One-dimensional Multilayer Structures Research Articles

Quantization of topological edge mode in a one-dimensional photonic crystal heterostructure

The study of topological phases of matter has seen significant advancements in recent years, largely driven by the discovery and exploration of their distinctive topological edge states. Here, we delve into the edge properties of a one-dimensional periodic multilayer structure. The analysis reveals that this system exhibits characteristics akin to the Su–Schrieffer–Heeger model in optics. The theoretical analysis explores the impact of multiple interfaces on the emergence of a topological edge mode (TEM) within the structure. The proposed heterostructure functions as a general beam splitter. Moreover, when the interface is doubled, the heterostructure exhibits two TEM states, resulting from the quantization of an incoming beam into its two equally orthogonal constituents. As the number of interfaces increases, more quantized TEM states occur within the photonic bandgap. Also, it identifies that the quality factor of the original TEM mode at 382.08 THz frequency linearly increases with respect to the number of interfaces. The outcome suggests potential applications in photonic sensors, optoelectronics, and photonic devices, indicating the heterostructure’s pivotal role in advancing these fields.

Study of the photothermal response of a multilayer structure doped with VO2@Au nanoshells

In this paper, we demonstrate a theoretical study of a multiphysics problem to solve for the photothermal response of a one-dimensional multilayer structure containing a layer doped with VO2@Au nanoshells. The VO2@Au nanoshell consists of a gold (Au) shell and a core of the phase change material vanadium dioxide (VO2) where the VO2 core transitions from a semiconductor state to a conductor state at the critical temperature of 68 °C. This behaviour results in thermal induced optical tunability through this reversible phase change of the VO2, due to the temperature dependent optical and thermal properties. The presence of the VO2 core, functioning as an ultra-fast and reversible optical phase-change material, leads to the emergence of photothermal induced bistability. The layer doped with the VO2@Au nanoshell is approximated as an effective medium using the Maxwell-Garnett Theory to enable an analytical solution. In this study, the optical response of the multilayer structure is obtained using the Transfer Matrix Method, while the thermal response for both stationary and transient states is solved using the Green’s Function Method and Kirchhoff’s Transformation. These equations are interconnected through the heat source term in the heat diffusion equations, representing the local heat generation induced by the continuous-wave laser applied to the structure. Our findings indicate that at the wavelengths of 658 nm and 747 nm, there are two distinct photothermal responses arising from the phase change of the VO2 core. At these wavelengths, the absorption of light increases and decreases, respectively, because of the VO2 phase change. This analytical method not only offers a thorough exploration of the fundamentals of induced photothermal responses in multilayer structures but also holds considerable potential for various applications, including solar cells, photothermal therapy, and nanothermal sensors.

General deep learning framework for emissivity engineering

Wavelength-selective thermal emitters (WS-TEs) have been frequently designed to achieve desired target emissivity spectra, as a typical emissivity engineering, for broad applications such as thermal camouflage, radiative cooling, and gas sensing, etc. However, previous designs require prior knowledge of materials or structures for different applications and the designed WS-TEs usually vary from applications to applications in terms of materials and structures, thus lacking of a general design framework for emissivity engineering across different applications. Moreover, previous designs fail to tackle the simultaneous design of both materials and structures, as they either fix materials to design structures or fix structures to select suitable materials. Herein, we employ the deep Q-learning network algorithm, a reinforcement learning method based on deep learning framework, to design multilayer WS-TEs. To demonstrate the general validity, three WS-TEs are designed for various applications, including thermal camouflage, radiative cooling and gas sensing, which are then fabricated and measured. The merits of the deep Q-learning algorithm include that it can (1) offer a general design framework for WS-TEs beyond one-dimensional multilayer structures; (2) autonomously select suitable materials from a self-built material library and (3) autonomously optimize structural parameters for the target emissivity spectra. The present framework is demonstrated to be feasible and efficient in designing WS-TEs across different applications, and the design parameters are highly scalable in materials, structures, dimensions, and the target functions, offering a general framework for emissivity engineering and paving the way for efficient design of nonlinear optimization problems beyond thermal metamaterials.

Rational design of one-dimensional skin-core multilayer structure for electrospun carbon nanofibers with bicontinuous electron/ion transport toward high-performance supercapacitors

The fast transport of electrons and ions within electrodes is crucial to the final electrochemical properties. Herein, we have developed a unique ultra-long one-dimensional (1D) skin-core multilayer structure based on electrospun carbon nanofibers mainly through a facile Stöber method combined with resorcinol–formaldehyde resin, which not only achieves bicontinuous electron/ion transport during the charge/discharge process, but also provides large surface area for ion adsorption. Particularly, controlling the number of active layers as well as regulating the active sites in layer both can obviously improve capacitive properties. Benefiting from the synergistic effects of the desirable architecture, such the rational-designed skin-core structural carbon nanofibers as supercapacitor electrode can deliver a high specific capacitance up to 255 F g−1 at 0.5 A g−1, favorable rate capability with 89% capacitance retention of initial capacitance at 8 A g−1, and excellent cycling stability with nearly 93% capacity retention after 10,000 cycles at 2 A g−1. Furthermore, the as-assembled symmetric supercapacitor devices also present a maximum energy density of 8.77 Wh kg−1 at 0.25 kW kg−1 and a maximum power density of 3.70 kW kg−1 at 6.74 Wh kg−1. Such skin-core carbon nanofibers provide an effective strategy to design high-performance supercapacitor electrode for the next-generation energy storage devices.

Bragg reflector one-dimensional multi-layer structure sensor for the detection of thyroid cancer cells

In the proposed work, a defect cavity multi-layer Bragg reflector structure is proposed theoretically to find the presence of thyroid cancer cells in the given sample. The modelling, design and analysis of the sensor is performed using characteristic matrix method (CMM). Proposed structure has central defect cavity with 6 pairs of low and high refractive index layers on each side of the defect. To enhances the sensor sensitivity, the incident light in mid-infrared frequency range is used as input light source. The refractive index of normal and thyroid cancer cells is analysed for the performance of the sensor. The obtained Q factor and sensitivity of the sensor design is 3729 and 2828 nm/RIU respectively. The proposed sensor is a best choice of optical sensor for the detection of thyroid cancer cells in the given test sample for accurate analysis in medical applications.

Tunable nonreciprocal transmission based on non-Hermitian optical system with magnetic optical materials in a one-dimensional multilayer structure

In this study, a one-dimensional composite structure composed of a PT-symmetric system and magnetic optical (MO) materials is designed. The nonreciprocal propagation of a one-dimensional multilayer structure is investigated both theoretically and numerically based on the transfer matrix theory. Different from the single nonreciprocal frequency in the parity-time (PT) system, two adjacent band gaps are changed into a pair of nonreciprocal bands under the effect of MO materials and a PT system above the PT exceptional point, and extraordinary transmissions are inspired in some nonreciprocal frequencies. At the same time, the nonreciprocal propagation bands can be tuned based on the different choices of external magnetic field directions. Furthermore, with an increase in the gain/loss factor, the two nonreciprocal band gaps both disappear and form two bands with an extraordinary transmission at certain frequencies. Such peculiar properties in the composite structure may have broad potential applications in communication and integration devices.

Dodecanacci superconductor-metamaterial photonic quasicrystal

This paper presents the numerical study of Dodecanacci superconductor-metamaterial based one-dimensional quasiperiodic multilayer to determine their critical transmittance properties of photonic spectra using transfer matrix simulations. Initially, the transmission characteristics for Dodecanacci quasicrystal were examined along with various parametric effects including the thickness of building blocks and operating temperature for different generations of Dodecanacci quasiperiodic sequence. A vast number of distinct forbidden bandgaps and transmission peaks was observed until a few generations (≤3). Interestingly, the forbidden bandgaps were becoming wider, in other words, the transmission bands become narrower with an increase in generation number. However, there is a distinct red and blue shift was observed in the spectra with an increase in temperature and an increase in quasicrystal layer thickness respectively. Hence this study strongly supports that the Dodecanacci superconductor-metamaterial based one-dimensional quasiperiodic multilayered structures could be potentially used for applications like tunable optical reflectors or tunable narrowband filters based on its generation number and operating conditions.

Investigating the Second Harmonic Generation in One-Dimensional Multi-layer Structure Consisting of Polar Ferroelectric Called 𝐋𝐢𝐓𝐚𝐎𝟑 Using the Transfer Matrix Method

The transfer matrix method is widely used to calculate the electromagnetic waves dispersion. In this paper, we have investigated the second harmonic generation in a one-dimensional structure including LiTaO3 ferroelectric. Using the transfer matrix method, we obtain the second harmonic efficiency. In this article, in the structure of nonlinear photonic crystals, the linear and nonlinear optical parameters are changed periodically, which causes the second harmonic conversion efficiency to be several times greater than the conversion efficiency of a nonlinear structure based on conventional quasi-phase matching (QPM). The reason for this is that in the system discussed in this paper, the presence of effects of band gap edges causes the density of states of the electromagnetic fields is increased, the group speed of the electromagnetic waves is decreased (as a result, the interaction time is increased) and local field is boosted. As a result of these three factors, the nonlinear optical interaction is effectively strengthened.

Wideband absorption in one dimensional bilayer-graphene embedded photonic multilayer structure

Abstract In this article, we propose a one-dimensional graphene-based multilayer structure which composed of traditional dielectric material and graphene. The dependence of absorption characteristics of this structure on the chemical potential of graphene, the optical thickness of the dielectric layer, the loss of the dielectric material and the incident angle are investigated by using the transfer matrix method. It is shown that the absorption bandwidth of the structure can be modulated by the chemical potential of graphene and the absorption is insensitive to the refractive index and geometric thickness of the dielectric material within a certain range. It is also shown that the absorption is generally insensitive to the angle of incidence. These findings have potential applications for designing tunable broadband absorbers and related optoelectronic devices.

Second harmonic generation in a multi-layer LiTaO3 structure using transfer matrix method

ABSTRACTIn this paper, the second harmonic generation in one-dimensional multi-layer LiTaO3 structure has been studied. To study and review the conversion efficiency, fundamental and second harmonic wave propagation inside the designed structures in this paper, we use the transfer matrix method. In the structures investigated due to the existence of the gap, density of passing electromagnetic modes in the edge of the gap and the defect modes is large. Also, the electromagnetic wave velocity is small. These factors produce a strong nonlinear optical interaction.

Disorder Effect on the Transmission of Second Harmonic Waves in One-Dimensional Periodically Poled LiTaO<sub>3</sub>

One of the methods for calculating electromagnetic wave dispersion in multi-layer structures is the transfer matrix method. In this paper, we use the transfer matrix method for second harmonic generation in a nonlinear multilayer structure. The nonlinear photonic crystals investigated in this paper are as one-dimensional multi-layered structures including ferroelectric materials such as LiTaO3. Our goal is to investigate the effect of the disorder on the transmission spectrum of electromagnetic waves. Our results showed that positional disorder has different effects on the transmitting band and the gap band. The disorder in the transmitting band reduces the transmission coefficient of the waves and increases the transmission coefficient of the waves in the gap band. Such work has not yet been done on nonlinear photonic crystals producing the second harmonic.

Experimental sol-gel fabrication and theoretical simulation of one-dimensional photonic crystals with a defect state

One-dimensional multilayer structures of the periodically alternating low refractive index (silica) and high refractive index (titania) materials have been deposited by sol–gel spincoating. The possibility of creating an optical filter by introducing a structural defect in the form of a layer of double thickness is shown theoretically and experimentally. All experimental spectra are in agreement with theoretical spectra calculated by transfer matrix method.

Modulation of electromagnetic local density of states by coupling of surface phonon-polariton

We studied the electromagnetic local density of state (EM-LDOS) near the surface of a one-dimensional multilayer structure (1DMS) alternately stacked by SiC and Si. EM-LDOS of a semi-infinite bulk appears two intrinsic peaks due to the resonance of surface phonon-polariton (SPhP) in SiC. In contrast with that of SiC bulk, SPhP can exist at the interface of SiC and Si for the 1DMS. The SPhPs from different interfaces can couple together, which can lead to a significant modulation of EM-LDOS. When the component widths of 1DMS are large, the spectrum of EM-LDOS exhibits oscillation behavior in the frequency regime larger than the resonance frequency of SPhP. While the component widths are small, due to the strong coupling of SPhPs, another peak appears in the EM-LDOS spectrum besides the two intrinsic ones. And the position of the new peak move toward high frequency when the width ratio of SiC and Si increases. The influences of distance from the surfaces and period of 1DMS on EM-LDOS have also been studied in detail. The results are helpful in studying the near-field radiative heat transfer and spontaneous emission.

Energy-transport models for spin transport in ferromagnetic semiconductors

Explicit energy-transport equations for the spinorial carrier transport in ferromagnetic semiconductors are calculated from a general spin energy-transport system that was derived by Ben Abdallah and El Hajj from a spinorial Boltzmann equation. The novelty of our approach are the simplifying assumptions leading to explicit models which extend both spin drift-diffusion and semiclassical energy-transport equations. The explicit models allow us to examine the interplay between the spin and charge degrees of freedom. In particular, the monotonicity of the entropy (or free energy) and gradient estimates are shown for these models and the existence of weak solutions to a time-discrete version of one of the models is proved, using novel truncation arguments. Numerical experiments in one-dimensional multilayer structures using a finite-volume discretization illustrate the effect of the temperature and the polarization parameter.

Design criteria for improving insulation effectiveness of multilayer walls

Energy savings in buildings can be achieved to a large amount by optimizing the insulation capabilities of its external walls. Typically such walls are multilayer structures whose insulation properties have a crucial dependence on the type, thickness and ordering of the materials employed in their construction. In this work, the heat transfer matrix approach is used for a quantitative analysis of heat conduction in one-dimensional multilayer structures under steady periodic conditions. In this way, some of the results previously suggested by numerical data are accounted for in a rigorous way. In particular, a fundamental inequality concerning layer order and its effect on the modulus of the temperature decrement factor introduced by a wall is derived. This provides a design criterion for building effective insulation structures. Another factor that can significantly affect the insulating performance of a wall is the number of employed layers, once the total extension of the wall, the total material amounts, and therefore the total thermal resistance of the wall, have been fixed. It is shown that, under specific circumstances, an optimum number of layers can be identified. The influence of layer order and distribution on the time delay that a wall introduces between outer and inner temperatures is also addressed. The presented results are illustrated by means of numerical examples that show how to control to a large extent modulus and phase of the temperature decrement factor of a multilayer wall.

Sol-gel fabrication of one-dimensional photonic crystals with predicted transmission spectra

One-dimensional multilayer structures of periodically alternating low refractive index (silica) and high refractive index (titania) materials have been deposited by sol-gel spincoating. Experimental spectra of the structures are in agreement with spectra calculated by transfer matrix technique. As an example, theoretical and experimental spectra with a stop band corresponding 600 nm-reflection are shown.

Bound states in one-dimensional acoustic parity-time-symmetric lattices for perfect sensing

In this letter, we study the propagation of acoustic waves through a one-dimensional multilayer structure composed of a thin defect layer sandwiched by two phononic crystals. Two kinds of defect states will generate in band gaps and both of them cause unitary transmission. However, they have very unlike field distributions due to the different contrasted acoustic impedances between the defect layer and its neighboring layers. Spectral positions of transmission peaks can be exactly determined by the resonant phase condition. In a non-dissipative system, these resonant states correspond to single crossing point of two eigenvalues of scattering matrix. When gain and loss are introduced to judiciously construct an acoustic parity-time-symmetric lattice, the crossing point will split into a pair of exceptional points (EPs). Interestingly, the EPs correspond to unidirectional zero reflection that is very sensitive to the thickness of defect layer. Taking advantage of this virtue, a very sensitive acoustic sensor can be designed, which has potentially applications in ultrasonic inspection, noise detection, ultrasonic medicine, etc.

Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization

We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that seek to maximize Purcell factors at individual frequencies is that our method not only aims to achieve frequency matching (across an entire octave) and large radiative lifetimes, but also optimizes the equally important nonlinear--coupling figure of merit $\bar{\beta}$, involving a complicated spatial overlap-integral between modes. We apply this method to the particular problem of optimizing micropost and grating-slab cavities (one-dimensional multilayered structures) and demonstrate that a variety of material platforms can support modes with the requisite frequencies, large lifetimes $Q > 10^4$, small modal volumes $\sim (\lambda/n)^3$, and extremely large $\bar{\beta} \gtrsim 10^{-2}$, leading to orders of magnitude enhancements in SHG efficiency compared to state of the art photonic designs. Such giant $\bar{\beta}$ alleviate the need for ultra-narrow linewidths and thus pave the way for wavelength-scale SHG devices with faster operating timescales and higher tolerance to fabrication imperfections.

A continuation fixed-point iterative method on harmonic generations with strong nonlinear optical effects in multi-layer structures

A continuation fixed-point iterative method for harmonic generations with strong nonlinear optical effects in one-dimensional nonlinear multi-layer structures, which are governed by the nonlinear Helmholtz systems, is presented in this paper. Three kinds of harmonic generations via \(\chi ^{(2)}\) or \(\chi ^{(3)}\) nonlinear process, which are important phenomena in nonlinear optics, are modeled as the application of our proposed method. In the regime of strong nonlinearity, the theoretical and computational analysis of the model problems encounters enormous challenges due to the discontinuity across layers and the strongly nonlinear coupling of modes. To overcome the difficulties in the nonlinearity and discontinuity, a fixed-point iteration with the finite element method is used to study the nonlinear conversion efficiencies by solving the weak formulations. Furthermore, a continuation technique that depends on the weak formulations to solve three model problems, is introduced to handle the iterative procedure for cases with large nonlinearity. The theoretical framework and numerical algorithm towards a uniform process is offered to study almost all the harmonic generations in \(\chi ^{(2)}\) or \(\chi ^{(3)}\) interaction. With the continuation fixed-point iterative technique, the convergence of the iterative procedure can be ensured, even in the presence of strong nonlinearity. Three numerical experiments with high conversion efficiencies are also presented to show the accuracy and efficiency of our proposed method.

Numerical investigation of optical Tamm states in two-dimensional hybrid plasmonic-photonic crystal nanobeams

Optical Tamm states (OTSs) in analogy with its electronic counterpart confined at the surface of crystals are optical surface modes at the interfaces between uniform metallic films and distributed Bragg reflectors. In this paper, OTSs are numerically investigated in two-dimensional hybrid plasmonic-photonic crystal nanobeams (HPPCN), which are constructed by inserting a metallic nanoparticle into a photonic crystal nanobeam formed by periodically etching square air holes into dielectric waveguides. The evidences of OTSs can be verified by transmission spectra and the field distribution at resonant frequency. Similar to OTSs in one-dimensional multilayer structures OTSs in HPPCN can be excited by both TE and TM polarization. The physical origin of OTSs in HPPCN is due to the combined contribution of strong reflection imposed by the photonic band gap (PBG) of the photonic crystal (PC) nanobeam and strong backward scattering exerted by the nanoparticle. For TE, incidence OTSs can be obtained at the frequency near the center of the photonic band gap. The transmissivity and the resonant frequency can be finely tuned by the dimension of nanoparticles. While for TM incidence OTSs are observed for relatively larger metallic nanoparticles compared with TE polarization. The differences between TE and TM polarization can be explained by two reasons. For one reason stronger backward scattering of nanoparticles for TE polarization can be achieved by the excitation of localized surface plasmon polariton of nanoparticles. This assumption has been proved by examining the scattering, absorption, and extinction cross section of the metallic nanoparticle. The other can be attributed to the deep and wide PBG available for TE polarization with less number of air holes compared with TM polarization. Our results show great promise in extending the application scope of OTSs from one-dimensional structures to practical integrated photonic devices and circuits.