Comparison between optical interconnection processors: folded perfect-shuffle versus three-dimensional butterfly

The differences between folded perfect shuffle and three-dimensional (3-D) multi-channel butterfly optical interconnection architectures are quantified. The three-dimensional butterfly network, in particular, is used to implement Hartley transform operation.     

Research on optical multistage butterfly interconnection and optoelectronic logic operations

We briefly study butterfly interconnection construction and propose an experimental approach to implementing multistage butterfly interconnection networks by using a special interconnection grating with the reflection ladder structure and liquid crystal light valves (LCLVs), and implementing the optical butterfly interconnections and primary optical digital logic operations. With this foundation, we analyse and discuss the features of the approach by computer simulations. In terms of our theoretical analyses, we improve the ring-circuit approach, based on the reflection ladder structure gratings, into a more suitable form based on transmission gratings, and we substitute the LCLVs with optoelectronic switches. Finally we give the experimental results of both the transmission grating and optoelectronic switches.     

Butterfly wing color: A photonic crystal demonstration

We have theoretically modeled the optical behavior of a natural occurring photonic crystal, as defined by the geometrical characteristics of the Teinopalpus Imperialis butterfly. In particular, following a genetic algorithm approach, we demonstrate how its wings follow a triclinic crystal geometry with a tetrahedron unit base. By performing both photonic band analysis and transmission/reflection simulations, we are able to explain the characteristic colors emerging by the butterfly wings, thus confirming their crystal form.     

Optical Digital Fast Fourier Transform System

A system for optical digital fast Fourier transform (FFT) is proposed. Data exchange, adder, and multiplier circuits required for the optical FFT system are designed. Each circuit contains the same basic element of an optical beam switch composed of a polarization rotator and a birefringent plate. In the FFT algorithm, butterfly switching for data exchange is important and the method of optical switching networks is very suitable for such operations. FFT calculation for one-dimensional data of a sinusoidal signal is experimentally demonstrated using the optical system. The throughput of the proposed system is estimated and its future perspective is discussed.     

Replication of homologous optical and hydrophobic features by templating wings of butterflies Morpho menelaus

The revealed “Christmas-tree” nanostructures in the cover and ground scales of the butterfly Morpho menelaus are responsible for the observed iridescent blue color and the diffraction pattern of the wings. The aspect ratio of nanostructures in ground scales is more than 5 times higher than that of Morpho peleides cover scales. Inspired by the butterfly, artificial nanostructures are fabricated successfully by templating the scales imbricating in the wings with low-temperature atomic layer deposition (ALD) methods. Through structural characterizations and optical measurements, we reveal that the hybrid structures inherit not only the morphology of the scales with high fidelity but also the homologous optical features including iridescence and diffraction. Besides, water contact angle measurements on both uncoated and coated wings show hydrophobic results. The integration of bio-templates and ALD methods provide a potential route to fabricate the nanostructures with multi-functional features, which may be especially crucial in the applications of innovative functional optical devices.     

光寻址2×2光学开关及3－D集成光学蝶形互连网络的实现

在光学多级互连网络的实现中，光学２×２开关的构造是至关重要的。本文介绍一种构成光寻址２×２光学开关的方法，该方法是在方解石晶体的双折射性质的基础上，利用普克尔斯只读光调制器（ＰＲＯＭ）来控制入射光的偏振态，从而实现光寻址２×２光学开关，这种开关具有许多优点，并且可以在３－Ｄ方向堆栈集成。利用该开关可以很方便地实现３－Ｄ集成的蝶形互连网络     

Colour characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method

In certain species of moths and butterflies iridescent colours arise from subwavelength diffractive structures. The optical properties of such a structure depend strongly on wavelength, incidence angle and state of polarization of illuminating radiation and on the viewing angle. Such structures can be analyzed only by solving Maxwell's equations, but since analytical solutions exist for only a few simple, highly symmetric structures numerical methods must be employed. We investigated the optical properties of butterfly wings in two dimensions by simulating a scale structure using a high accuracy version of nonstandard finite-difference time-domain algorithm. The simulated structure is a computer-generated model of a certain quasi-periodic arrangement of tree-like structures observed in the transmission electron micrograph (TEM) image of a transverse cross-section of a single scale from Morpho butterfly wings. We assumed that the structure is made of a slightly lossy dielectric material. We checked the accuracy and validity of our approach, by computing scattered field intensities due to an infinite cylinder and compared the results with analytical calculations using Mie theory. Next we deduced the wavelength dependence of a real refractive index and an absorption coefficient for the ground scales on the wings of Morpho sulkowskyi butterfly by computing the reflectivity and transmissivity spectrum of a scale at normal incidence, and comparing with experimental measurements. Finally, we calculated the tristimulus values and corresponding colour coordinates for various viewing directions from the scale's far-field reflectivity and transmissivity spectra to characterize its colour rendering abilities.     

Butterfly interconnection networks and their applications in Walsh-Hadamard transform-based information processing and optical computing

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Correlation in a Gaussian chain with the ends fixed

We consider an ideal chain whose ends are fixed without fluctuation at different points, possibly by optical tweezers. We derive a two-point probability distribution of a corresponding random walk and explicitly calculate the scattering function. We find that the contour plot of the resulting function shows a kind of normal butterfly pattern, contaminated by wavy texture. These results are compared with some representative previous models.     

Hofstadter's butterfly energy spectrum of ultracold fermions on the two-dimensional triangular optical lattice

We study the energy spectrum of ultracold fermionic atoms on the two-dimensional triangular optical lattice subjected to a perpendicular effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations and numerically solve them, then we obtain the Hofstadter's butterfly-like energy spectrum, which has a novel fractal structure. The observability of the Hofstadter's butterfly spectrum is also discussed.     

Light-Induced Hofstadter＇s Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper＇s equations from the Schr？dinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper＇s equations. We analyze the properties of the Hofstadter＇s butterfly spectrum and discuss its observability.     

Light-Induced Hofstadter＇s Butterfly Spectrum in Optical Lattices

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on A-type three-level atoms. When the dimensionless parameter a, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter＇s butterfly.     

Fault-tolerant polarization-insensitive photonic delay line architectures using two-dimensional digital micromirror devices

A binary multichannel photonic delay line (PDL) module is introduced that gives balanced loss switched states and a polarization-insensitive operation via the use of binary operation Digital Micromirror Devices (DMDs). Experimental demonstration of a DMD-based PDL architecture is performed for a 6.84-ns time delay design. Experimental results include a 25-beam feed interchannel crosstalk test indicating a <−60 dB optical interchannel crosstalk level for a 0.381 mm interchannel distance in the multichannel PDL. An average optical signal-to-leakage noise ratio of 35.33 dB is measured for this PDL. A butterfly design PDL optical architecture is proposed for minimizing loss and improving assembly accuracy. These DMD-based variable PDLs can be used in applications ranging from radio frequency (RF) fiber-optic signal processing systems to adaptive optics for astronomical and laser radar arrays.     

Bioinspired fabrication of magneto-optic hierarchical architecture by hydrothermal process from butterfly wing

We developed a green solution to incorporate nano-Fe₃O₄ into the hierarchical architecture of a natural butterfly wing, thus obtaining unique magneto-optic nanocomposites with otherwise unavailable photonic features. Morphological characterization and Fourier Transform Infrared-Raman Spectroscope measurements indicate the assembly of Fe₃O₄ nanocrystallites. The magnetic and optical responses of Fe₃O₄/wing show a coupling effect between the biological structure and magnetic material. The saturation magnetization and coercivity values of the as-prepared magneto-optic architecture varied with change of subtle structure. Such a combination of nano-Fe₃O₄ and natural butterfly wing might create novel magneto-optic properties, and the relevant ideas could inspire the investigation of magneto-optical devices.     

Cold atoms in non-Abelian gauge potentials: from the Hofstadter "moth" to lattice gauge theory

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.     

Optical bistabilities of higher harmonics: Inhomogeneous and transverse effects

The steady state behavior of optical bistable system in a ring cavity with transverse field variations and inhomogeneousely broadened two-level atoms is investigated outside the rotating wave approximation (RWA). Analytical and numerical investigation is presented for different cases of transverse field variations with Lorentzian or Gaussian line widths. When both (transverse and inhomogeneous) features taken into account, the first harmonic output field component outside the RWA exhibits a one-way switching down processes (butterfly OB) or reversed (clockwise) OB behavior, depending on the atomic linewidth shape.     

Trapped Fermi gases in rotating optical lattices: realization and detection of the topological hofstadter insulator

We consider a gas of noninteracting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the Streda formula.     

Contrast ratio and hysteresis width of optical bistability in quantum-dot vertical-cavity semiconductor optical amplifiers integrated with MEMS membrane

The characteristics of optical bistability in quantum dot vertical cavity semiconductor optical amplifier integrated with MEMS membrane have been investigated, and a closed-form model is derived taking into account the effect of the quantum dot discrete states and the membrane deflection and reflectivity. We show that small membrane deflection significantly adjusts the resonant wavelength, the contrast ratios and the hysteresis width. The shape of the input–output characteristics of the device can be adjusted to display clockwise, butterfly and counterclockwise hysteresis loops depending on the membrane deflection and the initial wavelength detuning. Our analysis reveals that the contrast ratios of the upper and lower bistable levels are totally different. Also, it has been shown that the characteristics of the bistability are strong function of the active layer linewidth enhancement factor and the membrane reflectivity.     

Replication of butterfly wing microstructures using molding lithography

This study employed a soft lithography technique to fabricate a polydimethylsiloxane (PDMS) replica of the multi-layered scales on the upper surface of a Morpho butterfly. The bionic photonic crystal microstructure of the replicated scales was examined using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The absorptivity, reflectivity and fluorescent characteristics of the wing were measured. The results showed that the microstructural and optical characteristics of the replicated wing qualitatively agree with those of the actual wing. The contact angle for the natural wing structure and the replicated wing were about 143° and 120°, respectively. As a result, it can be inferred that the soft lithography technique employed in this study represents a viable approach for the mass production of artificial photonic crystal structures for a variety of commercial applications, including optical elements for computing and communications purposes, photonic integrated circuits, anti-counterfeiting mechanisms, and so forth.     

Investigation of the helicity of magnetic fields on the Sun within the Parker dynamo model

Construction of the butterfly diagrams for the magnetic helicity in several approximations of a Parker dynamo has been carried out. The diagrams are constructed both for the cases of efficient generation of the magnetic field (large dynamo numbers) and for the weak generation (a small dynamo number). The corresponding asymptotic solution to the solar dynamo is used in the first case. The butterfly diagrams for different values of the meridional circulation were studied due to this solution. The butterfly diagrams are constructed and based on the few-mode approximation, which is valid for moderate dynamo numbers. The issue of which butterfly diagram features are common in all these approximations and can be compared with observational data is discussed.