Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appear when the lattice intensity at the defect site is {\em non-zero} rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.
We experimentally demonstrate a type of waveguiding mechanism for coupled surface-wave defect modes in a surface-wave photonic crystal. Unlike conventional spoof surface plasmon waveguides, waveguiding of coupled surface-wave defect modes is achieved through weak coupling between tightly localized defect cavities in an otherwise gapped surface-wave photonic crystal, as a classical wave analogue of tight-binding electronic wavefunctions in solid state lattices.
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 …
Specific features of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic defect, as well as their photonic density of states, Q factor, and emission, have been investigated. The effect of the thicknesses of the defect layer and the system as a whole, the position of the defect layer, and the dielectric boundaries on the features of the defect modes have been analyzed.
We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in the defected photonic lattices. The propagation properties and beam self-bending are controlled with modulation depth and period of the photonic lattices, positive and negative defects, beam distribution factor and nonlinearity change. For positive defects, the pseudo-period oscillation and localization of the AiG beam may be formed under a certain condition, while the beam is diffused for negative defects. Moreover, the solitons may appear during the propagation process when the self-focusing …
The aim of this paper is to present the analysis of influence of defects in 1D photonic crystal (PC) on the density of states and simultaneously spontaneous emission, in both spatial and frequency domains. In our investigations we use an analytic model of 1D PC with defects. Our analysis reveals how presence of a defect causes a defect mode to appear. We show that a defect in 1D PC has local character, being negligible in regions of PC situated far from the defected elementary cell. We also analyze the effect of multiple defects, which lead to photonic band gap splitting.
Some properties of defect modes of cholesteric liquid crystals (CLC) are presented. It is shown that when the CLC layer is thin the density of states and emission intensity are maximum for the defect mode, whereas when the CLC layer is thick, these peaks are observed at the edges of the photonic band gap. Similarly, when the gain is low, the density of states and emission intensity are maximum for the defect mode, whereas at high gains these peaks are also observed at the edges of the photonic band gap. The possibilities of low-threshold lasing and obtaining high-Q microcavities have been inve…
We have theoretically investigated a general function photonic crystals (GFPCs) with defect layer, and choose the line refractive index function for two mediums $A$ and $B$, and analyze the effect of defect layer's position, refractive indexes and period numbers on the transmission intensity and the electric field distribution. We obtain some new characters that are different from the conventional PCs, which should be helpful in the design of photonic crystals.
We predict that interfaces of modulated photonic lattices can support a novel type of generic surface states. Such linear surface states appear in truncated but otherwise perfect (defect-free) lattices as a direct consequence of the periodic modulation of the lattice potential, without any embedded or nonlinearity-induced defects. This is in a sharp contrast to all previous studies, where surface states in linear or nonlinear lattices, such as Tamm or Shockley type surface states, are always associated with the presence of a certain type of structural or induced surface defect.
In this paper, the characteristic matrix method is employed to theoretically investigate the propagation of electromagnetic waves through one-dimensional defective lossy photonic crystals (PCs) composed of negative index materials (NIMs) and positive index materials (PIMs). We consider symmetric and asymmetric geometric structures with two different types of NIM defect layers at the center of the structure. The effects of the polarization and the angle of incidence on the defect modes in the transmission spectra of both structures are investigated. The results show that the number of the defec…
We propose an improved structure of an optical biosensor based on a photonic crystal (PC) with a defect layer (DL), which can detect the concentration of SARS-CoV-2 in water by defect mode (DM) shift. We investigated 4 types of defective PCs with different arrangements of layers inside the perfect PCs and their impact on the performance of the sensor. The sensitivity and amplitude of DM were examined as a function of DL thickness. Also, the peculiarities of edge modes in the presence of DL were investigated. Finally, we obtained a characteristic equation to determine the wavelengths of DMs for…
We demonstrate that twisting one part of a chiral photonic structure about its helical axis produces a single circularly polarized localized mode that gives rise to an anomalous crossover in propagation. Up to a crossover thickness, this defect results in a peak in transmission and exponential scaling of the linewidth for a circularly polarized wave with the same handedness as structure. Above the crossover, however, the linewidth saturates and the defect mode can be excited only by the oppositely polarized wave, resulting in a peak in reflection instead of transmission.
We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of bandgaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing non-linear effects and light-matter interactions in structured fibers.
We propose a novel method to generate vector beams in planar photonic crystal cavities with multiple missing-hole defects. Simulating the resonant modes in the cavities, we observe that the optical fields in each defect have different phase and polarization state distributions, which promise the compositions of vector beams by the scattered light from the defects. The far-field radiation patterns of the cavity modes calculated via the Sommerfeld diffraction theory present vector beams possessing hollow intensity profiles and polarization singularities. In addition, the extraction efficiencies …
Structured materials like photonic crystals require for optimal use a high precision both on position and optical characteristics of the components which they are made of. Here, we present a simple tomographic algorithm, based on a specific Green's function together with a first-order Born approximation, which enables us to localize and characterize identical defects in finite-size photonic crystals. This algorithm is proposed as a first step to the monitoring of such materials. Illustrative numerical results show in particular some possibility of focalization beyond the Rayleigh criterion.
The use of an optically thick slab may provide versatile solutions for the realization of a current injection type laser using photonic crystals. Here, we show that a transversely higher-order defect mode can be designed to be confined by a photonic band gap in such a thick slab. Using simulations, we show that a high-Q of 10^5 is possible from a finely tuned second-order hexapole mode. Experimentally, we achieve optically pumped pulsed lasing at 1347 nm from the second-order hexapole mode with a peak threshold pump power of 88 uW.
The polarization properties of perfectly periodical and defective one-dimensional photonic bandgap structures with nonreciprocal chiral (bi-isotropic) layers are studied. The method of solution is based on the 2x2-block-representation transfer-matrix formulation. Numerical simulations are carried out for different type of structures (symmetrical or asymmetrical) in order to reveal the dependence of the reflection and transmission coefficients on frequency, chirality, nonreciprocity parameters, and the angle of wave incidence.
Current quantum cascade lasers based upon conduction band electron transitions are predominantly TM (electrical field normal to the epitaxial direction) polarized. Here we present a study of localized defect modes, with the requisite TM polarization, in connected square and hexagonal lattice two-dimensional (2D) photonic crystals for application as quantum cascade laser resonators. A simple group-theory based analysis is used to produce an approximate description of the resonant modes supported by defects situated at different high symmetry points within the host photonic lattice. The results …
We propose and experimentally demonstrate a tunable band-notched line-defect waveguide in a surface-wave photonic crystal, which consists of a straight line-defect waveguide and side-coupled defect cavities. A tunable narrow stopband can be observed in the broadband transmission spectra. We also demonstrate that both the filtering levels and filtering frequencies of the band-notched line-defect waveguide can be conveniently tuned through changing the total number and the pillar height of the side-coupled defect cavities. The band-notch function is based on the idea that the propagating surface…
In this article, localized linear defect modes due to bandgap guidance in two-dimensional photonic lattices with localized or non-localized defects are investigated theoretically. First, when the defect is localized and weak, eigenvalues of defect modes bifurcated from edges of Bloch bands are derived analytically. It is shown that in an attractive (repulsive) defect, defect modes bifurcate out from Bloch-band edges with normal (anomalous) diffraction coefficients. Furthermore, distances between defect-mode eigenvalues and Bloch-band edges are exponentially small functions of the defect streng…
We demonstrate how to achieve reversible nonreciprocal optical response in a periodic photonic structure with a pair of defects, one of them being a nonlinear liquid crystal defect layer. The twin defect layers structure is symmetric at low intensity and becomes asymmetric above a power threshold corresponding to the optical reordering of the liquid crystal. We show that nonreciprocal effects can be reversed by changing the wavelength as a consequence of the defect mode dependent light localization inside the structure.
Electromagnetic topological insulators have been explored extensively due to the robust edge states they support. In this work, we propose a topological electromagnetic system based on a line defect in topologically nontrivial photonic crystals (PCs). With a finite-difference supercell approach, modal analysis of the PCs structure is investigated in detail. The topological line-defect states are pseudospin polarized and their energy flow directions are determined by the corresponding pseudospin helicities. These states can be excited by using two spatially-symmetric line-source arrays carrying…
Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of $\sim$$3(λ/n)^{3}$. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical…
We have studied spectral properties of a cholesteric liquid crystal with a combined defect consisting of a nanocomposite layer and a twist. The nanocomposite layer is made of metallic nanoballs dispersed in a transparent matrix and featuring effective resonant permittivity. A solution has been found for the transmission spectrum of circularly polarized waves in the structure. We have analyzed spectral splitting of the defect mode in the bandgap of the cholesteric when its frequency coincides with the nanocomposite resonant frequency. Defect modes have characteristics strongly dependent on the …
Two dimensional (2D) photonic crystals are well known for its ability to manipulate the propagation of electromagnetic wave inside the crystal. 1D and 2D photonic crystals are relatively easier to fabricate than 3D because the former work in the microwave and far infrared regions whereas the later work in the visible region and requires smaller lattice constants. In this paper, simulation for a modified 2D PC with two symmetric waveguide channels where a defect is located inside one of the channel is performed. The simulation results show that optical switching is possible by modifying the ref…
We demonstrate the dynamics of stimulated Raman scattering in designed high-Q/Vm silicon photonic band gap nanocavities through the coupled-mode theory framework towards optically-pumped silicon lasing. The interplay of other chi(3) effects such as two-photon absorption and optical Kerr, related free-carrier dynamics, thermal effects, as well as linear losses such as cavity radiation and linear material absorption are included and investigated numerically. Our results clarify the relative contributions and evolution of the mechanisms, and demonstrate the lasing and shutdown thresholds. Our stu…
The peculiarities of defect modes and reflection spectra of chiral photonic crystals (CPC) with an isotropic defect for various thicknesses of the defect layer was investigated. The peculiarities of the spectra of photonic density of the state (DOS) and those of the intensity at the center of the defect were investigated, too. It was shown that there is one more possibility of tuning of laser emission - by the change of the defect layer thickness - in CPCs doped with laser dyes (with resonance atoms) and with an isotropic defect. It was shown that the given system can work as a tunable narrow-…
We introduce topological defect to a square lattice of elliptical cylinders. Despite the broken translational symmetry, the long-range positional order of the cylinders leads to residual photonic bandgap in the density of optical states. However, the band-edge modes are strongly modified by the spatial variation of ellipse orientation. The $Γ-X$ band-edge mode splits into four regions of high intensity and the output flux becomes asymmetric due to the formation of crystalline domains with different orientation. The $Γ-M$ band-edge mode has the energy flux circulates around the topological defe…
We report for the first time the bandgap engineering of Tamm plasmon photonic crystals - Tamm plasmon structures of which the metalic layer is periodically patterned into lattice of subwavelength period. By adopting a double period design, we evidenced experimentally a complete photonic bandgap up to $150\,nm$ in the telecom range. Moreover, such design offers a great flexibility to tailor on-demand, and independently, the band-gap size from $30\,nm$ to $150\,nm$ and its spectral position within $50\,nm$. Finally, by implementing a defect cavity within the Tamm plasmon photonic crystal, an ult…
The employment of magneto-optical materials to fabricate photonic crystals gives the unique opportunity to achieve optical tuning by applying a magnetic field. In this study we have simulated the transmission spectrum of a microcavity in which the Bragg reflectors are made with silica (SiO2) and yttria (Y2O3) and the defect layer is made with TGG (Tb3Ga5O12). We show that the application of an external magnetic field results in a tuning of the defect mode of the microcavity. In the simulations we have considered the wavelength dependence of the refractive indexes and the Verdet constants of th…
As an attractive degree of freedom in electromagnetic (EM) waves, the orbital angular momentum (OAM) enables infinite communication channels for both classical and quantum communications. The exploration of OAM generation inspires various designs involving spiral phase plates, antenna arrays, metasurfaces, and computer-generated holograms. In this work, we theoretically and experimentally demonstrate an approach to producing OAM carrying EM waves by a point defect in three-dimensional (3D) photonic crystals (PCs). Simultaneous excitation of two vibrational-defect states with an elaborately eng…
In this paper, we study the excitation of guided resonances (GRs) in photonic-crystal slabs based on point-defected aperiodically-ordered supercells. With specific reference to perforated-slab structures and the Ammann-Beenker octagonal lattice geometry, we carry out full-wave numerical studies of the plane-wave responses and of the underlying modal structures, which illustrate the representative effects induced by the introduction of symmetry-preserving and symmetry-breaking defects. Our results demonstrate that breaking the supercell mirror symmetries via the judicious introduction of point-…
We theoretically investigate the design of cavities in a three-dimensional (3D) inverse woodpile photonic crystal. This class of cubic diamond-like crystals has a very broad photonic band gap and consists of two perpendicular arrays of pores with a rectangular structure. The point defect that acts as a cavity is centred on the intersection of two intersecting perpendicular pores with a radius that differs from the ones in the bulk of the crystal. We have performed supercell bandstructure calculations with up to $5 \times 5 \times 5$ unit cells. We find that up to five isolated and dispersionle…
Topological defects, such as quantum vortices, determine the properties of quantum fluids. The study of their properties has been at the center of activity in solid state and BEC communities. On the other hand, the non-trivial behavior of wavepackets, such as the self-accelerating Airy beams, has also been intriguing physicists. Here, we study the formation, evolution, and interaction of optical vortices in wavepackets at the Dirac point in photonic graphene. We show that even in a non-interacting two-component system the topological excitations appearing in a wavepacket can still be considere…
We investigate interactions by means of direct numerical simulations between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss different lattice structures in which the beams with different intensities and phases are launched into the medium, but accelerate in opposite directions. During interactions we see the interference fringe, breathers and soliton pairs generated that are not accelerating. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift …
Phase changing materials (PCM) are widely used for optical data recording, sensing, all-optical switching, and optical limiting. Our focus here is on the case when the change in the transmission characteristics of the optical material is caused by the input light itself. Specifically, the light-induced heating triggers the phase transition in the PCM. In this paper, using a numerical example, we demonstrate that incorporating the PCM in a photonic structure can lead to a dramatic modification of the effects of light-induced phase transition, as compared to a stand-alone sample of the same PCM.…
We present a novel differential refractive index sensor based on arrays of photonic molecules (PM) of dielectric cylinders and two structural defect cavities. The transmission spectrum of the photonic proposed structure as sensor shows a wide photonic stop band with two localized states. One of them, the reference state, is bound to a decagonal ring of cylinders and the other, the sensing state, to the defect cavities of the lattice. It is shown that defect mode is very sensitive to the presence of materials with dielectric permittivity different from that of the surrounding cylinders while th…
Perfect, narrow-band absorption is achieved in an asymmetric 1D photonic crystal with a monolayer graphene defect. Thanks to the large third order nonlinearity of graphene and field localization in the defect layer we demonstrate the possibility to achieve controllable, saturable absorption for the pump frequency.
Nonreciprocal (NOR) transmission with magneto-optical materials plays a critical role in a broad range of applications, such as optical isolation, all-optical signal processing, and integrated photonic circuits. The underlying mechanism is that a static magnetic field can break the time-reversal symmetry in the presence of magneto-optical materials. However, the typical NOR devices usually need a large size because the weak magneto-optical activity of materials. Here, our theoretical investigations show that the NOR transmission can be obtained in the one-dimensional photonic crystal with a ma…
Whispering gallery modes (WGMs) in circularly symmetric optical microresonators exhibit integer quantized angular momentum numbers due to the boundary condition imposed by the geometry. Here, we show that incorporating a photonic crystal pattern in an integrated microring can result in WGMs with fractional optical angular momentum. By choosing the photonic crystal periodicity to open a photonic bandgap with a band-edge momentum lying between that of two WGMs of the unperturbed ring, we observe hybridized WGMs with half-integer quantized angular momentum numbers ($m \in \mathbb{Z}$ + 1/2). More…
In this paper, we study the radiation from embedded sources in two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab, and that the beamwidth is directly proportional to the leaky-wave attenuation constant, which provides a…
Photonic crystals with a sufficiently high refractive index contrast display partial or full band gaps. However, imperfections in the metamaterial cause light scattering and extinction of the interfering propagating waves. Positive as well as negative defect volumes may contribute to this kind of optical perturbation. In this study, we fabricate and characterize three-dimensional woodpile photonic crystals, with a pseudo-bandgap for near-infrared optical wavelengths. By direct laser writing, we intentionally introduce random defects in the periodic structure. We show that we can model random d…
Topological defects (TDs) in crystal lattices are elementary lattice imperfections that cannot be removed by local perturbations, due to their real space topology. We show that adding TDs into a valley photonic crystal generates a lattice disclination that acts like a domain wall and hosts topological edge states. The disclination functions as a freeform waveguide connecting a pair of TDs of opposite topological charge. This interplay between the real-space topology of lattice defects and band topology provides a novel scheme to implement large-scale photonic structures with complex arrangemen…
We report trapping and propagation of photonic Dirac mode in a helically twisted hollow core photonic crystal fiber (HC-PCF) where the trapped light in the hollow (air) defect can preserve the orbital angular momentum (OAM). We show that a photonic Dirac point can emerge even in a twisted system for a suitable choice of curvilinear coordinate and the related waveguide defect modes defined in the new basis can preserve the associated OAM during axial translation. The effect of twist rate, defect geometry and crystal dimension on the propagation of OAM carrying trapped Dirac modes is critically …
We propose a new optical biosensor based on a photonic crystal with a defect layer, which can determine the SARS-CoV-2 concentration in water by the defect mode shift. Two models of the dependence of the refractive index of the defect layer on the concentration of the pathogen in water were considered. The optimal parameters for the photonic crystal in our device and the optimal thickness of the defect layer were determined. It was also demonstrated that in the presence of absorption in the investigated structure it is much more advantageous to work in the reflection mode compared to the trans…
We fabricated two dimensional photonic crystal structures in zinc oxide films with focused ion beam etching. Lasing is realized in the near ultraviolet frequency at room temperature under optical pumping. From the measurement of lasing frequency and spatial profile of the lasing modes, as well as the photonic band structure calculation, we conclude that lasing occurs in the strongly localized defect modes near the edges of photonic band gap. These defect modes originate from the structure disorder unintentionally introduced during the fabrication process.
We derive the expression for spontaneous emission rate in finite one-dimensional photonic crystal with arbitrary defects using the effective resonator model to describe electromagnetic field distributions in the structure. We obtain explicit formulas for contributions of different types of modes, i.e. radiation, substrate and guided modes. Formal calculations are illustrated with a few numerical examples, which demonstrate that the application of effective resonator model simplifies interpretation of results.
Photonic crystal is a dielectric material which has a refractive index or permittivity which vary periodically, thus preventing the propagation of light with specific frequency and direction. The frequency range is called a photonic bandgap (PBG). If the structure of photonic crystals is modified by taking one line of rod in a photonic crystal is obtained a waveguide. Giving structures with symmetrical defects around the waveguide channel with the parameters given occurs coupling between the waveguide and cavity. Coupling indicates transfer part or all of the EM field depends on the frequency …
We present a novel, real-time, experimental technique for linear and nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies on excitation with random-phase waves and far-field visualization of the spatial spectrum of the light exiting the lattice. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion within each zone. For photonic lattices with defects (e.g., photonic crystal fibers), our technique enables far-field visualization of the defect mode overlaid on the extended Brillouin zone structure o…
