Properties of Defect Modes in Periodic Lossy Multilayer with Negative-Index-Materials

Employing the characteristic matrix method, this study investigates transmission properties of onedimensional defective lossy photonic crystals composed of negative and positive refractive index layers with one lossless defect layer at the center of the crystal. The results of the study show that as the refractive index and thickness of the defect layer increase, the frequency of the defect mode decreases. In addition, the study shows that the frequency of the defect mode is sensitive to the incidence angle, polarization, and physical properties of the defect layer, but it is insensitive to the small lattice loss factor. The peak of the defect mode is very sensitive to the loss factor, incidence angle, polarization, refractive index, and thickness of the defect layer. This study also shows that the peak and the width of the defect mode are affected by the numbers of the lattice period and the loss factor. The results can lead to designing new types of narrow filter structures and other optical devices.     

One-dimensional photonic crystals with a planar oriented nematic layer: Temperature and angular dependence of the spectra of defect modes

Transmission spectra of a one-dimensional photonic crystal (PC) formed by two multilayer dielectric mirrors and a planar oriented layer of 5CB nematic liquid crystal (LC) that is sandwiched between these mirrors and serves as a structure defect are investigated experimentally. Specific features of the behavior of the spectrum of defect modes as a function of the angle of incidence of light on the crystal are studied for two polarizations: parallel and perpendicular to the director of the LC; the director either lies in the plane of incidence or is perpendicular to it. It is shown that, for the configurations considered, the maxima of the defect modes shift toward the short-wavelength region as the tilt angle of incidence radiation increases; this tendency is more manifest for the parallel-polarized component, when the director lies in the plane of incidence. In the latter case, the width of the photonic band gap (PBG) appreciably decreases. The temperature dependence of the polarization components of the transmission spectra of a PC is investigated in the case of normal incidence of light. The spectral shift of defect modes due to the variation of the refractive index of the LC at the nematic-isotropic liquid phase transition point is measured. It is shown that, in real PCs, the amplitude of defect modes decreases when approaching the center of the band gap, as well as when the number of layers in the dielectric mirrors increases. Theoretical transmission spectra of the PCs calculated by the method of recurrence relations with regard to the decay of defect modes are in good agreement with experimental data.     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明:在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Near-infrared tunable narrow filter properties in a 1D photonic crystal containing semiconductor metamaterial photonic quantum-well defect

The near-infrared (NIR) narrow filter properties in the transmission spectra of a one-dimensional photonic crystal doped with semiconductor metamaterial photonic quantum-well defect (PQW) were theoretically studied. The behavior of the defect mode as a function of the stack number of the PQW defect structure, the filling factor of semiconductor metamaterial layer, the polarization and the angle of incidence were investigated for Al-doped ZnO (AZO) and ZnO as the semiconductor metamaterial layer. It is found that the frequency of the defect mode can be tuned by variation of the period of the defect structure, polarization, incidence angle, and the filling factor of the semiconductor metamaterial layer. It is also shown that the number of the defect mode is independent of the period of the PQW defect structure and is in sharp contrast with the case where a common dielectric or metamaterial defect are used. The results also show that for both polarizations the defect mode is red-shifted as the number of the defect period and filling factor increase. An opposite trend is observed as the angle of incidence increases. The proposed structure could provide useful information for designing new types of tuneable narrowband filters at NIR region.     

Giant Asymmetric Transmission and Circular Dichroism with Angular Tunability in Chiral Terahertz Metamaterials

Inspired by the chiral structure from mode interaction, a chiral terahertz metamaterial and its complementary structure with the coexistence of asymmetric transmission and circular dichroism response are designed. The asymmetric transmission happens in the presence of electric and magnetic modes perpendicular to each other, resulting from intrinsic chirality under normal incidence. Circular dichroism exists in the presence of electric and magnetic modes parallel to each other under oblique incidence because of extrinsic chirality. Both asymmetric transmission and circular dichroism are enhanced by complementary structures, benefitting from the coupling between adjacent units. The maximum of chiral parameter κ can achieve 450, which is one hundred times higher than previously reported. The chiral response can be tuned by the incident angle and is sensitive to the environmental refractive index. The results highlight the potential applications of these metamaterials in chiral sensing and polarization transformation devices.     

Angular tuning of defect modes spectrum in the one-dimensional photonic crystal with liquid-crystal layer

A one-dimensional ZrO₂/SiO₂ photonic crystal with a 4-n -pentyl-4' -cyanobiphenyl (5CB) nematic defect layer was used to investigate the transmission spectra of light polarized parallel and perpendicular to the liquid-crystal director at different angles of incidence. The spectra of the photonic crystal were shown to split into four polarized components T_ij at oblique incidence. When the incident angle increased, the bandgap edges and the defect modes shifted towards short wavelengths, while the amplitudes of the defect modes increased for the transverse magnetic polarization and decreased for the transverse electric polarization. The observed discrepancy between the defect mode amplitudes in the center and near the edges of the photonic bandgap was found to be related to the radiation losses inside the defect layer of a non-ideal photonic crystal. The simulated transmission spectra obtained using recurrence relations and taking into account the decay of defect modes are in good agreement with the experimental data.     

色散光子晶体GHz波段的传输特性

将两单负材料耦合后,再与一双负材料交替生成光子晶体。然后利用传输矩阵法对该光子晶体的能带和缺陷模进行了研究。结果表明:这种结构的光子晶体具有一种新型的光子带隙,不随晶格常数的缩放而移动;当引入普通电介质缺陷层时,缺陷模对入射角的改变不敏感,但缺陷模个数随着缺陷层厚度的增加而增多。     

Optical transmission spectra in symmetrical Fibonacci photonic multilayers

We study the transmission properties of light through the symmetric Fibonacci photonic multilayers, i.e, a binary one-dimensional quasiperiodic structure, made up of both positive (SiO₂) and negative refractive index materials with a mirror symmetry. These spectra are calculated by using a theoretical model based on the transfer matrix approach for normal incidence geometry, in which many perfect transmission peaks (the transmission coefficients are equal to the unity) are numerically obtained. Besides, the transmission coefficient exhibits a six-cycle self-similar behavior with respect to the generation number of the Fibonacci sequence.     

Abnormal behaviour of one-dimensional photonic crystal with defect

The effect of introduction a defect in a conventional one-dimensional photonic band gap (PBG) structure in respect of the dispersion relation, reflectivity, group velocity and effective group index of such a structure has been studied. In particular, the dependence of various properties of such a structure on the angle of incidence of the electromagnetic waves has been given more importance in the present study. The study shows that inside the conventional PBG structure as well as defect PBG structure, the group velocity and effective group index become negative for certain ranges of normalized frequency. In a defect PBG structure, it is possible to achieve desired values (negative or positive) of group velocity and effective group index by choosing appropriate angle of incidence, whereas in conventional PBG structures, the maximum (negative and positive) values of group velocities and effective group index are found to be almost independent of the angle of incidence. This is a unique property of defect PBG structure which is different from the properties of conventional PBG structures. Because of this unique property, defect PBG structure may be widely used for construction super lenses, lasing without inversion and other optical systems in photonics.     

含复合缺陷层的光子晶体的光学特性

运用传输矩阵法研究了在一维光子晶体中插入缺陷层的透光特性。在无缺陷层的一维光子晶体中能产生467~510 nm、1 279~1 715 nm两处明显的光子带隙。重点研究了插入缺陷层后,在1 279~1 715 nm的光子带隙中缺陷层厚度和入射角度大小分别与透射光谱变化的关系。研究发现：缺陷模的位置对入射角变化很敏感;出现缺陷模的数量和插入缺陷层的数量相同;一维光子晶体厚度的增大不会改变缺陷模的数量和位置,只改变透射峰的宽度和透射率。     

Band structures of phononic-crystal plates in the form of a sandwich-layered structure

This study investigates the propagation of Lamb waves in phononic-crystal plates in the form of a sandwich-layered structure. The composite plates are composed of periodic layers bilaterally deposited on both sides of the homogeneous core layer. Using the analyses of the band structures and the transmission spectra, it is revealed that the core layer may induce significant modulations to the lower-order Lamb modes. The modulations are ascribed to the reshaped particle displacement fields of the eigenmodes. Prominently, the core layer made of soft material (rubber) combines the identical eigenmodes of the periodic layers into a pair of asymmetric and symmetric modes in which case the periodic layers vibrate independently. However, the core layer made of hard material (tungsten) or medium hardness material (silicon) couples the periodic layers tightly, in which case the composites vibrate as a whole. In addition, it is found that the phononic band gaps are very sensitive to the thickness of the core layer; this could be indispensable to practical applications such as bandgap tuning.     

Traveling of light through a 1D photonic crystal containing a defect layer with resonant dispersion

Spectral properties of a 1D photonic crystal that is comprised of two multilayered dielectric mirrors and a nanocomposite layer between them as a structural defect are studied. The nanocomposite consists of silver nanoballs dispersed in a transparent matrix and is characterized by an effective resonant permittivity. The spectral manifestation of the defect mode splitting for the s-polarized waves is studied as a function of the angle of incidence and concentration of nanoballs. Specific features of the transmission spectra for the s- and p-polarized waves are established for the angle of incidence equal to the Brewster angle of the seeding photonic crystal. It is shown, in particular, that, in the region of the continuous transmission spectrum of the spolarized waves, there arises an additional bandgap caused by mixing of the resonant mode with photonic modes.     

Investigation of one-dimensional photonic crystals composed of dispersive materials

One-dimensional photonic crystals (1DPCs) composed of dispersive materials (including negative refractive index materials, negative μ materials, and negative ? materials) are proposed. The dependence of the band gaps on the angle of incidence and thickness scale are investigated by using the transfer matrix method. Simulation results show that the band gaps of these dispersive material 1DPC are insensitive to the thickness scale. The defect modes of these doped 1DPCs behave specially when the thickness of the defect layer, the angle of incidence and the thickness scale of PC change.     

Photonic band gap and defect mode from a layered periodic structure with anisotropic nonmagnetic right-handed and left-handed metamaterials

We demonstrate a photonic band gap (PBG) from a layered periodic structure containing anisotropic nonmagnetic right-handed and left-handed metamaterials whose permittivity elements are partially negative. A set of criteria imposed on materials and structures to realize a PBG is derived, and the transmission spectra are also discussed. When a defect layer is introduced, some unusual properties are found in contrast to that of a defect mode in ordinary PBG structures.     

Investigation of defect modes in a defective photonic crystal with a semiconductor metamaterial defect

In this work, we theoretically investigate the properties of defect modes in a defective photonic crystal containing a semiconductor metamaterial defect. We consider the structure, (LH)^N/D^P/(LH)^N, where N and P are respectively the stack numbers, L is SiO₂, H is InP, and defect layer D is a semiconductor metamaterial composed of Al-doped ZnO (AZO) and ZnO. It is found that, within the photonic band gap, the number of defect modes (transmission peaks) will decrease as the defect thickness increases, in sharp contrast to the case of using usual dielectric defect. The peak height and position can be changed by the variation in the thickness of defect layer. In the angle-dependent defect mode, its position is shown to be blue-shifted as the angle of incidence increases for both TE and TM waves. The analysis of defect mode provides useful information for the design of tunable transmission filter in semiconductor optoelectronics.     

Tunable plasmon-induced transparency based on asymmetric H-shaped graphene metamaterials

We propose and numerically demonstrate a tunable plasmon-induced transparency(PIT) phenomenon based on asymmetric H-shaped graphene metamaterials. The tunable PIT effect is realized through varying the applied polarization angles rather than changing the structure geometry. By simply adjusting the polarization angle, the transmission spectra can be controlled between the switch-on state and switch-off state. The physical mechanism of the induced transparency is revealed from magnetic dipole inductive coupling and phase coupling. Importantly, by varying the Fermi energy of the graphene or the refractive index of the substrate, the resonant position of the PIT can be dynamically controlled and the maximum modulation depths can reach up to 60.7%. The sensitivity(nm/RIU) of the graphene structure, which is the shift of resonance wavelength per unit change of refractive index, is 5619.56 nm/RIU. Moreover, we also extend our research to the x-axis symmetric H-shaped structure, and the tunable PIT transmission window can also be realized. The physical mechanism of the induced transparency is revealed from the electric dipole hybridization coupling. Our designed H-shaped graphene-based structures is a promising candidate for compact elements such as tunable sensors, switches and slow-light devices.     

Wide angular range operation of a dielectric multilayer film with a photonic-crystal-type defect

Light can tunnel through a high-reflectivity dielectric multilayer film when a photonic-crystal-type defect is introduced in the structure, which is useful for optical signal processing. We consider chirped structures with a defect in layer thickness for which high reflectivity is achieved over a broad wavelength range except within a narrow spectral window. The useful transmission window, while it shifts toward shorter wavelengths as the angle of incidence of the light beam is increased, does not, in general, survive; i.e., transmission disappears progressively. We show that wide angular range operation can, however, be achieved by a proper design of the chirped structure. Analytical expressions for the design parameters are derived on the basis of a semi-infinite photonic crystal model. Theoretical reflectance spectra of defect SiO2/TiO2 chirped multilayer films are presented and discussed in terms of the dispersion of the electromagnetic radiation modes of the finite photonic crystal. These devices offer a simple way to mechanically tune (through inclination of the film) the wavelength transmitted from a fixed white-light beam.     

含负折射率介质非线性Bragg腔的双稳态特性

研究了含负折射率介质一维光子晶体非线性Bragg腔的透射特性、光学增强和双稳态特性.对负折射率介质无色散和有色散非线性Bragg腔及由两种正折射率介质构成的非线性Bragg腔的透射谱、光学增强、缺陷模的线宽、入射光的红移量、双稳态开关阈值进行了比较.含负折射率介质的非线性Bragg腔可显著增大腔内光学增强效应，降低缺陷模的线宽、入射光的红移量和双稳态开关阈值.     

含负折射率材料的一维光子晶体缺陷模式的研究

采用光学传输矩阵方法,研究了由正折射率材料和负折射率材料交替组成的一维光子晶体中带有缺陷层时的光学传输特性.计算了含有普通电介质插层和有吸收的介质插层两种情况下的透射谱.结果表明,在正入射时,对于普通电介质插层,随插层厚度的增大,缺陷模的个数增多;对于有吸收特性的介质插层,随插层厚度的增大和吸收特性的增强,缺陷模式并没有出现,而是表现为对透射峰的明显增益.     

Influence of the polarization and optical axis on the transmission behavior in a one dimensional photonic crystal containing uniaxial metamaterial

In this letter, we introduce a one-dimensional photonic crystal (1DPC) structure with a uniaxial metamaterial defect layer. It is proposed to control the transmitted wave of the defect mode by adjusting the orientation of the optical axis and incidence angle for both polarization states. The 4 × 4 transfer matrix method was employed to calculate the transmittance spectrum of the proposed structure. It is shown that the photonic band gaps, the intensity and the peak wavelength of the defect mode depends on the polarization, the orientation of the optical axis and the incidence angle of the wave, due to the strong anisotropy of the metamaterial. The transmittance spectrum curves at different optical axes of the uniaxial metamaterial and the distinct incidence angles are illustrated graphically. It is shown that the defect mode appears as a peak in the transmission spectrum. Pronounced contrasts in the intensity, wavelength positions of the defect mode and photonic band gap were demonstrated depending on the incidence angle and the orientation of the optical axis of the uniaxial metamaterial defect layer for both polarizations. Our structure offers a great variety of possibilities for designing and controlling the transmitted intensity of the defect mode.