The dispersion relation for TM-Polarized millimeter nonlinear electromagnetic surface waves propagating along the interface of a ferromagnet cover, whose magnetic permeability depends on the absolute value of the magnetic field and a linear substrate has been derived exactly.
Consider a waveguide structure consisting of a pair of metamaterial and dielectric slabs inserted in vacuum. A plane polarized wave is obliquely incident on it. Metamaterials (sometimes termed left-handed materials (LHMs)) are materials whose real parts of permittivity ε and permeability μ are both negative and consequently have negative index of refraction. The transmission of the electromagnetic waves through the structure is analyzed theoretically and numerically with the emphasis on the dissipation factor. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves in each region. Then, Snell's law is applied and the boundary conditions of the fields are imposed at each layer interface to obtain a number of equations with unknown parameters. The MAPLE is used to solve these equations for the unknown parameters to calculate the reflection and transmission coefficients. These coefficients are used to determine the reflected, transmitted and loss powers of the structure. In the numerical results the mentioned powers are computed and illustrated as a function of frequency, angle of incidence and slab thickness when the dissipation factor changes.
Three-layer slab waveguide with the substrate layer made of a left-handed material (LHM) of negative and complex
permittivity (ε) and permeability (μ) is investigated as an optical sensor. The effect of the negative optical
parameters of the substrate on the effective index, the power, the penetration depth, and the sensitivity of the senor is
studied in details. The structure is also treated as an evanescent wave optical sensor.
The effect of a metal layer with negative permittivity on the behavior of nonlinear-magnetoopic isolator is studied.
The isolator consists of Metal film, nonlinear cladding, and magnetooptic substrate. It is found that difference between
forward and backward propagation for TM<sub>0</sub> mode increases with increasing the absolute value of the tuning parameter
which is the permittivity of the metal film, ε<sub>f</sub>. It is also found that the maximum cutoff thickness of the isolator occurs
in selfdefocusing case around η=0.65 and at the highest assumed value of ε<sub>f</sub> = -8. The results are interesting since they
assure the possibility to get maximum optimization of the isolator behavior by adding metallic materials.
Optical sensors have wide range of application such as in medicine, astronomy, industry, and others. Sensitivity of
symmetric three layered optical waveguide sensor is investigated. The proposed sensor consists of dielectric slab
surrounded by metamaterial (MTM) cladding and MTM substrate. MTMs are new artificial materials which have
simultaneously negative permittivity ε and negative permeability μ. Different values of MTMs parameters ε and μ are
chosen to optimize the sensitivity of the sensor. However, the value of ε<sub>μ</sub> is kept content and equal to 4. The
dispersion equation which represents the effective index <i>n<sub>e</sub></i> for transverse electric modes (TE) as a function of slab
thickness has been derived. A close form solution of the sensitivity (S) which is defined as the variation of the effective
index with respect to Temperature variation is introduced. The sensitivity then numerically calculated as function of the
film thickness at different values of Metamaterial parameters. It is found that sensitivity varies with the film thickness
and depends on the MTMs parameters. These results are important for designing sensors.
Optical waveguide isolators are vital integrated optic modules in advanced optical fiber communication systems. This
study demonstrates an integrated optical isolator which has simple structure consisting of three layers. The thin magnetic
garnet film is sandwiched between linear dielectric cover and metamaterial (MTM) substrate. The effective refractive
indexes for both forward and backward fields are analytically calculated by deriving the dispersion equation of the TM
fields. The difference Δβ between the phase constant for forward and backward propagation is calculated numerically for
different values of MTMs permittivity (ε<sub>s</sub>) and permeability (μ<sub>s</sub>). In all the calculations, the value of ε<sub>s</sub>μ<sub>s</sub> is kept equal to
4. Δβ is also plotted as a function of the film thickness. Results show that the value of Δβ changes with the parameters of
MTMs and the film thickness. This helps in selecting the optimal design for the isolator at which Δβ approaches zero.
The results are encouraging to propose an optical isolator.
Stress effect on the behavior of optical waveguide sensor consists of dielectric slab inserted between metamaterial
(MTM) cladding and substrate is investigated by using numerical calculations. Several MTMs with different values of ε
and μ with ε μ = 4 are chosen in order to clarify the variation of stress effect with respect to the material constants.
Numerical calculations of the effective index for both transverse electric modes (TE) and transverse magnetic modes
(TM) as a function of stress and slab thickness have been performed. It is found that stress affects the performance of
the waveguide sensor.
TE waves can propagate in metal film of three waveguide structure if at least one of the covering media is nonlinear. The waveguide sensor under consideration consists of a metal wave guiding film coated with two nonlinear claddings. Contrary to what has been recently predicted, it is shown here that uniform field profile may be achieved under the suitable choice of the dielectric constants of the surroundings. Electric fields and fraction of power flow down the sensor layers are studied here. We expect this kind of planar waveguide sensors may be realized experimentally and will have applications in future opto-electronic devices. Uniform field approach has been discussed and implemented for the first time in investigating the waveguide sensors.
The dispersion relations for TE polarized waves guided by thin dielectric film surrounded by a nonlinear cladding
and a linear substrate are presented. The sensitivity of the effective refractive index on the cladding index in
evanescent optical waveguide sensor is derived. Closed form analytical expressions and normalized charts are given
to provide the conditions for the maximum sensitivity of nonlinear sensors when the measurand is homogeneously
distributed in the semi-infinite waveguide cover (homogeneous sensing). The results will be compared with those of
the well known linear evanescent wave sensors.
Electromagnetic surface waves in magnetic superlattices (LANS) film bounded by a nonlinear dielectric cover are
discussed as a function of the film parameters. Magnetic superlattices (antiferromagnetic-non magnetic) which are
linear frequency-dependent gyromagnetic media are described with an effective - medium theory, we found that,
surface waves are reciprocal for <i>H<sub>o</sub>= 0</i> and non reciprocal for <i>H<sub>o</sub>≠ 0</i>. We also calculate and illustrate the variation of the wave index with the power flow for various values of the thickness of (LANS) t and the magnetic fraction <i>f</i><sub>1</sub>
where <i>f</i><sub>1</sub> is the fraction of the superlattice occupied by the magnetic material.
The paper is concerned with the propagation characteristics of TE surface waves in a planer wave-guide structure of
a lateral antiferromagnetic -non magnetic superlattices (LANS)film bounded by a nonlinear dielectric cover and a
left handed substrate (LHM). In (LHM) substrate both permittivity and magnetic permeability are negative in
definite frequency range. We study nonlinear dispersion properties of the TE surface waves and illustrate power
flow variation with the wave index when both permittivity and magnetic permeability are negative. We found that
surface waves are backward traveling and the wave power variation with the wave index shows bistability behavior.
In recent years, optical wave guided sensors have attracted scientists for the development of biochemical and biomedical optical sensors in addition to optical communicative devices. These sensors show immunity to electromagnetic fields and have no danger of ignition so that they are used in cases of risky environments. Optical sensors have additional advantages: higher sensitivity, higher stability and lower price. Surface sensing, in particular, is used in recognition of adsorption or deposition on a certain surface such as the detection of adsorbed proteins, antibodies and bacteria cells. In this work, a sensing layer (extra ultra-thin film) iss assumed to rest on surface of a thin film covered with a nonlinear clad of lief dependent refractive index. A normalized analysis for the design of evanescent wave sensors is carried out for linear waveguide sensors with normal asymmetry (i.e., substrate refractive index is higher than that of clad). Sensitivity of such sensors is evaluated and the condition for them to achieve maximum sensing is also introduced. A computer program was developed for the computation and then plotting results in the so called universal charts from which one can specify the appropriate dimension for the required sensor.
The nonlinear characteristics of TM surface waves at microwave frequencies in a layered structure of left-handed metamaterial filme, a nonlinear antiferromagnet cover, and a linear dielectric substrate have been performed. The complex wave number of TM surface wave is computed by solving the dispersion equation in order to find out the reduced phase and attenutation constants. The effects of the frequency and nonlinearity of antiferromagnet on the reduced phase and attenuation constants have been examined. The power flow has also been studied as a function of the reduced phase and attenuation constants.
In this communication, we present an extensive theoretical analysis of nonlinear wave guide structure sensor and derive the conditions of the maximum sensitivity of TE nonlinear surface plasmons. The theoretical requirements for reaching high sensitivity of the proposed nonlinear waveguide sensor will be determined. Exact maximum sensitivity expressions for nonlinear surface plasmons in sensing schemes will be obtained, which will allow the designer to find the work basis of maximum sensitivity and to create the right dimensioning of the proposed structure. We believe that the theoretical predictions and numerical modeling could realize future versatile sensors. The above concepts could be experimentally demonstrated and carried out.
In this paper, the propagation characteristics of nonlinear surface waves at a lateral antiferromagnetic/nonmagnetic superlattices (LANS) substrate and a nonlinear dielectric cover have been investigated. LANS super-lattices (antiferromagnetic-non magnetic) which are linear frequency-dependent gyromagnetic media, described with an effective-medium theory. We found that the nonlinear magnetic waves are reciprocal for <i>H<sub>o</sub></i> = <i>O</i> and nonreciprocal for <i>H<sub>o</sub></i> ≠ <i>O</i>. We also calculate and illustrate the variation of the wave index with the power flow for various values of the magnetic fraction <i>f<sub>1</sub></i>. We found that the nonlinearity interface is a very frequency dependent.
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. The present paper proposes a new approach of FDTD technique to simulate the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we found a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
An efficient Finite Difference Time Domain approach is proposed for analyzing the propagation characteristics of 2-Dimensional planar scatter. An improved finite difference time domain method for the analysis of planar scatters is formulated. In order to solve an open initial boundary value problem, an absorbing boundary condition should be used as there are many forms of absorbing boundary conditions. We try to solve the scattering problem by using some absorbing boundary condition (ABC) at boundaries. Excitation pulses are used as sinusoidal and Gaussian. An illustrated example is also presented with the use of Mur's order boundary conditions. The proposed approach could be used easily in designing various waveguide structures. The scattering parameters for various geometrical structure are computed and results found consistent with either proposed values or values previously published. The strength of this approach to boundary conditions is also noticed in terms of the economical use of personal computer memory.
We study theoretically the nonlinear frequency characteristics of the transverse magnetic surface waves on the interface of an antiferromagnet and superconductor structure. The complex wave number of TM wave is computed by solving the dispersion equation in order to find out the effect of the temperature of superconductor on the reduced phase and attenuation constants. Both effects of the nonlinearity and the temperature of superconductor have been studied on the power flow as a function of the reduced phase and attenuation constants.
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
This paper presents two methods of analysis of the complex moving waveguide. One approach is a numerical technique based on Davidenko's method, the other is a perturbation method. It is clear that if one wants to obtain more accurate results over a wide range it is necessary to develop numerical techniques capable for solving lossy waveguides that has a complex propagation constant or a complex dielectric constant. Newton's method is one of these methods which requires several iterations in the complex plane, but this method fails in most cases in producing satisfactory results. Davidenko technique offers an alternative which is efficient and reliable and which relaxes the extent of the restriction placed on initial guess to be sufficiently close to the solution. The main idea of Davidenko's algorithm is to reduce Newton's method for the numerical solution of n-coupled nonlinear algebraic equations into n-coupled first-order differential equations in a dummy variable. The second one is a simple and accurate perturbation method, where the real part (beta) ' of the complex modal index (beta) equals (beta) ' + i(beta) '' is obtained by solving the corresponding real eigenvalue equation and the imaginary part (beta) '' is given by ((partial)(beta) '/(partial)(epsilon) ')(epsilon) '', where (epsilon) equals (epsilon) ' + i(epsilon) '' is the dielectric constant of the absorptive layer, and ((partial)(beta) '/(partial)(epsilon) ') is obtained by numerical differentiation. Numerical results by Davidenko's method are compared with these obtained from the perturbation method. It is found that the perturbation method is in a good agreement with the numerical one. Furthermore, for the first time in our knowledge, the complex propagation characteristics are presented for moving waveguides. These results could be used in designing many optical moving sensors.
A new exact analytical dispersion relation for TM p-polarized millimeter nonlinear electromagnetic surface waves propagating along the interface of nonlinear ferromagnet cover and linear magnetic media has been derived theoretically. A nonlinear magnetic permeability of the cover can be considered as a function of the absolute value of the magnetic field of the wave and can be written as (mu) <SUP>nl</SUP> equals (mu) <SUB>1</SUB> + (mu) H, which is contacted with an isotropic linear dielectric substrate. The existence conditions for these waves to be propagated are studied. The power flow expressions versus the wave index have also been obtained. This new behavior could be used in Microwave Electronics and Integrated Circuits (IC) Technology.
This paper presents the dispersion relation for TE s-polarized nonlinear elextron-ia.-nttic surface waves guided by a grounded gyrornagnetic slab, surrounded by a nonlinear dielectric cover with intensity dependent refractive indicies. Wave will be in a direction transverse to the applied magnetic field . Numerical results are also illustrated to show the effective wave index as a function of the power flow carried by the structure for different values of the slab thickness.
Analytical dispersion relations and the power flow expressions for TM (p-polarized) non-linear electromagnetic surface wave propagating along the interface of an inhomogeneous and dielectric non-linear media have been investigated theoretically_ An inhomogeneous dielectric cover has the dielectric permittivity of the form e = a + bz, which is contacted with strongly non-linear Kerr like layer. The existence conditions for these waves to be propagated are studied. These waves have no counterpart in the linear isotropic regime. The power flow versus the wave index, and the consequence interference non-linearity might be evaluated for a variety of inhomogeneity parameters, which are found to be inhomogeneity dependent, and could lead to optical hysteresis and bistability.