Defect Mode Frequency Research Articles

Investigation of non-reciprocity and behavior of defect modes in photonic crystals incorporating Weyl semimetals

Abstract The ability to control the frequency of defect modes in photonic crystals has led to the emergence of novel applications. Researchers have recognized the unique properties of Weyl semimetals and explored their utilization in photonic crystals. This study investigates the non-reciprocal properties in photonic crystals incorporating Weyl semimetals and examines the behavior of defect modes within these crystals. This paper employs a photonic crystal containing Weyl semimetals with two different structures. Initially, the non-reciprocal properties in both structures are examined, followed by an analysis of the behavior of defect modes. The results indicate that only utilizing Weyl semimetal in the photonic crystal does not result in non-reciprocity. The arrangement of layers next to each other, or the geometry, plays a crucial role in non-reciprocity. Additionally, the behavior of defect modes varies depending on the structure type and propagation direction.

Defect mode properties of self-similar symmetry order in triadic Cantor photonic crystals

The discovery of quasi-crystal tells us that not only the translational symmetry order (TSO) but also other orders can produce Bragg diffraction. As far as we know, in one dimensional (1D) photonic crystals (PCs) there are two symmetry orders, TSO and self-similar symmetry order (SSO). There has been a lot of researches exploring the properties of defect of TSO in the 1D PCs, but until now we do not find any studies related to the defect of SSO. In this work we consider the triadic Cantor set (TCS) PCs to stage 6, and attempt to create the defect of SSO by changing the scale factor of stage 2 to 3 and stage 3 to 4, where for the high-refractive-index layer only the thickness of stage 3 changes. It's well known that the defect of TSO governs the frequency of a kind of transmission peaks, called defect mode. Our results show that the defect of SSO influences the background intensity of the transmittance spectrum rather than the transmission peaks. We note that the defect mode frequency and the transmittance background intensity interchange their roles for the two symmetry orders, and it follows that the long neglected transmittance background intensity should be a significant optical property.

High-Performance Dual-Channel Photonic Crystal Terahertz Wave Modulator Based on the Defect Mode Disappearance of a Combined Microcavity

With the working frequency of wireless communication systems moving to a higher terahertz (THz) band, the design of high-performance THz wave modulators has become a pivotal issue to be tackled urgently in THz communication. In this paper, we design a high-performance dual-channel photonic crystal modulator to enable ON–OFF regulation of the THz wave based on the defect mode disappearance of combined microcavities. The modulator introduces Y-type line defects into silicon rod photonic crystals as a dual-channel waveguide and the point defects and ring resonator form a combined microcavity. Due to the refractive index of the ring resonator filler, gallium arsenide, it is tunable with pump light excitation, and the defect mode frequency of the combined microcavity can be dynamically changed. Under pump excitation with a wavelength of 810 nm and an intensity of 0.4 μJ/cm2, 1.34 THz and 1.83 THz dual-channel waves can be OFF due to the defect mode disappearance of the combined microcavity. This is simulated by the time-domain steady-state response and steady-state THz wave field intensity distribution of the modulator by the finite-difference time-domain method. The results indicate that the dual-channel modulator has large modulation depths of 100% and 99.7%, high modulation rates of 4.05 GHz and 4.17 GHz, and low insertion losses of 0.31 dB and 0.18 dB, which lays foundation for the development of high-speed and low-loss THz communication technology.

Design and analysis of 1D photonic crystal doped with magnetized cold plasma defect for application of single/multi-channel tunable narrowband filter

The present research demonstrates the tunable filtering properties of a single/multi-channel filter based on 1D photonic crystal (PhC), which is designed with dielectric materials (A, B) and magnetized cold plasma (P). The proposed filter has a configuration of Transmission spectra of the structure is investigated for both right-hand polarization and left-hand polarization configurations of the plasma material by employing the well-known transfer matrix method. It is found that number of periods of the plasma layer (N) decides the single-channel and multi-channel operations of the filter. It is revealed that the external magnetic field can be manipulated to tune the frequency of the filter. Also, it is found that the geometrical parameters such as thickness of the plasma layer, plasma density, and incident angle play a significant role in tuning the defect mode frequency. Moreover, the color map plot is studied to provide a clear insight of shifting nature of the defect mode frequency. Quality factor of the filter is evaluated vis-à-vis different geometrical parameters. Our considered structure can be the mainstay for filtering applications in microwave regions, and can find suitable applications in dense wavelength division multiplexing and high speed signal processing.

Gas sensing applications using magnetized cold plasma multilayers

In this paper, we theoretically propose a novel magnetic field-dependent sensor using omnidirectional magnetized cold plasma photonic crystal in one dimension for TE polarization. The structure consists of asymmetric two periodic arrays from magnetized cold plasma and sample cavity layer. Between the periodic arrays, a sample cavity is sandwiched between two quartz layers. The methodology of the proposed detector depends on the appearance of a sensitive defect mode. The results clear that the defect mode frequency depends significantly on the refractive index of the sample, and it is extremely sensitive to incident angle changes, applied magnetic field, the number density of electrons, and sample layer thickness. The optimized proposed sensor has high sensitivity of 15.14 GHz/RIU, quality-factor of 527.32, and figure of merit of 1066.20 RIU−1, where RIU means refractive index unit. So, the proposed sensor can aid in solving many challenges in chemical and environmental applications.

Identifying delamination in carbon fiber composites based on defect modes in imperfect phononic crystals

Delamination is one of the most common types of damage in fiber-reinforced composites. In this paper, borrowing from the concept of defect modes in imperfect phononic crystals, we propose a method for identifying delamination damages in composite materials. Specifically, by periodically arranging concentrated masses on the surface of a finite carbon fiber beam, the carbon fiber beam becomes a phononic crystal, and defect modes in Bragg bandgaps can be observed when there is delamination. With the spectral element method formulation, we show that the frequencies of defect modes are directly related to the length and location of the delamination. By performing algebraic addition and subtraction on the generated defect mode frequencies when applying excitations at the two ends of a defected carbon fiber composite beam, an approximately linear correlation with the length and location of delamination can be obtained. Our analytical and experimental results indicate that, by introducing periodicity on the carbon fiber composite beam and applying appropriate post-processing algorithm to the generated defect modes, rapid and accurate identification of the delamination length and location can be achieved based on the bandgap characteristics of the imperfect phononic crystals.

Tunable reflectance characteristics of magnetized cold plasma based one-dimensional defective photonic crystal

In this work, we analyze the reflectance property of a MCP based 1DPC with symmetrically introduced defect layer of air. The reflectance spectra of the defective PC are obtained by employing TMM with variation in the thickness of the defect. It is reported that the PC with the defect thickness of zero having the form, (AB)N/2(BA)N/2, exhibits two adjacent completely reflected bands separated by a defect mode with reflectance zero. The conventional extrinsic PC offers a single completely reflected band lying in the range 4–6 GHz that splits into two parts by defect mode when we operate the PC in defective mode. By increasing the defect thickness up to 15 mm, the low frequency band becomes narrower and the defect mode frequency is shifted towards a lower value, whereas the second band becomes wider. The defect mode frequency shows a similar decreasing behavior with increase in the thickness of air defect below and above its particular value of 20 mm. In this investigation, the disappearance of defect mode at a critical thickness and reappearance of new defect mode at higher frequency with further increase in defect thickness, are considered as important features of this defective PC. Such kind of tunability in the reflected band, defect mode frequency, and reappearance of new defect mode, all are in a good agreement with the computed results reported by the researchers. The insights of the analysis can be employed in design of optical filters, waveguides, detectors, and similar tunable microwave and switching devices.

Magnetically controlled three-channel phononic switch

This study includes the design procedure of a novel three-channel switch based on solid–solid phononic crystals. This elastic switch is externally controlled by the magnetic field. Proposed 1 × 3 switch is designed using Young’s modulus variations (ΔE effect) of magnetostrictive materials due to change in the magnetic field intensity. The change in the elastic constant shifts the defect mode frequency position. A fundamental phenomenon in this switch is the major frequency shift, which is equal to 100 kHz for Terfenol-D Young’s modulus reduction of 18%. It should be noted that this frequency shift occurs in presented phononic structure with a lattice constant equals to 500 μm. The major frequency shift is due to Terfenol-D high sensitivity to the magnetic field and using the hollow cylinders in output waveguides of structure. The elastic switch simulation is accomplished by finite element method. The crosstalk worst case in the proposed switch is −17 dB, which shows the device suitable performance.

Terahertz flat-top broadband defect modes generated in periodically undulated waveguides

We propose a tunable flat-top broadband defect mode in the terahertz (THz) frequency range by inserting multiple defects into a periodic waveguide with undulated tube walls. When introducing a defect into periodic structures, we can achieve a defect mode with a very sharp transmission peak in the forbidden band due to the local resonance effect. Here, in the proposed multi-defect structure, we find a broadband defect mode with a bandwidth of 38.3 GHz appearing in the transmission spectrum, which is over 21 times that of the traditional defect mode. The simulations reveal that the broadband defect mode is caused by the competition between Bragg scattering and local resonances in multiple defect mode coupling. The bandwidth and center frequency of this broadband defect mode can be manipulated by altering the number and size of defects, which could be applied in various THz systems as functional devices.

Novel Design for the Temperature Sensing Using Annular Photonic Crystals

In this research, a high-performance temperature sensor of a one-dimensional defective annular photonic crystal is proposed. The structure design of our proposed defective annular photonic crystal is: [(Si/SiO2) N/2 TiO2 (Si/SiO2) N/2] with TiO2 as a defect layer. The transmission spectrum of the defective annular photonic crystal is calculated by using the well-modified transfer matrix method in cylindrical coordinates. Thermal characteristics of the defect mode that emerged in the transmission spectrum are studied in the visible region. Dependence of the defect mode frequency on the defect layer thickness is also discussed. As temperature increases, the defect mode is shifted to new positions due to thermal expansion and thermo–optical effects. Numerical results show that the core radius has an important effect on the transmission intensity of the defect mode. Moreover, our proposed temperature sensor showed a sensitivity of about 11 nm / 1000 °C, figure of merit of 0.218 / oC and a very small full width at half maximum of about 0.049 nm. The proposed annular photonic crystals temperature sensor could present a novel method to overcome the limited performance of the planar photonic crystals temperature sensors besides the possibility of using in many potential filtering applications.

Two-channel all-elastic solid-solid phononic switch

We have investigated the elastic wave switching based on nonlinear phononic crystals. The phononic crystal structure contains of an input waveguide and two output waveguides that acts as elastic 1 × 2 switch. The input wave with low intensity propagates through bar waveguide; in this case the performance of structure is linear. By increasing the intensity of input wave, nonlinear behavior is appeared and the applied wave propagates through cross waveguide. Increment of the gradient of displacement results in the nonlinear behavior in phononic structure and changing the mass density of the propagation medium. Changing the mass density of constituent materials shifts the frequency of defect modes. By these feature, designing of elastic 1 × 2 switch is realized.

Application of a Microwave Coaxial Bragg Structure for the Measurement of Parameters of Insulators

A method for the measurement of the complex permittivity of insulators using a microwave coaxial photonic crystal is proposed and implemented. The method is based on a solution to an inverse problem using minimization of the difference of experimental and calculated frequency dependences of the transmission and reflection coefficients at the defect-mode frequency in the band gap of a photonic microwave crystal containing a structure with the parameters that must be determined. An unambiguous solution to the inverse problem can be obtained using a defect mode in the band gap at the frequency of which a maximum of the standing wave is obtained in the region of the structure under study.

Nonlinear elastic switch based on solid–solid phononic crystals

Mass density nonlinearity in a solid–solid phononic crystal and its effect on phononic band gap tunability are investigated. Also, a phononic On–Off switch is designed based on nonlinear phononic crystals. The proposed switch is formed of tungsten scatterers with a square arrangement, embedded in a poly methyl methacrylate background. Also, this structure contains a linear channel that creates a defect mode in the phononic band gap. Increment of input intensity causes the wave propagation medium to be dynamic. This effect allows phononic band gap to be tuned, and the defect mode frequency of the linear channel to be shifted to higher frequencies. Due to these features, the On–Off switch is designed and controlled by the excitation wave intensity. In the linear regime the switch is On, and by increasing the intensity of applied wave, it becomes Off. To the best of our knowledge, this is the first time a nonlinear phononic crystal switch is proposed. The calculated extinction ratio for the proposed structure is equal to − 19.96 dB, which seems to be suitable for switching applications.

Designing tunable narrow band filters using a plasma photonic crystal structure with sinusoidal modulated plasma defect layer

In this work, we have designed tunable narrow band filters using symmetric and asymmetric one-dimensional plasma photonic crystal structures. Both proposed structures contain a plasma defect layer that its electron density and therefore the refractive index can be modulated sinusoidally by an external electric or acoustic fields. The transmittance spectrum is obtained by using the transfer matrix method. The results have shown that in symmetric and asymmetric structures, one and two very sharp localized defect mode appears in the photonic band gap, respectively. The frequency of the defect modes and their transmittance intensity are studied by changing the amplitude and frequency of the applied external field to the plasma defect layer. It is observed that by increasing the modulation frequency and its amplitude, the defect mode frequencies change and shift toward the lower frequencies that can be introduced as tunable narrow band filters.

Properties of omnidirectional gap and defect mode of one-dimensional graphene-dielectric periodic structures

We theoretically investigate the optical response of one-dimensional graphene based photonic crystal (1D-GPC) structures with and without defect layer in the low terahertz (THz) frequency region. The 1D-GPC is composed of alternated layers of isotropic dielectric material (SiO2) and graphene monolayer sheets. Using the transfer matrix method (TMM), the effects of several parameters such as the incidence angle, width, thickness, and refractive index of the defect layer and the chemical potential of graphene sheets on the device response will be explored in detail for both TE and TM polarizations. Our simulation results indicate that when a defect layer is introduced, the structure may support two kinds of defect modes. One kind is created in the Bragg gap and the other one is created in the graphene-induced photonic band gap (GIPBG). Our results reveal that a defect mode can appear within the GIPBG only for an optical thickness of the defect layer greater than that of the alternated dielectric layers of the 1D-GPC. While, the defect modes in the Bragg gap may be created by simply breaking of the periodicity of the dielectric lattice. In addition, the resonance frequency of defect mode in the GIPBG is found to be almost insensitive to the incident angle for both polarizations. Moreover, we show that an effective Brewster angle for our structure can be deduced from the variation of the amplitude of defect mode with the incident angle. Our analysis has shown an innovative idea for the realization of tunable broadband reflectors and narrowband filtering devices.

The properties of a tunable terahertz multichannel filter from one-dimensional photonic crystal dope by magnetized plasma defect

The terahertz magnetize-field tunable filtering properties in a multichannel filter based on a one-dimensional photonic crystal doped by magnetized plasma are theoretically investigated. The considered structure of (AB)4(ACB)N(AB)4 is designed, where A and B are two dielectric layers, C is the plasma layer, and N is the defect number. First, the structure can be worked as a multichannel filter whose channel number equals N. Second, the defect mode frequencies are all red-shifted as the ratio of dielectric refractive index or the sum of the A and B layer length increases. Third, we find that the channel frequencies can be shifted as a function of the applied magnetic field and the defect mode frequencies are all red-shifted as the plasma density increases. And the thickness of a plasma layer also affects the intensity, position and number of the defect modes. Therefore, these unusual properties may provide a novel design idea of a tunable terahertz multichannel transmission filter in future.

Two Types of Localized States in a Photonic Crystal Bounded by an Epsilon near Zero Nanocomposite

The spectral properties of a one-dimensional photonic crystal bounded by a resonant absorbing nanocomposite layer with the near-zero permittivity have been studied. The problem of calculating the transmittance, reflectance, and absorptance spectra of such structures at the normal and oblique incidence of light has been solved. It is shown that, depending on the permittivity sign near zero, the nanocomposite is characterized by either metallic or dielectric properties. The possibility of simultaneous formation of the Tamm plasmon polariton at the photonic crystal/metallic nanocomposite interface and the localized state similar to the defect mode with the field intensity maximum inside the dielectric nanocomposite layer is demonstrated. Specific features of field localization at the Tamm plasmon polariton and defect mode frequencies are analyzed.

Tunable Bragg defect mode in one-dimensional photonic crystal containing a graphene-embedded defect layer.

Using the transfer matrix method, the transmission properties of defective one-dimensional photonic crystal are analyzed in the terahertz region. The defect layer is composed of a graphene-embedded dielectric layer. We investigate the variation of the defect mode's frequency as a function of graphene chemical potential for different values of incident angles. The numerical results show that the frequency of the defect mode can be tuned effectively as the chemical potential of graphene nanolayers changes using an applied gate voltage. The present results can be useful in designing tunable graphene-based photonic devices such as filters and sensors in terahertz regions.

Periodic multilayer magnetized cold plasma containing a doped semiconductor

The present work is to numerically investigate the properties of the defect mode in a one-dimensional photonic crystal made of magnetized cold plasma, doped by semiconductor. The defect mode of such kind of multilayer structure is analyzed by applying the character matrix method to each individual layer. Numerical results illustrate that the defect mode frequency can be tuned by varying the external magnetic field, the electron density, and the thickness of the defect layer. Moreover, the behavior of the defect mode was found to be quite interesting when study the oblique incidence. It was found that for both right- and left-hand polarized transversal magnetic waves, the defect mode of the proposed defective structure disappears when the angle of incidence is larger than a particular oblique incidence. For the left-hand polarized transversal electric wave, however, an additional defect mode was noticed. The results lead to some new information concerning the designing of new types of tunable narrowband microwave filters.

Photonic band-gap and defect modes of a one-dimensional photonic crystal under localized compression

The rupture of periodicity caused by one defect (defect layer) in a one-dimensional photonic crystal (1DPhC) results in a narrow transmission spectral line in the photonic band-gap, and the field distribution shows a strong confinement in the proximity of the defect layer. In this work, we present a theoretical model to calculate the frequency of defect modes caused by defect layers induced by localized mechanical stress. Two periodical arrangements were studied: one with layers of poly(methyl-methacrylate) (PMMA) and polystyrene (PS), PMMA-PS; the other with layers of PMMA and fused silica (SiO2), PMMA-SiO2. The defect layers were induced by localized compression (tension). The frequencies of the defect modes were calculated using elasto-optical theory and plane wave expansion and perturbation methods. Numerical results show that the frequency of the defect mode increases (decreases) when the compression (tension) increases. Based on the theoretical model developed, we show that compression of n layers of a 1DPhC induces n defect modes whose frequencies depend on the compression magnitude in the case of normal incidence of electromagnetic waves, in accordance with the results reported for other types of defect layers. The methodology shows the feasibility of the plane wave expansion and perturbation methods to study the frequency of the defect modes. Both periodical arrangements are suitable for designing mechanically tunable (1DPhC)-based narrow pass band filters and narrow reflectors in the (60, 65) THz range.