We studied the optical properties of a dielectric photonic crystal structure with spirals arranged in a hexagonal lattice. The dielectric constant of the material is 9 and the filling ratio is 15.2%. We found that this kind of structure exhibits a significant polarization gap for light incident along the axis of the spirals. The eigenmodes inside the polarization gap are right-hand (left-hand) circularly polarized depending on the whether the spirals are left-handed (right-handed). The transmission spectrum of a slab of such a structure has been calculated and matches well with the analysis of the eigenmodes.
We present a numerical study on photonic bandgap and bandedge modes in the golden-angle spiral array of air cylinders in dielectric media. Despite the lack of long-range translational and rotational order, there is a large PBG for the TE polarized light. Due to spatial inhomogeneity in the air hole spacing, the bandedge modes are spatially localized by Bragg scattering from the parastichies in the spiral structure. They have discrete angular momenta that originate from different families of the parastichies whose numbers correspond to the Fibonacci numbers. The unique structural characteristic…
We introduce a novel optimization method to design the first examples of photonic quasicrystals with substantial, complete photonic band gaps (PBGs): that is, a range of frequencies over which electromagnetic wave propagation is forbidden for all directions and polarizations. The method can be applied to photonic quasicrystals with arbitrary rotational symmetry; here, we illustrate the results for 5- and 8-fold symmetric quasicrystals. The optimized band gaps are highly isotropic, which may offer advantages over photonic crystals for certain applications.
We present designs of 2D isotropic, disordered photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest gaps are obtained by a constrained optimization method that starts from a hyperuniform disordered point pattern, an array of points whose number variance within a spherical sampling window grows more slowly than the volume. We argue that hyperuniformity, combined with uniform local topology and short-range geometric order, can explain how complete photonic band gaps are possible without long-range translational order…
We explore the effects of random link removal on the photonic band gaps of honeycomb networks. Missing or incomplete links are expected to be common in practical realizations of this class of connected network structures due to unavoidable flaws in the fabrication process. We focus on the collapse of the photonic band gap due to the defects induced by the link removal. We show that the photonic band gap is quite robust against this type of random decimation and survives even when almost 58% of the network links are removed.
Recently, a silicon micromachining method to produce tetrahedral silicon particles was discovered. In this report we determine, using band structure calculations, the optical properties of diamond-lattice photonic crystals when assembled from such particles. We show that crystal structures built from silicon tetrahedra are expected to display small stop gaps. Wide photonic band gaps appear when truncated tetrahedral particles are used to build the photonic crystals. With truncated tetrahedral particles a band gap with a width of 23.6% can be achieved, which is more than twice as wide compared …
Based on the rigorous generalized Mie theory solution of Maxwell's equations for dielectric cylinders we theoretically investigate the optical properties of two-dimensional deterministic structures based on the Fibonacci, Thue-Morse and Rudin-Shapiro aperiodic sequences. In particular, we investigate band-gap formation and mode localization properties in aperiodic photonic structures based on the accurate calculation of their Local Density of States (LDOS). In addition, we explore the potential of photonic structures based on aperiodic order for the engineering of radiative rates and emission …
In this work we show theoretically that it is possible to design a large band gap in the infrared range using a one-dimensional Photonic Crystal heterostructure made of porous silicon. Stacking together multiple photonic crystal substructures of the same contrast index, but of different lattice periods, it is possible to broad the narrow forbidden band gap that can be reached by the low contrast index of the porous silicon multilayers. The main idea in this work is that we can construct a Giant Photonic Band Gap -as large as desired- by combining a tandem of photonic crystals substructures by …
The effects of electric and magnetic loss factors on zero-mu and zero-epsilon gaps in a one-dimensional lossy photonic crystal composed of double-negative and double-positive materials are theoretically investigated by employing the characteristic matrix method. This study contradicts the previous reports as it indicates that by applying the inevitable factors of electric and magnetic losses to the double-negative material, the zero-mu and zero-epsilon gaps appear simultaneously in the transmission spectrum, being independent of the incidence angle and polarizations. Moreover, the results show…
In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed …
We present, theoretically and experimentally, amorphous photonic lattices exhibiting a band-gap yet completely lacking Bragg diffraction: 2D waveguides distributed randomly according to a liquid-like model responsible for the absence of Bragg peaks as opposed to ordered lattices containing disorder, which always exhibit Bragg peaks. In amorphous lattices the bands are comprised of localized states, but we find that defect states residing in the gap are more localized than the Anderson localization length. Finally, we show how the concept of effective mass carries over to amorphous lattices.
In this paper, theoretically, the characteristics matrix method is employed to investigate and compare the properties of the band gaps of the one-dimensional ternary and binary lossy photonic crystals which are composed of double-negative and -positive materials. This study shows that by varying the angle of incidence, the band gaps for TM and TE waves behave differently in both ternary and binary lossy structures. The results demonstrate that by increasing the angle of incidence for the TE wave, the width and the depth of zero-n, zero-μ, and Bragg gap increase in both ternary and binary struc…
We study a hybrid system consisting of a narrowband atomic optical resonance and the long-range periodic order of an opaline photonic nanostructure. To this end, we have infiltrated atomic cesium vapor in a thin silica opal photonic crystal. With increasing temperature, the frequencies of the opal's reflectivity peaks shift down by >20% due to chemical reduction of the silica. Simultaneously, the photonic bands and gaps shift relative to the fixed near-infrared cesium D1 transitions. As a result the narrow atomic resonances with high finesse (f/df=8E5) dramatically change shape from a usual di…
We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability μor the electric permittivity εof the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when μ= 0 or when ε= 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to μ= 0 occurs only for TE polarized waves, whereas a gap correspond…
We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton like) resonator gap in the dispersion relation. The origin and physical significance of the two types of gaps are discussed. The coupled-mode equations derived from the effective field formalism are valid deep within the Bragg gaps and resonator gaps.
Vortices are whirling disturbances commonly found in nature ranging from tremendously small scales in Bose-Einstein condensates to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a resu…
Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency-dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency-dependent property of topol…
We identify different types of the photonic band gaps (PBGs) of two dimensional magnetic photonic crystals (MPCs) consisting of arrays of magnetic cylinders and study the different tunability (by an external static magnetic field) of these PBGs. One type of the band gaps comes from infinitely degenerate flat bands and is closely related to those in the study of plasmonics. In addition, such PBGs are magnetically tunable and robust against position disorder. We calcualte the transmission of the PBG's and found excellent agreement with the results of the photonic band structure calculation. Posi…
We study the direction- and wavelength-dependent polarization anisotropy in light scattering at the air-photonic crystal interface as a function of angle of incidence for TE and TM polarized light. This is done using optical reflectivity measurements at high-symmetry points in the Brillouin zone of a three-dimensional photonic crystal with fcc symmetry. Polarized reflectivity measurements indicate the presence of stop gap branching for TE polarization, which is absent for TM polarization till the Brewster angle at K point. In contrast, stop gap branching is present for both TE and TM polarizat…
We propose a microscopic model to describe the scattering of light by atoms in optical lattices. The model is shown to efficiently capture Bragg scattering, spontaneous emission and photonic band gaps. A connection to the transfer matrix formalism is established in the limit of a one-dimensional optical lattice, and we find the two theories to yield results in good agreement. The advantage of the microscopic model is, however, that it suits better for studies of finite-size and disorder effects.
A plasmonic nanostructure conceived with periodic layers of a doped semiconductor and passive semiconductor is shown to generate spontaneously surface plasmon polaritons thanks to its periodic nature. The nanostructure is demonstrated to behave as an effective material modeled by a simple dielectric function of ionic-crystal type, and possesses a fully tunable photonic band gap, with widths exceeding 50%, in the region extending from mid-infra-red to Tera-Hertz.
We present a systematic study of photonic band gaps (PBGs) in three-dimensional (3D) photonic amorphous structures (PAS) with short-range order. From calculations of the density of optical states (DOS) for PAS with different topologies, we find that tetrahedrally connected dielectric networks produce the largest isotropic PBGs. Local uniformity and tetrahedral order are essential to the formation of PBGs in PAS, in addition to short-range geometric order. This work demonstrates that it is possible to create broad, isotropic PBGs for vector light fields in 3D PAS without long-range order.
We experimentally investigate the Bragg reflection of light at one-dimensionally ordered atomic structures by using cold atoms trapped in a laser standing wave. By a fine tuning of the periodicity, we reach the regime of multiple reflection due to the refractive index contrast between layers, yielding an unprecedented high reflectance efficiency of 80%. This result is explained by the occurrence of a photonic band gap in such systems, in accordance with previous predictions.
In this paper we analyze theoretically how the introduction of the third component into the two-dimensional photonic crystal influences the photonic band structure and the density-of-states of the system. We consider the periodic array of cylindrical air rods in a dielectric, and the third medium is introduced as a ring-shaped intermediate layer between the air pores and the dielectric background. Using the plane wave method, we have obtained the band structures for the 2D triangular lattice photonic crystals. The dependencies of TE and TM band gaps' widths and gaps' edges position on the inte…
Zak phase labels the topological property of one-dimensional Bloch Bands. Here we propose a scheme and experimentally measure the Zak phase in a photonic system. The Zak phase of a bulk band of is related to the topological properties of the two band gaps sandwiching this band, which in turn can be inferred from the existence or absence of an interface state. Using reflection spectrum measurement, we determined the existence of interface states in the gaps, and then obtained the Zak phases. The knowledge of Zak phases can also help us predict the existence of interface states between a metasur…
We study the density of states (DOS) in band gaps of ideal and disordered three-dimensional photonic crystals of finite size. The ideal crystal is a diamond lattice of resonant point scatterers (atoms) whereas the disordered one is obtained from it by displacing the scatterers by random distances in random directions. We find that DOS inside a band gap of the ideal crystal decreases as the inverse of the crystal size. Disorder narrows the band gap and DOS exhibits enhanced fluctuations near the new band edges. However, the average DOS still exhibits the same scaling with the crystal size withi…
Using the Floquet Hamiltonian derived based on the time-dependent perturbation theory, we investigated the quasienergy bands of a one-dimensional time-Floquet photonic crystal. The time-Floquet photonic crystal contains two alternating layers labeled as A and B, and the permittivity of A layer is modulated periodically in time. We showed that the quasienergy bands are reciprocal when the modulation function is a function of time only, while the quasienergy bands could be nonreciprocal when the permittivity is modulated in both time and space through an unique combination. In the former case, t…
We show theoretically that, in the limit of weak dispersion, one-dimensional (1D) binary centrosymmetric photonic crystals can support topological edge modes in all photonic band gaps. By analyzing their bulk band topology, these "harmonic" topological edge modes can be designed in a way that they exist at all photonic band gaps opened at the center of the Brillouin Zone, or at all gaps opened at the zone boundaries, or both. The results may suggest a new approach to achieve robust multi-frequency coupled modes for applications in nonlinear photonics, such as frequency up-conversion.
Dirac points, new photonic band gaps and effect of magnetically induced transparency in dichroic cholesteric liquid crystals with wavelength dependent magnetooptical activity parameter
By exploiting the concepts of magnetic group theory we show how unidirectional behavior can be obtained in two-dimensional magneto-photonic crystals (MOPhC) with uniform magnetization. This group theory approach generalizes all previous investigations of one-way MOPhCs including those based on the use of antiparallel magnetic domains in the elementary crystal cell. Here, the theoretical approach is illustrated for one MOPhC example where unidirectional behavior is obtained by appropriately lowering the geometrical symmetry of the elementary motifs. One-way transmission is numerically demonstra…
Photonic components based on structured metallic elements show great potential for device applications where field enhancement and confinement of the radiation on a subwavelength scale is required. In this paper we report a detailed study of a prototypical metallo-dielectric photonic structure, where features well known in the world of dielectric photonic crystals, like band gaps and defect modes, are exported to the metallic counterpart, with interesting applications to infrared science and technology, as for instance in quantum well infrared photodetectors, narrow-band spectral filters, and …
Ordinary metallic photonic crystals (PCs) have photonic band gaps in which the density of states (DOS) is strongly modified. Thermal emission of photons can be suppressed and enhanced accordingly. We consider the thermal emission characteristics of a metallic photonic crystal slab with a tunable thickness which in the thick limit approaches that of a photonic crystal and in the thin limit approaches that of a textured surface. We find that a thick photonic crystal suppresses emission in a specific range while a thin slab suppresses low frequency emission.
Interface states in a 1-D photonic crystal heterostructure with multiple interfaces are examined. It is found that the behavior of the localized modes in the photonic band gaps is dependent on whether there is an even or odd number of photonic crystal interfaces in the heterostructure. With certain sequences of all dielectric photonic crystals, topological states are shown to split in two, whereas for other heterostructures they are shown to vanish. Additional resonant modes appear depending on how many crystals are in the heterostructure.
We study photonic band gap formation in two-dimensional high refractive index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropi…
Here, we present a mechanism for tailoring the photonic band structure of a quarter-wave stack without changing its physical periods by embedding conductive sheets. Graphene is utilized and studied as a realistic, two-dimensional conductive sheet. In a graphene-embedded quarter-wave stack, the synergic actions of Bragg scattering and graphene conductance contributions open photonic gaps at the center of the reduced Brillouin zone, that nonexistent in conventional quarter-wave stacks. Such photonic gaps show giant, loss-independent density of optical states at the fixed lower-gap-edges, of even…
Photonic band gaps for the soft x-rays, formed in the periodic structures of solids or dense plasmas, are theoretically investigated. Optical manipulation mechanisms for the soft x-rays, which are based on these band gaps, are computationally demonstrated. The reflection and amplification of the soft x-rays, and the compression and stretching of chirped soft x-ray pulses are discussed. A scheme for lasing with atoms with two energy levels, utilizing the band gap, is also studied.
Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the first experimental realization of an isotropic complete photonic band gap (PBG) in a two-dimensional (2D) disordered dielectric structure. This structure is designed by a constrained-optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design co…
The existence of topological interface states is investigated at the boundary between a binary photonic crystal and a quaternary photonic crystal, with each possessing inversion symmetric unit cells. Conditions are established that describe where the quaternary crystal can exist in parameter space subject to constraints. The closing of band gaps is discussed for different optical path ratios. When the binary and quaternary crystals share an interface, optical states appear at the interface when the two crystals have different signs for the surface impedance. The evolution of the states is disp…
We theoretically study light propagation in guided Bloch surface waves (BSWs) supported by photonic crystal ridges. We demonstrate that low propagation losses can be achieved just by a proper design of the multilayer to obtain photonic band gaps for both light polarizations. We present a design strategy based on a Fourier analysis that allows one to obtain intrinsic losses as low as 5 dB/km for a structure operating in the visible spectral range. These results clarify the limiting factors to light propagation in guided BSWs and represent a fundamental step towards the development of BSW-based …
We study the bandgap properties of two-dimensional photonic crystals created by a lattice of rods or holes conformed in a symmetric or asymmetric triangular structure. Using the plane-wave analysis, we calculate a minimum value of the refractive index contrast for opening both partial and full two-dimensional spectral gaps for both TM and TE polarized waves. We also analyze the effect of ellipticity of rods and holes and their orientation on the threshold value and the relative size of the bandgap.
Photonic time-crystals (PTCs) are spatially-homogeneous media whose electromagnetic (EM) susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by gaps (rather than energy bands and gaps, as in photonic crystals). Here, we show that a free electron moving in a PTC spontaneously emits radiation, and, when associated with momentum-gap modes, the radiation of the electron is exponentially amplified by the mo…
We analyze the existence, stability, and mobility of gap solitons in a periodic photonic structure with nonlocal nonlinearity. Within the Bragg region of band gaps, gap solitons exhibit better stability and higher mobility due to the combinations of non-locality effect and the oscillation nature of Bloch waves. Using linear stability analysis and calculating the Peierls-Nabarro potentials, we demonstrate that gap solitons can revive a non-trivial elastic-like collision even in the periodic systems with the help of nonlocal nonlinearity. Such interesting behaviors of gap solitons in nonlocal no…
The optical properties of photonic structures made with more than two materials are very interesting for optical filtering and lighting applications. Herein, we compared the transmission properties of one-dimensional photonic crystals made with three, four and five materials, showing that, with a photonic crystal made of t different materials, the band gap splits in t-1 bands. The same optical thickness for the different materials layers results in split photonic band gaps with the same intensity. Photonic crystals with more than two materials result in a simple structure that could be used fo…
In this report we present an investigation of the optical properties and band structure calculations for the photonic structures based on the functional materials- ferroelectrics. A theoretical approach to the optical properties of the 2D and 3D photonic crystals which yields further insight in the phenomenon of the reflection from different families of lattice planes in relation to the presence of photonic gaps or photonic bands. We calculate the photonic bands and optical properties of LiNbO3 based photonic crystals. Calculations of reflection and transmission spectra show the features corre…
