Launching transverse-electric Localized Waves from a circular waveguide

In this paper, a cylindrical coordinate system-based finite difference time domain (FDTD) method is proposed for resonant frequency computation of dielectric material loaded circular waveguide. The computation is carried out by discretizing a model of circular waveguide resonator which has the radius of 10.12mm and the length of 60mm using FDTD notation and numerically computed to determine its resonant frequency in transverse electric (TE) mode. Some scenarios are applied for loading the waveguide by dielectric materials to analyze its resonant frequency to be compared with the hollow circular waveguide. From the results, it is shown that the TE mode resonant frequency for loaded circular waveguide is lower than of hollow circular waveguide which satisfies the numerical prediction. Meanwhile, from the scenario of circular waveguide partially loaded with dielectric material which is coated from outer region in a certain depth, it is found that the resonant frequency varies depending on the depth of dielectric material or on the volume proportion of dielectric material in the waveguide. The result shows when the proportion of dielectric material is 36% the lower resonant frequency is similar with the waveguide fully loaded with dielectric material.

A compact polarization demultiplexer (P-DeMux) is proposed and characterized to enable wavelength-divisionmultiplexing and mode-division-multiplexing simultaneously. The proposed structure is composed of a microring resonator in ultrathin waveguide and two bus channels in the novel silicon nitride silica silicon horizontal slot waveguides. In the slot waveguide, the transverse electric (TE) mode propagates through the silicon layer, while the transverse magnetic (TM) mode is confined in the slot region. In the designed ultra-thin waveguide, the TM mode is cutoff. The effective index of the TE modes for ultrathin and slot waveguides have comparable values. Thanks for these distinguishing features, the input TE mode can be efficiently filtered through the ultra-thin microring at the resonant wavelength, while the TM mode can directly output from the through port. Simulation Results show that the extinction ratio of the proposed P-DEMUX for TE and TM modes are ∼36.5 and 31.27 dB, and the insertion losses are ∼0.22 and 0.249 dB respectively.

A technique for creating a temperature-insensitive refractometer that utilizes transverse electric (TE) and transverse magnetic (TM) modes in an open-top ridge waveguide design is presented. By using the TE mode resonance as a temperature reference, the relative shift of the TM mode can be monitored in order to measure the refractive index of liquids under test. Specifically, the device fabricated here produces a resonance shift of 1 pm for every 1 × 10−4 of measured index change, with a temperature sensitivity less than 0.5 pm °C−1. To increase the sensitivity of these devices, a theoretical model is developed to investigate the performance of some potential waveguide structures. Relationships between the waveguide core size, refractive index distribution, as well as the relative evanescent sensitivity of TE and TM modes are examined.

A compact and fabrication friendly polarization demultiplexer (P-DEMUX) is proposed and characterized to enable wavelength-division-multiplexing and polarization-division-multiplexing simultaneously. The proposed structure is composed of a polarization-selective microring resonator in ultrathin waveguide and two bus channels in the silicon nitride-silica-silicon horizontal slot waveguides. In the slot waveguide, the transverse electric (TE) mode propagates through the silicon layer, while the transverse magnetic (TM) mode is confined in the slot region. In the designed ultra-thin waveguide, the TM mode is cut-off. The effective indexes of the TE modes for ultrathin and slot waveguides have comparable values. Thanks for these distinguishing features, the input TE mode can be efficiently filtered through the ultra-thin microring at the resonant wavelength, while the TM mode can directly output from the through port. Simulation results show that the extinction ratio of the proposed P-DEMUX for TE and TM modes are 33.21 dB and 24.97 dB, and the insertion losses are 0.346 dB and 0.324 dB, respectively, at the wavelength of 1551.64 nm. Furthermore, the device shows a broad bandwidth (>100 nm) for an extinction ratio (ER) of >20 dB. In addition, the proposed P-DEMUX also has a good fabrication tolerance for the waveguide width variation of –20 nm ≤ Δ w g ≤ 20 nm and the microring width variation of –20 nm ≤ Δ w r ≤ 20 nm for a low insertion loss of <0.75 dB and low ER of <–18 dB.

A polarization independent 1 × 3 equal optical power splitter (OPS) based on the self-collimation effect in two-dimensional (2-D) photonic crystal (PC) is proposed. Two splitter structures are introduced in the self-collimation 2-D PC, both of which have an air layer and a row of defect air holes. The proposed OPS is simulated using Rsoft software combined with plane wave expansion method and two finite-difference time-domain method. The results show that the beam for transverse electric (TE) mode and transverse magnetic (TM) mode can be self-collimated and divided equally into three outputs at the operating wavelength of 1310 nm. The transmission efficiencies are 95% for TE mode and 93% for TM mode, and the corresponding additional losses are 0.223 and 0.315 dB for TE mode and TM mode, respectively. The steady times are lower than 1.4 ps. The proposed polarization independent 1 × 3 equal OPS will have potential applications in optical fiber communication system.

In this paper, we propose a polarization-independent optoelectronic modulator based on the electrical absorption effect of graphene. Firstly, we use the simulation software COMSOL Multiphysics to design the structure, and find via changing the applied voltage on both ends of the graphene that the equivalent refractive index of graphene can be changed, thus changing the light absorption capacity of the modulator. The waveguides in the transverse magnetic (TM) and transverse electric (TE) modes have almost the same extinction coefficient by making a double-layer graphene ridge structure in the center of the silicon-based waveguide, which can achieve approaching modulation depth in the TM and TE modes. At 1550 nm wavelength, the two-dimensional cross-section of the structure is analyzed by the FEM method using COMSOL Multiphysics to obtain the effective refractive index of the structure. The simulation results show that when the distance between the double-layer graphene isolation layer is d = 20 nm, the TE and TM modes can achieve extinction ratios up to 110 dB over the wide communication band by selecting appropriate “ON” and “OFF” switching points. The bandwidth is 173.78 GHz and the insertion loss is only 0.0338 dB.

Omnidirectional light propagation in a realistic superlattice is investigated. This work complements two previous articles [Phys. Rev. E 59, 3624 (1999); 61, 5802 (2000)] that analyzed the cases of transverse electric (TE) and transverse magnetic (TM) polarization modes, respectively, of the dielectric superlattice modeled by means of Dirac delta functions. We present a quantitative analysis of the transmission functions, the band structures, the equifrequency surfaces, and the photon density of states (PDOS) for both TE and TM modes of the real superlattice without any approximations on the given dielectric function profiles. One of the advantages is that the Brewster effect can be manifested via our approach. In addition, the modes corresponding to TM evanescent waves that are absent from the Dirac comb model can be predicted. Finally, the exact PDOS of the realistic superlattice for the TE and TM modes can be obtained, respectively. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures.

Photonic integrated circuits (PICs) based on silicon-on-insulator (SOI) platform with the advantages of high-index-contrast and CMOS-compatible process can efficiently reduce the component sizes and densely integrate them at a chip scale. To meet the ever-increasing demand for the optical interconnect capacity, various multiplexing techniques have been used. However, it should still be proposed to effectively reduce the component size accompanied with the reasonable performance and wavelength division multiplexing (WDM) compatibility. To the best of our knowledge, there has no attempt so far to design a polarization demultiplexer based on a microring resonator in slot waveguide structures. In this paper, a compact silicon-based polarization demultiplexer is proposed, where two regular silicon-based waveguides are used as the input/output channels and a microring in slot waveguide structures is used as the polarization/wavelength-selective component. A full-vectorial finite-difference frequency-domain method is utilized to study the modal characteristics of the regular and slot silicon-based waveguides, where the effective indices and coupling for transverse magnetic (TM) and transverse electric (TE) modes are presented. With the unique modal characteristics of slot waveguides and the strong polarization-dependent features of microring resonator, we can show that the field distributions and the effective indices of the TM mode between the regular and slot waveguides are similar, while those of the TE mode show clearly different. As a result, the input TM mode outputs from the drop port at the resonant wavelength, while the input TE mode outputs from the through port directly with nearly neglected coupling, thus the two polarizations are separated efficiently. A three-dimensional finite-difference time-domain method is utilized to study the spectrum and transmission characteristics of the proposed device. From the results, a polarization demultiplexer with a radius of 3.489 m is achieved with the extinction ratio and insertion loss of ～ 26.12(36.67) dB and ～ 0.49(0.09) dB respectively for the TM(TE) mode at the wavelength of 1.55 m by carefully optimizing the key structural parameters. In addition, taking the fabrication errors into account during the practical process, the fabrication tolerances to the proposed device are analyzed in detail and the performance is assessed by the extinction ratio and insertion loss. For demonstrating the transmission characteristics of the designed polarization (de) multipexing (P-DEMUX) device, the evolution along the propagation distance of the input mode through the designed P-DEMUX is also presented. The present polarization demultiplexer is compatible with the WDM systems on-chip based on microring resonators and can be easily introduced into the WDM system to further increase the optical interconnect capacity.

Perfect metamaterial absorber (PMA) is an attractive optical wavelength absorber with potential solar energy and photovoltaic applications. Perfect metamaterials used as solar cells can improve efficiency by amplifying incident solar waves on the PMA. This study aims to assess a wide-band octagonal PMA for a visible wavelength spectrum. The proposed PMA consists of three layers: nickel, silicon dioxide, and nickel. Based on the simulations, polarisation-insensitive absorption transverse electric (TE) and transverse magnetic (TM) modes were achieved due to symmetry. The proposed PMA structure was subjected to computational simulation using a FIT-based CST simulator. The design structure was again confirmed using FEM-based HFSS to maintain pattern integrity and absorption analysis. The absorption rates of the absorber were estimated at 99.987% and 99.997% for 549.20 THz and 653.2 THz, respectively. The results indicated that the PMA could achieve high absorption peaks in TE and TM modes despite being insensitive to polarisation and the incident angle. Electric field and magnetic field analyses were performed to understand the absorption of the PMA for solar energy harvesting. In conclusion, the PMA possesses outstanding visible frequency absorption, making it a promising option.

The tunable propagation properties of transverse electric (TE) plasmonic modes have been investigated in the mid‐IR spectral region by using air‐Dirac semimetal (DSM)‐Si asymmetric structures, including the effects of Fermi levels, temperatures, and scattering times. The results manifest that on the condition that the Fermi level of DSM layer is not very large (2|μc|&lt;ℏω) and temperature is relatively high (about 100 K), the proposed DSM asymmetric structure supports obvious TE modes, which is quite different from the graphene symmetric structure limited to low liquid helium temperature. The transition frequency increases with Fermi level, the peak position of the real part and the saturation region of the imaginary part of effective index indicates an obvious blue shift. As temperature decreases, the contribution of interband transition becomes stronger, the 3D DSM indicates better dielectric properties and sustains stable TE mode. If scattering time is shorter than 0.1 ps, its effects on the propagation properties are very strong, resulting in a redshift of the real part of effective index. The results are very helpful to understand the tunable properties of DSM TE structures and aid the design of novel plasmonic devices, such as polarizers, modulators, and filters.

IntroductionThe problem of guided wave propagation in a wave guide with imperfectly reflecting boundaries arises in several applications, such as propagation in mine tunnels and in screened surface wave guides.In recent years, many studies have been carried out on the propagation characteristic of radio waves in tunnels in UHF band [1][2].From the theoretical point of view, tunnels can be regarded as hollow waveguides surrounded by a lossy dielectric medium, such as concrete, ground, and so on.The problem of radio communication in tunnels has found solutions using leaky transmission lines as supports for propagation of transverse electromagnetic modes [3][4].These modes are characterized by the fact that there is no cutoff frequency, and by an attenuation which increases with increasing frequency.However, when the frequency is high enough, natural propagation modes, which are transverse electric or transverse magnetic, can appear and interfere with the transmission line supported transverse electromagnetic modes [5].Natural propagation can be helpful to solve some specific problems, such as radio communications in mines with rooms and pillars which cannot be solved easily with the help of transmission lines.Natural propagation modes are also useful for short range communications, for example, in some road tunnels.For distances shorter than 200m, these modes can be more suitable the transmission line supported modes [6].In order to maximize the performance attainable feeding in the interior of tunnels with antenna systems, it is important to estimate the value and the attenuation of the electromagnetic strength inside the tunnel.Investigations concerning radiowave propagation in railways tunnels have been performed [7] and the results confirm the existence of a waveguide effect strongly related to the antenna positions.Recently, and Abo-Seida [9] studied the electromagnetic field due to vertical magnetic dipole buried in stratified media.Also, Abo-Seida [10] computed the attenuation below and above the cutoff frequency in a rectangular tunnel.It might be thought that waveguides with circular cross sections would be preferred to guides with rectangular cross sections, just as circular pipes are commonly used for carrying water a n d f l u i d s i n p r e f e r e n c e t o r e c t a n g u l a r p i p e s .H o w e v e r , c i r c u l a r w a v e g u i d e s h a v e t h e disadvantage that there is only a very narrow range between the cutoff wavelength of the dominant mode and the cutoff wavelength of the next higher mode.As with rectangular guides, the modes may be classified as transverse electric ( TE ) or transverse magnetic ( TM ), according to whether it is the electric or magnetic lines of force that lie in planes perpendicular www.intechopen.comElectromagnetic Waves 228 to the axis of the guide.The different modes are designated by a double subscript system analogous to that for rectangular guides.σ =10 -2 r = 4.08 σ =10 -1 TM 01 www.intechopen.com

A simple analytical calculation scheme to determine near field radiation through decomposing an emission domain into lots of thin thermal current sheets is presented. Through finding the orthogonal modes of thermal current of each thin layer, the thin current sheets can be treated as radiation sources of electromagnetic waves with determined analytical solutions. The outgoing electromagnetic waves from each thin current sheets can be either in transverse electric (TE) or transverse magnetic (TM) modes depending on the orientations of the current in the thin current sheets with respect to the directions of amplitude modulations of the orthogonal modes. Electromagnetic waves arriving to a collection domain are related to the electromagnetic waves leaving from each thin current thermal sheet with transfer coefficients. Transfer coefficient for TE and TM waves can be determined analytically with transfer matrix method or scattering matrix methods. Compared with existing dyadic Green's function method, the new calculation scheme allows material and temperature variations along one direction of the emission domain based on determined analytical expressions of TE and TM waves leaving from each thin current sheets. The simple calculation scheme is especially useful in near field radiation of layered structures with different material such as hyperbolic material with negative refractive indices. With this new approach, we recovered analytical solutions of near field radiation between two semi-infinite domains with uniform temperature and derived closed form solution of near field radiation between two semi-infinite domains with temperature profiles with/without laminated structures.

A previously developed field matching technique for the analysis of a metal disc-loaded circular waveguide, excited in a non-azimuthally varying transverse electric (TE) mode, was used to explore the advantage of the presence of a dielectric in controlling its dispersion characteristics for widening the bandwidth of a gyro-travelling-wave tube (gyro-TWT). The modelled structure, consisting of an axial dielectric insert and dielectric discs alternately placed between metal discs, was analysed considering the propagating and stationary waves in the disc-free and disc-occupied regions, respectively. While the axial dielectric insert gave no specific advantage with respect to dispersion control, the dielectric disc axial thickness, permittivity and periodicity and disc-hole radius quite effectively shaped the structure dispersion. In controlling the structure dispersion, the disc-hole radius, which was not as effective as the disc-periodicity in a conventional metal disc-loaded waveguide, became more effective, though the disc periodicity did not enjoy any additional advantage. The thickness or permittivity of dielectric discs controlled the passband frequencies and hence helped attain operating frequencies of a gyro-TWT. The passband of the lower and higher order modes remaining unchanged by a suitable choice of the structure parameters, a higher order mode, for instance the TE02 mode, gave a better wideband potential than the TE01 mode.

Transient electromagnetic (TEM) data can be seriously distorted by induced polarization (IP) phenomena when a polarizable body is present. The TEM field generated by a grounded-wire source contains transverse electric (TE) and transverse magnetic (TM) modes. The IP effect is most commonly studied with the TEM total field, rather than considering the difference between TE and TM fields. To investigate the effect of IP phenomena on the TE and TM fields, we have performed a detailed analysis on IP-distorted TEM data based on numerical and field examples. We first compare the IP effect on the TE and TM fields when polarizable bodies with different polarizable parameters are present. The TM field is more severely affected by the IP effect than the TE field. Compared to a single grounded-wire source, a double-line grounded-wire source can generate a larger TM field in the horizontal electric field. We compare the IP effect on TEM data from single- and double-line grounded-wire TEM configurations, and find that the data from the double-line configuration have a higher TM/TE ratio and are more severely affected by IP phenomena than in the single-line case. Thus, it would be easier to identify and extract the IP response from field data acquired with a double-line grounded-wire source configuration. These results have been verified by a field survey of the Kalatongke copper-nickel ore district, which has predominantly layered geology, in Xinjiang, China.

Triple-layer omni-directional reflectors (ODRs) consisting of a semiconductor, a transparent quarter-wavelength dielectric layer and metal layer have high reflectivities at all angles of incidence. In this paper, triple-layer ODRs are demonstrated that incorporate nanoporous SiO 2, a novel low-refractive-index (low-n) material with refractive indices n ≪ 1.46 as well as dense SiO 2 (n = 1.46). GaP and Ag serve as the semiconductor and metal layer materials, respectively. An angle-integrated transverse electric (TE) mode reflectivity of R avg | TE = 99.9 % and transverse magnetic (TM) mode reflectivity R avg | TM = 98.9 % are calculated for the triple-layer ODRs employing nanoporous SiO 2. Reflectivity measurements, including the angular dependence of R, are presented. Novel hybrid ODRs consisting of semiconductor, a several micron thick low-n dielectric material layer, a distributed Bragg reflector (DBR) and metal layer have outstanding reflectivities for all incident angles. GaP and Ag serve as the semiconductor and metal layer, respectively. Nanoporous SiO 2 is used as the low-n material. TiO 2 and dense SiO 2 serve as the DBR materials. The angle-intergrated reflectivities of the TE and TM modes are calculated to be larger than 99.9 % for the hybrid ODRs. The results indicate the great potential of the ODRs for light-emitting diodes with high light extraction efficiency.