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Analysis of Finite 2-D Photonic Crystals of Columns and Lightwave Devices Using the Scattering Matrix Method
Abstract
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 ]
... In fact (9) defines the matching condition for each PhC waveguide port considering any guided mode involved. Here we just used the spatial shift between real an imaginary part of any traveling wave to be a quarter of a wavelength, which is easily testable by direct substitution of such guided modes into (9). As a result, we obtain the field solution for the waveguide discontinuity but now without any reflections at the output ports 0 ( ) . ...
... Let E 0 m denote the amplitude of the transmitted wave in each output port. The resulting error in fulfilling condition (9) can be determined as follows ...
... The MAS model is described here by a matrix equation, which contains 6576 equations with 6576 unknowns and three right hand sides due to the existence of one auxiliary IWGA source per port (see Table 1). The unknown amplitudes of the IWGA sources are determined according to condition (9), i.e. the reflections suppression condition at the cutoff slice x 0 = ± (12·a + r base ). We shall not care about the matching condition at the input port y 0 = 8·a + r base because there is always a reflected wave present coming from the discontinuity (i.e. ...
We presented a novel method for the accurate and
efficient computation of the reflection and transmission coefficients
of waveguide discontinuities within planar photonic crystals (PhCs).
This method proposes a novel kind of field source that optimally
excites the dominant waveguide mode and mimics procedures that
are typically used for the measurement of reflection coefficients.
This technique may be applied to arbitrary field simulators working
in the frequency domain. The presented reflection compensation
scheme is elucidated along the Method of Auxiliary Sources (MAS).
In order to verify the results, we compare two test cases with the
rigorous connection technique provided by the Multiple Multipole
Method (MMP).
... As per their analysis, it is easy to introduce 90 0 bend in square lattices and 60 0 or 120 0 bend in hexagonal lattices. The defects with 90 0 , 60 0 and 120 0 bends are analyzed in detail by Yonekura et al. [39] using scattering matrix method on photonic crystal based conventional light wave devices. Zhang and Li [40] also discusses various bending waveguides with different bending angles. ...
... The rest of the defects (Crystal defects 2, 4, 6, 7, 9, 10, and 11) are newly discussed. Reflection losses for crystals 3, 5, 8, and 12 have been obtained by Yonekura et al. [39]. ...
Photonic Bandgap crystals are avidly studied because of their application of optical waveguides, optical diodes, defect mode photonic lasers, to name a few. This paper presents a comparative study of 14 bandgap crystals [13 defective and 1 without defect]. The design, simulation, and classification-based analysis of these defective crystals obtained by modifying dielectric arrangement in photonic bandgap lattice (PBG) lattice is carried out. In addition, the study of the dielectric structure of rods in the air is carried out concerning photonic bandgap for a 9 × 10μm wafer size. The discrete pulse components in real data, imaginary data, and intensity data were obtained using Fast Fourier Transforms and were converted to a clean dataset. With context to defective Photonic Crystal analysis and design explored the predictive and generative models for data-driven approaches. Within the predictive modeling framework, Microsoft AzureML is used to give classification performance using five different algorithms. The relative effectiveness of these algorithms has been studied. The created data have been classified using Multiclass Artificial Neural Network, Multiclass Decision Jungle, Multiclass Logistic Regression, Multiclass Random Forest, and 2-Clsaas Support Vector Machine classifiers. The Multiclass Decision Jungle and Multiclass Random Forest exhibit the maximum accuracy of 91.01% and 91.20%, respectively, while the other three algorithms give the classification accuracy of 87.5%.
... Recently, scattering matrix method has found many new applications such as the analysis of finite size photonic crystal devices [8][9][10] and metamaterials [11,12]. Moreover, the authors of [13] proposed an innovative way to apply this method to 3D photonic crystal structures. ...
... Unlike mesh based numerical methods such as finite difference time domain (FDTD) and finite element method (FEM), T-matrix method takes advantage of the specific structure of photonic crystals and uses cylindrical harmonics to express the field distributions. Although this semi-analytical approach is found to be nearly ten times faster than FDTD or FEM [9], it is still cumbersome to be used for the design of large photonic crystal structures due to its relatively higher computational complexity. ...
Abstract—The lowering and raising operators of cylindrical harmon- ics are used to derive the general fast multipole expressions of arbitrary order Hankel functions. These expressions are then employed to trans- form the dense matrix in the scattering matrix method (SMM) into a combination of sparse matrices (aggregation, translation and disag- gregation matrices). The novel method is referred to as fast multipole accelerated scattering matrix method (FMA-SMM). Theoretical study shows FMA-SMM has lower complexity O(N ,), where N stands for total harmonics number used. An empiri- cal formula is derived to relate the minimum,group size in FMA-SMM to the highest order Hankel functions involved. The various imple- mentation parameters are carefully investigated to guarantee the algo- rithm’s accuracy and efficiency. The impact of the cylinders density on convergence rate of iterative solvers (BiCGStab(2) here), memory cost as well as CPU time is also investigated. Up to thousands of cylinders can be easily simulated and potential applications in photonic crystal devices are illustrated. 106,Zhang and Li
... In the frequency domain, it is possible to develop more efficient computational methods by taking advantage of the geometric features. The multipole method (also called multipole expansion method, cylindrical wave expansion method, scattering-matrix method, and multiple-scattering method) [4][5][6][7][8][9][10] is quite popular; it solves a system of equations for the coefficients of local cylindrical wave expansions around each cylinder, and it is usually more efficient than the general FDTD method and FEM. The multipole method has been extended to multicylinder structures with a layered background medium involving one or more planar interfaces [11][12][13][14][15], but it becomes relatively complicated for these cases. ...
... For structures concerned here, general numerical methods such as the FEM are certainly applicable, but the multipole method [4][5][6][7][8][9] is more competitive. The multipole method produces a linear system with a dense coefficient matrix. ...
A simple model for two-dimensional photonic crystal devices consists of a finite number of possibly different circular cylinders centered on lattice points of a square or triangular lattice and surrounded by a homogeneous or layered background medium. The Dirichlet-to-Neumann (DtN) map method is a special method for analyzing the scattering of an incident wave by such a structure. It is more efficient than existing numerical or semianalytic methods, such as the finite element method and the multipole method, since it takes advantage of the underlying lattice structure and the simple geometry of the unit cells. The DtN map of a unit cell is a relation between a wave field component and its normal derivative on the cell boundary, and it can be used to avoid further computation inside the unit cell. In this paper, an improved DtN map method is developed by constructing special DtN maps for boundary and corner unit cells using the method of fictitious sources.
... It is a semi-analytic method and can give both filed distributions and transmission spectra against a static field excitation. Compared with FDTD method, scattering matrix can save computation time [3] By applying DC magnetic field along the axis of ferrite cylinders, their scattering properties will be affected. The scattering properties also change with the changing of the magnetic filed intensity. ...
... The Transmissions band for left port and right port are different, it is due to the different applied DC magnetic field intensity. By adjusting the applied DC magnetic field intensity, the filter becomes an adjustable filter, which is more flexible compared with conventional filter [3] [6].Fig.9 shows the electric filed distribution of Ybranch against different wavelength when the applied DC magnetic field in left discontinuity ...
This paper presents a novel approach to alternate the electromagnetic properties of the electromagnetic band gap (EBG), where a ferrite defect is introduced, and in addition, a DC magnetic field is applied to alternate the EBG's electromagnetic property. Numerous devices are examined, including a coupler and a Y-branch filter. The numerical experiments demonstrate that the devices electromagnetic characteristics can be easily adjusted by varying the DC magnetic-field intensity. In this paper, the examinations are performed using the scattering-matrix method. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 395–400, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20481
... The adaptation of PhC to optoelectronics makes it possible to envisage new perspectives, such as the production of integrated optical components and devices with reduced dimensions and the integration of several functions on the same substrate. Among these components: waveguides (Mekis et al. 1996;Mehmet et al. 2000;Lončar et al. 2000), lasers (Painter et al. 1999;Noda et al. 2001), splitters (Yonekura et al. 1999;Bayindir et al. 2000), fibers (Lebbal et al. 2013), and sensors (Benmerkhi et al. 2016;Bougriou et al. 2013). The realization of these dispositive is effected by creating a defect on the PhC structure consider. ...
In this paper, we propose an investigated sensor array based on two-dimensional photonic crystal air-slot width-modulated line-defect microcavity. This sensor consists of a waveguide coupled with microcavity. To achieve a high quality factor, we have tuned some parameters of the microcavity. The principle of sensing is based on the resonance wavelength shift when the refractive index is changed. For sensitivity analysis, we proposed various conventional designs (A–D). We demonstrated that the design D has the highest sensitivity. An air-slot is created within the line-defect. The existence of the slots enhances the light-matter interactions. The simulation results are obtained by using finite-deference time-domain method. The sensitivity can achieve 400 nm/RIU, with detection limit of 2.98 × 10⁻⁵ RIU.
... It is based on expanding the fields and matching them at the boundaries of different regions and thus lends itself naturally to the analysis of some nanoantenna structures. The most representative of mode-matching methods involves rigorous coupled-wave analysis (Moharam et al. 1995), scattering matrix method (Yonekura et al. 1999), plane-wave expansion method (Johnson and Joannopoulos 2001), and T-matrix method (Mishchenko et al. 2010). Using cheap computer resources, these methods are particularly useful in characterizing the optical response of periodic or multilayered nanoantennas, Yagi-Uda nanoantennas, and nanoantenna array. ...
The principal computational electromagnetics techniques for solving antenna problems are reviewed. An introduction is given on a historical review of how antenna problems were solved in the past. The call for precise solutions calls for the use of numerical methods as found in computational electromagnetics. A brief introduction on differential equation solutions and integral solutions is given. The Green’s function concept is introduced to facilitate the formulation of integral equations. Numerical methods and fast algorithms to solve these equations are discussed.
Then an overview of how electromagnetic theory relates to circuit theory is presented. Then the concept of partial element equivalence circuit is introduced to facilitate solutions to more complex problems. In antenna technology, one invariably has to have a good combined understanding of the wave theory and circuit theory.
Next, the discussion on the computation of electromagnetic solutions in the “twilight zone” where circuit theory meets wave theory was presented. Solutions valid for the wave physics regime often become unstable facing low-frequency catastrophe when the frequency is low.
Due to advances in nanofabrication technology, antennas can be made in the optical frequency regime. But their full understanding requires the full solutions of Maxwell’s equations. Also, many models, such as perfect electric conductors, which are valid at microwave frequency, are not valid at optical frequency. Hence, many antenna concepts need rethinking in the optical regime.
Next, an emerging area of the use of eigenanalysis methods for antenna design is discussed. This can be the characteristic mode analysis or the natural mode analysis. These analysis methods offer new physical insight not possible by conventional numerical methods.
Then the discussion on the use of the domain decomposition method to solve highly complex and multi-scale antenna structures is given. Antennas, due to the need to interface with the circuit theory, often have structures ranging from a fraction of a wavelength to a tiny fraction of a wavelength. This poses a new computational challenge that can be overcome by the domain decomposition method.
Many antenna designs in the high-frequency regime or the ray optics regime are guided by ray physics and the adjoining mathematics. These mathematical techniques are often highly complex due to the rich physics that come with ray optics. The discussion on the use of these new mathematical techniques to reduce computational workload and offering new physical insight is given.
A conclusion section is given to summarize this chapter and allude to future directions.
... Already the bending of the propagation path through a right angle with minimal loss has been theoretically demonstrated [3] and experimentally verified [4] and various interconnections such as Y- [5] and T- [2] junctions, and also channel-drop filters [6] have been proposed. Attention is now being turned to the modeling and fabrication of ultra-compact optical devices such as the folded directional coupler of Fig. 1 which comprises various elements connected through complex waveguide structures embedded in the photonic crystals [2]. ...
A rigorous semi-analytic approach to the modelling of coupling, guiding and propagation in complex microstructures embedded in photonic crystals is presented. The method, based on Bloch modes and generalized Fresnel coefficients, is outlined and a variety of applications of the design tool are presented.
... It is based on expanding the fields and matching them at the boundaries of different regions and thus lends itself naturally to the analysis of some nanoantenna structures. The most representative of mode-matching methods involves rigorous coupled-wave analysis (Moharam et al. 1995), scattering matrix method (Yonekura et al. 1999), plane-wave expansion method (Johnson and Joannopoulos 2001), and T-matrix method (Mishchenko et al. 2010). Using cheap computer resources, these methods are particularly useful in characterizing the optical response of periodic or multilayered nanoantennas, Yagi-Uda nanoantennas, and nanoantenna array. ...
The principal computational electromagnetics techniques for solving antenna problems are reviewed. An introduction is given on a historical review of how antenna problems were solved in the past. The call for precise solutions calls for the use of numerical methods as found in computational electromagnetics. A brief introduction on differential equation solutions and integral solutions is given. The Green’s function concept is introduced to facilitate the formulation of integral equations. Numerical methods and fast algorithms to solve these equations are discussed.
Then an overview of how electromagnetic theory relates to circuit theory is presented. Then the concept of partial element equivalence circuit is introduced to facilitate solutions to more complex problems. In antenna technology, one invariably has to have a good combined understanding of the wave theory and circuit theory.
Next, the discussion on the computation of electromagnetic solutions in the “twilight zone” where circuit theory meets wave theory was presented. Solutions valid for the wave physics regime often become unstable facing low-frequency catastrophe when the frequency is low.
Due to advances in nanofabrication technology, antennas can be made in the optical frequency regime. But their full understanding requires the full solutions of Maxwell’s equations. Also, many models, such as perfect electric conductors, which are valid at microwave frequency, are not valid at optical frequency. Hence, many antenna concepts need rethinking in the optical regime.
Next, an emerging area of the use of eigenanalysis methods for antenna design is discussed. This can be the characteristic mode analysis or the natural mode analysis. These analysis methods offer new physical insight not possible by conventional numerical methods.
Then the discussion on the use of the domain decomposition method to solve highly complex and multi-scale antenna structures is given. Antennas, due to the need to interface with the circuit theory, often have structures ranging from a fraction of a wavelength to a tiny fraction of a wavelength. This poses a new computational challenge that can be overcome by the domain decomposition method.
Many antenna designs in the high-frequency regime or the ray optics regime are guided by ray physics and the adjoining mathematics. These mathematical techniques are often highly complex due to the rich physics that come with ray optics. The discussion on the use of these new mathematical techniques to reduce computational workload and offering new physical insight is given.
A conclusion section is given to summarize this chapter and allude to future directions.
... Theoretical studies of basic directional coupler structure [1,2] and improved structures e.g. a structure with shorter coupling length [3] and experimental study [4], have been done. However, the major obstacle to the use of such devices as switching cell is that the switching between the input and output ports needs to be activated by an external signal. ...
We analyze and propose a directional optical coupler embedded in photonic crystal (PhC), which is driven by an external command signal. The switching method uses a low power external command signal, inserted in the central coupling region, which acts as another waveguide. The switching process is based on the change of the coupler from the bar state to the cross state owing to the external command signal.
... It is based on expanding the fields and matching them at the boundaries of different regions, and thus lends itself naturally to the analysis of multilayer optical devices. The most representative of modematching methods involves rigorous coupled-wave analysis [66], scattering-matrix method [67], and plane wave expansion method [68]. Using cheap computer resources, these methods are specially useful in characterizing the optical response of periodic OSC devices. ...
The book chapter provides a systematic study on plasmonic effects in organic solar cells (OSCs). We first introduce the concepts, significance, and recent progress of OSCs incorporating plasmonic nanostructures. On the basis of unique features of OSCs, we exploit versatile resonance mechanisms acting on the absorption enhancement of OSCs; for example, Fabry-Pérot mode, quasi-guided mode, and plasmonic mode. Next, we present rigorous theoretical models to characterize optical properties of OSCs. The key physical quantities, as well as the pros and cons of different models, are described in detail. After that, we show some theoretical results to unveil the fundamental and device physics of plasmonic effects in typical OSC structures. Finally, we conclude the chapter and identify future opportunities in this field.
... Les résonateurs peuvent aussi utiliser le couplage entre deux guides d'onde séparés par quelques inclusions [63], (figure 1.5.g). Le signal incident est injecté dans un premier guide d'onde et par couplage résonant via la structure, il est couplé dans le second guide d'onde. ...
Theoretical acousto-optic couplings mechanisms in nano-structured materials are investigated in the present thesis: the photonic and phononic crystals with simultaneous bandgaps, also named phoxonic crystals. The aim of the study consists in exploring their potential in order to reduce energy consumption, sizes of devices, by taking advantage ofthe confinement property and slow wave phenomena.For our investigations, numerical models, using finite element method, were developed to determine optimized conditions for a better efficiency and suitable parameters promoting wide bandgaps. Acoustic and optical confined modes search favorable for acousto-optic interaction is performed. Numerical models were created to compute the acousto-opticcouplings by taking into account various coupling mechanisms such as the photo-elastic, opto-mechanic and electro-optic effects.Many interaction configurations are investigated in order to determine the impact of material anisotropy, the cavity mode symmetries, various lattices or different materials such as silicon and lithium niobate.Finally, a first approach for a designed component is proposed. It shows the possibility to use coupling mechanisms for a device such as an optical modulator by using acousto-optic confined modes in a cavity.
... Mode-matching methods. Mode-matching method [76][77][78][79] is a commonly-adopted technique for modeling optical structures consisting of two or more separated regions. It is based on expanding the fields and matching them at the boundaries of different regions and thus lends itself naturally to the analysis of multilayer optical devices. ...
Organic solar cells (OSCs) have recently attracted considerable research interest. For typical OSCs, it is highly desirable to have optically thick and physically thin thickness for strong light absorption and efficient carrier collection respectively. In the meantime, most organic semiconductors have short exciton diffusion length and low carrier mobility [1-3]. As a consequence, the active layers of OSCs are generally thin with a thickness of a few hundred nanometers to ensure the efficient extraction of carriers, hence limiting the total absorption of incident light. Optimizing both the optical and electrical (i.e., multi-physical) properties of OSCs is in demands for rationally designed device architectures. Plasmonic nanomaterials (e.g., metallic nanoparticles [4-6], nanorods [7, 8], nanoprisms [9, 10], etc.) have recently been introduced into different layers of multilayered solar cells to achieve highly efficient light harvesting. The multilayered solar cells structures commonly have active layer, carrier (electron and hole) transport layer and electrode (anode and cathode). Through the localized plasmonic resonances (LPRs) [11-16] from metallic nanomaterials, very strong near-fields will be generated, which can provide a large potential for enhancing optical absorption in the multilayered OSCs. Besides the optical effects, it has been reported that metallic nanomaterials can modify the morphology, interface properties as well as the electrical properties of OSCs which will significantly modify the performances of OSCs [17-23]. In this article, the effects of various optical resonance mechanisms and the theoretical studies of the multiphysical properties of OSCs will be reviewed. Meanwhile, the experimental optical and electrical effects of metallic nanomaterials incorporated in different layers of OSCs will be studied. The morphology and interface effects of metallic nanomaterials in the carrier transport layers on the performances of OSCs will also be described.
... We performed approximate analysis only. We started from the transmission data on 2D triangular/hexagonal photonic crystals [13] and used our calculation results on stress-induced photonic bandgap shift and refractive index change to obtain total transmission through the channel waveguide for the case of an incident beam parallel to the input leg of the waveguide. One row of cells was omitted in the input leg, and two rows in the output leg. ...
We describe and numerically simulate a method for optical readout of microcantilever tip deflection utilizing a 2D photonic crystal-based channel waveguide with a 90O band. The structure is photolithographically built into the basis of the microcantilever structure in the zone of the maximum stress. The cantilever deflection causes a shift of the photonic bandgap edge and photoelastic refractive index change. If the operating wavelength is near the band edge, leakage of signal at the waveguide bend is increased, thus resulting in amplitude modulation of output signal proportional to deflection. The described approach can be applied for readout of deflection and stress in other microsystems as well.
... Typical refractive index contrast is about 2. Two-dimensional PBG waveguides can be used to fabricate a variety of passive components. They are utilized for waveguide intersections (crossings) with low cross-talk and high throughput [11], waveguide branches (Y-branches [12], T-branches [13]), channel add/drop filters for Wavelength Division Multiplexing (WDM) [14], etc. Their properties make them the ideal choice for downscaling of the dimensions of passive devices for optical communications. ...
I INTRODUCTION One of the significant emerging concepts in the field of optical telecommunications are materials with photonic band gap, also known as photonic crystals [1], [2]. These are readily applicable for highest bit transfer rates (tens and even hundreds of Gbit/s) and are inherently convenient for networks with WDM transmission. Photonic crystals were introduced by Yablonovitch in 1987 [3] and soon became one of the most important topics in optoelectronics generally, but also in numerous other fields, including e.g. microwave technique. A photonic crystal can be defined as material whose refractive index periodically varies along one, two or three axes with a period (lattice constant) comparable to the wavelength of light. If the refractive index contrast is sufficient, in such materials a photonic band gap (PBG) appears, a range of wavelengths in which no propagation of electromagnetic radiation is possible. A 3D photonic crystal is thus a perfect omnidirectional mirror in which no propagation of electromagnetic waves within the PBG is possible. A very important class of applications of photonic crystals in optical communication are PBG optical waveguides [4]. If a line defect is introduced in a photonic band gap structure, light is perfectly localized and guided within it, and thus a perfect (lossless) optical waveguide is obtained [5]. If a PBG guide sharply bends, light will follow its turns practically without losses, even if the bending angles are 90 0 and more over distances below one micrometer (as shown theoretically by Mekis et al [4] and experimentally by Lin et al [6]). This is the main advantage of PBG waveguides over conventional fiber-guides whose performance is limited by total internal reflection (TIR) and where the allowed radii of curvature are of the order of centimetres. An ideal solution for a photonic crystal waveguide would be to use a full 3D PBG for the confinement of the localized mode (line defect). However, the need to fabricate 3D structures with accurately controlled features with the dimensions of the order ~0.1 µm and incorporating controlled line defects at the same time are well beyond today's technological possibilities [7], [8]. A practical method used to overcome this problem are 2D photonic crystal waveguides. These are fabricated by planar technologies. Various solutions for practical 2D waveguides were described in e.g. [8], [10]. A 2D PBG structure consisting of an array of dielectric cylinders is shown in Fig. 1. The cylinders are presented stripped of the surrounding medium. In reality the embedding material should have either much higher or much lower refractive index than the cylinders. Typical refractive index contrast is about 2. x y z Fig. 1. 2D photonic crystal structure with triangular lattice of dielectric cylinders. Two-dimensional PBG waveguides can be used to fabricate a variety of passive components. They are utilized for wave-guide intersections (crossings) with low cross-talk and high throughput [11], waveguide branches (Y-branches [12], T-branches [13]), channel add/drop filters for Wavelength Division Multiplexing (WDM) [14], etc. Their properties make them the ideal choice for downscaling of the dimen-sions of passive devices for optical communications. A limitation of 2D photonic crystal waveguides is that they offer near-perfect optical confinement and guiding only within the xy plane, while being leaky along the third (z-) coordinate. This decreases the number of possible applica-tions and limits the use of guides to only a single mode. The issue of radiation losses and leaky modes in 2D PBG waveguides is analysed in [13].
... The former group has high directivity due to the limited angular propagation allowed within the EBG material, including EBG resonator/superstrate antennas [35,66,90,91] and EBG cavities [92]. The devices in the latter group can efficiently transmit electromagnetic waves, even for 90 • bands with zero radius of curvature [60,79], including EBG waveguide [93][94][95][96], power splitters, directional couplers [97,98], switches [65](and the references therein), and the EBG filters [99,100]. ...
... EM beam splitters have an important role in PhC-based optical components, and a 50/50 splitter is the most fundamental one. Based on regular (reciprocal) PhC waveguides, T-and Y-splitters have been proposed and studied previously [9][10][11][12][13][14][15][16]. For these splitters, wave transmission through the Tor Y-junctions depends strongly on the relationship between the modes that may propagate in the PhC waveguides and the modes of the junction regions. ...
Magneto-optical and regular photonic crystals with triangular lattice are designed to construct one-way waveguides. Accordingly, two types of efficient beam splitters with one-way input channels are proposed and investigated. One of the proposed beam splitters is a 1 × 2 splitter, which achieves 50/50 splitting based on the structural symmetry. Since both output channels are one-way waveguides, this splitter is immune to interferences at the output ends. The other is a 1 × 3 beam splitter, in which one output channel is a regular waveguide and the others are one-way waveguides. It is shown that the 1 × 3 splitter can provide equal splitting ratios in the guiding band if defects with proper parameters are introduced in the splitting region.
... The boundary integral equation (BIE) method is suitable for structures with piecewise constant refractive index profiles. The multipole method [7][8][9][10][11] is suitable for structures containing circular inclusions (dielectric rods or air holes). The Dirichlet-to-Neumann (DtN) map method [12,13] is an efficient numerical method for two-dimensional (2D) PhC devices. ...
Many photonic crystal (PhC) devices are nonperiodic structures due to the introduced defects in an otherwise perfectly periodic PhC, and they are often connected by PhC waveguides that serve as input and output ports. Numerical simulation of a PhC device requires boundary conditions to terminate PhC waveguides that extend to infinity. The rigorous boundary condition for terminating a PhC waveguide is a nonlocal condition that connects the wave field on the entire surface (or line in two-dimensional problems) transverse to the waveguide axis, and it is relatively difficult to use, especially for realistic devices, such as those in PhC slabs. In this paper, a simple approximate boundary condition involving a few points in the waveguide axis direction is introduced. The new boundary condition is used with the Dirichlet-to-Neumann map method to take advantage of the lattice structures and identical unit cells in PhC devices. Comparisons with the rigorous nonlocal boundary condition indicate that the simple boundary condition gives accurate solutions if the computational domain is enlarged by a few lattice constants in each direction.
... As a result of this coupling, electromagnetic waves propagating along one waveguide excite modes of the neighboring waveguide, thus power coupling takes place. Among different methods for implementing optical directional couplers [2][3][4][5], those in which optical waveguides are implemented using periodic dielectric structures have found great attention. For the same token, photonic-crystal waveguides can be exploited in implementation of optical couplers. ...
It is shown that the modal analysis of coupled waveguides in a two-dimensional photonic crystal can be reduced to the evaluation of natural frequencies of an equivalent network. This network is constituted of ideal transmission lines and transformers and is directly derived from Maxwell's equations without any simplifying assumptions. The natural frequencies of the proposed equivalent network are computed after its subdivision into a series of cascaded sub-networks. These sub-networks are then described by their multi- port impedance matrices so that the entire network can be described by the cascaded connection of these matrices. Resonance conditions of this cascaded connection yield the natural frequencies and consequently the propagation constants of various modes of the original coupled photonic-crystal waveguides. Under the resonance condition, the voltages and currents of the equivalent network are nonzero, and they can be used to determine all the field components of the corresponding mode. The obtained numerical results verify the fact that the coupling length of photonic-crystal directional couplers can be reduced considerably.
... Meade et al. [7], first discussed the line defect waveguide. Later on, sharp bending of light was theoretically calculated by Mekis et al. [8] and Yonekura et al. [9]. The line defect waveguide in the photonic crystal allows a wide design window and a wide transmission band. ...
In the present paper, we have made an analysis to observe the effect of introduction of defect on dispersion relation, group velocity, and effective group index in a conventional photonic band gap (PBG) structure. The study shows that inside the PBG materials group velocity and effective group index becomes negative in both types (conventional as well as defect PBG structure) of structure at a certain range of frequencies. Also, near the edges of the bands it attains very high values of index of refraction. A defect PBG structure gives a very unique feature that group velocity becomes exactly zero at a particular value of frequency and also becomes several hundred times greater than the velocity of light which is not attainable with the conventional PBG structure. Defect PBG structures with such peculiar characteristics are seen in lasing without inversion, in construction of perfect lens, in trapping of photon and other optical devices.
... Beam splitting has key importance in all-optical applications of photonic crystals (PCs), such as interferometers [1] and analog-to-digital converters [2]. An input beam can be split into two equal amplitude branches by Y-and T-shaped linear defect3456 and coupled-cavity [7] waveguides in PCs. Beam splitting can also be achieved by directional coupling between linear defect waveguides [8]. ...
Splitting of light waves by a two-dimensional photonic crystal associated with source size and dispersion relation of photonic crystal at a wavelength of 1,550 nm without disturbing periodicity is numerically demonstrated via finite-difference time-domain simulations. Split branches in either polarization state make plus or minus 45° with the [11] direction and propagate in a self-collimated manner with equal amplitude and phase. Sixty-four percent of total transmittance is attained provided that the waves are coupled and collected through appropriate planar waveguides. Alternatively, approximately 50 % total transmittance for both polarizations can be obtained by application of an anti-reflection coating layer at the input face. Polarization-independent beam splitting occurs in a narrow range around the target wavelength, while its transverse-magnetically polarized sub-harmonic can also be split. The photonic crystal can also operate as a polarizing splitter at oblique incidence.
... Optical power splitter is an important component in integrated optical circuits. Photonic crystal optical power splitters based on T-junction or Yjunction have been analyzed [8], [24]. In this paper we present a new design of power splitter based on multimode-interference (MMI) effect in photonic crystal waveguides. ...
Photonic crystals have the capability to control electromagnetic waves
due to the existence of photonic bandgap. The devices based on photonic
crystal structures usually have the advantage of substantial size
reduction compared to their conventional counterparts, which may lead to
miniaturization and large-scale integration of optical and
opto-electronic devices. In this dissertation, several novel optical
devices based on photonic crystals are designed and analyzed, including
a compact power splitter, a compact polarizing beam splitter, an optical
intersection of nonidentical optical waveguides, and a single mode
coupled resonator optical waveguide. The simulation results show
superior advantages compared to their conventional counterparts. In
addition, a new fabrication method based on combining a custom-built
blue laser writer and the technique of optical holography is developed
for the purpose of mass production of useful photonic crystal devices.
... U in E to the nanometer dimension of the periodicity found photonic crystals (PhCs), we can use directional coupler embedded in photonic crystal to act as switching cell within photonic integrated circuits (PICs). Theoretical studies of basic directional coupler structure [1, 2] and improved structures e.g. a structure with shorter coupling length [3] and experimental study [4], have been done. However, the major obstacle to the use of such devices as switching cell is that the switching between the input and output ports needs to be activated by an external signal. ...
We analyze and propose a directional optical coupler embedded in photonic crystal (PhC), which is driven by an external command signal. The switching method uses a low power external command signal, inserted in the central coupling region, which acts as another waveguide. The switching process is based on the change of the coupler from the bar state to the cross state owing to the external command signal.
... However, in the frequency domain, special and more efficient numerical methods can be developed to take advantage of special geometric features of the PhC devices. For ideal two-dimensional (2D) PhCs composed of infinitely long and parallel circular cylinders (rods or air-holes), the multipole method (Felbacq et al. 1994; Yonekura et al. 1999; Martin 2006) based on cylindrical wave expansions around each cylinder is particularly efficient. If a main propagation direction can be identified for the PhC device, the scattering matrix method (McPhedran et al. 1999; Yasumoto et al. 2004 ) can be used. ...
A typical photonic crystal (PhC) device has only a small number of distinct unit cells. The Dirichlet-to-Neumann (DtN) map
of a unit cell is an operator that maps the wave field to its normal derivative on the boundary of the cell. Based on the
DtN maps of the unit cells, a PhC device can be efficiently analyzed by solving the wave field only on edges of the unit cells.
In this paper, the DtN map method is further improved by an operator marching method assuming that a main propagation direction
can be identified in at least part of the device. A Bloch mode expansion method is also developed for structures exhibiting
partial periodicity. Both methods are formulated on a set of curves for maximum flexibility. Numerical examples are used to
illustrate the efficiency of the improved DtN map method.
In this paper, a photonic crystal based encoder consisting of two hexagonal shaped couplers in 2D square lattice of dielectric rods in air is proposed. Waveguides have been created by removing dielectric rods in the structure, and rods with smaller radii have been used to achieve the proper couplers operations. The proposed structure can generate a two-bit binary code in the output, according to the order of active inputs, without the use of nonlinear effects. To realize this structure, an OR gate is designed, then the two OR gates are combined to consolidate the desired encoder. Best delay time and the dimensions of the proposed structure are about 166 fs and 390 μm2, respectively, and the switching rate is 6THz.
The principal computational electromagnetics techniques for solving antenna problems are reviewed. An introduction is given on a historical review of how antenna problems were solved in the past. The call for precise solutions calls for the use of numerical methods as found in computational electromagnetics. A brief introduction on differential equation solutions and integral solutions is given. The Green’s function concept is introduced to facilitate the formulation of integral equations. Numerical methods and fast algorithms to solve these equations are discussed.
Then an overview of how electromagnetic theory relates to circuit theory is presented. Then the concept of partial element equivalence circuit is introduced to facilitate solutions to more complex problems. In antenna technology, one invariably has to have a good combined understanding of the wave theory and circuit theory.
Next, the discussion on the computation of electromagnetic solutions in the “twilight zone” where circuit theory meets wave theory was presented. Solutions valid for the wave physics regime often become unstable facing low-frequency catastrophe when the frequency is low.
Due to advances in nanofabrication technology, antennas can be made in the optical frequency regime. But their full understanding requires the full solutions of Maxwell’s equations. Also, many models, such as perfect electric conductors, which are valid at microwave frequency, are not valid at optical frequency. Hence, many antenna concepts need rethinking in the optical regime.
Next, an emerging area of the use of eigenanalysis methods for antenna design is discussed. This can be the characteristic mode analysis or the natural mode analysis. These analysis methods offer new physical insight not possible by conventional numerical methods.
Then the discussion on the use of the domain decomposition method to solve highly complex and multi-scale antenna structures is given. Antennas, due to the need to interface with the circuit theory, often have structures ranging from a fraction of a wavelength to a tiny fraction of a wavelength. This poses a new computational challenge that can be overcome by the domain decomposition method.
Many antenna designs in the high-frequency regime or the ray optics regime are guided by ray physics and the adjoining mathematics. These mathematical techniques are often highly complex due to the rich physics that come with ray optics. The discussion on the use of these new mathematical techniques to reduce computational workload and offering new physical insight is given.
A conclusion section is given to summarize this chapter and allude to future directions.
Localized Surface Plasmon (LSP) characteristics of the metallic nano-rod, the promising candidate for the optical nanoantenna, are investigated. Geometrical parameters including size, number, and gap dimensions of the nano-rods clearly affect the optical field enhancement and evanescent electric field distribution. The hollow nano-rod exhibits higher field enhancement compared to that of other rod geometries and the maximum electric field is found at the so called, resonant wavelength. As the number of solid nano-rods increases, the optical field of the first order decreases. It is found that the coupling fields in the gaps between solid nano-rods can be optimized to obtain desirable radiation patterns.
The properties of surface plasmon modes and switching gaps for extraordinary mode in the 3-D magnetized plasma photonic crystals (MPPCs) with body-centered-cubic lattices, that are composed of the core tellurium (Te) spheres with surrounded by the magnetized plasma shells inserted in the air, are theoretically investigated in detail by the plane wave expansion method, as the magneto-optical Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). Our computing results show that the complete photonic bandgaps for extraordinary mode and two flatbands regions can be observed. The optical switching can be realized by such MPPCs, which can be tuned by the radius of core Te sphere, the plasma density and the external magnetic field, respectively. The flatbands regions are determined by the existence of surface plasmon modes. The numerical simulations also demonstrate that the interesting properties of surface plasmon modes can be found. If the thickness of magnetized plasma shell is larger than a threshold value, the band structures for extraordinary mode will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this condition, the inserted core sphere also has no effect on the band structures. It is worth to be noticed that the upper edge frequencies of two flatbands regions will not depend on the topology of lattice. However, to the different topologies of lattices, if the thickness of magnetized plasma shell is close to zero, the frequencies of lower edges will be convergence to two different constants.
In this paper, the properties of photonic band gaps (PBGs) for three-dimensional (3-D) magnetized plasma photonic crystals (MPPCs) composed of homogeneous magnetized plasma spheres immersed in the anisotropic dielectric (the uniaxial material) background with diamond lattices are theoretically studied by the plane wave expansion method, as the Faraday effects of magnetized plasma are considered. The equations for calculating the anisotropic PBGs in the first irreducible Brillouin zone are theoretically deduced. The anisotropic PBG and one flatbands region can be achieved. The effects of the ordinary-refractive index, extraordinary-refractive index, plasma filling factor, plasma frequency, and the external magnetic field on the characteristics of first anisotropic PBG are studied in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in diamond lattices, and the complete PBG can be obtained compared to the conventional 3-D MPPCs doped by the isotropic material (the relative bandwidth of PBG is increased by 0.1108). The bandwidth of PBG also can be enlarged by introduced the magnetized plasma into 3-D PCs containing the uniaxial material, and the relative bandwidth of PBG is increased by 0.0266. It also is shown that the first anisotropic PBG can be manipulated by the ordinary-refractive index, extraordinary-refractive index, plasma filling factor, plasma frequency, and the external magnetic field, respectively. The PBG can be enlarged by introducing the uniaxial material into 3-D MPPCs as the Faraday effects are considered. It also provides a way to enlarge the complete PBG for the 3-D MPPCs.
A major drawback of conventional dielectric waveguides is that their bending radii are limited to several millimeters due to the degradation of total internal reflection. Since the guiding of light in a PhC defect waveguides is not given through total internal reflection but the photonic bandgap (PBG) effect they can provide bending within the subwavelength range. Hence, PhC waveguides offer a promising scheme for low loss and ultra-dense optical integration. In this paper we have investigated and optimized 60° and 90° waveguides bends that are implemented in a planar photonic crystal (PhC) with triangular and square lattice symmetry. The in-plane guiding within the planar PhC structure is based on a W1 defect waveguide (a single line defect acting as a light channel in the Λ-K-direction) whereas for the vertical light confinement we rely in a slab waveguide formed by the low index contrast material system InGaAsP/InP. To achieve a reasonable bandgap around 1.55 μm the PhC consists of a lattice of holes with a filling factor of 39%. Key optical design parameters are characterized using 2D Finite difference time domain (FDTD) solution of the full-Wave Maxwell's equations. We show a significant improvement in both the transmission efficiency (up to 97%) and the transmission bandwidth by performing an optimization based on a sensitivity analysis.
A novel 2×1 beam combiner in two-dimension photonic crystal (PC) is presented. The rate-matching condition is analyzed based on coupled-mode theory. The transmittance performance of T-shaped branch in square lattice is simulated by the finite-difference time-domain (FDTD) method. By altering the radius of dielectric rods at vertex, we match the amplitude decay rates of three waveguides. Numerical simulation results show the PC combiner has a perfect transmittance when the rate-matching condition is satisfied.
The dispersive properties and unusual surface plasmon modes in three-dimensional (3-D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic lattices that are composed of the core tellurium (Te) spheres surrounded by the magnetized plasma shells inserted in the air are theoretically studied in detail by the plane-wave expansion method, as the magneto-optical Faraday effects of magnetized plasma are considered. Our analysis shows that the proposed 3-D MPPCs can obtain the complete photonic band gaps, which can be manipulated by the radius of core Te sphere, the plasma density, and the external magnetic field, respectively. We also find that a flatband region can be achieved, which is determined by the existence of surface plasmon modes. If the thickness of the magnetized plasma shell is less than a threshold value, the band structures of such 3-D MPPCs will be similar to those obtained from the same structure containing the pure magnetized plasma spheres. In this case, the inserted core sphere also will not affect the band structures. It is also noticed that the upper edge of flatband region does not depend on the topology of lattice.
In this paper, we design a novel Y-junction power splitter which is optimized according to coupled mode theory. Two rods are added in the junction. One rod is a silicon rod and another one is a ferrite rod, the refractive index of which can be varied by adjusting the external magnetic field. So, it not only can split the power, but also controls the output energy of the two branches automatically. The transmission spectrum is calculated by finite difference time domain (FDTD) method, which shows that the output energy of the two branches is closely related to the frequency of the incident terahertz (THz) wave and the refractive index of the ferrite rod. The device is a good candidate for integrated optical circuit, the tuning rate of which is about a few microseconds.
Dispersion properties of two types of three-dimensional plasma photonic crystals are theoretically investigated by a modified plane wave expansion method, which is composed of isotropic dielectric and nomagnetized plasma. The eigenvalue equations of two types of structures depend on the diamond lattice realization (dielectric spheres inserted in plasma background or vice versa), are deduced respectively. The band structures can be obtained by solving the nonlinear eigenvalue equations. The influences of relative dielectric constant and plasma frequency with different filling factors on dispersive relation are demonstrated, respectively. The numerical results show that the band structures can be modulated by the parameters for the two types of plasma photonic crystals.
The propagation performances of a double-chain splitter waveguide consists of coupled silver nanowires are investigated for different structures. We show that the efficiency of energy transport along the waveguide and split at a Y-junction due to surface plasmonic coupling is significantly depends on the parameters chosen for the structure such as radius of nanowire, opening angle of splitter and illuminating wavelength. The optimal structure for efficiently guiding and splitting the light at 600 nm is discussed in detail.
Due to the period 3-D structure, photonic crystals would form photonic bandgap. They are more important and widely used in optical communication, energy and display regime. The relationship between distances of circular photonic crystals and wavelength in perpendicular corner propagation is investigated in this study. There are six types of propagation found in the results. With the maximum propagation efficiency, the relationship between distances of circular photonic crystals and wavelength is the curve of decay ripple wave like. It is found under different distances of photonic crystals, there are three types between the propagation efficiency and wavelength
We investigate the electrodynamics properties and especially the in-plane light-wave propagation mechanism in photonic crystal circuits doped with active lattice points, using a rigorous semi-analytical technique.
Scattering matrix method is used to simulate the finite size 2D periodic structures. Coated or dielectric ring electromagnetic band gap structure is simulated and some novel properties are discussed. The numerical results show that coating layer has great impact on band gap characteristics. This provides additional freedom to tune or modify the properties of photonic crystal devices.
Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.
A monopole antenna in front of a conducting cylinder is analyzed by the modal-expansion method and scattering matrix method. An infinite perfectly conducting plate is introduced at the top of the monopole antenna to facilitate the modal-expansion analysis. Scattered fields due to the reflecting cylinder are obtained by the scattering matrix method with the aid of cylindrical function's addition theorem. Enforcement of continuity conditions of the tangential field components across the regional surfaces results in the matrix equation for determining the expansion coefficients. Numerical results for the return loss and radiation pattern of a monopole antenna in front of a conducting cylinder are presented and are in good agreement with experimental ones. The effect of the cylindrical reflector's radius and its distance from the monopole on the antenna's radiation performance is also examined.
Citation
Shanhui Fan and J. D. Joannopoulos, "PHOTONIC CRYSTALS: Towards Large-Scale Integration of Optical and Optoelectronic Circuits," Optics & Photonics News 11(10), 28-33 (2000)
http://www.opticsinfobase.org/opn/abstract.cfm?URI=opn-11-10-28
We propose a directional coupler design based on coupled cavity waveguide in photonic crystals. The plane wave expansion is used to give the dispersion of the coupled cavity waveguides and two parallel such waveguides. The couple length is got from the dispersion curves. Based on the research of the dispersion, we present a directional coupler and the transmission property is given. This structure is potentially important for highly efficient directional coupler in integrate optical circuit.
Main modelling approaches used for investigating the Photonic bandgap (PBG) devices are reviewed. In particular, the model based on Leaky Mode Propagation (LMP) method is described.
A complete analysis of the propagation characteristics, including the determination of modal propagation constants, electromagnetic field harmonics and total field distribution, transmission and reflection coefficients, total forward and backward power flow in the structure, guided and radiated power, and total losses, can be carried out by a computer program based on the LMP approach.
The numerical results have been validated by comparisons with those obtained by using other more complex and expensive models.
The new model shows some significant advantages in terms of very low computational time, absence of any a priori theoretical assumptions and approximations, capability of simulating the actual physical behaviour of the device and fast determination of the bandgap position.Copyright © 2003 John Wiley & Sons, Ltd.
Development of fast, flexible, and accurate methods for the analysis (and design) of photonic crystals devices is a relevant topic in order to optimize existing devices and/or developing new design solutions. Within this framework, in this article, we present an improved version of the scattering matrix method [1] for the evaluation of the electromagnetic behavior of two-dimensional finite-extent photonic crystals made of a finite set of parallel dielectric rods. In particular, by relying on features of the fields to be computed within the device and a suitable aggregation into “macrocells”, a considerable reduction of the number of unknowns of the linear system to be solved is achieved. A numerical analysis confirms the accuracy of the proposed method and the remarkable computational benefit. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2564–2570, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21998
Photonic crystal angle elements fabricated in silicon-on-insulator (SOI) are reported. These elements are modelled using three-dimensional finite difference time domain (FDTD) method. Photonic crystals have a two-dimensional trigonal lattice structure with cylindrical air columns. The period of the crystal is approximately 420 nm and the cylinder diameter is about 330 nm. Defect creation is performed by removing air columns from certain lattice sites. The SOI-layer is one micron thick and it also defines the column height. The FDTD modelling results imply that photonic crystal angle elements with lower height do not exhibit proper light transmission at the telecommunications wavelength window, 1550 nm. FDTD modelling results give higher transmission for TE-polarised light than for TM-polarisation. For better light coupling a taper element with widened waveguide end is designed.
A new approach for modal analysis of coupled cavity waveguides (CCW) in two-dimensional photonic crystals is presented. The mode propagation constants and the mode field profiles can be accurately derived by a simple matrix calculation, using a one-dimensional lattice sums, a T-matrix of an isolated circular cylinder, and generalized reflection matrices. Numerical examples have confirmed that the convergence of numerical solutions is very fast and the accuracy is very high.
A novel and numerically efficient treatment of electromagnetic modes localized at defects in two-dimension (2D) photonic crystals is presented in this paper. The method represents the fields in terms of scattered fields by each column of the photonic crystals. With the method, the field distributions in two photonic crystal structures are calculated with satisfying results.
Several of frailty has been identified in designing the DEMUX/MUX in PhC. For example, the power transfer inside the device not transfers 100% at the output arms. Light propagates inside the devices might dissipate along the waveguide. To minimize this losses, the design need to be alter, such as incorporate the defect pillar inside the space between two pillars so that the light will reflect back when the light incident with the defect pillar. Development of planar lightwave circuit (PLC) devices by combining the conventional waveguides and PhCW need to be study. One of the mechanisms how to minimize the coupling loss between conventional waveguide and PhCW is by introduces taper waveguide at the end of PhCW. By introducing taper waveguide, the bigger spot size from conventional waveguide will slowly shrink when enter the taper waveguide at the PhCW. Most of the work in this thesis focuses on optical communication PLC technology. Application area of photonic crystal devices can be extends into other applications. PhC can also be implemented in other applications such as bio-sensing, imaging, illumination, etc. The investigation on how the existing devices can be used for such applications and new devices/materials will have to be developed to address these areas. In the future, PhC components will by widely used in optical telecommunications. Since the invention of the concept of PhC in the end of of the 80's, their properties have been studied intensively. New applications have been proposed and realized. The only components that are so far in commercial use are the photonic crystal fibers. They have many extraordinary properties that cannot be achieved using conventional fibers and thus will have a profound effect on the fiber optics industry. In the near future, other PhC components, such as fiber lasers, will also be brought into market.
La denominada sociedad de la información en la que nos encontramos actualmente ha sido posible gracias a la revolución tecnológica derivada del desarrollo espectacular de la microelectrónica desde hace poco más de medio siglo. Desde la aparición del transistor como componente básico la evolución tecnológica ha seguido una trayectoria de miniaturización considerable. El número de componentes que pueden ser insertados en un chip se ha doblado cada 18 meses según las predicciones que en los años setenta realizó G. Moore. En la actualidad se ha llegado a una frontera tecnológica de escala nanométrica donde se han originado graves problemas, derivados de la alta integración, que han frenado este ritmo de evolución. Con vistas a la superación de los problemas surgidos en la microelectrónica se ha venido proponiendo el empleo de los fotones, más rápidos y con menos disipación de energía, para continuar el desarrollo tecnológico. Avances en esta dirección favorecerían el desarrollo de las redes ópticas dentro del campo de las telecomunicaciones al dotarlas de funcionalidades que permitan eliminar los "cuellos de botella" generados en los conversores optoelectrónicos. Además hay otros campos de investigación que se verían beneficiados como por ejemplo la computación o los sensores fotónicos. Surge un complejo y vasto campo conocido como la Nanofotónica. En esta tesis se estudian los cristales fotónicos planares como una de las tecnologías incluidas dentro del campo de la Nanofotónica. Concretamente se estudia la implementación de un acoplador direccional en cristales fotónicos. Esta estructura es básica en todo tipo de aplicaciones ya que permite la implementación de funcionalidades básicas tan importantes como son los divisores de potencia, multiplexores y demultiplexores, interferómetros Mach-Zehnder o incluso conmutadores. A lo largo de toda la tesis se abordan temas que van desde el modelado de las estructuras de cristal fotónico y el diseño teórico del acoplador direcci
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