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 interlayer dielectric constant and interlayer thickness were analyzed. In the framework of this approach, we have estimated the influence of the surface oxide layer on the band structure of macroporous silicon. We observed the shift of the gaps' edges to the higher or lower frequencies, depending on the interlayer thickness and dielectric constant. We have shown that the existence of a native oxide surface layer should be taken into consideration to understand the optical properties of 2D photonic crystals, particularly in macroporous silicon structures.
Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional 5-fold and 8-fold symmetric quasiperiodic photonic crystals
Surface modes (SM) are highly spatially localized modes existing at the core-cladding interface of photonic-bandgap hollow-core fiber (PBG-HCF). When coupling with SM, the air modes (AM) in the core would suffer a higher loss despite being spectrally within the cladding photonic bandgap, and would be highly dispersive around the avoided crossing (anti-crossing) wavelength. In this paper, we numerically demonstrate that such avoided crossings can play an important role in the tuning of the temperature dependence of group delay of AM of PBG-HCF. At higher temperatures, both the thermal-optic eff…
We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the holes and/or the distance between them, multiple transitions between normal and topological photonic band gaps (PBGs) can appear. The time-reversal symmetric topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states. We search for optimal topological transitions, i.e., sharp transitions sensitive to the g…
We show that slightly polydisperse disordered 2D foams can be used as a self-assembled template for isotropic photonic band gap (PBG) materials for transverse electric (TE) polarization. Calculations based on in-house experimental and simulated foam structures demonstrate that, at sufficient refractive index contrast, a dry foam organization with threefold nodes and long slender Plateau borders is especially advantageous to open a large PBG. A transition from dry to wet foam structure rapidly closes the PBG mainly by formation of bigger fourfold nodes, filling the PBG with defect modes. By tun…
We demonstrate that disorder in photonic crystals could lead to pronounced modification of spontaneous emission rate in the frequency region corresponding to the photonic band gap (PBG). Depending on the amount of disorder, two different regimes of the Purcell effect occurs. For the moderate disorder, an enhancement of spontaneous emission occurs at the edge of PBG due to modification of the properties of the edge state. This effect is responsible for recently observed mirrorless lasing in photonic crystals at the edge of PBG. When the level of disorder increases, the spontaneous emission rate…
A previous work, ref. 2 experimentally confirmed that measured special polarization characteristic features of a three-dimensional terahertz (THz) photonic-crystal did not apparently apply to general physical- and optical- basic rules. It is said that three-dimensional (3D) photonic crystals (PC) have no polarization anisotropy within photonic band gap (PBG, stop gap, stop band) of high symmetry points in normal incidence. None the less because two directions at right angles to each other on the plane (001) are constitutionally and optically identical in appearance, the polarization orientatio…
An ultra-broadband transverse magnetic (TM) pass hyperuniform disordered photonic crystal (HUDPC) polarizer is proposed and demonstrated on a silicon-on-insulator platform. Propagation of the transverse electric mode is blocked by three combined effects, including the photonic bandgap (PBG) effect, diffusive (non-resonant) scattering, and bandedge resonances. Specially, the designed 30-dB bandwidth in polarization extinction ratio (PER) of 265 nm is much larger than the spectral width of the PBG (149 nm) due to using the bandedge resonances. The TM mode is in the subwavelength regime of the HU…
We investigate numerically the effect of Kerr nonlinearity on the transmission spectrum of a one dimensional $δ$-function photonic crystal. It is found that the photonic band gap (PBG) width either increases or decreases depending on both sign and strength of Kerr nonlinearity. We found that any amount of self-focusing nonlinearity $(α>0)$ leads to an increase of the PBG width leading to light localization. However, for defocusing nonlinearity, we found a range of non-linearity strengths for which the photonic band gap width decreases when the nonlinearity strength increases and a critical non…
Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast $α$ for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity $\mathcal{S}(α)\equiv dΔ(α)/dα$, the first derivative of the optimal gap-to-midgap ratio $Δ(α)$. In particular, for all our crystal networks, $\mathcal{S}(α)$ takes a universal form that is well approximated by the analytic formula for a one-dimensional quarter-wave stack, $\mathcal{S}_{\text{QWS}}(α)$. Even more surpris…
Dirac points, new photonic band gaps and effect of magnetically induced transparency in dichroic cholesteric liquid crystals with wavelength dependent magnetooptical activity parameter
The approach based on the generalized Kirchhoff's law for calculating photoluminescence (PL) spectra of one-dimensional (1D) multi-layered structures, in particular, 1D photonic crystals has been developed. It is valid in the local thermodynamic equilibrium approximation and leads to simple and explicit expression for the photoluminescence intensity. In the framework of the present theory the analytical expression for the spontaneous emission intensity enhancement factor (IEF) for a 1D photonic crystal has been derived. It takes a particularly simple form in the case of a sufficiently large nu…
In this paper, the photonic quantum spin Hall effect (PQSHE) is realized in dielectric two-dimensional (2D) honeycomb lattice photonic crystal (PC) by stretching and shrinking the honeycomb unit cell. Combining two honeycomb lattice PCs with a common photonic band gap (PBG) but different band topologies can generate a topologically protected edge state at the combined junction. The topological edge states and their unidirectional transmission as the scatterers with triangular, pentagonal, and heptagonal shapes are researched. Meanwhile, the unidirectional transmission in an inverted Ω-shaped w…
In this paper, the transfer matrix method is used to investigate the reflectance properties in a symmetric defective annular photonic crystal (APC) containing semiconductor, high-$T_c$ superconductor and a radial defect layer. Numerical results offer many noteworthy features that can be very useful in designing optical devices. In this regard, the geometric effects of alternate layers on the optical reflectance of our defective APC structure by changing the thickness of different layers would be investigated. Then, the possibility of controlling the spectral position of existed photonic band g…
Coupling Analysis of Electromagnetic Field Transverse Magnetic (TM) on 2D Photonic Crystals with Symmetrical Refractive Index Defect Using Tensor Green Method
The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to the different signs of Berry curvature at the K and K$'$ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to finite values including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berr…
We investigate supercontinuum generation in several suspended-core soft-glass photonic crystal fibers pumped by an optical parametric oscillator tunable around 1550 nm. The fibers were drawn from lead-bismuth-gallium-cadmium-oxide glass (PBG-81) with a wide transmission window from 0.5-2.7 micron and a high nonlinear refractive index up to 4.3.10^(-19) m^2/W. They have been specifically designed with a microscale suspended hexagonal core for efficient supercontinuum generation around 1550 nm. We experimentally demonstrate two supercontinuum spectra spanning from 1.07-2.31 micron and 0.89-2.46 …
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…
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.
