White-Light Nonlinear Photonic Lattices in Self-Defocusing Media

Using fully incoherent white light emitted from an incandescent lamp and amplitude mask, we experimentally investigate the influence of several factors on the fabrication of the lattice in photovoltaic self-defocusing LiNbO3：Fe crystal, the factors include the orientation of the crystalline c axis relative to the principal axis of the photonic lattice and the filament, the diameter of input dark spot and the separation of the adjacent input dark spots. Experimental results reveal that the best fabricating condition of photonic lattices is that the principal axis of lattice is tilted for 45^o relative to the crystalline c axis which is parallel to the filament of the lamp. In addition, it is necessary that the diameter of the input dark spot is larger than the half of their separation.     

Supercontinuum generation in a two-dimensional photonic kagome crystal

We demonstrate the generation of ultrabroad spectra in a photonic crystal fiber with a kagome-lattice transverse structure. This two-dimensional periodic photonic lattice allows for strong confinement of light without employing defect states nor using photonic bandgap guiding. Light guiding is mediated by total internal reflection in the intersections of the lattice structure, similar to tapered or micro-structured fibers. The kagome lattice structure is manufactured from a soft glass with a high nonlinearity. Using a Ti:sapphire oscillator as a pump source, we observe for the first time impressive supercontinuum generation in the guided modes of a 2D photonic lattice. Supercontinuum generation is caused by fission and radiation of higher-order solitons in the anomalous dispersion range. Our spectrum encompasses the spectral range from 200 to 1750 nm. The dependence of the continuum on coupling spot location, fiber length, and pump wavelength and power as well as on pulse duration and polarization state is investigated. Using a numerical simulation for the lattice structure, pulse propagation through this structure is theoretically studied. Our model reveals the mechanism of supercontinuuum generation in the 2D photonic structure and explains the essential experimental findings.Electronic supplementary material to this article is avaiable at and accessible for authorized users.     

Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice

We have fabricated photonic quasicrystal lasers with a Penrose lattice that does not possess translational symmetry but has long-range order, and observed coherent lasing action due to the optical feedback from quasiperiodicity, exhibiting a variety of 10-fold-symmetric lasing spot patterns. The lattice constant dependence of lasing frequencies and spot patterns show complicated features very different from photonic crystal/random lasers, and we have quantitatively explained them by considering their reciprocal lattice. Unique diversity of their reciprocal lattice opens up new possibilities for the form of lasers.     

Resonant modes in quantum well structure of photonic crystals with different lattice constants

The resonant modes in a quantum well (QW) structure composed of three slabs of two dimensional (2D) photonic crystals with different lattice constants are analyzed with plane-wave-based transfer matrix method (TMM). It is found that the energy band of the well slab submerged into the band gap of barrier slab is discretized into quantized modes and the number of the resonant modes changes with the well slab thickness. A model structure of asymmetrical photonic QW consisting of two slabs of 2D photonic crystals with different lattice constants and one uniform dielectric slab in between is proposed and the resonant modes in it are investigated with the same method. A useful numerical simulation method for theoretical discussion as well as for practical application about photonic QW structure of photonic crystals with different lattice constants is proposed.     

Negative Refraction and Near-Field Imaging of an Elliptical-Rod Photonic Crystal Slab in the Second Band

Negative refraction and imaging properties of the electromagnetic wave through a two-dimensional photonic crystal （PC） slab, which consists of a square lattice of elliptical dielectric rods immersed in the air background, is studied by the plane-wave expansion method and the finite-difference time-domain method. A point source placed in the vicinity of the PC slab can form a good-quality image spot through the PC slab for the incident frequencies within the second photonic band. The calculated result also shows that negative refraction occurs in this kind of PC slab.     

Tunneling control of strongly correlated particles on a lattice: a photonic realization

We propose a photonic realization of tunneling control for two strongly correlated particles moving on a one-dimensional lattice, based on light transport in a square waveguide lattice with a periodically curved axis. We show the photonic analogue of dynamic localization of correlated particles and suggest the possibility to coherently suppress particle interaction.     

Dynamical tunneling of counterpropagating beams mediated by an optical photonic lattice

In a numerical study, we demonstrate the dynamical tunneling (DT) of two counterpropagating (CP) mutually incoherent beams in a two-dimensional photonic lattice, recorded in a photorefractive (PR) crystal. The beams are launched head-on from the opposite faces of a PR crystal in which an optically induced two-dimensional photonic lattice is established. The DT is caused by the spontaneous symmetry breaking of CP beams, which is induced by the nonlinear interaction between the beams and is mediated by the lattice. To observe DT we found no need to introduce a specific external tilt potential, as is done in the conventional Zener tunneling; the tilting is provided by the repulsive interaction between the beams, which causes ejection of one beam from the launching region of the other. As the beams propagate, they move laterally in real time, causing the leakage of radiation from the first Brillouin zone to the second and higher zones. In the process the beams also tunnel from the first photonic band zone to the higher zones, which by definition is the DT.     

Controllable Photonic Band Gap and Defect Mode in a 1D CO2-Laser Optical Lattice

We propose a new method to form a novel controfiable photonic crystal with cold atoms and study the photonic band gap （PBG） of an infinite 1D CO2-laser optical lattice of SSRb atoms under the condition of quantum coherence. A significant gap generated near the resonant frequency of the atom is founded and its dependence on physical parameters is also discussed. Using the eigenquation of defect mode, we calculate the defect mode when a defect is introduced into such a lattice. Our study shows that the proposed new method can be used to optically probe optical lattice in situ and to design some novel and controllable photonic crystals.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

A dark hollow beam from a selectively liquid-filled photonic crystal fibre

This paper reports that, based on the electromagnetic scattering theory of the multipole method, a high-quality hollow beam is produced through a selectively liquid-filled photonic crystal fibre. Instead of a doughnut shape, a typical hollow beam is produced by other methods; the mode-field images of the hollow-beam photonic crystal fibre satisfy sixth-order rotation symmetry, according to the symmetry of the photonic crystal fibre (PCF) structure. A dark spot size of the liquid-filled photonic crystal fibre-generated hollow beam can be tuned by inserting liquid into the cladding region and varying the photonic crystal fibre structure parameters. The liquid-filled PCF makes a convenient and flexible tool for the guiding and trapping of atoms and the creation of all-fibre optical tweezers.     

Large forbidden angles for a two-dimensional photonic crystal of connected-honeycomb lattice

The off-plane band structures of a two-dimensional photonic crystals of connected-honeycomb lattice are calculated by the plane-wave expansion method. To investigate how the band gaps vary with the off-plane angle, an effective refractive-index model is employed to work out the corresponding angular gap map. We find that the connected-honeycomb lattice can provide forbidden angles taking up as much as 58.6% of the solid angle. The result will be helpful in the design of photonics devices incorporating two-dimensional photonic crystal structures.     

Photonic crystal waveguides utilizing a modulated lattice structure

We experimentally demonstrate a new class of optical waveguide consisting of a-Si/SiO(2) autocloned photonic crystals with modulated lattice structure. The waveguide utilizes the macroscopic form birefringence of photonic crystals and confines light by the difference in the effective refractive index. A monopole modal field with spot diameters of 6.9 micromx6.5 microm was observed at a wavelength of 1.55 microm. The propagation loss of the waveguide at the wavelength was found to be ~4.2 dB/mm at most.     

Enlargement of complete two-dimensional band gap by using photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure, which consists of two photonic crystals of a square lattice of circular columns with reverse dielectric configurations, is proposed. Photonic band gap properties are calculated using a plane-wave method and the transmission spectra are obtained. After optimization, the relative width of the complete band gap reached 13.8% based on the simple unit-cell shape and crystal lattice. The photonic crystal heterostructure opens up new ways of engineering photonic band gap materials and designing photonic crystal devices.     

Polaritonic and photonic gap interactions in a two-dimensional photonic crystal

If an ionic material is used in a photonic crystal, the lattice resonance creates a polaritonic gap in the infrared range. The interaction between a polaritonic gap and the structure gap in a 2D square photonic crystal is studied by transfer matrix photonic band structure calculations. The polaritonic gap appears for a surprisingly low volume density of the ionic material. The TM gaps are larger than the TE gaps, as in the dielectric case. By varying the lattice constant, the structure gaps can be shifted across the polaritonic gap, and the effects of merging the two gaps can be studied.     

Analysis of two-dimensional photonic band gap structure with a rhombus lattice

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.     

Microwave control of spontaneous emission of a driven four-level atom in photonic crystals

We study the coherent control of spontaneous emission of a double-driven four-level atom embedded in photonic crystals. Combined effect of different relative locations between the upper band edge and the two upper levels and the phase of microwave coupling field is discussed. It is shown that quantum interference effect such as laser-induced dark line depends strongly on the phase of microwave field.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

Anyons in one-dimensional lattices: a photonic realization

Anyons are nonlocal quasi-particles carrying fractional statistics that interpolate between bosons and fermions. Here we propose a photonic realization of anyons moving on a one-dimensional lattice, which is based on light transport in an engineered square array of optical waveguides with a helically bent axis. Our photonic simulator enables visualization of the nonlocal nature of anyons in Fock space and the persistence of correlated tunneling even in the absence of particle interaction.