Modulation of Photonic Bandgap and Localized States by Dielectric Constant Contrast and Filling Factor in Photonic Crystals

The band structure of 2D photonic crystals (PCs) and localized states resulting from defects are analyzed by finite-difference time-domain (FDTD) technique and Padé approximation.The effect of dielectric constant contrast and filling factor on photonic bandgap (PBG) for perfect PCs and localized states in PCs with point defects are investigated.The resonant frequencies and quality factors are calculated for PCs with different defects.The numerical results show that it is possible to modulate the location,width and number of PBGs and frequencies of the localized states only by changing the dielectric constant contrast and filling factor.

Photonic Bandgap Properties of One-Dimensional Photonic Crystal Consisting of Complex Artificial Media

Propagation of electromagnetic waves in one-dimensional (1-D) stratifiedchiral structures is described by the 4X4 transfer-matrix method. The photonic bandgap (PBG)properties in 1-D periodical chiral media are investigated. The relation between PBGand chiralityadmittance has been analyzed. Under proper operating parameters, quite perfect multichannelfiltering properties can be obtained with the periodic structure. The photonic bandgap properties ofone-dimensional layered periodical structures that include of double negative (DNG) medium,so-called backward-wave (BW) medium are investigated. The simulation results show that the width ofthe PBG in the structure composed of chiral medium and BW medium is larger then that composed ofchiral medium and usual medium. Our analysis has shown that the usage of the negative material makesit possible to dramatically widen the band gap of one-dimensional photonic crystal.

Photonic Bandgap Properties of Atom-lattice Photonic Crystals in Polymer

The present paper covers the various photonic crystals（PhCs） structures mimicking real atom-lattice structures in electronic crystals by using the femtosecond laser-induced two-photon photopolymerization of SU-8 resin. The bandgap properties were investigated by varying the crystal orientations in 〈111 〉, 〈110〉 and 〈100〉 of diamond-lattice PhCs. The photonic stop gaps were present at λ=3.88 um in 〈111〉 direction, λ=4.01 um in 〈110〉 direction and λ=5.30 um in 〈100〉 direction, respectively. In addition, defects were introduced in graphite-lattice PhCs and the strong localization of photons in this structure with defects at λ=5 um was achieved. All the above work shows the powerful capability of femtosecond laser fabrication in manufacturing various complicated threedimensional photonic crystals and of controlling photons by inducing defects in the PhCs samples.

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings is proposed. In this model calculated are only the potential modes of a unit cell, which is a high-index ring in the low-index background for this fibre, rather than the whole cladding periodic structure based on Bloch＇s theorem to find the bandgap. Its accuracy is proved by comparing its results with the results obtained by using the accurate full-vector plane-wave method. High speed in computation is its great advantage over the other exact methods, because it only needs to find the roots of one-dimensional analytical expressions. And the results of this model, mode plots, offer an ideal environment to explore the basic properties of photonie bandgap clearly.

Zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres

This paper investigates the zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres （PBGFs） by using a full-vector finite element method. By simulation we found that theoretically the zero dispersion wavelength can be tailored by respectively changing the rounded diameter of air holes, pitch, refractive index, normalized thickness of core rings, and hole diameter to pitch ratio. At the same time the tailoring of dispersion slope can also be realized by changing the rounded diameter of air holes or pitch or normalized thickness of core rings. To illustrate the reasonability of fibre designs, this paper also gives the variance of normalized interface field intensity which measures the scattering loss relatively versus wavelength for different designs. From the viewpoint of loss, varying the rounded diameter and the thickness of core ring could shift zero wavelength but it is difficult to get the required parameters within so tiny range in practical drawing of PBGFs, on the other hand, it is possible in practice to respectively alter the pitch and refractive index to shift zero wavelength. But varying hole diameter to pitch ratio is not worthwhile because they each induce large increase of loss and narrowness of transmission bandwidth. The zero dispersion wavelength can be engineered by respectively varying the rounded diameter of air holes, pitch, refractive index, and normalized thickness of core rings without incurring large loss penalties.

Modulated spatial transmission signals in the photonic bandgap

This paper describes the spatial transmission of electromagnetically induced transparency and four-wave mixing signals in the photonic bandgap structure,which are modulated using the adjustable parameters of light fields.The spatial transmission patterns of the relevant signals are experimentally investigated with respect to the optical nonlinear Kerr effect that occurs in the modulation process.The experimental results reveal the spatial transmission patterns of the probe transmission and the four-wave mixing signals,such as focusing,defocusing,shifting,and spatial splitting.This study explains how the tunable parameters of light fields and their interactions with each other can regulate the spatial transmission of the light fields by changing the refractive indices of media,which provides a new research perspective and a degree of experimental technology support for more efficient all-optical communications.

Effect of single point defects on the confinement losses of air-guiding photonic bandgap fibers

The confinement losses in air-guiding photonic bandgap fibers （PBGFs） with air hole missing are studied with the full-vector finite-element method. It is confirmed that there are two loss peaks （1.555 and 1.598 μm） if there is a hole missing in the cladding far from the core. The closer to the core the hole missing is, the larger the confinement losses are, and even no mode could propagate in the core. The main power of the fundamental mode leaks from the core to the cladding defect. The quality of PBGFs can be improved through controlling the number and position of defects.

Characteristics of Bragg Gratings in All-Solid Photonic Bandgap Fiber

We report on fiber Bragg gratings in all-solid photonie bandgap fiber that was composed of a triangular array of high-index Ge-doped rods in pure silica background with fluorine-doped index-depressed layer surrounding the Ge-doped rod. Fiber Bragg gratings were photowritten with 193 nm ArF excimer laser and characterized for their response to strain, temperature, bending, and torsion. These gratings couple light from the forward core mode to not only backward core mode but also backward rod modes. This results in multiple resonance peaks in the reflection spectrum. All resonance wavelengths exhibited the same temperature and strain response with coefficient similar to that of Bragg gratings in standard single-mode fiber. The strength of the resonance peaks corresponding to the backward rod modes showed high sensitivity to bending and torsion.

Spectrally U-shaped profile of beam propagation factor in all-solid photonic bandgap fiber

We found the beam quality factor M^(2)of the fundamental mode as a function of wavelength is U-shaped in the working photonic bandgap(PBG) of an all-solid PBG fiber(AS-PBGF) for the first time,to the best of our knowledge,and our simulation results also match well with the phenomenon.The normal band that is near the high-frequency edge of the third PBG integrates the lowest M^(2)and single-mode operation simultaneously,while the other two edge regions suffer from anomalous variation of M^(2)versus wavelength.The general applicability of this finding can be further extended to other PBGs and also other representative structures in the AS-PBGF field.

Mode converter based on dual-core all-solid photonic bandgap fiber

In this paper, we present a mode-selective coupler based on a dual-core all-solid photonic bandgap fiber（AS-PBGF）. Because they are all-solid, AS-PBGF-based mode converters are easier to splice to other fibers than those based on air-hole photonic crystal fibers. Mode conversions between the LP01 and LP11modes, LP01 and LP21modes, and LP01 and LP02modes are obtained at the wavelength λ=1550 nm. The 3 dB wavelength bandwidth of these mode converters are 47.8,20.3, and 20.3 nm, respectively.

An investigation of numerical aperture of air-core photonic bandgap fiber

Air-core photonic bandgap fiber(PBF)is the perfect choice of the next-generation fiber optical gyroscope(FOG),with excellent temperature,electromagnetism and radiation adaptability.Numerical aperture is an important optical parameter of PBF for application in FOG.The PBF’s maximum theoretical numerical aperture(NAmax)is calculated and compared with the far-field numerical aperture(NAeff)through experiments.The result indicates that the relationship between NAmax and NAeff has much stronger dependence on wavelength than that of the conventional fiber,and they get close at wavelengths near the middle of the photonic bandgap with the error less than 5%.Furthermore,photonic bandgap fiber optical gyroscope(PBFOG)with no fusion splicing points is proposed,and the optimization method and results of the PBF’s structure parameters for application in PBFOG are given from the aspect of numerical aperture.

Large-mode-area neodymium-doped all-solid double-cladding silicate photonic bandgap fiber with an index step of ～0.5%

A large-mode-area neodymium-doped silicate photonic bandgap fiber was theoretically designed and experimen- tMly demonstrated. The relative index step between the high-index rods and the background glass was -0.5%, which is the lowest cladding index difference reported on rare-earth-doped all-solid photonic bandgap fibers to our knowledge. An output power of 3.6 W with a slope efficiency of 31- was obtained for a 100-cm-long fiber.

Effect of Dielectric Constant Contrast and Filling Factor to Photonic Bandgap

The effect of dielectric constant contrast and the filling factor to the photonic bandgap in a 2-D square lattice photonic crystal is discussed. The location, width and number of photonic bandgap can be modulated.

Complete photonic bandgap in silicon nitride slab assisted by effective index difference between polarizations

The slab effective index difference between the transverse-electric(TE)and transverse-magnetic(TM)polarizations was utilized to obtain complete photonic bandgap(CPBG)in a silicon nitride(Si_(x)N_(y))photonic crystal slab.For this,coincident frequency range in the TE photonic bandgap(PBG)and TM PBG,which denotes the CPBGs of the slab,must be found with the same structure.Through adjusting the effective index pair of TE and TM polarizations by changing the thickness of the Si_(x)N_(y)core layer,and also optimizing the structure parameters within the photonic crystal plane,a large normalized CPBG of 5.62%was theoretically obtained in a slab of Si_(x)N_(y)with a refractive index of 2.5.Moreover,based on the obtained CPBG,a microcavity which could support both TE and TM polarization was theoretically demonstrated.The cavity modes for different polarizations were both well confined,which proved the reliability of the CPBG.In addition,using the same method,the lowest refractive index of Si_(x)N_(y)on silica slab for a CPBG could be extended to as low as 2.The results indicate that there is potential for development of various high-performance CPBG devices based on Si_(x)N_(y)slab technology.

Improved gas sensor with air-core photonic bandgap fiber

The propagation loss of a fiber can be increased by coupling core mode and surface mode which will deteriorate the performance of photonic bandgap fiber （PBGF）. In this paper, we presented an aircore PBGF for gas sensing applications. By designing A = 2.63 μm, d = 0.95 A, and Reore= 1.13 A, where A is the distance between the adjacent air holes, the fiber was single-mode, no surface mode was supported with fiber, and more than 90% of the optical power was confined in the core. Furthermore, with optimizing the fiber structural parameters, at wavelength of 2 = 1.55 μm that is in acetylene gas absorption line, significant relative sensitivity of 92.5%, and acceptable confinement loss of 0.09 dB/m, were simultaneously achieved.

Novel 1-D Sandwich Photonic Bandgap Structure

A sandwich photonic bandgap (PBG) structure is a novel PBG structure whose periodic lattice is buried in the middle of a substrate. Neither drilling nor suspending the substrate is required, and the integrity of the ground plane is maintained. This paper presents several modification techniques for sandwich PBG structure fabrication. The forbidden gap can be improved by adopting the chirping technique, applying the tapering technique, enlarging the periodic elements, adjusting the location of the periodic lattice in the sub-strate, and using different dielectric media H-shape elements. A finite difference time domain method is ap-plied to analyze the structures. Deep and wide stopbands can be obtained using the modified sandwich structures. Experimental measurement results agree well with the theoretical analysis.

Photonic bandgap structure and long-range periodicity of a cumulative Fibonacci lattice

In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(DBR)structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.

Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method

One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO2/SiO2, TiO2/SnO2, SiO2/SnO2, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO2/SiO2 and SiO2/SnO2, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO2/SiO2 layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.

Application of Padé Approximation in Simulating Photonic Crystals

To save finite-difference time-domain（FDTD） computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Pad6 approximation with Baker＇s algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000, the intensity spectrum obtained by the Padé approximation from a 2^8-item sequence output is more exact than that obtained by fast Fourier transformation from a 2^20-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method, and then the band diagrams are obatined. In addition, mode frequencies and Q-factors are calculated for photonic crystal microcavity.

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional（2D） metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters（dielectric constant and filling factor） are investigated for two types of 2D metal/dielectric（M/D） photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.