These results should be helpful in guiding the design of THz tunable devices such as optical switches, smart absorbers, and imaging.

Frequency Selective Surface for Ultra-Wide Band Filtering and Shielding.

A frequency selective surface for spatial filtering in the standardized Ultra-Wide Band (UWB) frequency range is proposed. A very large stop-band of 1.75–15.44 GHz has been obtained, with good polarization insensitivity and an angular stability of more than 60 and more than 50 in TE and TM incidence, respectively. Circuit models have been devised. The structure has been assessed by electromagnetic simulation and implemented on an FR4 substrate of 1.6 mm thickness, with an edge of the square-shaped unit cell of 15 mm. Tests in an anechoic chamber demonstrated good matching between simulation and experimental results and proper operation of the device.

Sensitive detection of orthogonal polarization intensity ratio via metal-cladding waveguide

A rapid and sensitive detection method of incident light with different orthogonal polarization intensity ratios based on the double metal-cladding waveguide has been demonstrated. The middle layer of the waveguide is a uniaxial negative crystal lithium niobate, resulting in distinct coupling angles for TE and TM polarization. The isolation of the device can reach 42 dB due to well separation of TE and TM polarization. The quantitative experiments to measure ratio of TE to TM incident light have been carried out. Meanwhile, this method can support polarization detection in ultraviolet, visible, and infrared region. This method will play a significant role in optical information processing system and the integrated system.