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Two-Dimensional Photonic-BandGap Structures Operating at Near-Infrared Wavelengths
Abstract
Photonic crystals are artificial structures having a periodic dielectric structure designed to influence the behaviour of photons in much the same way that the crystal structure of a semiconductor affects the properties of electrons *RF 1*. In particular, photonic crystals forbid propagation of photons having a certain range of energies (known as a photonic bandgap), a property that could be incorporated in the design of novel optoelectronic devices [2]. Following the demonstration of a material with a full photonic bandgap at microwave frequencies [3], there has been considerable progress in the fabrication of three-dimensional photonic crystals with operational wavelengths as short as 1.5 micrometer [4], although the optical properties of such structures are still far from ideal [5]. Here we show that, by restricting the geometry of the photonic crystal to two dimensions (in a waveguide configuration), structures with polarization-sensitive photonic bandgaps at still lower wavelengths (in the range 800-900 nm) can be readily fabricated. Our approach should permit the straightforward integration of photonic-bandgap structures with other optical and optoelectronic devices.
... [42][43][44][45][46] Periodic structures further provide precise control over wave propagation and dispersion. For instance, photonic crystals manipulate electromagnetic waves to create peculiar phenomena such as photonic bandgaps, [47][48][49] resonant field enhancement and localization, [50][51][52] and slow-light effects, [53][54][55] which have been leveraged to achieve high sensitivities in PhC-based sensors. [56][57][58] Similarly, phononic [59] and magnonic [60] crystals enable the control of acoustic and spin waves, respectively. ...
The development of high‐sensitivity magnetic field sensors is crucial for precise magnetic field detection. In this context, a theoretical model is presented for a highly sensitive surface acoustic wave (SAW) magnetic field sensor incorporating phononic crystal (PnC) structures composed of Au pillars embedded within a SiO2 guiding layer. Rectangular and triangular PnC configurations are studied and their potential for improving sensor performance are assessed. In the design, the PnC is integrated into the SiO2 guiding layer to preserve the continuous magnetostrictive layer, enhancing its interaction with the SAW. Results from the simulations indicate that the proposed sensor can achieve a nearly two orders of magnitude increase in sensitivity compared to a continuous delay line of similar dimensions, and an eightfold improvement over a previous sensor design with PnCs composed of magnetostrictive pillars. This improved performance is attributed to the enhanced interaction between the SAW and the continuous magnetostrictive layer, driven by resonance effects within the PnC. These findings highlight the significant potential of incorporating PnCs into SAW sensors for future high‐performance magnetic field sensing.
... We start from Maxwell's equations in an anisotropic medium, incorporating correction terms representing nonlinear polarization and higher-order electromagnetic effects [10,19] : ...
Given the rapid urbanisation, acceleration of the anthropogenic transformation of landscapes and the escalating ecological imperatives facing India, robust and effective green building codes have become paramount in ensuring sustainable housing development. This paper reviews the effect of the development of green building codes on sustainable housing across India, especially as far as their compliance with SDGs. While prior literature targets policy formulation, more attention should be paid to researching the policy impacts and the difficulties in the corresponding policies’ implementation. To evaluate the effectiveness of the Green Buildings codes, the study uses systematic review of literature and policy documents, which works hand-in-hand with qualitative analysis. The research hypothesis posits that in regions having policies closely aligned with SDGs, there has been greater development of policies of sustainability and these areas exhibit enhanced development of policies and sustainability outcomes as evidenced by development of codes on maintaining resilience, environmental performance, and socio-economic equity This relationship is basis of the study hence the question; what factors enhance the potential for improved sustainability outcomes in green building codes aligned with SDGs? Research evidence indicates that despite intended high ambitions in formulation of codes, the eventual effectiveness is negated by weak operational compliance and geographical inequalities. This research forms part of a broader investigation into specific sections of the green building codes, covering energy efficiency, material utilisation, urban planning, and green space development. The study offers policy implications to policy makers and maps out a general guideline to enhance the implementation of sustainable features in housing delivery systems across the country.
... We start from Maxwell's equations in an anisotropic medium, incorporating correction terms representing nonlinear polarization and higher-order electromagnetic effects [10,19] : ...
This study investigates the influence of anisotropic metamaterials on electromagnetic wave propagation in cylindrical waveguides. Through rigorous mathematical modeling and numerical simulations using MATLAB, we analyze how the anisotropy factor modulates power flux direction, dispersion, and stopping light conditions at specific frequencies. The results demonstrate that anisotropy enables dynamic switching between forward and backward propagation, allowing the design of high-precision wave filters and sensors. The proposed model’s accuracy is validated through computational simulations, offering valuable insights into advanced photonic applications.
... Photonic crystal (PhC) membrane waveguides, both in silicon and III-V semiconductors, are promising sources of non-classical states of light since they enable extreme light confinement that provides a strong enhancement of optical nonlinearities [143][144][145] . Line-defect, slow-light, PhC waveguides can reduce the group velocity of light to less than 1/50 of its natural speed while keeping the propagation losses low 146 . ...
The ability to generate complex optical photon states involving entanglement between multiple optical modes is not only critical to advancing our understanding of quantum mechanics but will play a key role in generating many applications in quantum technologies. These include quantum communications, computation, imaging, microscopy and many other novel technologies that are constantly being proposed. However, approaches to generating parallel multiple, customisable bi- and multi-entangled quantum bits (qubits) on a chip are still in the early stages of development. Here, we review recent developments in the realisation of integrated sources of photonic quantum states, focusing on approaches based on nonlinear optics that are compatible with contemporary optical fibre telecommunications and quantum memory infrastructures as well as with chip-scale semiconductor technology. These new and exciting platforms hold the promise of compact, low-cost, scalable and practical implementations of sources for the generation and manipulation of complex quantum optical states on a chip, which will play a major role in bringing quantum technologies out of the laboratory and into the real world.
... real-valued frequencies as functions of real-valued wave vectors) of photonic crystals composed of loss-less and non-dispersive materials have been studied in detail [3,4], as well as additional investigations of loss-less, but dispersive problems [5]. This includes the retrieval of effective permittivities and permeabilities in the long-wavelength limit [6][7][8], the study of stop band and complete band gaps [9][10][11][12], and the investigation of singular points, such as Dirac [13] or Weyl points [14], van-Hove singularities and the densityof-states [15], and band edges in the context of slow * cwo@mci.sdu.dk light [16,17]. ...
We study bandstructure properties of periodic optical systems composed of lossy and intrinsically dispersive materials. To this end, we develop an analytical framework based on adjoint modes of a lossy periodic electromagnetic system and show how the problem of linearly dependent eigenmodes in the presence of material dispersion can be overcome. We then formulate expressions for the bandstructure derivative (complex group velocity) and the local and total density of transverse optical states. Our exact expressions hold for 3D periodic arrays of materials with arbitrary dispersion properties and in general need to be evaluated numerically. They can be generalized to systems with two, one or no directions of periodicity provided the fields are localized along non-periodic directions. Possible applications are photonic crystals, metamaterials, metasurfaces composed of highly dispersive materials such as metals or lossless photonic crystals, metamaterials or metasurfaces strongly coupled to resonant perturbations such as quantum dots or excitons in 2D materials. For illustration purposes, we analytically evaluate our expressions for some simple systems consisting of lossless dielectrics with one sharp Lorentzian material resonance. Finally, we show how the perturbation of a periodic system with a sharp resonance modifies the bandstructure. By combining several Lorentz poles, this provides an avenue to perturbatively treat quite general material loss bands in photonic crystals.
Diabetes mellitus is a pervasive health challenge requiring efficient monitoring for effective management. Non-invasive glucose detection methods, such as analyzing glucose levels in human urine, offer a promising alternative to traditional blood-based tests. This study explores the design and application of one-dimensional (1D) photonic crystal waveguides (PCWs) for glucose detection in urine, emphasizing their potential to enhance sensitivity, accuracy, and response speed. The proposed PCW structure comprises 11 alternating layers of silicon dioxide (SiO2) and titanium dioxide (TiO2), with thicknesses of 300 nm and 500 nm, respectively, forming a periodic optical lattice to generate a photonic bandgap. This structure confines light effectively and exhibits strong light-matter interaction. The waveguide utilizes a 1.55 µm light source to detect refractive index changes induced by glucose molecules, enabling real-time, label-free sensing. Simulation results demonstrate the sensor’s ability to differentiate glucose concentrations ranging from normal (0–1.5 mmol/L) to extremely high (10 mmol/L). At normal glucose levels, transmittance is 0.8482, increasing to 0.87957 for the highest glucose concentration. Sensitivity varies between 0.0020 and 0.0050 dL/mg, with peak sensitivity observed at normal glucose levels. The resolution is highest for extremely high glucose concentrations, exceeding 2.5, while stabilizing around 0.5 for intermediate levels. The quality factor improves linearly with glucose concentration, starting at approximately 1670 for normal levels and reaching 2100 for extreme levels. The response time shows a marginal increase with rising glucose levels, from 2.225 ps at normal concentrations to 2.245 ps at the highest concentration, ensuring fast detection. These results highlight the efficacy of the proposed photonic crystal waveguide as a compact, sensitive, and reliable biosensor for glucose detection. With its potential for high sensitivity, superior resolution, and rapid response time, this device is well-suited for on-chip integration and point-of-care diagnostics, offering enhanced accessibility and convenience in diabetic management.
In this chapter, designs of breath analyzer and toxic gas detection sensors are demonstrated by using nanomaterial multilayered structures. This breath analyzer can be used to detect alcohol content in human breath. This breath analyzer contains multiple layers of repeated three dielectric materials and an air groove in between the structure. The breath sample to be tested is passed through the air groove and the light spectrum is observed on the output side. The breath sample without alcohol content will generate a normal light spectrum (treated as a reference spectrum), while, the breath sample with alcohol content will generate a light spectrum different from normal (reference) light spectrum. Thus, alcohol content in the blood can be detected, if we monitor light spectrum. In addition to this, the abovementioned nanomaterial multilayered structure can also be used to detect toxic gas present in the air. The principle of detection is same. This structure generates a light spectrum depending on the material composition, lattice parameters, and gas present in the air groove. First, the light spectrum generated by this structure is recorded for normal air, when there is no toxic gas present in the atmosphere. This spectrum acts as a reference spectrum. After this, if there is a toxic gas leakage anywhere in the surrounding, then this toxic gas will pass through the air groove in the photonic structure and will cause a change in light spectrum. The new light spectrum will be different from the reference light spectrum. So, in this way, the toxic gas present in the atmosphere can also be detected by monitoring the light spectrum of photonic nanomaterial multilayered structure.
We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{\"o}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector \Bk and frequency plus a modulated Bloch carrier wave having crystal wave vector \Bm and frequency . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless and (\Bk-\Bm)\odot\Lambda \in 2\pi \mathbb Z^d, where is the periodicity cell of the medium and for any two vectors the product is defined to be the vector This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.
We investigate in this paper different aspects of the absolute photonic bandgap (PBG) formation for a two-dimensional periodic dielectric structure. In particular we examine how the symmetry of the filling pattern in a periodic dielectric material influences the photonic gap parameters. We present the results of the calculations and discuss the existence of the absolute PBG, the maximization of its width as a function of the parameters of a two-dimensional dielectric crystal as well as the practical technological feasibility of these optimized structures.
The technology to generate laser light from semiconductor microstructures is developing rapidly. New techniques for epitaxial growth and surface processing allow great flexibility in laser architecture. Highly efficient lasers with submicrometre dimensions, operating independently or packed together in dense two-dimensional arrays, will soon be used for transmitting, storing and manipulating information with unprecedented speed.
Many major discoveries in physics this century originate from the study of waves in periodic structures. Examples include X-ray and electron diffraction by crystals, electronic band structure and holography. Analogies between disciplines have also led to fruitful new avenues of research. An exciting example is the recent discovery of three-dimensionally periodic dielectric structures that exhibit what is called a "photonic band gap" (PBG), by analogy with electronic band gaps in semiconductor crystals. Photons in the frequency range of the PBG are completely excluded so that atoms within such materials are unable to spontaneously absorb and re-emit light in this region; this has obvious beneficial implications for producing highly efficient lasers. Given that electrons and photons obey almost the same differential wave equation, the idea of a PBG is clearly far from crazy. It does, however, demand a radical rethink of how light behaves in periodic structures.
Structures arranged so as to exhibit a complete photonic bandgap (PBG) have been proposed for a variety of technological applications. McCall et al. have reported an experimental and numerical investigation of microwave propagation in a two-dimensional array consisting of low-loss high-dielectric-constant cylinders. This system was shown to have a complete PBG, as well as a defect mode. Here we present an experimental investigation of the properties of a variety of defect modes, created by altering a region in the otherwise periodic lattice of dielectric cylinders. These alterations include removing one or more cylinders from the lattice in a variety of spatial separations and orientations, and also a procedure whereby the defect mode frequency may be tuned by slightly perturbing those cylinders closest to the defect region. The implication of these results for supercell numerical simulations and potential technical applications are discussed.
Third‐order, one‐dimensional, semiconductor‐air gratings have been designed, fabricated, and evaluated by optical waveguide transmission measurements. Gratings with as little as six unit cells show a clear band edge around 840–850 nm. Owing to our approach of semiconductor‐rich lattices with small airgaps, the diffractive spreading loss is sufficiently small (∼50% in the passband) for meaningful results to be extracted. The measurements indicate that the optical waveguide approach is a good starting point for the study of photonic microstructures and that practical device concepts can be implemented. © 1996 American Institute of Physics.
We introduce and analyze a new type of high‐Q microcavity consisting of a channel waveguide and a one‐dimensional photonic crystal. A band gap for the guided modes is opened and a sharp resonant state is created by adding a single defect in the periodic system. An analysis of the eigenstates shows that strong field confinement of the defect state can be achieved with a modal volume less than half of a cubic half‐wavelength. We also present a feasibility study for the fabrication of suspended structures with micron‐sized features using semiconductor materials. © 1995 American Institute of Physics.
It has been recognized for some time that the spontaneous emission by atoms is not necessarily a fixed and immutable property of the coupling between matter and space, but that it can be controlled by modification of the properties of the radiation field. This is equally true in the solid state, where spontaneous emission plays a fundamental role in limiting the performance of semiconductor lasers, heterojunction bipolar transistors, and solar cells. If a three-dimensionally periodic dielectric structure has an electromagnetic band gap which overlaps the electronic band edge, then spontaneous emission can be rigorously forbidden.