Confinement of Bloch surface waves in a graphene-based one-dimensional photonic crystal and sensing applications

Bloch surface waves(BSWs) are excited in one-dimensional photonic crystals(Ph Cs) terminated by a graphene monolayer under the Kretschmann configuration. The field distribution and reflectance spectra are numerically calculated by the transverse magnetic method under transfer-matrix polarization, while the sensitivity is analyzed and compared with those of the surface plasmon resonance sensing method. It is found that the intensity of magnetic field is considerably enhanced in the region of the terminated layer of the multilayer stacks, and that BSW resonance appears only in the interface of the graphene and solution. Influences of the graphene layers and the thickness of a unit cell in Ph Cs on the reflectance are studied as well. In particular, by analyzing the performance of BSW sensors with the graphene monolayer,the wavelength sensitivity of the proposed sensor is 1040 nm/RIU whereas the angular sensitivity is 25.1?/RIU. In addition,the maximum of figure of merit can reach as high as 3000 RIU-1. Thus, by integrating graphene in a simple Kretschmann structure, one can obtain an enhancement of the light–graphene interaction, which is prospective for creating label-free,low-cost and high-sensitivity optical biosensors.     

Bloch oscillations in one-dimensional photonic crystal coupled microcavity composed of single-negative materials

We have studied the propagation properties of electromagnetic waves in one-dimensional photonic crystal coupled microcavity structure composed of single-negative materials. Two Wannier-Stark ladders can be obtained by employing only one type of microcavity. The dynamics behavior of a Gaussian pulse transmitting through the structure is simulated theoretically. We demonstrated for the first time that even in this multilayered structure completely made of single-negative materials, the optical Bloch oscillations and Zener tunneling can also be attained.     

Ultrasmall demultiplexer by use of one-dimensional photonic crystal

Silica-based one-dimensional photonic crystal (1D-PC) is fabricated by use of a high-spatial-frequency grating with input and output surfaces tilted with respect to its periodic direction. An incident beam is coupled with the first photonic band in the second Brillouin zone of the 1D-PC. The output beam angle changes 3 degrees with a wavelength change of 1%. A prototype of an ultrasmall demultiplexer is demonstrated by use of a silica slab waveguide with 1D-PC.     

Phase engineering of one-dimensional defective photonic crystal and applications

It is shown in this paper that many new sensitive phase photonic crystal devices will be developed, if some existing problems can be overcome. The main problems are the rapid change of light intensity around the defect mode and the influence of the substrate. The method for overcoming these problems is to construct the defective photonic crystal in a heterostructure or an asymmetric structure. The phase properties of asymmetric one-dimensional photonic crystals with couple defects are revealed in this paper. As examples, a phase modulator and a phase switch with very high sensitivity are demonstrated. PACS 42.70.Qs; 42.79.-e; 42.60.Da; 74.62.Dh     

New regions of diffraction reflection in apodized one-dimensional photonic crystals with a large modulation depth

The specific features of light transmission in a cholesteric liquid crystal (LC) cell with a director rotated by 90° have been investigated. In this structure, where a light wave is incident at a large angle with respect to the LC surface, the light is reflected (refracted) in the LC layer near the opposite boundary. It is shown that the application of an electric field changes the character of extraordinary wave refraction, as a result of which light starts passing through a cell. The transmission threshold voltage is determined, and its dependence on the angle of incidence of light is obtained. The dependence of the transmitted-light intensity on the voltage across the cell is obtained as well. The same dependences are also derived by numerical calculations with allowance for the turning points and extinction.     

Phase control of group velocity in one-dimensional photonic crystal with a dispersive defect layer

Propagation of an electromagnetic pulse through one-dimensional photonic crystal doped with three-level ο-type atomic systems is discussed. It is found that in the presence of quantum interference and incoherent pump, the transmitted pulse becomes completely phase dependent. So, the group velocity of the transmitted pulse can be switched from subluminal to superluminal light propagation just by adjusting the relative phase of applied fields.     

Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal

Dispersion curves of surface electromagnetic waves (SEWs) in 1D silicon nitride photonic crystals having periodic surface corrugations are considered. We experimentally demonstrate that a bandgap for SEWs can be obtained by fabricating a polymeric grating on the multilayered structure. Close to the boundary of the first Brillouin zone connected to the grating, we observe the splitting of the SEW dispersion curve into two separate branches and identify two regions of very low group velocity. The proper design of the structure allows the two folded branches to lie beyond the light line in a wide spectral range, thus doubling the density of modes available for SEWs and avoiding light scattering.     

Method of measuring one-dimensional photonic crystal period-structure-film thickness based on Bloch surface wave enhanced Goos-Hänchen shift

This paper puts forward a novel method of measuring the thin period-structure-film thickness based on the Bloch surface wave (BSW) enhanced Goos-Hänchen (GH) shift in one-dimensional photonic crystal (1DPC). The BSW phenomenon appearing in 1DPC enhances the GH shift generated in the attenuated total internal reflection structure. The GH shift is closely related to the thickness of the film which is composed of layer-structure of 1DPC. The GH shifts under multiple different incident light conditions will be obtained by varying the wavelength and angle of the measured light, and the thickness distribution of the entire structure of 1DPC is calculated by the particle swarm optimization (PSO) algorithm. The relationship between the structure of a 1DPC film composed of TiO₂ and SiO₂ layers and the GH shift, is investigated. Under the specific photonic crystal structure and incident conditions, a giant GH shift, 5.1×10³ times the wavelength of incidence, can be obtained theoretically. Simulation and calculation results show that the thickness of termination layer and periodic structure bilayer of 1DPC film with 0.1-nm resolution can be obtained by measuring the GH shifts. The exact structure of a 1DPC film is innovatively measured by the BSW-enhanced GH shift.     

Back-propagating surface polaritons of a one-dimensional photonic crystal containing single negative metamaterials

The existence of the surface polaritons at the interface separating a semi-infinite uniform left-handed metamaterial and a one-dimensional photonic crystal composed of alternating layers of two kinds of single-negative materials is theoretically investigated. The dispersion characteristics of the surface polaritons are analyzed and demonstrated that in the presence of metamaterial, the surface polaritons are sensitive to light polarization, so that there exist only backward TM-polarized (or TE-polarized) kind of the surface polaritons depending on the ratio of the thicknesses of the two periodic stacking layers. The existence regions of the surface polariton modes are determined for both TM-polarized and TE-polarized surface polariton modes.     

Effect of anisotropy on the photonic band gap and surface polaritons of a one-dimensional single-negative photonic crystal

The effect of anisotropy on the photonic band structure and surface polaritons of a one-dimensional photonic crystal made of uniaxially anisotropic epsilon-negative (ε<0,μ>0) and mu-negative (ε>0,μ<0) metamaterials is theoretically investigated. Two different cases of uniaxially anisotropic epsilon-negative and mu-negative metamaterials are considered. It is found out that for one case of anisotropy, one-dimensional photonic crystal does not have any single-negative band gap. As a result, it can not support the surface polaritons. While, for another case, the structure shows single-negative band gaps. So, the surface polaritons can be excited at the interface of such a photonic crystal. However, these surface polaritons, unlike the isotropic case, are not omnidirectional and they are restricted to a limited rang of the propagation constant.     

Prediction of interface states in liquid surface waves with one-dimensional modulation

We theoretically study the interface states of liquid surface waves propagating over the heterojunctions formed by a bottom with one-dimensional periodic undulations. By considering the periodic structure as a homogeneous one, our systematic study shows that the signs of the effective depth and gravitational acceleration are opposite within the band gaps whether the structure is symmetric or not. Those effective parameters can be used to predict the interface states which could amplify the amplitudes of liquid surface waves. These phenomena provide new opportunities to control the localization of water-wave energy.     

Wave propagation in a one-dimensional photonic crystal with metamaterial

This paper deals with the study of the transmission of electromagnetic waves through a one-dimensional multilayer periodic structure consisting of alternating slabs of negative- and positive-index media. It also focuses on the behavior of the transmission with the angle of incidence for both polarizations. The proposed structure works as a tunable p-polarization filter i.e. a filter which completely blocks the s-polarized wave but partially allows the p-polarized wave to pass through it for an angle of incidence greater than 20 ^°. For angles of incidence less than 50 ^° the structure works as a tunable edge filter.     

Magneto-optical activity of a one-dimensional photonic crystal with a magnetic defect

The influence of a magnetic defect on the field distribution and magneto-optical properties of a one-dimensional photonic crystal has been investigated. It has been shown that the maximum localization of the wave field in the defect layer is achieved in an asymmetric photonic crystal structure. A greater Faraday rotation, which significantly exceeds the angle of rotation of the polarization plane in an isolated magnetized layer, and a higher degree of localization of the wave field can be achieved when the magnetic layer is surrounded by layers of photonic crystal mirrors with a lower refractive index. An increase in the Faraday rotation angle is determined not only by an increase in the thickness of the magnetic defect but also by a symmetric increase in the number of periods in the photonic crystal mirrors.     

Spectral properties of a one-dimensional resonant photonic crystal

The eigenexcitation and transmission spectra of a one-dimensional resonant photonic crystal are studied for TM and TE polarized electromagnetic waves. The crystal considered is a layered structure consisting of alternating isotropic layers and layers of a resonantly absorbing gas. The performed calculations show that the band structure of the spectra of the resonant photonic crystal significantly changes as the angle of incidence and the density of the resonant gas are varied. The structure of the spectra of additional transmission in the bandgap of the resonant photonic crystal is studied taking into account the decay of electromagnetic modes. The possibilities of controlling the spectrum of electromagnetic modes are indicated.

     

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.     

Dispersion and attenuation of Rayleigh waves at a one-dimensional random roughness of the free surface of a hexagonal crystal

Analytical expressions are derived for dispersion and attenuation of Rayleigh waves propagating along the statistically rough free surface of a hexagonal crystal (Z cut). The roughness under consideration is one-dimensional (the profile function of the roughness depends on one coordinate) and has the form of hollows of a random lattice. The results obtained earlier in the solution of an analogous problem for a two-dimensional roughness are used in the one-dimensional case. The relationships derived for the dispersion and attenuation of Rayleigh waves are treated analytically and numerically over the entire range of frequencies acceptable in the framework of the perturbation theory. It is shown that the dispersion and attenuation of Rayleigh waves are qualitatively similar to those observed in an isotropic medium.     

Propagation of surface magnetostatic waves in a one-dimensional magnon crystal of a variable thickness

The propagation of surface magnetostatic waves in a ferromagnetic film of variable thickness having a planar periodic structure in the form of a grating of etched parallel strips (one-dimensional magnon crystal) has been investigated. The dispersion characteristics of surface magnetostatic waves have been calculated using the Wentzel-Kramers-Brillouin method. The intrinsic error of the method has been estimated, and the magnon spectrum of the surface magnetostatic wave has been studied. An analysis of the dispersion characteristics and the transmission capacity of these structures has demonstrated that they can be used for designing narrow-band and comb filters.     

Density of states of a one-dimensional disordered photonic crystal

An analytic theory of the density of states in one-dimensional disordered photonic crystals is proposed. It is shown that the problem of the density of optical modes can be reduced in the small dielectric contrast approximation to solving a generalized Fokker-Planck equation for the distribution function of the logarithmic derivative of the electric field (the wave phase). The exact analytic solution and density-of-states asymptotics deep in the band gap of the photonic crystal and close to the band gap edge are derived. The results obtained agree well with the empirical relations derived earlier from numerical experiments.     

Surface states in the one-dimensional model of a crystal with an arbitrary potential at the boundary

The approximate formula for the number of surface states and the approximate equation for its energy values has been obtained for the model of a one-dimensional semi-infinite crystal with an arbitrary potential at the boundary and the Kronig-Penney-type potential inside the crystal.     

Temperature and external field-driven microrelief at free surface of smectic-A liquid crystal

A homeotropically oriented smectic-A film on a solid substrate with periodical microrelief is considered. Periodical distortions of the free surface of the film induced by this microrelief are theoretically investigated. The dependence of these distortions on the film thickness, the temperature, and external magnetic (electric) field is obtained. It is shown that, for a certain choice of the shape of the substrate surface microrelief, one can realize a temperature and external magnetic (electric) field control on the microrelief at the free surface of the smectic-A film.