Effective medium parameters for 1D photonic crystal containing single-negative material layers using the envelope function approach

Nonlinear wave propagation in a 1D photonic crystal containing single-negative layers is investigated using the multiple-scale method. In this approach, the electric field is decomposed into a slowly varying envelope function and a fast Bloch-like function to obtain the analytic expressions of the effective parameters of an equivalent medium. The periodic structure has an equivalent left-handed medium for the envelope function. Gap soliton formation is discussed and compared with that associated with the Bragg gap.     

A method to measure the Brillouin frequency shift of the medium through Brillouin amplification ratio

In order to measure the Brillouin frequency shift (BFS) of the medium, this paper proposes a method using mixtures in a two-cell stimulated Brillouin scattering system, which uses a medium to be measured as amplifier medium and a mixture medium as generator medium. The seed light from the generator gains effective amplification in the amplifier and the amplification ratio changes with the mixing fraction. Only when the BFS of the mixture medium is equal to that of the medium in the amplifier does the seed light obtain the maximum amplification ratio. The method has the advantage of independence of the wavelength of the incident light.     

Solving a class of burning disturbed problem with shock layers

A class of combustion problem with shock layers is considered.A modified perturbation method is presented.Using this simple and valid technique,we construct the boundary and the shock layers solution to the problem,and the asymptotic behavior of the solution is discussed.The modifying perturbation method is shown to be a valid method.     

A New 1×K Tunable Multi-wavelength Router and its Features

Tunable wavelength routers (TWRs) for multiple wavelength selection are key devices in dynamic wavelength-routing wavelength division multiplexing (WDM) networks. In this paper, by cascading conventional 2×2 TWRs, a new 1×K TWR is proposed for large-scale dynamic wavelength-routing WDM networks. When the cascading numbers are smaller, the 1×K TWR can be directly applied to networking WDM networks. When the cascading numbers are larger, the 1×K TWR can be carried out by the integrating method and be extensively used to networking various multi-wavelength optical networks by the way of “EDFA+TWR”. Though the cascading method proposed is based on the acousto-optic TWRs, it can be also applied to cascading other kinds of TWRs.     

Nonreciprocal transmission of electromagnetic waves by three-layer magneto-optical mediums

We investigate the non-reciprocal transmission properties of a three-layer structure filled with magneto–optical medium and normal medium. Based on the transfer matrix method, we deduce the total transmission coefficient for a one-dimensional(1 D) structure with anisotropic mediums. When two-side layers with magneto–optical medium loaded in opposite external magnetic field, the time-reversal symmetry of transmission properties will be broken. Our numerical results show that the non-reciprocal transmission properties are influenced by external magnetic fields, incident angle, and thickness of the normal medium layer. Since the non-reciprocal properties can be easily realized and adjusted by the simple structure, such a design has potential applications in integrated circulators and isolators.     

Analytical model of an acoustic diode comprising a superlattice and a nonlinear medium

We give an analytical analysis to the acoustic propagation in an acoustic diode (AD) model formed by coupling a superlattice (SL) with a nonlinear medium. Analytical solutions of the acoustic transmission are obtained by studying the propagations in the SL and the nonlinear medium separately with the conventional transfer-matrix method and a perturbation technique. Compared with the previous numerical method, the proposed approach contributes a better physical insight into the intrinsic mechanism of acoustic rectification and helps us to predict the performance of an AD within the effective rectifying bands in a simple way. This is potentially significant for the practical design and fabrication of AD devices.     

A Hybrid Method of Solving the Electromagnetic Inverse Scattering Problem in Lossy Medium

A hybrid method of solving the electromagnetic inverse scattering problem in a lossy medium is proposed. The gradient search method is first used to determine the spatial distribution of the target, then the Monte Carlo method is selected to calculate the conductivity and permittivity of the scatterer. The results of numerical experiments verify that the hybrid method of combining the two ways is high-precision, efficient, and suited to global optimization.     

The determination of the relative permittivity of periodic stratified media based on the iterative time-reversal method

In this paper, we present a new method to determine the relative permittivity of periodic stratified media using the iterative time-reversal method. Based on transmission line theory, the focal peak value of iterative time-reversal electro- magnetic waves, which contain information about the periodic stratified medium, is computed in pulse-echo mode. Using the relationship between the focal peak value and the relative permittivity of the periodic stratified medium, the relative permittivity can be obtained by measuring the focal peak value. Numerical simulations are conducted, and the results demonstrate the feasibility of the proposed approach to the measurement of the relative permittivity of a periodic stratified medium.     

Phase Transition in Acoustic Localization in a Soft Medium Permeated with Air Bubbles

Propagation of an acoustic wave in a soft medium permeated with air bubbles is theoretically investigated by using a self-consistent approach. The soft medium is assumed to be viscoelastic to estimate the effect of acoustic absorption on the acoustic localization in such a medium. The oscillation phases of bubbles are examined by employing a phase diagram method. A collective oscillation of the bubbles is observed once the acoustic localization occurs, which is known as a phenomenon of ＇phase transition ＇, and such a phenomenon persists as we manually increase the viscosity factor of the soft medium. Therefore it is proven that the phenomenon of phase transition may serve as a unique criterion to effectively identify acoustic localization in a bubbly soft medium even in the presence of viscosity, and the directions of the phase vectors help to determine the extent of localization. This is of practical significance for experimental research studying the acoustic localization in such a medium, for which the presence of viscosity generally causes great ambiguity in distinguishing the effects of localization and acoustic absorption.     

A new method for measuring the threshold of stimulated Brillouin scattering

A new method for measuring the threshold of stimulated Brillouin scattering (SBS) based on the generation location of a Stokes beam is proposed for the first time to our knowledge. The length of the medium cell is selected to be longer than the free gain length of pump pulses in the Brillouin medium. The reflected light from a certain mirror in front of the medium cell is chosen as the reference beam, and the SBS threshold is measured by the "jump" of the delay between the Stokes beam and the reference beam. An 8-ns Q-switched single-longitudinal-mode pulse is used as the pump and the typical SBS medium FC-72 is selected as the nonlinear medium in our experiment. The SBS threshold intensity is measured to be 173-178 mW/cm 2 , which is consistent with existing results measured with the transmitted energy limiting method.     

High efficiency,small size,and large bandwidth vertical interlayer waveguide coupler

Since the advent of three-dimensional photonic integrated circuits,the realization of efficient and compact optical interconnection between layers has become an important development direction.A vertical interlayer coupler between two silicon layers is presented in this paper.The coupling principle of the directional coupler is analyzed,and the traditional method of using a pair of vertically overlapping inverse taper structures is improved.For the coupling of two rectangular waveguide layers,a pair of nonlinear tapers with offset along the transmission direction is demonstrated.For the coupling of two ridge waveguide layers,a nonlinear taper in each layer is used to achieve high coupling efficiency.The simulation results show that the coupling efficiency of the two structures can reach more than 90%in a wavelength range from 1500 nm to 1650 nm.Moreover,the crosstalk is reduced to less than-50 d B by using multimode waveguides at intersections.The vertical interlayer coupler with a nonlinear taper is expected to realize the miniaturization and dense integration of photonic integrated chips.     

Research on synthetic aperture radar imaging technology of one-dimensional layered rough surfaces

A quick and exact imaging method for one-dimensional layered rough surfaces is proposed in this paper to study the scattering characteristics of a layered medium that exists widely in nature.The boundary integral equations of layered rough surfaces are solved by using the propagation-inside-layer expansion combined with the forward and backward spectral acceleration method(PILE+FB-SA),and the back scattering data are obtained.Then,a conventional synthetic aperture radar(SAR) imaging procedure called back projection method is used to generate a two-dimensional(2D) image of the layered rough surfaces.Combined with the relative dielectric permittivity of realistic soil,the random rough surfaces with Gauss spectrum are used to simulate the layered medium with rough interfaces.Since the back scattering data are computed by using the fast numerical method,this method can be used to study layered rough surfaces with any parameter,which has a great application value in the detection and remote sensing areas.     

Application of Equivalent Air Gap Method in Uniaxial Crystal Plate

The equivalent air gap method is a simple way to trace the ray propagation in an isotropic medium, but it cannot be applied to an anisotropic medium. We present the exact general expressions of the equivalent air gap thicknesses and the displacements for the plane-parallel uniaxial crystal plates. They are also suitable for the isotropie medium. This method is useful when one determines whether certain size plane-parallel plates can be fitted into the available air of an optical system, and also in the prism system design.     

Coordinate Transformation for Fast Simulation of Z-Scan Measurements

We apply a new method consisting of a coordinate transformation and two-step scheme to simulate numerically Zscan characteristics of a nonlinear medium. A comparison of numerical results obtained by this new method with those by the conventional numerical method is made. The results show that the new scheme yields a large, orders-     

Shrinking device realized by using layered structures of homogeneous isotropic materials

We propose the practical realization of a shrinking device by using layered structures of homogeneous isotropic materials.By mimicking the shrinking device with concentric alternating thin layers of isotropic dielectrics,the permittivity and the permeability in each isotropic layer can be properly determined from the effective medium theory in order to achieve the shrinking effect.The device realized by multilayer coating with dielectrics is validated by TE wave simulation,and good shrinking performance is demonstrated with only a few layers of homogeneous isotropic materials.     

Optimal Acoustic Attenuation of Weakly Compressible Media Permeated with Air Bubbles

Based on fuzzy logic （FL） and genetic algorithm （GA）, we present an optimization method to obtain the optimal acoustic attenuation of a longitudinal acoustic wave propagating in a weakly compressible medium permeated with air bubbles. In the optimization, the parameters of the size distribution of bubbles in the medium are optimized for providing uniformly high acoustic attenuation in the frequency band of interest. Compared with other traditional optimization methods, the unique advantage of the present method is that it can locate the global optimum quickly and effectively in need of knowing the mathematical model precisely. As illustrated by a numerical simulation, the method is effective and essential in enhancing the acoustic attenuation of such a medium in an optimal manner. The bubbly medium with optimized structural parameters can effectively attenuate longitudinal waves at intermediate frequencies with an acoustic attenuation approximating a constant value of lO（dB/cm）. Such bubbly media with optimal acoustic attenuations may be applied to design acoustic absorbent by controlling broader attenuation band and higher efficiency.     

Ultrasound-Modulated Optical Tomography in Reflective and Coaxial Configuration

Ultrasound-modulated optical tomography affords a very promising noninvasive imaging method for biomedical diagnosis.With this technique, an ultrasound beam is focused into a scattering medium to provide an accurate localization and, simultaneously, a modulation of laser light inside the medium. Based on the high-sensitivity detection technique, we have developed a unique reflective configuration, which was more convenient and practical than other existing configurations. Furthermore, the configuration also introduced a new scheme to hnprove the spatial resolution in the imaging. A phantom was imaged to validate the feasibility of the proposed configuration.     

Conformational Transition of Poly （Acrylic Acid） Detected by Microcantilever Sensing

Poly （acrylic acid） （PAA） chains are grafted on one side of a microcantilever by the self-assembled method and the deflections of the microcantilever are detected as a function of medium pH from 3 to 11. It is found that when the pH varies, the microcantilever deflects because of the changing surface stress. By analysing the electrostatic repulsive effect, the surface stress change is related to the conformation transition of PAA from a collapse state to a swelling state. This method offers the interaction information among the polymer chains during the conformational transition and affords an alternative way to study conformational change of polymers.     

Low Threshold Bistable Switching by the Nonlinear One—Dimensional Photonic Crystal

In the approximation of the fast Debye relaxation of a nonlinear Kerr medium,the nonlinear finite-difference timedomain method is derived to simulate numerically the one-dimensional nonlinear photonic crystqal sandwiched by the Kerr medium.Bistable switching with a low threshold intensity of 0.01kW/cm^2 is obtained,and the corresponding refractive index change of the Kerr media is about 0.038.