Defect Mode Frequency Research Articles

各向异性介质缺陷单负媒质光子晶体的新型缺陷模

A kind of zero-phase-shift gap appears in the one-dimensional photonic crystal composed ofalternate epsilon-negative materialand mu-negative material,and the gap does not vary with electromagnetic wave incident angle and polarization direction.To tune the defect mode frequency,a layer of anisotropic media is introduced into the center of that photonic crystal.The transmission spectra are investigated by Berreman 4×4 matrix.The result indicatesthat frequency of defect mode can be tuned by rotating the anisotropic media around z-axis in laboratory coordinate,and does not changed by different incident angles.These phenomena can be applied to tunable single tunnel omnidirectional filter in light wave.

Planar defects and heterostructure in diamond structure photonic crystals

Three dimensional diamond structure photonic crystals with planar defects and heterostructure fabricated by rapid prototyping and gel casting with alumina were studied. The influence of ordinary planar defect and twinned planar defect on the transmission properties of the electromagnetic wave in the photonic crystals was first investigated. The normalized resonant intensities are 0.5 and 0.58 for ordinary and twinned planar defect photonic crystals (PCs). The resonant intensity of electromagnetic wave in the twinned planar defect PC is stronger than that in the ordinary planar defect PC and the resonant peak width of the twinned planar defect PC is narrower and steeper than that of the ordinary planar defect PC. The resonant peak intensity and frequency of planar defect modes increase firstly and then decrease with the increase of the planar defect sizes. The strongest resonant peak intensity lies at the defect size with 0.5 mm. If the defect size is more than 2.5 mm, the resonant mode will disappear. In the heterostructure PC, which was realized by combining two perfect PCs with different lattice constants of 9 mm and 12 mm, the band gaps of the two different PCs can be united together.

Single Defect in Finite one Dimensional Photonic Crystals

Applying transfer matrix method, we get reflection and transmission coefficient of finite one dimensional photonic crystals. At the same time, we consider the position influence of single defect. We find the frequency of defect mode is same, but the height of transmission peak is not same when single defect is in different position of crystal. The transmission peak is maximum when the defect is in center of finite one dimensional photonic crystals.

Temperature‐dependent absorbance spectra of semiconductor‐dielectric photonic crystals

AbstractTerahertz absorbance spectra of defective and non‐defective semiconductor‐dielectric photonic crystals are theoretically investigated. Two structures with a strongly temperature‐dependent permittivity will be considered at different temperatures. First, non‐defective structure of (Si02/InSb)N and second, defective structure of (Si/SiO2)N InSb(SiO2/Si)N which is completely similar to the structure reported by Hung et al. (J. Appl. Phys. 110, 093110 (2011)). We have shown that in the non‐defective structure the peak of absorbance takes place at band edges and the peak height is nearly 55% of incidence at 325 K and decrease to 12% at 225 K. In the second structure the most absorption takes place in defect mode frequency which is at least three times larger than band edge absorption. By increasing the temperature from 225 K to 325 K, the height of absorption increases from 6.8% to 50% of incident radiation and is slightly shifted to upper frequencies (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Tunable defect mode in a semiconductor-dielectric photonic crystal containing extrinsic semiconductor defect

In this work, we theoretically investigate the tunable properties in the defect mode for a defective semiconductor-dielectric photonic crystal (SDPC). Here, the defect layer is an extrinsic semiconductor of n type InSb, n-InSb, which has a strong temperature- and concentration-dependent dielectric constant. With the use of n-InSb, the defect mode can be tuned as a function of temperature and concentration. The defect mode frequency is blue-shifted as the concentration or the temperature increases. In addition, this defect mode frequency shows a nearly linear dependence on the concentration but a nonlinear dependence on the temperature. Finally, by increasing the defect thickness leads to the presence of multiple defect modes which can be used to design a multichanneled filter.

Optical Defect Modes in Chiral Liquid Crystals at Birefringent Defect Layer

An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) for the case of a birefringent defect layer is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, a birefringent layer (with the averaged dielectric susceptibility equal to the average dielectric susceptibility of CLC) sandwiched between two CLC layers inserted in an isotropic medium with the dielectric constant equal to the average dielectric constant of CLC is studied. The chosen model allows one to get rid off the polarization mixing at the external surfaces of the defect structure (DMS) and to reduce the corresponding equations to the equations for light of diffracting in CLC polarization only. The dispersion equation determining connection of the defect mode frequency with the layer birefringence and other parameters of the defect structure is obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC- birefringent defect layer-CLC) are presented and analyzed. It is shown that generally speaking the layer birefringence reduces the DM lifetime in comparison with the DMS with an isotropic defect layer and only at discrete values of DMS parameters it achieves the value of the corresponding DMS with an isotropic defect layer. Correspondingly, generally speaking, the effect of anomalously strong light absorption at the defect mode frequency and the lowering of the lasing threshold are not so pronounced as in the case of the DMS with an isotropic defect layer. The case of DMS with low defect layer birefringence is studied in details. The options of effectively influence at the DM parameters by changing the defect layer birefringence are discussed.

Optical Defect Modes in Chiral Liquid Crystals at Active Defect Layer

An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) for the case of an active defect layer is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, an isotropic absorbing or amplifying layer (with the dielectric susceptibility equal to the average dielectric susceptibility of CLC) sandwiched between two CLC layers is studied. The chosen model allows one to get rid off the polarization mixing and to reduce the corresponding equations to the equations for light of diffracting in CLC polarization only. The dispersion equation determining connection of the defect mode frequency with the isotropic layer gain and thickness is obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-active defect layer-CLC) are presented and analyzed for absorbing and amplifying defect layers. The effect of anomalously strong light absorption at the defect mode frequency for absorbing defect layer is discussed. It is shown that in DFB lasing in a defect structure with an amplifying defect layer an adjusting of the lasing frequency to the DM frequency results in a significant lowering of the lasing threshold and the threshold gain is lowering with increase of defect layer thickness. Numerical estimates of the threshold gain are performed for typical values of the related parameters and analytic expressions for thick CLC layers in the defect structure are presented.

Defect mode suppression in a photonic crystal structure with a resonance nanocomposite layer

This paper examines the key features of the transmission and reflection spectra of a one-dimensional photonic crystal structure in which a nanocomposite layer is sandwiched between dielectric Bragg mirrors. Two orthogonal polarisations of an incident wave correspond to different plasmon resonance frequencies of the nanocomposite. If one of the plasmon frequencies coincides with the defect mode frequency in one of the photonic bandgaps, complete suppression of the defect mode in the transmission spectrum is possible, which makes the spectra of such structures polarisation-sensitive.

Defect modes in one-dimensional granular crystals

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values.

Properties of defected one-dimensional terahertz plasmonic crystal films in a metal air-gap waveguide

We investigated properties of localized modes of one-dimensional terahertz plasmonic crystal films with defects in a metal air-gap waveguide by terahertz time-domain spectroscopy experiments and finite-difference time-domain simulations. A defect was created by varying the width of an air slit at the center of the plasmonic crystal film. The donor (accept)-like defect modes were observed when the width of the defect air slit increases (decreases) from an initial width. The quality factor increases abruptly as the air-gap size decreases, while the defect mode frequency slightly decreases. The high quality-defect mode was examined for terahertz sensor applications.

Optical Defect Modes in Photonic Chiral Liquid Crystals

An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) is developed. The analytic study is facilitated by a special choice of the problem parameters. The dispersion equation determining connection of the defect mode frequency with the isotropic (defect) layer thickness is given. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-defect layer-CLC) are presented and analyzed for nonabsorbing, absorbing and amplifying CLC. The effect of anomalously strong light absorption at the defect mode frequency is revealed. It is shown that in DFB lasing in a defect structure adjusting of the lasing frequency to the DM frequency results in a significant lowering of the lasing threshold. Numerical solutions of the DM dispersion equation are performed for typical values of the related parameters.

Optical defect modes in chiral liquid crystals

An analytic approach to the theory of optical defect modes in chiral liquid crystals (CLCs) is developed. The analytic study is facilitated by the choice of the problem parameters. Specifically, an isotropic layer (with the dielectric susceptibility equal to the average CLC dielectric susceptibility) sandwiched between two CLC layers is studied. The chosen model allows eliminating the polarization mixing and reducing the corresponding equations to the equations for light of diffracting polarization only. The dispersion equation relating the defect mode (DM) frequency to the isotropic layer thickness and an analytic expression for the field distribution in the DM structure are obtained and the corresponding dependences are plotted for some values of the DM structure parameters. Analytic expressions for the transmission and reflection coefficients of the DM structure (CLC-defect layer-CLC) are presented and analyzed for nonabsorbing, absorbing, and amplifying CLCs. The anomalously strong light absorption effect at the DM frequency is revealed. The limit case of infinitely thick CLC layers is considered in detail. It is shown that for distributed feedback lasing in a defect structure, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold. The DM dispersion equations are solved numerically for typical values of the relevant parameters. Our approach helps clarify the physics of the optical DMs in CLCs and completely agrees with the corresponding results of the previous numerical investigations.

Properties of defect modes in geometrically chirped one-dimensional photonic crystals

The variation of the transmission coefficient with defect mode frequency in a geometrically chirped photonic crystal with central defect layer has been investigated theoretically using transfer matrix method and validated experimentally by fabricating and characterizing such photonic crystals. The defect mode frequency is extracted by modeling the defect layer as a Fabry–Perot resonant cavity with mirrors replaced by two geometrically chirped photonic crystals. It is shown that the structural asymmetry of the chirped photonic crystals with respect to the central defect layer affects the width of the photonic band gap and also induces coupling variation between the eigenmodes of the defect layer and those at the band edges of the constituent photonic crystals. This leads to variation in the defect mode transmittance across the photonic band gap and introduces notches at positions where the eigenmodes of the band edges have maximum transmission.

Defect mode properties of two-dimensional unmagnetized plasma photonic crystals with line-defect under transverse magnetic mode

The piecewise linear current density recursive convolution finite-difference time-domain method of plasma is used to study the defect mode properties of transverse magnetic wave propagation in the two-dimensional unmagnetized plasma photonic crystals with a line-defect layer. In frequency domain, the transmission coefficients of electromagnetic differential Gaussian pulses are computed, and the effect of lattice constant, dielectric column radius, periodic constant, parameters of plasma and parameters of line-defect layer on defect mode properties of two-dimensional unmagnetized plasma photonic crystals are analyzed. The results illustrate that the frequency of defect mode cannot be tuned by changing periodic constant, position of the defect layer and plasma collision frequency, but be tuned by changing relative permittivity and radius of dielectric column in the defect layer, and central distance between defect layer and dielectric layer with the width of prohibit band gaps fixed. Furthermore, the defect mode and the width of prohibit band gaps can also be tuned by changing lattice constant, dielectric column radius and plasma frequency.

The defect mode and the quantum effect of light wave in cylindrical anisotropic photonic crystal

The quantum effect of light wave mode is studied under restriction condition of light wave in 1-D cylindrical anisotropic doped photonic crystal. The defect mode character of TE wave and TM wave are calculated by characteristic matrix method . New defect mode structure of 1-D cylindrical anisotropic doping photonic crystal was obtained. The defect mode frequency and transmission angle increases with increasing quantum number. The defect mode frequency of the same pattern decreases with increasing cylinder radius.

Influence of filling fraction on the defect mode and gap closing of a one-dimensional photonic crystal: An analytical approach

Study of the optical properties of the one-dimensional defective photonic crystals using the gap map is improving through the emergence of new analytical methods, which are easy and without any physical restrictions. Gap map is able to monitor the changes in the defect mode frequencies and photonic band gap regions as a function of filling fractions, and all visible spectra in a single graphic presentation. In this paper, by utilizing a novel technique based on Green’s function method for analyzing the defect modes, the gap map and gap closing point of a one-dimensional defective photonic crystal have been demonstrated. This method enables study of the defect modes inside the omnidirectional band gap, which is an important object in the designing of the optical filters. Moreover, as a designing criterion, obtaining the gap closing points inside the gap map enables finding of some filling fraction intervals that each one contains several distinct omnidirectional band gaps simultaneously, using a single photonic crystal. This method has been employed for the design of an optical filter at 1.3 and 1.55 μm, which is applicable for telecommunication.

A one-dimensional photonic crystal with a superconducting defect layer

A one-dimensional dielectric photonic crystal with a complex defect layer, consisting of ultrathin superconducting and dielectric sublayers, is theoretically studied. It is shown that the position of the defect mode and the transmittivity at the defect mode frequency strongly depend on the thickness of the superconducting sublayer as well as on the temperature.

Platonic crystals: Bloch bands, neutrality and defects

We consider the properties of flexural waves in a periodically-constrained thin elastic plate. A square array of rigid pins is embedded into the plate. We show that such a system supports a stop band commencing at zero frequency, and we evaluate analytically the frequency limits of its first three bands. We show that each band has neutral directions, in which its dispersion relation and group velocity coincide with those of two corresponding plane waves. We construct the stop band Green’s functions and analyse strongly localized defect modes, and we also find the frequency of the resonant defect mode lying in the first band gap.

Defect mode properties of magnetized plasma photonic crystals

The piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) method for magnetized plasmas is applied to study the characteristic of one_dimensional magnetized plasma photonic crystals with a defect layer. In frequency domain, the transmission ratio of electromagnetic Gaussian pulses is computed, and the effects of periodic constant, parameters of plasma and parameters of defect layer such as dielectric length and position on defect mode properties of magnetized photonic crystals are analysed. The results show that the frequency of defect mode cannot be tuned by changing the parameters of position and periodic constant, changing the length of the defect layer can increase the number of defect mode, and the frequency and peak of defect mode can be changed by different parameters of plasma.

Defect Modes in Chiral Liquid Crystals: An Analytic Approach

An analytic approach to the theory of the optical defect modes in chiral liquid crystals (CLC) is developed. The analytic study is facilitated by the choice of the problem parameters. Namely, an isotropic layer (with the dielectric susceptibility equal to the average dielectric susceptibility of CLC) sandwiched between two CLC layers is studied. The chosen model allows one to get rid off the polarization mixing and to reduce the corresponding equations to the equations for light of diffracting in CLC polarization only. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (CLC-layer-CLC) are obtained as well as the dispersion equation determining connection of the defect mode frequency with the isotropic layer thickness. A limiting case of infinitely thick CLC-layers is considered in details. The developed approach helps to clarify the physics of the optical defect modes in CLC and manifests an excellent agreement with the corresponding results of the previous investigations obtained by a numerical approach.