High-order Bandgap Research Articles

Design of high-index broken-ring-based all-solid photonic bandgap fibers

The design of all-solid photonic bandgap fibers based on a high-index broken ring is investigated, where the background material is silica and the broken ring consists of several individual high-index rods. Density of states maps and Bloch mode field distributions obtained by plane wave expansion method show that a high-order bandgap in such fibers can be engineered and broadened. The principle is that both the azimuthal and the radial orders of the LP modes of the high-index rods in the cladding can be controlled by the broken ring. It is demonstrated that the highest azimuthal order of the group of less affected LP modes is determined by the rod number and the bandgap width is largely affected by the rod size. The high-order bandgap can be used to design all-solid photonic bandgap fiber with broad transmission ranges of 488 nm and 944 nm for a center wavelength of 800 nm and 1550 nm, respectively, and the transmission window features the typical normal-zero-anomalous dispersion profile.

Broken-Ring-Based All-Solid Photonic Bandgap Fibers

The design of bandgap-engineered all-solid photonic bandgap fibers based on a broken-ring structure is investigated in detail. Both density of states maps and Bloch mode field distributions are used to show how the bandgap structure can be engineered and a higher-order gap be greatly expanded by replacing the high-index germanium-doped rod in a repeating cell with a ring of several individual high-index rods. The strategy is that both the azimuthal and radial orders of the cladding LP modes can be controlled by the broken-ring parameters. In particular, the rod number determines the highest azimuthal order of the LP mode that is less affected by the broken-ring, and the bandgap width is largely affected by the rod size. The result of bandgap engineering is that the higher-order bandgap can be utilized to design all-solid photonic bandgap fibers with very broad transmission windows of 488 nm and 944 nm centered at 800 nm and 1550 nm, respectively, and with typical normal-zero-anomalous dispersion profiles.

Linear discrete diffraction and transverse localization of light in two-dimensional backbone lattices

We study the linear discrete diffraction characteristics of light in two-dimensional backbone lattices. It is found that, as the refractive index modulation depth of the backbone lattice increases, high-order band gaps become open and broad in sequence, and the allowed band curves of the Floquet-Bloch modes become flat gradually. As a result, the diffraction pattern at the exit face converges gradually for both the on-site and off-site excitation cases. Particularly, when the refractive index modulation depth of the backbone lattice is high enough, for example, on the order of 0.01 for a square lattice, the light wave propagating in the backbone lattice will be localized in transverse dimension for both the on-site and off-site excitation cases. This is because only the first several allowed bands with nearly flat band curves are excited in the lattice, and the transverse expansion velocities of the Floquet-Bloch modes in these flat allowed bands approach to zero. Such a linear transverse localization of light may have potential applications in navigating light propagation dynamics and optical signal processing.

High-order bandgaps in one-dimensional photonic crystals

Bandgaps, including high-order ones, of one-dimensional photonic crystals are analysed.Accurate analytical expressions for band edges for both s and p polarized light are derived.As a consequence, the conditions for bandgap closing are obtained in a simple analyticalform. The derivation is based on a perturbative expansion of the dispersion equation using anew parameter which remains small around the band edges of all physically feasibleone-dimensional photonic crystals.

Bandgap characteristics of one-dimensional plasma photonic crystal

When two pump laser pulses intersect in an underdense plasma, plasma Bragg grating (PBG) is induced by the slow-varying ponderomotive force [Z. M. Sheng et al., Appl. Phys. B: Lasers Opt. 77, 673 (2003)]. Such a PBG can be considered as a one-dimensional (1D) plasma photonic crystal (PPC). Here the bandgap characteristic of 1D PPC composed of plasma layers of different densities is investigated theoretically and numerically. It is found that when the maximum density is lower than the critical density of the pump laser, there is only one normal-incidence bandgap. When the maximum density is higher than the critical density of the pump laser, high-order bandgaps are found. The theoretical results are verified by 1D particle-in-cell simulations.

Double photonic bandgap hollow-core photonic crystal fiber

We report on the design, fabrication and characterization of hollow-core photonic crystal fiber with two robust bandgaps that bridge the benchmark laser wavelengths of 1064 nm and 1550 nm. The higher-order bandgap arises due to the extremely thin struts of the silica cladding and their fine-tuning relative to the apex size. The optimum strut thickness was found to be approximately one hundredth of the cladding pitch.

Analysis of Optical Reflection in a Chirped Distributed Bragg Reflector

A theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR) is presented. The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio, ρ = d 2/d 1, where d 2 and d 1 are the thicknesses of two constituent dielectric layers. Reflection spectra are numerically calculated and analyzed by making use of the transfer matrix method in a stratified medium. The results show that such a chirped structure has a weak effect on the fundamental bandgap, but the higher order bandgaps are strongly affected. The second bandgap is apparently broadened due to the shift in its lower band edge. Results of spectra for both TE and TM waves at different incident angles are also given and discussed.

Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals

A large absolute higher-order stop-band is achieved in two-dimensional (2D) photonic crystals of square lattice. A genetic algorithm is used to search through a large number of possible structures. In this algorithm, the unit cell is divided into a grid of square pixels and a 2D binary chromosome is assigned to each filling pattern of the pixels. An initial structure with a small higher-order stop-band is included in the initial population to accelerate the search procedure. This initial structure is formed by breaking the symmetry of the supercell of a photonic crystal having a square lattice of square dielectric rods in air. In the optimization process, the effect of reducing the symmetry of the unit cell on the photonic band-gap is investigated. A structure showing an absolute higher-order band-gap as large as 0.1522(2πc/a) is obtained, which is larger than the values reported so far for photonic stop-bands.

Achieving large higher-order stop-bands in two-dimensional photonic crystals using a real-valued genetic algorithm

A real-valued genetic algorithm is used for the realization of higher-order stop-bands in two-dimensional photonic crystals with a square lattice. In this procedure, a number of square rods are arranged in the unit cell of the crystal. Using a genetic algorithm, we determine the dimensions and centers of the rods for a maximum stop-band. In this algorithm, the dimensions and positions of the square rods are represented as real number chromosomes. Some linear decimal crossovers without crossover sites are used. The plane-wave expansion method is used for calculating the photonic band structure corresponding to each chromosome. Four optimized photonic crystal structures are presented. The maximum absolute bandwidth of the optimized higher-order band-gaps is 0.0806(2πc/a).

Novel Low-Loss Bandgaps in All-Silica Bragg Fibers

We demonstrate that higher order bandgaps in all-silica Bragg fibers can have modes with four orders of magnitude lower confinement loss than those using the fundamental bandgap. A scheme for exploiting the higher order gaps for any specific wavelength via a global scaling of the fiber geometry is proposed. This approach provides lower losses than by reducing the confinement loss of the fundamental gap by scaling the core. Using a variety of modeling techniques, we have examined the band structure and guidance of idealized air-core all-silica Bragg fibers. It is demonstrated that the higher order, low loss, bandgaps analyzed here are uniquely accessible to single-material Bragg fibers, and are fundamentally different from the higher order gaps typically associated with depressed-index Bragg fibers such as the ldquoOmniguiderdquo fibers. Further analysis suggests that some of the key features of the guided modes of Bragg fibers can be understood by considering the properties of single hollow-core homogeneous dielectric waveguides (ldquoboreholesrdquo).

Effect of rotation on photonic band gap of two-dimensional square lattice photonic crystal with hollow rod

The plane-wave expansion method is used to calculate TE and TM mode band gaps for two-dimensional square lattice photonic crystal with hollow anisotropic tellurium (Te) rods under three different rotation operations. The effect of rotation on TE and TM mode band gaps and absolute band gap is investigated. The calculated results show that the high order band gaps of TM mode have a close relationship with structure rotation symmetry, and the rotation symmetry and the distribution of Te in x-y plane together influence TE mode band gaps.

Optical response of high-order band gap in one-dimensional photonic crystal applying in-plane integration

A new broadband filter, based on the high-order band gap in one-dimensional photonic crystal (PCs) of the form Si∣air∣Si∣air∣Si∣air∣Si∣air∣Si∣air∣Si, has been designed by the plane wave expansion method (PWEM) and transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device.

Extension of photonic band gaps in one-dimensional photonic crystals

A method is proposed for extending photonic band gaps by constructing periodic structures from two or more consecutively located photonic crystals with different lattice constants or filling factors. The photonic band gaps with a maximum extension are predicted by superposing the photonic band gap maps on one another. It is demonstrated that both the lowest and higher order band gaps can be merged in photonic crystals with a high refractive index contrast.

Higher-Order Bragg Resonance in Gravity Surface Waves overPeriodic Bottoms

A calculation method based on the Bloch theorem is developed for thegravity surface waves over the periodic bottoms of large undulations. Thestudy shows the existence of comparable high-order bandgaps, which aredemonstrated to result from the higher-order Bragg resonances, i.e. theresonant interactions between surface waves and the harmonic components of thefluctuating bottom. It is also shown that the band widths of the high-ordergaps are quite sensitive to the amplitudes of high-order harmonics of thebottom.

Microvoid channel polymer photonic crystals with large infrared stop gaps and a multitude of higher-order bandgaps fabricated by femtosecond laser drilling in solid resin

Photosensitive polymer materials are ideally suited for laser-induced micro- and nanostructuring, as structural and compositional changes are achieved already under exposure to moderate intensities of high-repetition rate ultrashort-pulsed light. Photonic crystals with bandgaps in the infrared or the visible spectral region are a particularly interesting application, because highly correlated structural elements at a size of only a few hundred nanometers are required. We fabricated infrared photonic crystals based on microvoid channels inside solid polymer material. Femtosecond-pulsed visible light was focused into UV-cured Norland NOA63 resin by a high numerical aperture objective. In the focal spot microexplosions drive the material out of the center of the focus. Void channels of 0.7–1.3 μm diameter are generated by translating the sample along a preprogrammed pathway. Woodpile structures of void channels at layer spacings of 1.6–2.6 μm and in-plane channel spacings of 1.2–1.3 μm allowed for bandgap-induced suppression of infrared transmission in the stacking direction of as much as 86% by only 20 layers. As these structures are highly correlated and do not contain many imperfections, up to three higher-order stop gaps are observed. Consistent with theory, the number and gapwidth of higher-order gaps strongly increases with the ratio between layer- and in-plane spacing. Due to their low refractive index contrast and the missing interconnectivity of voids our structures do not provide complete photonic bandgaps. However, their manifold of sizable higher-order gaps allows for the engineering of photonic stop gaps down to the near-infrared wavelength region using comparatively large structural dimensions.

A new slant on photonic crystal fibers

We present the novel use of microstructured optical fibers not as "light-pipes", but in a transverse geometry to manipulate the light propagating across the fiber. Fundamental and higher-order bandgaps were observed experimentally in this geometry using a number of techniques. The comparison of the measured spectra with photonic band structure and Finite-Difference Time-Domain simulations provide strong evidence that the spectral features are a result of the periodic nature of the fiber microstructure in the transverse direction.

Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization

Three-dimensional photonic crystals with bandgaps of 1.5-2.3 mum in wavelength and with gap/midgap ratios of as much as 18% were generated efficiently by two-photon photopolymerization in a liquid resin. From 0.5-1.1-mW femtosecond-pulsed 540-nm light, woodpile structures consisting of 40 layers of elliptically shaped rods spaced at 350-500 nm were fabricated by focusing with a 1.3-N.A. objective. The high degree of correlation in these structures allowed the suppression of infrared transmission by as much as 50% as well as the observation of higher-order bandgaps. We also investigated the decrease in the gap wavelength on reduction of layer spacing, in-plane rod spacing, and rod size.

Voltage references: from diodes to precision high-order bandgap circuits [Book Review

Voltage references: from diodes to precision high-order bandgap circuits [Book Review

Voltage references: from diodes to precision high-order bandgap circuits

Preface. Acknowledgments. List of Tables. List of Figures. Summary. 1. The Basics. 1.1 The Diode. 1.2 Current Mirrors. Appendix A.1: Temperature Dependence of the Diode Voltage. 2. Current References. 2.1 PTAT Current References. 2.2 Startup Circuits and Frequency Compensation. 2.3 CTAT Current References. 2.4 Temperature-Independent Current References. 2.5 PTAT[superscript 2] Current Generators. 3. Voltage References. 3.1 Zero-Order References. 3.2 First-Order References. 3.3 Second-Order References (Curvature Correction). 3.4 State-of-the-Art Curvature-Correction Techniques. 4. Designing Precision Reference Circuits. 4.1 Error Sources. 4.2 The Output Stage. 4.3 Designing for Power Supply Rejection and Line Regulation. Appendix A.4: Error Sources in a Typical First-Order Bandgap. Appendix B.4: Effect of the Resistors' Temperature Coefficient on a Reference with a Current-Mode Output Stage. 5. Considering the System and the Working Environment. 5.1 Design of the Trim Network. 5.2 Package-Shift Effects. 5.3 System-Related Issues. 5.4 Characterization. Appendix A.5: Bandgap Trimming Procedure for a Mixed-Mode (Both Voltage-Mode and Current-Mode) Output Stage. Appendix B.5: Package Shift-Effects in Bandgap Reference Circuits. Appendix C.5: Derivation of the Time Required for a Reference Circuit to Change a Finite Amount upon a single-Step Stimulus. Index. About the Author.

Photonic gap in amorphous photonic materials

Two-dimensional amorphous photonic materials are created, which do not possess any long-range order but have only short-range order. Our calculation of the multiple-scattering method shows that, for S-polarized waves, these materials have photonic gap that is independent of incident directions. Even though the detailed structures of amorphous photonic materials are different with each other, they possess a common photonic gap, if only they have the same short-range order. Based on our studies it may be confirmed that, for S-polarized waves, the first band gap of photonic crystals comes mainly from the short-range order, while the higher-order band gaps are related to the long-range order. The measured transmission spectrum of an amorphous photonic material agrees perfectly with the calculation.