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Observation of Light Propagation in Photonic Crystal Optical Waveguides with Bends
Electronics Letters
Abstract
Light propagation is investigated in two-dimensional photonic
crystal waveguides with bends, which were composed of closely-packed
holes formed in a GaInAsP thin film. Wavelength and polarisation
dependence on propagation characteristics were observed in the
wavelength range 1.47-1.60 μm
... Indeed high-resistivity intrinsic Si has proven to yield low-loss [13], low-dispersion waveguides combined with strategic design considerations. Photonic crystals [14][15][16][17][18], which are typical photonic nanostructures, are examples of built-in all-Si waveguide platforms, where the wave confinement and waveguiding function are based on the photonic bandgap (PBG) effect [19]. The first notion of THz integrated circuits based on an all-Si platform was proposed in 2012 by Fujita et al. [20]. ...
... In TE bandgap region, the propagation of THz waves with in-plane polarization is inhibited. Early reports on photonic crystal waveguides go back to 1999 when light transmission in photonic crystal waveguides at light-wave region [19] Indeed, there is extensive literature exploring PBG and its potential for manipulating THz waves but not as much on a proof of concept for real-life applications. In their work, Hasek et al. provided experimental proof of concept to theories on measurements methods for fluids and deoxyribonucleic acid (DNA) for sensing application in the healthcare industry [76,77] using a 2D photonic crystal waveguide implemented in a high-density polyethylene [78]. ...
Recent advances in silicon (Si) microphotonics have enabled novel devices for the terahertz (THz) range based on dielectric waveguides. In the past couple of years, dielectric waveguides have become commonplace for THz systems to mitigate issues in efficiency, size, and cost of integration and packaging using metal-based waveguides. Therefore, THz systems have progressively evolved from cumbersome collections of discreet components to THz-wave integrated circuits. This gradual transition of THz systems from numerous components to compact integrated circuits has been facilitated at each step by incredible advances in all-Si waveguides allowing low-loss, low dispersion, and single-mode waveguiding operation. As such, all-Si waveguides position themselves as highly efficient interconnects to realize THz integrated circuits and further large-scale integration in the THz range. This review article intends to reevaluate the evolution stages of THz integrated circuits and systems based on all-Si waveguides.
... De cette manière, il est aussi possible d'étudier la propagation de la lumière dans des guides d'onde sur cristaux photoniques (réalisés par l'introduction de défauts dans la structure périodique). Ces guides peuvent être droits [136,[144][145][146] ou à virage [142,144]. ...
... De cette manière, il est aussi possible d'étudier la propagation de la lumière dans des guides d'onde sur cristaux photoniques (réalisés par l'introduction de défauts dans la structure périodique). Ces guides peuvent être droits [136,[144][145][146] ou à virage [142,144]. ...
... Ils sont réalisés en créant un défaut linéaire. Cette idée est apparue en 1994 sous l'impulsion de Joannopoulos, Chapitre 1 -Les cristaux photoniques 30 Meade et al. [3,65] mais les premières réalisations sont arrivées cinq à six ans plus tard [66,67,68]. La Figure 1 Les pertes sont pour l'instant encore importantes, mais il y a fort à penser que l'amélioration des procédés d'élaboration diminuera cette contrainte. ...
... Couplage par la trancheC'est la méthode issue de l'optique intégrée. Elle permet de sonder les modes guidés de la structure et consiste à injecter de la lumière (lampe tungstène, laser accordable ou non) par la tranche clivée de l'échantillon en utilisant une fibre ou un objectif de microscope[7,32,66,70].Il est alors nécessaire d'utiliser un substrat qui permet le clivage. Cette méthode est relativement délicate à mettre en oeuvre du fait de la petite taille des guides d'onde utilisés et parce que des problèmes d'adaptation modale entre le mode injecté et le mode du guide peuvent apparaître. ...
Photonic crystals (PCs), i.e. periodic dielectric structures, allow the control of light. For example, propagation of photons can be suppressed in certain directions and for frequencies contained in what is called the photonic band gap (PBG). This thesis report on the conception, fabrication and characterization of guides, filters, planar micro-cavities and light extractors based on two-dimensional silicon photonic crystals. This structures can be etched in the planar waveguide of silicon-on-insulator (SOI) substrates and they can take advantage of well known microelectronic fabrication technology. Furthermore, the fabrication with CMOS-type technology on 8 in. wafers allows to prepare the integration of optical functions within silicon microelectronic chips. The first part of this manuscript focuses on passive structures: guides and filters. An original optical bench was build in order to perform transmission measurements on a wide wavelength range (1.1 to 1.7 µm). Monolayer waveguides, mirrors and unidimensional cavities are investigated. Resonant modes with quality factors higher than 150 are measured. This results are in very good agreement with the FDTD (Finite Difference Time Domain) simulations and with the calculated band diagrams. The second part of the thesis concerns the out-of-plane light emission from photonic crystal structures. Confinement of photons in planar micro-cavities and light extraction properties of particular points on the photonic crystal band diagram are studied. Both approaches are investigated on SOI substrates and on a new kind of substrates, called “optical substrates”, developed especially for our applications and composed of a monocrystalline silicon layer bonded a buried distributed Bragg reflector. That way, the influence of the light confinement in the third direction have been investigated. On SOI substrate, a light extraction efficiency higher than 45 % have been measured on one side and in a reduced solid angle.
... PCs display photonic band gap (PBG) similar to their electronic counterparts in which no electromagnetic (EM) waves could be transmitted. EM wave transmission for frequencies lying in the PBG of a PC can be achieved by introducing, for instance, linear defects to form waveguides (WGs) in which EM waves are confined in and decay abruptly in the transverse direction [2][3][4][5]. Linear defect WGs have found widespread utility in applications such as wavelength division de/multiplexing [6,7] and unidirectional light transmission [8,9]. EM waves in two parallel WGs were shown to couple and decouple and thus enable EM power transfer in between if the dielectric region between the WGs is properly designed [10,11]. ...
Guiding and evanescent coupling properties of surface modes bound to the interfaces of two-dimensional photonic crystals in close proximity are numerically demonstrated. Interacting photonic crystals are composed of silicon pillars in air, where their outermost layers facing each other are annular. Surface modes are identified through supercell band structure computations, while their excitation by the electromagnetic waves through a perpendicular insertion waveguide is demonstrated using finite-difference time-domain simulations. Lifting the degeneracy between the surface modes as a consequence of bringing two identical photonic crystal surfaces to a sufficient distance results in evanescent coupling in a beating manner whose beat length linearly varies between 10 and 20 periods up to a frequency at which both surface modes travel with the same group velocity. The surface mode coupling phenomenon could be employed either to enhance sensitivity or to reduce device size in bio/chemical sensor applications since the effective travelling length of surface waves increases by about 3.5 times due to evanescent coupling.
... Experimentally, PC waveguides and bends have recently gained much attention. Lin S. Y.[177], reported near 100% transmission for a 90° sharp comer in the microwave region, while Baba et al.[178] observed light propagation in a 2D PC with bends of varying angles in a triangular lattice of air rods in GalnAsP in the 1.38p,m region.However it was only till recently, when the complete characterisation of light propagating through a sharp 120° bend was presented in the 1.55 jam region by Tokushima et al[179].Charlton et al.[180] of our group also fabricated waveguide bends and splitters for the operation in the visible region in 1999. These were composed of a triangular array of air rods etched in a Silicon Nitride waveguiding core. ...
p>Photonic crystals are attracting much interest due to their ability to inhibit spontaneous emission of light. This and related properties arise from the formation of photonic bandgaps, whereby multiple scattering of light by lattices of periodically varying refractive indices act to prevent the propagation of electromagnetic waves having certain wavelengths. The etching of regular two-dimensional vertical air rods has formed a popular method for the formation photonic crystals in a dielectric planar waveguide. However, the ability for such a structure to possess a complete photonic bandgap is only possible by the use of large air rod diameters and high dielectric constants. Such structures lead to significant losses due to refractive index mismatch and large out-of-plane scattering when coupled with current fibre optical networks of low refractive index.
In this thesis the use of a quasicrystalline structure is proposed instead of the regular crystal lattice. For the first time, a twelve-fold symmetric photonic quasicrystal is designed and successfully modelled using the finite-difference time-domain method. It was shown to possess a complete and absolute photonic bandgap with small air rods in a relatively low refractive index material Silicon Nitride (n=2.02). It is also shown that such complete and absolute photonic bandgaps are also realisable in low refractive index materials such as glass (n=1.45). This would provide a whole range of optical devices based on the photonic quasicrystal that are directly compatible with current fibre optical networks.
The first photonic quasicrystal embedded in a Silicon Nitride waveguide to operate in the visible to infrared region of the electromagnetic spectrum was also shown. The quasicrystal was experimentally shown to possess the complete and absolute photonic bandgap.</p
... 90 The introduction of linear defects in an otherwise perfectly periodic structure can lead to the appearance of guided modes within a photonic bandgap, forming a photonic crystal waveguide (PhC-wg). 91 One way to see this is that the defect is surrounded by media that reflect any incoming light so that the light is confined to the defect. PhC-wg's offer unparalleled possibilities for dispersion engineering, thanks to the generally large index contrast between the different elements of the structure and to the large number of degrees of freedom to be tuned. ...
Solitons are wave packets that can propagate without changing shape by balancing nonlinear effects with the effects of dispersion. In photonics, they have underpinned numerous applications, ranging from telecommunications and spectroscopy to ultrashort pulse generation. Although traditionally the dominant dispersion type has been quadratic dispersion, experimental and theoretical research in recent years has shown that high-order, even dispersion enriches the phenomenon and may lead to novel applications. In this Tutorial, which is aimed both at soliton novices and at experienced researchers, we review the exciting developments in this burgeoning area, which includes pure-quartic solitons and their generalizations. We include theory, numerics, and experimental results, covering both fundamental aspects and applications. The theory covers the relevant equations and the intuition to make sense of the results. We discuss experiments in silicon photonic crystal waveguides and in a fiber laser and assess the promises in additional platforms. We hope that this Tutorial will encourage our colleagues to join in the investigation of this exciting and promising field.
... The investigation of photonic crystal (PhC) structures has been a fruitful area of research since it was pioneered in the late-1980s [1][2][3][4]. However, despite the fact that the first 1D periodic dielectric waveguide was first demonstrated as early as 1978 [5] in the form of a fiber Bragg grating, it was not until the development of the first hole-defined line-defect PhC waveguides (PCWs) in the early 2000s [6][7][8][9] that the practical applicability of silicon-on-insulator (SOI) PCWs to telecommunications and sensing applications became obvious. PhCs are an attractive technology to work with because of the many interesting phenomena that can be engineered in them. ...
In this paper we demonstrate that by breaking the left/right symmetry in a bi-planar double-silicon on insulator (SOI) photonic crystal (PhC) fin-waveguide, we can couple the conventionally used transverse-electric (TE) polarized mode to the transverse-magnetic (TM) polarization slot-mode. Finite difference time domain (FDTD) simulations indicate that the TE mode couples to the robust TM mode inside the Brillouin zone. Broadband transmission data shows propagation identified with horizontal-slot TM mode within the TE bandgap for fully mismatched fabricated devices. This simultaneously demonstrates TE to TM mode conversion, and the narrowest Si photonics SiO<sub>2</sub> slot-mode propagation reported in the literature (10 nm wide slot), which both have many
potential telecommunication applications.
... Photonic Crystals (PCs) are promising candidates for many applications, and they might act as a waveguide or microcavity laser (Painter et al. 1999;Baba et al. 1999) because PCs are engineered to provide controlled optical properties. Such optical properties are not available in homogeneous materials. ...
Due to the fabrication processes, inaccurate manufacturing of the photonic crystals (PCs) might occur which affect their performance. In this paper, we examine the effects of tolerance variations of the radii of the rods and the permittivity of the material of the two-dimensional PCs on their performance. The presented stochastic analysis relies on plane wave expansion method and Mote Carlo simulations. We focus on two structures, namely Si-Rods PCs and Air-Holes PCs. Numerical results show—for both structures—that uncertainties in the dimensions of the PCs have higher impact on its photonic gap than do the uncertainties in the permittivity of the Si material. In addition, Air-Holes PCs could be a good candidate with least alteration in the photonic gap considering deviations that might occur in the permittivity of Si due to impurities up to 5%.
... Photonic Crystals (PCs) are promising candidates for many applications, and they might act as a waveguide or microcavity laser [1,2] because PCs are engineered to provide controlled optical properties. ...
Due to the fabrication processes, inaccurate manufacturing of the photonic crystals (PCs) might occur which affect their performance. In this paper, we examine the effects of tolerance variations of the radii of the rods and the permittivity of the material of the two-dimensional PCs on their performance. The presented stochastic analysis relies on plane wave expansion method and Mote Carlo simulations. We focus on two structures, namely Si-Rods PCs and Air-Holes PCs. Numerical results show – for both structures – that uncertainties in the dimensions of the PCs have higher impact on its photonic gap than do the uncertainties in the permittivity of the Si material. In addition, Air-Holes PCs could be a good candidate with least alteration in the photonic gap considering deviations that might occur in the permittivity of Si due to impurities up to 5%.
... It is not possible to mention all the previously reported 2D-PhC bend waveguides. However, we have tried our best to cite the most prominent bend waveguides based on PhC structure [14][15][16][17][18][19]. ...
An attractive and realizable scheme of a compact two-dimensional (2D) photonic crystal (PhC) heterostructure is proposed for flexible light steering formed by integrating two PhC structures having diverse optical properties. The first PhC allows both TE-and TM-polarized light to propagate through it with minimum transmission loss (TL), whereas the second PhC structure is designed in such a way that TE-polarized light faces a photonic bandgap while self-collimated TM-polarized light travels without any diffraction. The study is conducted via a 2D finite element method. By the distinctive arrangement of both PhC structures, it is possible to obtain a TM-polarization maintaining device that offers a high polarization extinction ratio of ∼49 dB as well as a compact 180 • bend for TE-polarized light with low TL. The proposed study is useful in designing PhC waveguides with sharp bends, which can be employed for multiple applications in photonic integrated circuits.
... For many years, photonic crystals (PCs) of metal-dielectric structures designed to control and manipulate the propagation of electromagnetic fields have been widely studied, both theoretically and experimentally [1][2][3][4][5][6][7][8][9]. Among the various methods, used to calculate the transmittance or reflectance of photonic crystals, stands out the scattering matrix method based on multipole expansions, which has been further developed and extended according to the particular geometries of the PC structures. ...
We study the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Resonant band structures of transmission coefficients are obtained as functions of the incidence angle, the geometric parameters, and the number of unit cells of the superlattices. The theory of finite periodic systems that we use is free of assumptions, the finiteness of the periodic system being an essential condition. We rederive the correct recurrence relation of the Chebyshev polynomials that carry the physical information of the coherent coupling of plasmon modes and interface plasmons and surface plasmons, responsible for the photonic bands and the resonant structure of the surface plasmon polaritons. Unlike the dispersion relations of infinite periodic systems, which at best predict the bandwidths, we show that the dispersion relation of this theory predicts not only the bands, but also the resonant plasmons’ frequencies, above and below the plasma frequency. We show that, besides the strong influence of the incidence angle and the characteristic low transmission of a single conductor slab for frequencies ω below the plasma frequency ω p , the coherent coupling of the bulk plasmon modes and the interface surface plasmon polaritons lead to oscillating transmission coefficients and, depending on the parity of the number of unit cells n of the superlattice, the transmission coefficient vanishes or amplifies as the conductor width increases. Similarly, the well-established transmission coefficient of a single left-handed slab, which exhibits optical antimatter effects, becomes highly resonant with superluminal effects in superlattices. We determine the space-time evolution of a wave packet through the λ / 4 photonic superlattice whose bandwidth becomes negligible, and the transmission coefficient becomes a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with the centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs.
... Photonic crystal based optical sensors work based on the resonance wavelength principle [11]. Based on this sensing principle, any mechanical deformation caused from within or without the sensor, the resonance wavelength or output intensity of the sensor will vary, thereby showing sensitivity towards effects triggered internally or externally. ...
p>The motivation for this paper is the strikingly sad statistics, obtained from various research bodies globally, regarding the effect of cancers on the global populace and the impact of current methods put in place for the early diagnosis of cancer. This paper is novel for many reasons. Primarily, it presents the use of an optical biosensor based on photonic crystal for cancer cell detection. This biosensor was recently developed as an ultra-compact biochemical sensor based on a 2D photonic crystal cavity known for altering its spectrum in proportion to minute changes in refractive index. Secondarily, The Finite Difference Time Domain (FDTD) and Plane Wave Expansion (PWE) techniques were applied to analyze the possibility of using photonic crystals as biosensors for the detection of cancer cells. The obtained resonant wavelength from the analysis of simulated results was 1.54964 µm and transmitted power obtained from the analysis was 51.9%. For the cancerous cell sample, The PC 12 Cell, the obtained resonant wavelength from analysis of the simulated results was 1.54964 µm and the transmitted power obtained from the analysis was 55.6%.</p
... two-dimensional triangular lattice photonic crystals with rod-shaped air holes in silicon where the line defect waveguide is obtained by removing out a row of holes from the middle of the photonic crystal along the propagation direction as shown infigure 35. The waveguide can guide light from one location to another, Light propagates through the defect, confined by total internal reflection in the vertical direction and Bragg reflection, due to the PBG, in the lateral direction[59] [60]. Our objective in this chapter is to provide a better understanding of the slow light in photonic crystal waveguide, for this purpose, we will discuss the results and do a re-simulation of the paper that reported by Li et al in ref[61] as follow:The photonic crystal structure, sequentially, from top to bottom an air layer / silicon (Si) / silica (SiO2) The SOI (silicon on insulator) substrate consisting of silicon (Si) layer with thickness of 220 nm and silica layer with thickness of 2000 nm. ...
Photonic crystals (PhCs) are artificially constructed periodic arrangements of dielectric materials. The discovery of photonic crystals with a photonic band gap, has opened up new methods for controlling light, leading to proposals for many novel devices. An important element of optical circuits is a linear waveguide to carry light to and from components, in addition, photonic crystals provide unique advantages for waveguides. Photonic-crystal waveguides, guided by the band gap of the PhC and it is one of the most suitable and attractive structures for realizing the slow light effect, because such a line defect structure operates at room temperature and has a high potential for on-chip integration by modifying the initial PhC structure. Slow light promotes a stronger light–matter interaction; it offers additional control over the spectral bandwidth of the interaction, and it allows us to delay and temporarily store light in all-optical memories. In this context, the aim of this thesis is to study and design two photonic crystal waveguides PCW1 and PCW2 designed to achieve slow light in the flat band region of guided modes with large normalized delay bandwidth product (NDBP) while maintaining smaller values of group velocity dispersion. To further test the applicability of our waveguide PCW2, the buffering capacity is calculated, which is found to be as high as 148 bits on the assumption that the device length is L=1mm. The reported results can be useful in making on-chip optical buffers and delay lines.
... Photonic Crystals (PCs) can be considered as a promising candidate in the areas of photonics and optical communications technology including microcavity lasers [1] and waveguides [2]. Photonic Crystal (PC), that is a repeated structure which is composed of two different alternating materials, have the ability to control and manipulate the propagation of optical waves resulting in new optical properties of these structures. ...
Tolerance variations of the design parameters of the photonic crystals due to fabrication processes have a strong effect on the performance of the photonic crystals and their operating wavelengths. In this work, the uncertainties of the design parameters of one-dimensional photonic crystals (1D-PCs) and their impacts on the PCs optical properties and the operating performance are investigated. The effects of these uncertainties for different tolerances are studied for both defect-free PCs and PCs with a defect air layer. The probability distribution function and the standard deviations of the photonic gap bandwidth, the defect mode wavelength and the trust gap width are studied. These stochastic analyses and modeling are based on the transfer matrix and Monte Carlo simulations.
... two-dimensional triangular lattice photonic crystals with rod-shaped air holes in silicon where the line defect waveguide is obtained by removing out a row of holes from the middle of the photonic crystal along the propagation direction as shown infigure 35. The waveguide can guide light from one location to another, Light propagates through the defect, confined by total internal reflection in the vertical direction and Bragg reflection, due to the PBG, in the lateral direction[59] [60]. Our objective in this chapter is to provide a better understanding of the slow light in photonic crystal waveguide, for this purpose, we will discuss the results and do a re-simulation of the paper that reported by Li et al in ref[61] as follow:The photonic crystal structure, sequentially, from top to bottom an air layer / silicon (Si) / silica (SiO2) The SOI (silicon on insulator) substrate consisting of silicon (Si) layer with thickness of 220 nm and silica layer with thickness of 2000 nm. ...
Recently, slow light with low group velocity attracted wide attention because it is regarded as a promising technology for future all-optical communication networks. It can be used for the enhancement of light-matter interaction; it also offers the possibility to miniaturize high sensitivity sensors. Slow light occurs due to a large first-order dispersion arising from the resonance of light with a material or structure. Photonic crystal waveguides are especially attractive for generating slow light in a wideband with a high group index and low group-velocity dispersion. Slow light in photonic crystal waveguides can be used for a wide range of applications, such as delay lines or buffers and enhanced light-matter interaction.
In our work, we present a novel type of a slow-light photonic crystal waveguide obtained by changing the position of the second rows of holes of a line defect photonic crystal waveguide in the direction of light propagation; the modified photonic crystal is optimized through simulation performed by the 2-D PWE method of the RSoft software.
... Due to such property and other properties of PCs, optical photonic crystal waveguides (PCWs) are used widely in optical network systems. By constructing a waveguide in a perfect photonic crystal, the symmetry of the crystal is broken and PC permits propagating of light in the waveguide path [3,4]. ...
... give rise to an interaction between the TM-like and TE -like photonic modes. Prevention of this type of vertical symmetry breaking was already a significant concern during the development of traditional photonic crystal slab waveguides [9,226,373]. Such effects in the presence of disorder require further investigation. ...
In this thesis we investigate designer disordered complex media for photonics and phononics applications. Initially we focus on the photonic properties and we analyse hyperuniform disordered structures (HUDS) using numerical simulations. Photonic HUDS are a new class of photonic solids, which display large, isotropic photonic band gaps (PBG)comparable in size to the ones found in photonic crystals (PC). We review their complex interference properties, including the origin of PBGs and potential applications. HUDS combine advantages of both isotropy due to disorder (absence of long-range order) and controlled scattering properties from uniform local topology due to hyperuniformity (constrained disorder). The existence of large band gaps in HUDS contradicts the longstanding intuition that Bragg scattering and long-range translational order is required in PBG formation, and demonstrates that interactions between Mie-like local resonances and multiple scattering can induce on their own PBGs. The discussion is extended to finite height effects of planar architectures such as pseudo-band-gaps in photonic slabs as well as the vertical confinement in the presence of disorder. The particular case of a silicon-on-insulator compatible hyperuniform disordered network structure is considered for TE polarised light. We address technologically realisable designs of HUDS including localisation of light in point-defect-like optical cavities and the guiding of light in freeform PC waveguide analogues. Using finite-difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities in planar
hyperuniform disordered solids with isotropic band gaps that efficiently confine TE polarised radiation. We thus demonstrate that HUDS are a promising general-purpose design platform for integrated optical micro-circuitry. After analysing HUDS for photonic applications we investigate them in the context of elastic waves towards phononics applications. We demonstrate the first phononic band gaps (PnBG) for HUDS. We find that PnBGs in phononic HUDS can confine and guide elastic waves similar to photonic HUDS for EM radiation.
... PhC waveguides, formed by introducing a linear defect into a perfect PhC structure, is one of the essential ingredients in PICs. 2D PhC waveguides were proposed [6] and demonstrated experimentally [7,8] . Based on this structure, many components such as Mach-Zehnder devices [9] , filters [10,11] , modulators [12] , detectors [13] , sensors [14] , and directional couplers [15] can be created. ...
In this Letter, the effects of material/structure parameters of photonic crystal (PhC) parallel waveguides on the coupling length are investigated. The results show that, increasing the effective relative permittivity of the PhC leads to a downward shift of the photonic bandgap and a variation of the coupling length. A compact PhC 1.31/1.55 μm wavelength division multiplexer (WDM)/demultiplexer with simple structure is proposed, where the output power ratios are more than 24 dB. This WDM can multiplex/demultiplex other light waves efficiently.
... two-dimensional triangular lattice photonic crystals with rod-shaped air holes in silicon where the line defect waveguide is obtained by removing out a row of holes from the middle of the photonic crystal along the propagation direction as shown infigure 35. The waveguide can guide light from one location to another, Light propagates through the defect, confined by total internal reflection in the vertical direction and Bragg reflection, due to the PBG, in the lateral direction[59] [60]. Our objective in this chapter is to provide a better understanding of the slow light in photonic crystal waveguide, for this purpose, we will discuss the results and do a re-simulation of the paper that reported by Li et al in ref[61] as follow:The photonic crystal structure, sequentially, from top to bottom an air layer / silicon (Si) / silica (SiO2) The SOI (silicon on insulator) substrate consisting of silicon (Si) layer with thickness of 220 nm and silica layer with thickness of 2000 nm. ...
We present a novel type of slow light photonic crystal waveguide obtained by changing only the position of the second rows of holes of a line defect photonic crystal waveguide in the direction of light propagation. A nearly constant group index is achieved for 30, 32 and 33 over 10.5, 13.5 and 15.5 nm, respectively. In addition, a large normalized delay-bandwidth product ranging from 0.201 to 0.344 is obtained at the operation wavelength 1550 nm.
... However, this type of PC structure has not been used for realizing high spatial resolution biosensor imaging since its Bloch surface modes are not confined laterally (rather they propagate along the plane of the substrate surface). Another type of important PC structure is the PC slab, which consists of a periodicity of RI contrast in the plane of the substrate surface introduced by alternating a high-RI guiding layer (e.g., TiO2, GaAs) with low-RI materials (e.g., air, water, Si) [7,27,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74]. The PC slabs are typically comprised of 1D (e.g., linear) or 2D (e.g., quadratic and triangular) structures [7,46,51,63,75], and here we focus on the 1D PC slab since it is the simplest to use for PCEM. ...
... PBGs are a specific energy bands in the band structure that light cannot propagate there, in fact PBGs are a forbidden wavelength band that any electromagnetic wave with these wavelengths cannot propagate in there. So we can use them to confine the waves into the waveguides and prevent them to propagate in the PhC structure [10,1112]. At recent years, various applications of PhC based devices have been presented such as power splitters [13], optical filters [14], demultiplexers [15], waveguides [16], etc. Optical power splitters are one of the mostlyused components in modern optical communication systems. ...
In this paper a high efficiency optical power splitter based on two-dimensional photonic crystals is proposed. The photonic crystal cavity is assumed to be constructed by TiO2 nanorods with refractive index n = 2.609. To do so, first we implement some techniques to design a 1*2 optical power splitter, which include Y-shape waveguides and various types of defects such as point and line defects. The results of numerical simulations show that at the wavelength range of DWDM systems, the proposed 1*2 power splitter has the maximum efficiency of 99.616 %. A similar method is employed to design a 1*4 splitter with high performance operation at the same wavelength range which relates to the efficiency of 99.21% that is the highest amount between these type of power splitters. The final size of these high efficiency power splitters is 130μm2 (10μm*13μm) which make them suitable for integrated optical circuits.
... Photonic crystal (PhC), as a kind of periodic dielectric structure, has been studied extensively for several applications because of the strong capability to manipulate light propagation, including optical waveguides and interconnects [1][2][3][4], modulators and switches [5,6], lasers [7,8], and sensors . PhC sensors have met practical demands: high sensitivity, cheap, ultra-compactness, low power consumption, and disposable. ...
We introduce an alternative method to establish a nanoscale sensor array based on a photonic crystal (PhC) slab, which is referred to as a 1 × 4 monolithic PhC parallel-integrated sensor array (PhC–PISA). To realize this function, four lattice-shifted resonant cavities are butt-coupled to four output waveguide branches, respectively. By shifting the first to the two closest neighboring holes around the defect, a high Q factor over 1.5 × 10 4 has been obtained. Owing to the slightly different cavity spacing, each PhC resonator shows an independent resonant peak shift as the refractive index changes surrounding the resonant cavity. The specific single peak with a well-defined extinction ratio exceeds 25 dB. By applying the finite-difference time-domain (FDTD) method, we demonstrate that the sensitivities of each sensor in PhC-PISA S 1 = 60.500 nm / RIU , S 2 = 59.623 nm / RIU , S 3 = 62.500 nm / RIU , and S 4 = 51.142 nm / RIU (refractive index unit) are achieved, respectively. In addition, the negligible crosstalk and detection limit as small as 1 × 10 − 4 have been observed. The proposed sensor array as a desirable platform has great potential to realize optical multiplexing sensing and high-density monolithic integration.
... This propagation loss is two or three orders of magnitude less than that reported for metallic lines (4–25 dB/cm) at the 0.3-THz band[8][9][10][11][12]. To the best of our knowledge, this value is also the smallest ever reported among various PC waveguides, including those in the light-wave region (2–100 dB/cm)[20,34,35,[37][38][39][40][41][42][43][44][45]. This indicates that the limiting factor of propagation loss for the PC waveguide in the terahertz region is not the radiation loss from structural errors because of the fabrication process as reported for the light-wave region but the material absorption of Si when the resistivity is less than 30 kΩ-cm, which is in our experimental condition. ...
We pursued the extremely low loss of photonic-crystal waveguides composed of a silicon slab with high resistivity (20 kΩ-cm) in the terahertz region. Propagation and bending losses as small as <0.1 dB/cm (0.326–0.331 THz) and 0.2 dB/bend (0.323–0.331 THz), respectively, were achieved in the 0.3-THz band. We also developed 1.5-Gbit/s terahertz links and demonstrated an error-free uncompressed high-definition video transmission by using a photonic-crystal waveguide with a length of as long as 50 cm and up to 28 bends thanks to the low-loss properties. Our results show the potential of photonic crystals for application as terahertz integration platforms.
... However, this type of PC structure has not been used for realizing high spatial resolution biosensor imaging since its Bloch surface modes are not confined laterally (rather they propagate along the plane of the substrate surface). Another type of important PC structure is the PC slab, which consists of a periodicity of RI contrast in the plane of the substrate surface introduced by alternating a high-RI guiding layer (e.g., TiO2, GaAs) with low-RI materials (e.g., air, water, Si) [7,27,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74]. The PC slabs are typically comprised of 1D (e.g., linear) or 2D (e.g., quadratic and triangular) structures [7,46,51,63,75], and here we focus on the 1D PC slab since it is the simplest to use for PCEM. ...
We review the development and application of nanostructured photonic crystal surfaces and a hyperspectral reflectance imaging detection instrument which, when used together, represent a new form of optical microscopy that enables label-free, quantitative, and kinetic monitoring of biomaterial interaction with substrate surfaces. Photonic Crystal Enhanced Microscopy (PCEM) has been used to detect broad classes of materials which include dielectric nanoparticles, metal plasmonic nanoparticles, biomolecular layers, and live cells. Because PCEM does not require cytotoxic stains or photobleachable fluorescent dyes, it is especially useful for monitoring the long-term interactions of cells with extracellular matrix surfaces. PCEM is only sensitive to the attachment of cell components within ~200 nm of the photonic crystal surface, which may correspond to the region of most interest for adhesion processes that involve stem cell differentiation, chemotaxis, and metastasis. PCEM has also demonstrated sufficient sensitivity for sensing nanoparticle contrast agents that are roughly the same size as protein molecules, which may enable applications in "digital" diagnostics with single molecule sensing resolution. We will review PCEM's development history, operating principles, nanostructure design, and imaging modalities that enable tracking of optical scatterers, emitters, absorbers, and centers of dielectric permittivity.
In this paper, a temperature-controlled angle selection device based on a photonic bandgap is proposed, consisting of MLC-6608 liquid crystal (MLC) and common electrolytes stacked in layers. This device has an angular transmission stability for electromagnetic waves over a wide frequency band (600–660 THz). A high transmissivity (T>0.85) area, also called an angle window, is formed at 25° and 75°, and an area of zero transmissivity is formed beyond the angle window. The MLC is temperature-responsive, and the range of angle selection can be expanded or narrowed by temperature adjustment. When the MLC is replaced by the biological sample, it shows good sensing performance. It can be used to detect in vitro dermis, in vivo stratum corneum, and in vivo epidermis and it is of great significance in medicine, with a sensing sensitivity of 90.91°/refractive index unit.
The absence of a suitable standard device platform for terahertz waves is currently a major roadblock that is inhibiting the widespread adoption and exploitation of terahertz technology. As a consequence, terahertz-range devices and systems are generally an ad hoc combination of several different heterogeneous technologies and fields of study, which serves perfectly well for a once-off experimental demonstration or proof-of-concept, but is not readily adapted to real-world use case scenarios. In contrast, establishing a common platform would allow us to consolidate our design efforts, define a well-defined scope of specialization for “terahertz engineering,” and to finally move beyond the disconnected efforts that have characterized the past decades. This tutorial will present arguments that nominate substrateless all-silicon microstructures as the most promising candidate due to the low loss of high-resistivity float-zone intrinsic silicon, the compactness of high-contrast dielectric waveguides, the designability of lattice structures, such as effective medium and photonic crystal, physical rigidity, ease and low cost of manufacture using deep-reactive ion etching, and the versatility of the many diverse functional devices and systems that may be integrated. We will present an overview of the historical development of the various constituents of this technology, compare and contrast different approaches in detail, and briefly describe relevant aspects of electromagnetic theory, which we hope will be of assistance.
We have experimentally demonstrated a very low cross talk in photonic crystal waveguide crossings of any kind. For cross talk reduction, we added a resonant cavity to the waveguide intersection designed to operate in microwave frequencies. The two-dimensional waveguide crossing structure was sandwiched between two parallel metal plates to eliminate radiation loss in the vertical direction. Transmission measurements revealed that when designed properly the cross talk reduction was as large as −30 dB at resonance, which is qualitatively consistent with simulation results. From the experimental results, the detailed resonant mode shape at the waveguide intersection was found to play a key role in relaying the input signal in the forward direction and therefore reducing cross talk.
We present here the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Based on the theory of finite periodic systems, we show that besides the strong influence of the incidence angle, the low transmission characteristic of a single conductor slab, for frequencies $\omega$ below the plasma frequency $\omega_p$, becomes in this domain highly oscillating. Similarly, the well-established transmission coefficient of a single left-handed slab becomes highly resonant with superluminal effects in superlattices with more than one unit cell. We determine the space-time evolution of a wave packet through the $\lambda/4$ photonic superlattice whose transmission coefficient is a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs. We show that besides the strong influence of the incidence angle, the coherent coupling of the bulk plasmon modes and the interface surface plasmon polaritons lead to oscillating transmission coefficients, and depending on the parity of the number of unit cells $n$ of the superlattice, the transmission vanishes or amplifies as the conductor width increases. We determine the space-time evolution of a wave packet through the $\lambda/4$ photonic superlattice whose bandwidth becomes negligible, and the transmission coefficient becomes a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with the centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs.
Photonic crystals have received great attention due to the potential for use as key devices, such as optical filters, optical switches, waveguides, and micro lasers. Photonic crystals fabricated so far via the sol-gel process are inverseopal photonic crystals (or inverted opals), in which colloidal crystal templates were used. The materials are made up of complex oxides, with two or more metal ions, as those that possess a variety of electric and/or optical properties with certain tunability that usual semiconductors like Si cannot afford. This chapter focuses on the fabrication and optical properties via solution-based routes including primarily the sol-gel process, including materials and structures for photonic crystals, fabrication procedures (synthesis of templates and deposition methods), and evaluation of geometry of crystal and properties (1D, 2D, and 3D). © Springer International Publishing AG, part of Springer Nature 2018.
Photonic crystal planar circuits designed and fabricated in silicon on silicon dioxide are demonstrated. Our structures are based on two-dimensional confinement by photonic crystals in the plane of propagation, and total internal reflection to achieve confinement in the third dimension. These circuits are shown to guide light at 1550 nm around sharp corners where the radius of curvature is similar to the wavelength of light.
Photonic crystal research is advancing at an astonishing pace. In this chapter photonic crystals are classified, from a crystal dimension viewpoint, into 2D and 3D crystals. They are further divided, from a material point of view, into semiconductors, organic dielectrics and fibers. Although ID crystals have occasionally been referred to in recent photonic crystal research, they are omitted from this chapter.
We present three-dimensional analysis of two-dimensional guided resonances in photonic crystal slab structures. This analysis leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and reflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes, and the strength of the index modulation.
Photonic crystals manipulate photons in a manner analogous to solid-state crystals, and are composed of a dielectric material with a periodic refractive index distribution. In particular, two-dimensional photonic-crystal slabs with high index contrasts (semiconductor/air) are promising for practical applications, owing to the strong optical confinement in simple, thin planar structures. This paper presents the recent progress on a silicon photonic-crystal slab as a technology platform in the terahertz-wave region, which is located between the radio and light wave regions (0.1–10 THz). Extremely low-loss (<0.1 dB/cm) terahertz waveguides based on the photonic-bandgap effect as well as dynamic control and modulation of a terahertz-wave transmission in a photonic-crystal slab by the effective interaction between photoexcited carriers and the terahertz-wave trapping due to the photonic band-edge effect are demonstrated. Terahertz photonic-crystal slabs hold the potential for developing ultralow-loss, compact terahertz components and integrated devices used in applications including wireless communication, spectroscopic sensing, and imaging. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Photonic crystals have received great attention due to the potential for use as key devices, such as optical filters, optical switches, waveguides, and micro lasers. Photonic crystals fabricated so far via the sol–gel process are inverse-opal photonic crystals (or inverted opals), in which colloidal crystal templates were used. The materials are made up of complex oxides, with two or more metal ions, as those that possess a variety of electric and/or optical properties with certain tunability that usual semiconductors like Si cannot afford. This chapter focuses on the fabrication and optical properties via solution-based routes including primarily the sol–gel process, including materials and structures for photonic crystals, fabrication procedures (synthesis of templates and deposition methods), and evaluation of geometry of crystal and properties (1D, 2D, and 3D).
Nearly fifteen years have passed since the study of photonic crystals first commenced. Initially, this study was undertaken as it was seen as an interesting new area in physics. In the last five years, an increasing number of studies have been carried out on device applications in applied physics and engineering in addition to fundamental studies since a breakthrough on the realization of photonic crystals in optical regime has been achieved. The unique properties of photonic crystals have also led to their studies being recognized as a new and major field in optoelectronics. Moreover, study of the physics of photonic crystals continues to grow, drawing on many other scientific fields such as radio techniques, chemistry, precision machinery, acoustics, and so on. This chapter chronologically introduces the milestones reached in the study and development of photonic crystals, as well as some of their physical background.
Developing terahertz integration technology is essential for practical use of terahertz electromagnetic waves (0.1–10 THz) in various applications including broadband wireless communication, spectroscopic sensing, and nondestructive imaging. In this paper, we present our recent challenges towards terahertz system integration based on photonic crystal technology such as the development of terahertz transceivers. We use photonic-crystal slabs consisting of a twodimensional lattice of air holes formed in a silicon slab to develop low loss compact terahertz components in planar structures. The demonstration of ultralow loss (< 0.1 dB/cm) waveguides and integrated transceiver devices in the 0.3 THz band shows the potential for the application of photonic crystals to terahertz integration technology. Improving the coupling efficiency between the photonic crystal waveguide and resonant tunneling diode is important to take full advantage of the ultralow loss photonic crystal waveguides.
In this chapter, 2D PC slab waveguides including several functional waveguides among various PC devices are taken up in particular. Namely, results on the design, fabrication and characterization of those 2D PC waveguides necessary for application to ultrafast optical planar integrated circuits are described in detail.
At the early stage of research, photonic crystals (PCs) were mainly discussed out of physical interest. However, studies of its device applications started and have expanded worldwide since the middle of the 1990s. Presently, PCs are expected to be one of the key technologies in the next era of optoelectronics. The first part of this chapter discusses the principles and future prospects of various PC devices.
In this chapter we take a survey of our current research work as well as fundamental features of PCs for non-spcialists or newcomers including undergraduate students. By grasping those first, it should be, we believe, easier for them to understand the later chapters. For this purpose, in addition to surveying a few representative PBSs, their prominent features, and PC-based devices, we also present and explain basic concepts and fundamental laws or relations needed to understand the underlying physics, by considering mainly a simple 1D PBS. In some other cases, we use the band structures without explaining here how to obtain those.
Compared with the photonic crystal(PC) structures composed of Si circular, the PC structures composed of triangular lattice of air holes in a dielectric slab are more easily fabricated and integrated. The tunability of directional band gap in a two-dimensional photonic crystal of air holes in a semiconductor matrix is demonstrated numerically, using the plane wave expansion calculation. Numerical simulations show that the photonic crystal band gaps are modulated by nematic liquid crystals infiltrated in the air holes. Then the band gap can be controlled easily under the influence of the external electric field. So the results can serve as a field-sensitive polarizer. These results are in agreement with that of Liu. However, the tunable field-sensitive polarizer based on the phenylacetylene liquid crystals instead of 5CB liquid crystals has the wider frequency range. Moreover, the transmission spectrum of the photonic crystal infiltrated by liquid crystal is analyzed, using finite difference time domain(FDTD) method. Numerical simulations show that the shift of the spectrum modulated by liquid crystal can be used to design a novel switch.
We have fabricated several two-dimensional photonic-crystal (2DPC) slab waveguides by using fine electron beam lithography and dry etching. The 2DPC waveguides include straight, bend, Y-branch, directional coupler, and coupled-cavity waveguides on the GaAs/AlGaAs substrate as an application to the ultra-small and ultra-fast all-optical switching device. Transmission spectra and near field patterns were characterized in a wide wavelength range from 850 to 1600nm with the sample finished to the air-bridge type 2DPC slab. These waveguides appear to be suitable for achieving the waveguide platform in the symmetrical-Mach-Zehnder device.
In this chapter, proposals for and examples of photonic crystal applications are reviewed, referring to the relevant publications from the body of literature covering this field of investigation. This chapter is composed of the following 11 sections:
Lasers
Light-emitting diodes (LEDs)
Resonators and filters
Waveguides
Fibers
Prisms and polarizers
Photonic integrated circuits
Nonlinear devices
Tunable crystals and optical switches
Antennas and electromagnetic wave techniques
Miscellaneous
Although many other papers treat ID crystals such as diffraction gratings and multilayer films as photonic crystals, we concentrate mainly on 2D and 3D photonic crystals in this chapter. Appropriate articles from each relevant research organization are introduced in accordance with the application. Note that all the published papers are not covered.
The design, fabrication, and measurement of photonic-band-gap (PEG) waveguides and resonators in two-dimensional photonic crystal slabs have been investigated. Although photonic crystal slabs have only partial gaps, efficient waveguides and resonators can be realized by appropriate design. As regards PBG waveguides, we show various designs for efficient single-mode waveguides in PhC slabs with SiO2 cladding, we report group dispersion measurements of PBG waveguides in PhC slabs, and describe the successful fabrication of PBG waveguides with adiabatic connectors that enable us to couple the light from single-mode fibers efficiently to PBG waveguides. As regards PBG resonators, we show how to realize very high-Q and small volume resonators in hexagonal PhC slabs, and report the fabrication of resonant tunneling filters that consist of PBG resonators coupled with PBG waveguides. We also describe the successful fabrication of resonant tunneling mode-gap filters with adiabatic mode connectors.
We theoretically investigated the resolution of the photonic crystal (PC) k-vector superprism, which utilized the wavelength-dependent refraction of light at an angled output end as a narrow band filter at 1.55 μm wavelength range. Similarly to the case of the conventional S-vector prism, we defined the equi-incident-angle curve against the dispersion surface, and calculated the beam collimation, wavelength sensitivity and resolution parameters for light propagation in the PC. We estimated that the resolution of the k-vector prism is the same as or higher than that of the S-vector prism and the PC can be significantly miniaturized. In addition, we clarified the relation of the S-vector prism phenomenon and the position of the output end in the k-vector prism, and different results for the reduced and repeated zone schemes, which are important for the detailed design. We also confirmed that the light propagation simulated by the FDTD method well agreed with the results of the dispersion surface analysis.
We discuss photonic crystals (PhCs) with advanced micro/nano-structres which are semiconductor quantum dots (QDs) and micro electro-mechanical systems (MEMS) for the purpose of realizing novel classes of PhC devices in future photonic network system. After brief introduction on advantages to implement QDs and MEMS with PhCs, we discuss optical characterization of PhC microcavity containing self-assembled InAs QDs. Modification of emission spectrum of a QD ensemble due to the resonant cavity modes is demonstrated. We also point out the feasibility of low-threshold PhC lasers with QD active media in numerical analysis. A very low threshold current of ∼10 μA is numerically obtained for lasing action in the multi dimensional distributed feedback mode by using realistic material parameters. Then, the basic concept for MEMS-controlled PhC slab devices is described. We show numerical results that demonstrate some of interesting functions such as the intensity modulation and the tuning of resonant frequency of cavity mode. Finally, a preliminary experiment of MEMS-based switching operation in a PhC line-defect waveguide is demonstrated.
Optical interconnection technologies are increasingly deployed in high-performance electronic systems to address challenges in connectivity, size, bandwidth, latency, and cost. Projected performance requirements are leading to formidable cost and energy efficiency challenges. Hybrid and integrated photonic technologies are currently being developed to reduce assembly complexity and to reduce the numbers of individually packaged parts. This chapter provides an overview of the important challenges that photonics currently face, identifies the various optical technologies that are being considered for use at the different interconnection levels, and presents examples of demonstrated state-of-the-art optical interconnection systems. Finally, the prospects and potential of these technologies in the near future are discussed.
We have fabricated optical waveguides in three-dimensional (3D) photonic crystals and observed propagation of light beams. Light beams with wavelengths of 1.15 μm propagate along the line defects formed in the 3D photonic crystals. The 3D photonic crystals consist of a-Si/SiO2 multilayers laminated alternately by rf bias sputtering on a periodically hollowed silica substrate with a triangular lattice. The pit diameter is 0.2 μm and the pitch of the lattice is 0.5 μm. The thickness of each laminated layer is 0.2 μm. Line defects are formed normal to the surface by laminating a-Si/SiO2 multilayers with ten periods on the substrate in which the corrugation patterns have been omitted in a certain area corresponding to the core. The measurements of transmittance normal to the surface show that the wavelength of 1.15 μm used in observation of propagation is in the passband for the one-dimensional periodic region corresponding to the core and in the stop band for the 3D periodic region corresponding to the cladding, respectively. Measurements show good agreement with finite-difference time-domain calculations.
We report the experimental demonstration of waveguides built around layer-by-layer photonic crystals. An air gap introduced between two photonic crystal walls was used as the waveguide. We observed full (100%) transmission of the electromagnetic (EM) waves through these planar waveguide structures within the frequency range of the photonic band gap. The dispersion relations obtained from the experiment were in good agreement with the predictions of our waveguide model. We also observed 35% transmission for the EM waves traveling through a sharp bend in an L-shaped waveguide carved inside the photonic crystal.
The scattering matrix method was applied to the analysis of finite two-dimensional photonic crystals and lightwave devices. Results indicated that 1) the light transmission at the photonic band gap (PBG) is suppressed to less than 30 dB in the densely packed and honeycomb crystals, both of which are composed of only four rows of unit cells of semiconductor columns and 2) this PBG effect is weakened to half when the nonuniformity from 10 to 30% is brought to the diameter of columns. Also, the light propagation in defect waveguides with abrupt bends, a branch and a directional coupler was demonstrated by this method. It was found that the coupling loss at the input end of the waveguide is drastically changed by the shape of the input end. The reflection loss at 60 bends was estimated to be less than 1 dB, and the excess loss at an abrupt Y-branch was estimated to be 0-4.6 dB, depending on the frequency of the input wave. The demultiplexing and power dividing functions were expected in a directional coupler with a submicron coupling length, which is considered to be due to antiguide characteristics of the waveguides. [IEEE ]
Since it was first published in 1995,Photonic Crystalshas remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written,Photonic Crystalsis an indispensable resource for students and researchers.
We demonstrate highly efficient transmission of light around sharp corners in photonic band-gap waveguides. Numerical simulations reveal complete transmission at certain frequencies, and very high transmission \(>95%\) over wide frequency ranges. High transmission is observed even for 90° bends with zero radius of curvature, with a maximum transmission of 98% as opposed to 30% for analogous conventional dielectric waveguides. We propose a simple one-dimensional scattering theory model with a dynamic frequency-dependent well depth to describe the transmission properties.