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Surface magnetoplasmons (SMPs) in the three-layer structure of semiconductor, dielectric, and photonic crystal (PhC) are theoretically investigated. The PhC portion in the structure is designed properly so that its band gap covers the one-way propagation range of SMPs. In such an all-dielectric system, robust one-way propagation is available for SMPs at terahertz frequencies, and SMP band gap also occurs due to the PhC effect. With the use of a heterostructure of dielectric layer in the all-dielectric system, two different approaches for trapping terahertz radiation are proposed and verified by numerical simulations.

In this work, spoof surface plasmon polaritons in a novel subwavelength periodic bilateral cross-metal diaphragm channel waveguide are theoretically and experimentally investigated. It is found that the propagation frequency range can be broadened due to the absence of the bandgap between the fundamental band and the second guiding band by tuning the geometric parameters. In addition, the dispersion curve of the second band can pass through the light line and then enter into the radiation region, leading to a frequency-based beam steering radiation. We also find that, below the light line, there exists an anomalous linear dispersion such that the guiding mode propagation length can be extended up to around 200λ. Good agreement has been achieved between experimental and numerical results.

We propose a new type of differential microstrip line that can reduce the crosstalk between this differential pair and conventional single-ended microstrip lines. The structure of the proposed differential microstrip line is based on coupled conventional microstrip lines with their edge replaced by hairpin periodic subwavelength pattern. We found, numerically and experimentally, that the spoof surface plasmon polaritons (SPPs) at microwave frequencies exist in such a structure. It is revealed by EM field simulation that the spoof SPPs mode is highly localized on the surface of the periodic differential microstrip line. This leads to the weak coupling and crosstalk between the differential structured microstrip line and single microstrip line. The observation can be hopefully applied to improve the signal integrity performance in high density microwave circuits.

The guiding properties of spoof surface plasmon polaritons (SPPs) in an array of hollowed-out metallic blocks standing on a metallic surface are theoretically investigated in this study. For such spoof SPPs, there exists an additional guiding mode except for the fundamental mode and the former is closely related to hollowing out metal blocks. The dispersion band of this additional mode has a negative slope (corresponding to a group velocity) and it intersects the light line and then enters the radiation region as the frequency grows, which leads to a frequency steering pencil-like radiation. The transmission and radiation properties of the additional mode of spoof SPPs are finally verified experimentally.

When an electromagnetic field propagates through a linear but dispersive medium, the front edge (the launching fringe of the waveform where the field is first turned on) propagates precisely at the speed of light in vacuum by first timing on t1=tfront=（z/c）and the main signal (the main part of the field) follows up with group velocity which is characterized by the frequency-dependent refractive index of medium by second timing on t2=tgroup=(z/vgroup)=[n(φ)z/c] .The distinct wave-packets progress from tfrontto tgroup(i.e. from the front-edge-timing to the main-signal-starting timing) are well known as optical precursors. It was believed that precursors are an ultra-fast phenomena, persisting only for a few optical cycles, and that they have an exceedingly small amplitude and two different kinds of spike-type wave-packet (i.e. Sommerfeld precursor and Brillouin forerunner). Both exact wave shape for electromagnetic wave while it goes into a linear time-invariant, lossless plasma system is reported.

Electromagnetic wave properties of a Fibonacci-sequence photonic crystal (FSPC) made of single-negative materials are theoretically investigated. It is found that, in the oblique incidence, such a kind of photonic crystal exhibits additional photonic bands or dips in the vicinity of either magnetic plasma frequency or electric plasma frequency. The additional photonic bands or dips corresponding to magnetic plasma frequency occur only for the TE wave, whereas those corresponding to electric plasma frequency occur only for the TM wave. In addition, we find that there exist omnidiretional gaps in such a single-negative FSPC.

We propose a cylindrical photonic quantum well made of photonic crystals containing liquid crystals, the properties of which are theoretically calculated and investigated by the transfer matrix method in the cylindrical symmetry system. Liquid crystals are introduced into the photonic quantum well structure as tunable defect layers. When the liquid crystals are pseudo–isotropic state and the azimuthal mode order of incident waves are m =0, there were two pass-bands around certain wavelength. When the liquid crystals are homeotropic state, the reflectance of pass-band at shorter wavelength decreases from 0.75 to 0.05 in the TM mode, but the reflectance does not change in the TE mode. When mode order m =1 and the liquid crystals are pseudo-isotropic state, the reflectance of defect mode stayed the same as m =0. However, the result is reversed while the phase of liquid crystals change from pseudo-isotropic to homeotropic state. The reflectance is the same as in the TM mode, but that in the TE mode decreases substantially from 0.75 to 0.05. The application of our structure to switching device is highly potential.

In this work, theoretical formulas for the H-polarization electromagnetic propagation in a cylindrical multilayer structure (CMS) are given. The relationships between two modes, H- and E-polarization are pointed out. With the derived formulae, we present the numerical results for three model structures such as the single cylindrical interface, the single cylindrical slab, and the cylindrical photonic crystal (CPC). In the single cylindrical interface, it is found that there exists a Brewster starting radius at which a minimum reflectance is attained in H-polarization. In the single cylindrical slab, the result illustrates that the reflectance response in the wavelength domain contains the oscillating and nonoscillating regions. As for the CPC, we find the PBG structure at zero azimuthal mode number is very similar to that of planar photonic crystal. The PBG, however, can be strongly influenced by increasing the azimuthal mode number in a CPC.

Effects of superconducting thin film on the defect mode in a dielectric photonic crystal heterostructure (PCH) are theoretically investigated. The considered structure is (12)NS(21)N, in which both layers 1 and 2 are dielectrics, layer S is a high-temperature superconducting layer, and N is the stack number. The defect mode is analyzed based on the transmission spectrum calculated by using the transfer matrix method. It is found that, in the normal incidence, the defect mode existing in the host PCH of (12)N(21)N will be blue-shifted as the thickness of layer S increases. In addition, the defect mode is also blue-shifted for both TE and TM modes in the case of oblique incidence. The embedded superconducting thin film plays the role of tuning agent for the defect mode of PCH. As a result, the proposed structure can be designed as a tunable narrowband transmission filter which could be of technical use in the optoelectronic applications.

The vortex distributions and dynamics in superconductors with triangular and honeycomb pinning arrays are investigated by numerical simulation of the two- dimensional (2-D) time-dependent Ginzburg–Landau equations. Periodic boundary conditions are implemented through specific gauge transformations under lattice translations. We model the pinning sites as holes. The simulation results at different magnetic fields are presented. For film with regular triangular pinning array, the vortices are all captured within the holes for a wide range of magnetic fields. For film with regular honeycomb pinning array, the interstitial vortices appear at relatively low magnetic fields. With an increase of magnetic field, the new vortices may enter the holes again and keep the number of vortices at the interstitial positions unchanged. These results confirm our explanations of the experimental results we obtained earlier.

The optical response of an atomic vapor can be coherently manipulated by tunable quantum interference occurring in atomic transition processes. A periodic layered medium whose unit cells consist of a dielectric and an EIT (electromagnetically induced transparency) atomic vapor is designed for light propagation manipulation. Such an EIT-based periodic layered medium exhibits a flexible frequency-sensitive optical response, where a very small change in probe frequency can lead to a drastic variation of reflectance and transmittance. As the destructive quantum interference relevant to two-photon resonance arises in EIT atoms interacting with both control and probe fields, the controllable optical processes that depend sensitively on the external control field will take place in this EIT-based periodic layered medium. Such a frequency-sensitive and field-controlled optical behavior of reflection and transmission in the EIT photonic crystal can be applicable to designs of new devices such as photonic switches, photonic logic gates and photonic transistors, where one laser field can be controlled by the other one, and would have potential applications in the areas of integrated optical circuits and other related techniques (e.g., all-optical instrumentations).

A kind of plasmonic open waveguide, which is a periodic subwavelength metallic Domino array, is investigated both theoretically and experimentally in this paper. Based on the guiding mechanism of spoof surface plasmon polaritions (spoof SPPs), the transmission properties of this waveguide are controllable by altering the geometric parameters of the periodic structure. Microwave experimental results verify the high efficiency of wave guiding in such open waveguide, as predicted in theoretic analysis.

Properties of wave transmission in a photonic quantum well (PQW) structure containing superconducting materials are theoretically investigated. We consider two possible PQW structures, (AB) P (CD) Q (AB) P -asymmetric and (AB) P (CD) Q (BA) P -symmetric, where the host photonic crystal (PC) (AB) P is made of dielectrics, A = SrTiO3, B = Al2O3, and the PQW (CD) Q contains C = A and superconducting layer D = YBa2Cu3O7ix, a typical high-temperature superconducting thin fllm. Multiple transmission peaks can be seen within the photonic band gap (PBG) of (AB) P and the number of peaks is directly determined by the stack number of PQW, i.e., it equals Q-1. Additionally, the results show that symmetric PQW structure is preferable to the design of a multichannel transmission fllter. The efiect of stack number of photonic barrier is also illustrated. Such a fllter operating at terahertz with feature of multiple channels is of technical use in superconducting optoelectronic applications.

In this report, the phenomena of low-frequency spoof surface plasmon polaritons (spoof SPPs) in a new metallic cylindrical antenna at terahertz (THz) frequencies are demonstrated. The antenna is designed as a periodic structure whose unit cell includes an open hollow ring (OHR) as compared with the conventional periodic subwavelength corrugated metallic wire (PSCMW) with cylindrical structure. Near- and far-field distributions, dispersion properties, and radiation efficiency are numerically evaluated and then compared for both PSCMW and PSCMW-OHR. It is indicated that when the dispersion line passes through the light line into a radiation zone, the field becomes a leaky mode. We find that the far-field radiation of the leaky mode can generate frequency scanning effects with a scanning angle of 23°, and the radiation efficiency can be increased to 90% as the number of periodic unit cells is large enough.

Based on a waveguide made of a subwavelength metal-block array with open slots, a kind of scanning antenna is proposed in this work. Low-frequency spoof surface plasmon polaritons (spoof SPPs) exist in this waveguide and under certain conditions, a leaky mode can be produced. The leaky mode could scan the radiation pencil-beam by angles of 53° when the input frequency changes. The leaky mode is derived from a negative slope dispersion curve of some new transmission modes. As this dispersion curve intersects with the light line, it becomes the leaky mode in high-frequency region. Numerical results reveal that the modal field of the transmission mode resides inside the interior of a hollow block as compared with that in a solid metal block array. Experimental verification of the leaky mode at microwave frequencies has been performed, and the results are found to be consistent with the theoretical analysis.

In this paper, the characteristics of a novel terahertz plasmonic microcavity consisting of a circular hole and a coaxial (metallic) cylindrical core machined on a planar metal surface is theoretically investigated. It is shown that such a structure can sustain plasmonic modes, whose resonant wavelengths are much larger than the hole diameter and fields tightly localized within the cavity. For this cavity, both high quality factor and ultrasmall mode volume can be achieved in the terahertz range. As this type of microcavity is particularly compatible with planar technology, it has promising applications in the miniaturization and integration of terahertz optical components.

The filtering properties for a narrowband reflection-and-transmission filter in an annular defective photonic crystal containing an ultrathin and strongly lossy metallic film are theoretically investigated based on the transfer matrix method for the cylindrical Bragg waves. At a certain design wavelength, simultaneous peaks in reflectance and transmittance can be found. The peak wavelength is shown to be dependent on the azimuthal mode number of the cylindrical waves. The peak heights in reflectance and transmittance can be directly varied by the stack numbers. In addition, the influence of the starting radius in reflectance and transmittance is also illustrated.

In this work, the enhancement in photonic band gap (PBG) in a dielectric-semiconductor photonic crystal (DS PC) is investigated. We consider two possible schemes that can be used to enhance the PBG in the near-infrared region. The flrst scheme is to add an ultrathin metal layer into the DS PC such that a structure of ternary metal-dielectric-semiconductor (MDS) PC is formed. The second scheme is to make use of the heterostructured PC. In scheme 1, it is found that the addition of metal layer will signiflcantly move the left band edge to the shorter wavelength position, leading to an enlargement in the PBG. This enlargement can be extended as the thickness of metal fllm is increased. In addition, a pronounced enhancement in PBG is achieved when the metal with a higher plasma frequency is used. In scheme 2, we flnd that the PBG can be signiflcantly enlarged compared to scheme 1. In addition, the increase in the band extension is shown to be four times larger than that in scheme 1. The results illustrate that, in order to enhance the PBG, the use of scheme 2 is superior to scheme 1. The enhancement of near- infrared (NIR) PBG is of technical use in the optical communications.

A tunable multichannel filter in the finite photonic crystal (PC) containing photonic quantum well (PQW) as a defect is proposed. The symmetric structure (AB)P(CD)Q( BA)P and the asymmetric structure (AB)P(CD)Q(AB)P are considered in this work. Here, the host PC of (AB)P is made of Si for layer A and of SiO2 for layer B. In the PQW, (CD)Q, C also is Si, but D is an extrinsic semiconductor, n-type silicon (n-Si). With the use of n-Si, it is found that both structures can function as a tunable multichannel filter in the infrared region. The number of channels is equal to Q + 1 in the symmetric structure, whereas it is Q for the asymmetric one. The positions of multiple resonant peaks can be tuned by the variation in the impurity concentration of n -Si. The proposed filter could be used to design the wavelength division multiplexer filter that is of technical use in optical communications.

A periodic layered medium, with unit cells consisting of a dielectric and an electromagnetically-induced transparency (EIT)-based atomic vapor, is designed for light propagation manipulation. Considering that a destructive quantum interference relevant to a two-photon resonance emerges in EIT-based atoms interacting with both control and probe fields, an EIT-based periodic layered medium exhibits a flexible frequency-sensitive optical response, where a very small variation in the probe frequency can lead to a drastic variation in reflectance and transmittance. The present EIT-based periodic layered structure can result in controllable optical processes that depend sensitively on the external control field. The tunable and sensitive optical response induced by the quantum interference of a multi-level atomic system can be applied in the fabrication of new photonic and quantum optical devices. This material will also open a good perspective for the application of such designs in several new fields, including photonic microcircuits or integrated optical circuits.

Since a two-level resonant atomic system can be simulated by a simple circuit, three- and four-level electromagnetically induced transparency (EIT) that occur due to light-atom interaction can find its classical counterpart in circuit analog. As the optical response of an EIT atomic medium (including atomic vapors and semiconductor-quantum-dot dielectrics) can be controlled via tunable quantum interference induced by applied external control fields, in the scheme of circuit analog, such a controllable manipulation is achieved via capacitor coupling, where two loops are coupled by a capacitor that can represent the applied control fields in atomic EIT. Both numerical simulation and experimental demonstration of three- and four-level EIT were performed based on such a scenario of circuit analog. The classical “coherence” relevant to quantum interference among transitions pathways driven by both probe and control fields in EIT atomic systems has been manifested in the present circuit analog of EIT.

The frequency-sensitive optical response due to two-photon resonance of electromagnetically induced transparency (EIT) in a tunable band structure of an EIT-based layered medium is considered. The unit cells of this periodic layered structure are composed of dielectric (e.g., GaAs) and EIT atomic vapor. The frequency-sensitive behavior of controllable reflectance and transmittance depending on the external control field can be applicable to new device design (e.g., it can serve as the fundamental working mechanism for photonic switches and photonic logic gates). Some two-input logic gates (e.g., OR and NAND gates) are designed based on the present effect of sensitive switching control that results from the two-photon resonance.

Optical properties of a periodic multilayer structure containing the superconducting and dielectric materials are theoretically investigated based on the Abeles theory for a stratified medium and the two-fluid model for a superconductor. It is found that, for the TM wave, at wavelength near the superconducting threshold wavelength, an additional high-reflectance band appears and some reflection dips exist, which are, however, not seen for the TE wave. The reflection dips behave as the strongly localized passbands that can be used to design a multichannel narrowband transmission filter without physically introducing any defect layer in the structure.

Dispersion properties, birefringence and confinement loss between the circular air-hole photonic crystal fiber (CAHPCF) and rotational elliptical air-hole photonic crystal fiber (REAHPCF) are investigated numerically by means of a plane-wave expansion method and a finite element method. Results show that the performances of REAHPCF on flatter dispersion curve, single mode, high birefringence and low confinement loss is better than that of CAHPCF.

The resonant transmission peaks in the asymmetric and symmetric multilayer narrowband transmission filters are theoretically investigated based on the transfer matrix method. In an asymmetric filter there exists only one resonant peak within the photonic band gap, and its position can be changed when the design wavelength is varied. In a symmetric filter, it is found that there are two resonant peaks. Using Bloch wave approximation, an investigation of these two resonant peaks has been made, and they are shown to correspond to the symmetric and antisymmetric field solutions in the defect layer.

By using lithium niobate (LiNbO3) as a defect layer, a tunable multilayer narrowband reflection-and-transmission filter containing an ultrathin metallic film is proposed. Due to the voltage dependence of the refractive index for LiNbO3, tunable optical filtering properties have been theoretically investigated based on the calculated wavelength-dependent reflectance and transmittance. The dependences of peak wavelength on the applied voltage and the angle of incidence are numerically illustrated. The results reveal that in addition to working as a tunable filter, it can also be expected to act as a refractometric optical sensor.

It is known that electromagnetic resonant tunneling phenomenon can be found in the single-negative (SNG) bilayer, a two-layer coating made of the epsilon-negative (ENG) and the munegative (MNG) media. In this work, we report that this resonant tunneling is strongly dependent on the static positive parameters in SNG materials. The values of the static permeability in ENG layer and the static permittivity in MNG layer for obtaining the resonant tunneling are theoretically analyzed and discussed for two possible cases of equaland unequal-thicknesses. Useful design guidelines in selecting positive parameters for the resonant tunneling are obtained. We also investigate the possible influence in the resonant tunneling due to the losses from the ENG and MNG materials. Additionally, we examine the polarization-dependent resonant tunneling, that is, the dependence of angle of incidence is examined.

In this work, we analyze the tunable multiple-filtering property at infrared frequency in a finite semiconductor-dielectric photonic crystal (SDPC), (AB) P A, where A is a strongly extrinsic semiconductor, n-type germanium (n-Ge). B is a dielectric material, and P is the number of periods. It is found that multiple filtering phenomenon can be obtained in the region where the permittivity of n-Ge is negative. The number of resonant peaks is found to be equal to P. With the permittivity of n-Ge being concentration-dependent, these resonant peaks can be shifted as a function of impurity concentration. The analysis indicates that such an SDPC can work as a tunable multichannel filter which is of technical use for the semiconductor applications in optical communications.

Optical flltering properties in a multichanneled transmis- sion fllter based on one-dimensional photonic crystal containing the coupled defects are theoretically investigated. The resonant transmis- sion peaks are designed to be located within the photonic band gap of a defect-free photonic crystal. The number of peaks is directly equal to the number of the coupled defects. The positions of resonant peaks can be tuned by varying the refractive index of the defect layer. In ad- dition, extremely resonant peaks can be produced by adding the Bragg mirrors at the front and rear sides of the structure.

A design of mid-infrared frequency multichanneled transmission filter in a one-dimensional photonic crystal heterostructure containing negative-permittivity materials is proposed. It is found that the number of resonant peaks in transmittance is just related to the stack number. These peaks are located within the pass band of the ideal host photonic crystal, which is fundamentally different from that of using photonic quantum well structure. The peak positions can be tuned by varying the thicknesses of the two constituent layers. In addition, they are also shifted as a function of angle of incidence for both the transverse electric (TE) and the transverse magnetic (TM) waves.

A new kind of leaky wave antenna based on low-frequency surface plasmon polaritons (SPPs) is proposed, which is constructed by periodic metallic blocks with an open slot on the top. Numerical analysis shows that by introducing the open slot on the metallic blocks, there will appear extra spoof SPPs modes in the band gap of metallic solid blocks. The dispersion curve of such spoof SPPs modes passes through the light line and enters into the radiation region, and consequently it can generate a frequency steering pencil-like radiation. Experimental verification agrees with the theory.

The optical response of an atomic vapor can be controlled by using tunable quantum interference induced by external control field. A periodic layered medium whose unit cells consist of dielectric (e.g., GaAs) and EIT (electromagnetically induced transparency) atomic vapor is suggested. It is demonstrated that such an EIT-based periodic layered medium shows more flexible optical response (sensitive to frequency) than a conventional photonic crystal does. The controllable band structure that depends on the external control field can be applicable to designs of new devices such as photonic switches and photonic logic gates, where one laser field can be controlled by the other one, and would have potential applications in the field of integrated optical circuits and other related areas, e.g., the all-optical technique.

A new type of stripline-based microwave transmission, which has relatively lower crosstalk compared with the conventional striplines, is proposed. The structure is formed by corrugated inward slit that is subwavelength scale on the edge of the stripline via the photolithography techniques. Numerical simulation is used to analyze the transmission and dispersion properties of this new stripline structure, and the results are experimentally verified in the frequency range from 200 MHz to 8 GHz. We found that spoof surface plasmon polaritons are supported on the new stripline structure whose electromagnetic fields are highly localized near the stripline, and hence the coupling is suppressed between the present type of stripline and the conventional stripline. For a structured stripline and a conventional stripline which are parallelly placed and separated by a distance of the stripline width, the crosstalk between them ranges from −17.13 to −64.89 dB, which is much lower than the crosstalk between two coupled conventional striplines. As this new type of stripline has such an important advantage, it would be applicable to high-density microwave circuits or high-speed circuits.

The angle- and thickness-dependent photonic band structures in a one-dimensional superconducting photonic crystal are theoretically investigated based on the transfer matrix method. The band structure is studied near and below the threshold frequency at which the superconducting material has a zero permittivity. The gap structure is analyzed as a function of the thicknesses of the two constituent superconducting and dielectric materials. In the angular dependence of the band structure, it is found that in the TM-polarization there exists a strongly localized superpolariton gap in the vicinity of the threshold frequency. This gap is shown to be enhanced as the angle increases.

The effects of losses on the photonic band gap (PBG) in a one-dimensional lossy double-negative (DNG)/double-positive (DPS) photonic crystal are theoretically investigated. Using the Lorentz expressions for the permittivity and permeability for the dispersive and lossy DNG material, it is found that the magnetic loss, in comparison with the electric loss, has a more salient influence on the PBG. The magnetic loss is shown to play a vitally important role in the analysis of PBG for this DNG/DPS photonic crystal.

The effective surface impedance of a high-temperature superconducting thin film on a semiconductor plasma substrate is calculated. Two possible configurations are considered. The first one is a superconducting film deposited on a semi-infinite semiconductor substrate. It is seen that there exists a critical film thickness for the superconductor such that a minimum effective surface resistance is attained. The effective surface resistance is strongly dependent on the high-frequency permittivity of semiconductor plasma. The second will be limited to the more practical case, that is, the semiconductor substrate is of finite thickness. The investigation of substrate resonance in the effective surface resistance shows some fundamental distinctions when a semiconductor plasma substrate is introduced.

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.

We summarize some results on the behavior of vortex dynamics and pinning effects in superconducting films with artificial pinning centers. Superconducting thin films with regular arrays of holes were fabricated using electron-beam lithography and reactive dry etching techniques. Vortex dynamics in the mixed state in type II superconductors is strongly influenced by the presence of defects, which act as pinning centers. Periodic critical current matching peaks were observed in magnetotransport measurements. The matching effect is caused by the interplay between the pinning centers and vortex lattice. Therefore, vortex lattice behaviors are changed for different temperatures and the geometry of the pinning centers. Molecular dynamic simulations are made to study this phenomenon. The ground state distribution of vortices obtained from simulations can give a reasonable explanation of the prominent matching peaks we found in the experiments.

Optical wave properties for a photonic crystal narrowband filter with a left-handed defect are theoretically investigated. The filter is made of a defect layer together with two quarter-wave dielectric photonic crystals in a symmetric manner. It is found that a narrowband transmission filter can be achieved with the value of negative refractive index in defect being an even integer when the defect thickness equals the quarter wavelength. It also can be implemented when the value of negative refractive index is equal to an integer if the defect thickness is taken to be the half wavelength. As for the asymmetric one, there is only one selection rule for the quarter wavelength defect. Additionally, the effects of losses coming from the left-handed defect are also examined. The results establish guiding rules for the choice of the negative refractive index that are of technical use in designing such a filter with a left-handed defect.