Self-collimation In Photonic Crystals Research Articles

Self-collimation in the square lattice photonic crystals composed of multi-circular ring scatterers

In this paper, fractal supercells are constructed according to the Thue-Morse theory and arranged in a square lattice to form fractal photonic crystals (PCs), which are called the first-order (1st) and second-order (2nd) approximate of Thue-Morse structure. The multi-circular ring scatterers (MCRSs) are innovatively applied in them and the effect of the number (H) and width (W) variation of the rings on the equifrequency contours (EFCs) of PCs is investigated. To calculate the energy band diagrams and EFC mappings of the first-order (1st) and second-order (2nd) approximate of Thue-Morse structure, an improved plane wave expansion (PWE) method is also introduced. Then, the possibility of achieving polarization-insensitive self-collimation (PISC) in the approximate of Thue-Morse structure and conventional square lattice (CSL) PCs are explored. This phenomenon was verified by simulations at normalized frequencies of 0.128, 0.068, and 0.27 (ωa/2πc), respectively, and the phenomenon of vertical incidence self-collimation of light (VISCOL) was proposed on this basis. Finally, a reflection on the value of the multi-ring nested type of scatterers is presented. Replacing the circular rings in the PCs with square rings, it is found that the EFCs for TE polarization change less while the EFCs for TM polarization have larger variations, which leads to a reduction in the VISCOL frequency range and provides a possibility for beam splitter design.

Band gap properties and self-collimation in a tenfold quasicrystal structure photonic crystals applying multicircular ring scatterers

In this paper, a kind of tenfold photonic quasicrystals based on the Penrose puzzle theory with the application of multicircular ring scatterers (MCRSs) is presented. It is divided into four kinds of square supercells and employed in a square lattice to constitute the first-order (1st), second-order (2nd), third-order (3rd), and fourth-order (4th) tenfold quasicrystal structure photonic crystals (TFQCSPCs) accordingly. In an attempt to evaluate the dispersion maps and equifrequency contour (EFC) profiles of such long-range ordered but not really periodic TFQCSPCs, an enhanced plane wave expansion (PWE) method is adopted. The photonic crystals (PCs) discussed in this paper are first classified into two major categories, air hole and dielectric column types which will be referred to as type 1, type 2 respectively in the following. The varying features of photonic band gaps (PBGs) of TFQCSPCs are inquired about by changing the refractive index (n) of the relevant medium and the number of rings (H) of MCRSs under two broad prerequisites of type 1 and type 2 PCs. The results are also compared with the associated properties of PBGs of traditional square lattice PCs (TSLPCs) and traditional triangular lattice PCs (TTLPCs) which employ MCRSs. Then, the 1st and 2nd TFQCSPCs and TSLPCs are fabricated in the form of hollow air holes dug in the silicon plate, and the transformation of their PBGs and EFCs is researched when the width (W) and H of the ring are adjusted. The possibility of implementing the phenomenon of polarization-insensitive self-collimation (PISC) in TFQCSPCs and TSLPCs is explored by examining the smoothest EFCs in EFC mappings. Eventually, our work actualizes the PISC phenomenon at seven normalized frequency (NF) values of 0.074, 0.168, 0.170, 0.172, 0.265, 0.270, and 0.297, which fills the gap of the PISC phenomenon in the low-frequency domain.

Formulation of Iterative Finite-Difference Method for Generating Large Spatially Variant Lattices

A new numerical method to generate spatially variant lattices (SVLs) is derived and implemented. The algorithm proposed solves the underlying partial differential equations iteratively with an update equation derived using the finite-difference method to obtain an SVL that is continuous, smooth, and free of unintended defects while maintaining the unit cell geometry throughout the lattice. This iterative approach is shown to be more memory-efficient when compared to the matrix-based approach and is, thus, suitable for the calculation of large-scale SVLs. The iterative nature of the solver allows it to be easily implemented in graphics processing unit to parallelize the computation of SVLs. Two spatially variant self-collimating photonic crystals are generated and simulated to demonstrate the functionality of the algorithm as a tool to generate fully three-dimensional photonic devices of realistic size.

Multi-optical effects in two-dimensional photonic crystals of metallic pairs

Beam steering in photonic crystals is significant in manipulating light beams. In this paper, we design self-collimation, beam splitting, and negative refraction effects in photonic crystals based on metallic pairs immersed in dielectric background. By using a single array of metallic pairs, a broadband and wide-angle self-collimation effect is achieved. Meanwhile, due to the extreme anisotropy, a beam splitting effect is achieved by utilizing the kissing of equi-frequency contours. We then restructure the unit cell with glide symmetry to achieve negative refraction effect in a wide frequency range and realize the effect of flat lens. To illustrate this phenomenon, a flat lens based on the restructured unit cell is designed and numerically demonstrated.

Design of mesoscopic self-collimating photonic crystals under oblique incidence.

Mesoscopic Photonic Crystals (MPhCs) are composed of alternating natural or artificial materials with compensating spatial dispersion. In their simplest form, as presented here, MPhCs are composed by the periodic repetition of a MPhC supercell made of a short slab of bulk material and a short slab of Photonic Crystal (PhCs). Therefore, MPhCs present a multiscale periodicity with a subwavelength periodicity within each PhC slab and with a few-wavelength periodicity for its supercell. Thanks to this mesoscopic structure, MPhCs allow the self-collimation of light, through a mechanism called mesoscopic self-collimation (MSC), along both directions of high symmetry and directions oblique with respect to the MPhCs slab interfaces. Here, we propose a new design method useful for conceiving MPhCs that allow MSC under oblique incidence, avoiding in-plane scattering and ensuring propagation via purely guided modes, without out-of-plane radiation losses. In addition, the proposed method allows a systematic search for optimal MSC structures, which also simultaneously satisfy the impedance matching condition at MPhC interfaces, thus reducing the effect of multiple reflections between bulk-PhC interfaces. The proposed design method has the advantage of an extreme analytical simplicity and it allows direct design of oblique-incidence MPhC structures. Its accuracy is validated through Finite Difference Time Domain simulations and the MSC performances of the designed structures are evaluated, in terms of angular direction, beam waist, overall transmittance, and through discussion of a Figure of Merit that accounts for residual beam curvature. This simple yet powerful method can pave the way for the design of advanced MSC-based photonic interconnects and circuits that are immune to crosstalk and out-of-plane losses.

Bistability phenomena based on frequency-sensitive self-collimation in nonlinear photonic crystals

By introducing the change of beam behavior near the frequency sensitive self-collimation point, a new kind of bistability is observed in a finite nonlinear photonic crystal (PhC). The mechanism of such a PhC bistability is from the complex interplay between cavity resonance, nonlinearity and beam behavior. Additionally, it has unique properties, including: high frequency sensitivity, small volume, short switching time, robustness and position flexibility. With the consideration of beam behavior, a new theory based on the coupled-mode equation has been constructed, whose result agrees with the numerical one very well. The new PhC bistability could be widely used to design various optical devices, as a bistable all-optical switch has also been demonstrated.

Independent control of phase and power in spatially variant self-collimating photonic crystals.

Self-collimating photonic crystals are a promising technology to control waves in optical devices. A technique was recently developed that can bend, twist, and otherwise spatially vary a photonic crystal without deforming the unit cells, as this would weaken or destroy the optical properties. Applying this to self-collimating photonic crystals allows us to control multiple properties of light at the same time. A spatially variant self-collimating photonic crystal is shown that decouples the phase and power of the wave and controls them independently and at the same time within the same volume. This creates new physical mechanisms from which to design optical systems. Some possible applications include miniaturization of optical systems, integrated optics, beam steering, and imaging, among others.

Multiple-wavelength conversion based on the anomalous Doppler effect induced by dynamic tuning in a self-collimation photonic crystal

The Doppler effect of relative motion-induced frequency shift as an interesting fundamental wave phenomenon draws significant research interest in many applied aspects of physics and engineering. Photonic settings represent an important class of platforms to observe and manipulate this effect. Here, an anomalous Doppler effect via dynamic index tuning in a photonic crystal (PhC) is proposed and investigated theoretically by considering the guided reflection of light from a moving front at near the speed of light. A virtual waveguide constructed in a square lattice PhC slab utilizing the self-collimation effect is proposed, and the moving equivalent reflector is realized by photonic band shift induced by a pump light for changing the refractive index dynamically. The anomalous Doppler shift occurs at multiple wavelengths, which depends on the Bloch nature of this photonic crystal and its band structure. Moreover, another kind of small spectral shift caused by adiabatic wavelength conversion is also observed. This nonstationary procedure is studied combining the full-wave numerical simulation and wavelet transform analysis. This work sheds light on the emergence of anomalous Doppler effect and wavelength conversion via dynamic index tuning in photonic crystals and can be important for manipulating such effects in practical photonic devices.

New Eras in Physics

Dear readers, authors and reviewers of Annalen der Physik, On 16 November 2018, the 26th meeting of the General Conference on Weights and Measures in Versailles adopted a resolution on the revision of the International System of Units (SI).1 With this, the French metrology institution BIPM will give up its traditional role as host of the famous “Grand K”, the kilogram prototype, which is to be replaced by a fixed value of the Planck constant h.2 At the same time, also the elementary charge e,3 the Boltzmann constant k,4 and the Avogadro constant NA5 received new definitions so that in the future all seven SI units will be defined in terms of physical constants. These changes will come into effect on 20 May 2019, and on this occasion Annalen der Physik will publish a special issue “The Revised SI: Fundamental Constants, Basic Physics and Units”, edited by our Editorial Advisory Board member Klaus Blaum (Max Planck Institute for Nuclear Physics Heidelberg), Dmitry Budker (Johannes Gutenberg University of Mainz), Andrey Surzhykov (Technical University and Physikalisch-Technische Bundesanstalt – PTB, Braunschweig), and Joachim H. Ullrich (President of the PTB, the National Metrology Institute of Germany) (Figure 1). It is planned to contain Review Articles on the fundamental constants and corresponding units, as well as a substantial collection of further overview articles and new research results around these and the required high-precision measurements. Watch out for many articles to be already online at http://www.ann-phys.org (Early View)! This special issue will clearly be one of the AdP highlights in the New Year, as it is of fundamental importance for physics and the foundations of physical measurements. However, there are also other fields of physics that currently undergo revolutionary developments. One of them is certainly gravitational wave astronomy. We have already been glad to publish the article by the LIGO and VIRGO Collaborations on “The basic physics of the binary black hole merger GW150914” (the first detection in September 2014) which has been downloaded more than three times a day on average since. Now we are even happier to follow up with the Nobel Lectures 2017 “LIGO and the Discovery of Gravitational Waves”, Parts I to III, authored by the Laureates Rainer Weiss (article number 1800349), Barry C. Barish (article number 1800357), and Kip S. Thorne (article number 1800350) in the present issue. They are being accompanied by an Expert Opinion (article number 1800442) from our Board member Bruce Allen of the Max Planck Institute for Gravitational Physics Hannover and a Review Article on Forecasting Gamma-Ray Bursts with Gravitational Waves by Sarp Akcay (Friedrich-Schiller-Universität Jena and University College Dublin). The spectrum of recent top Review and Feature Articles in Annalen der Physik spreads further from astrophysical black holes over self-collimation in photonic crystals to Bose–Einstein condensation (article numbers 1700430, 1700049, and 1700124). And, last but not least, special issues will continue to be a cornerstone of the journal, with the 2017 article collection on Many-Body Localization having been cited almost 400 times already at present, also to be followed by ‘Physics of Information’ and ‘Advances in Physics of Semiconductors’ later this year. Suggestions for new special issue topics are always welcome at ann-phys@wiley.com. Generally, we have noticed increasing submission numbers as well as better-quality contributions, and we intend to keep up the standards of the journals by a strict editorial and peer-review selection process that currently results in an acceptance rate below 20%. Recent trends also include increasing submission numbers in applied physics fields as well as from China (more than one third of contributions in 2018), most notably in current topical areas such as quantum information or photonics. To support this significant development, we have appointed four new Editorial Advisory Board members in 2018, among them Qihuang Gong, Peking University; Hong-Bo Sun, Jilin University Changchun; Dingyu Xing, Nanjing University; and Pu Yu, Tsinghua University, Beijing, and with our colleague Huan Wang we have now an Editor working in the Wiley Beijing office. A warm welcome to each of you, and to all authors joining the growing AdP community! Wishing you a peaceful, healthy, successful and pleasant year 2019. Stefan Hildebrandt, Editor-in-Chief Nadezda Panarina, Maria E. Stournara, Huan Wang, James Cook, Matthew Lock, Editors

Broadband self-collimation in C2 symmetric photonic crystals.

In this study, we report a low-symmetric photonic crystal (PhC) structure that exhibits high coupling efficiency in a broadband frequency range with a tilted self-collimating capability. First, the analytical approach is implemented as a starting point, and the ideal configuration is chosen for the self-collimation effect, which is analytically supported by group velocity dispersion and third-order-dispersion calculations. Then, numerical analyses in both time and frequency domains are performed to the ideal PhC design, which possesses a strong self-collimating characteristic, even at huge incident angles within the operating frequencies. Later, experimental measurements are conducted in microwaves, and the existing self-collimation property is still preserved at longer wavelengths in the millimeter scale. The microwave experiment as well as numerical analyses indicate that the designed PhC self-collimator allows overcoming possible misalignment problems at the PhC-source interface and enables a strong broadband beam channeling with a high transmission.

Broadband self-collimating phenomenon in a low-loss hybrid plasmonic photonic crystal.

A 2D planar self-collimating photonic crystal, based on a dielectric square lattice and a hexagonal lattice, is proposed. We demonstrate that the proposed structure can support the propagation of a hybrid surface plasmon polarition (SPP) mode with a loss of -0.017 dB/μm, and the mode size is only 0.33μm. The defined figure of merit is one order of magnitude higher than that of the dielectric-metal structure. In addition, the self-collimating angle of more than 10° can be tuned with a silica index change of 0.08. The proposed structure possesses broad operation bandwidth of 88nm and 58nm for a dielectric square lattice and a hexagonal lattice, respectively. These two kinds of photonic crystals promise potential applications in photonic modulators and SPP photonic devices.

Study on Tunable Self-Collimation in Photonic Crystals

Study on Tunable Self-Collimation in Photonic Crystals

An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection

Diffraction-free propagation of light has been demonstrated in free space for Bessel-like beams and for arbitrary beams in specially designed photonic crystals and metamaterials. The phenomenon is called self-collimation in photonic crystals and canalization in metamaterials, as the approaches to obtaining the effect are different. In both cases, however, diffraction-free propagation of light is achieved by making the dispersion surface of the material at a given frequency flat. In photonic crystals this is done by tuning the unit-cell dimensions close to the band-gap regime, and in metamaterials by tuning a hyperbolic-type metamaterial towards its transition to an ordinary elliptical metamaterial. In this work, we propose an alternative way to suppress optical diffraction in a metamaterial by adjusting the anisotropy of the finite-sized three-dimensional metamolecules and the material’s spatial dispersion. The approach allows matching the wave impedance of the material to that of the surrounding medium in a wide range of incidence angles and thereby also suppressing optical reflection from the material’s surface.

Spatially variant periodic structures in electromagnetics.

Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity.

Nonreciprocal self-collimation in two-dimensional gyromagnetic photonic crystals and its applications in signal separation

We investigate self-collimated electromagnetic waves in two-dimensional gyromagnetic photonic crystals (GPCs) fabricated by semi-cylinder rods. The nonreciprocal self-collimation transmission is found by means of band structure and equi-frequency contour (EFC) calculations. Progressively tilting flat EFC by optimizing the structure of GPC, we show that nonreciprocal spatial wavelength division can be achieved without any corrugations inside the structure. Further, the frequency range for the nonreciprocal spatial wavelength division can be flexibly manipulated by the external static magnetic field.

Optical switch based on the liquid–crystal-modulated self-collimating photonic crystals

In this paper, a compact optical switch for self-collimated light beams in a liquid–crystal-modulated photonic crystal is proposed. The designed optical switch is working at 1550 nm. The equi-frequency contours and band diagram of the structure are calculated by using plane wave expansion method. The transmission spectra for different liquid crystal rotation angle are computed with finite-difference time-domain method. Meanwhile, the steady-state field distributions of the light propagation in the structure are presented. The designed optical switch may find important applications in the photonic integrated circuits.

All-angle self-collimation in two-dimensional square array photonic crystals based on index contrast tailoring

A comprehensive study has been performed to achieve all-angle self-collimation in basic two-dimensional square array photonic crystals with cylindrical scatterers. Based on plane wave expansion and finite difference time domain analysis for both rod- and hole-type structures, we report on all-angle self-collimation (SC) in the first band of the structure, which results in loss suppression due to out-of-plane scatterings. A lower threshold for index contrast has been obtained to achieve all-angle SC, which offers more design flexibility regarding structural parameters. Furthermore, it has been shown that a minimum and maximum coupling efficiency enhancement of ∼40% and 80% can be achieved for the proposed structure, respectively, by introducing a row of scatterers with proper radius at the input and the output air/photonic crystal interfaces.

Complete photonic band gaps and tunable self-collimation in the two-dimensional plasma photonic crystals with a new structure

In this paper, the properties of complete photonic band gaps (CPBGs) and tunable self-collimation in two-dimensional plasma photonic crystals (2D PPCs) with a new structure in square lattices, whose dielectric fillers (GaAs) are inserted into homogeneous and nomagnetized plasma background are theoretically investigated by a modified plane wave expansion (PWE) method with a novel technique. The novel PWE method can be utilized to compute the dispersion curves of 2D PPCs with arbitrary-shaped cross section in any lattices. As a comparison, CPBGs of PPCs for four different configurations are numerically calculated. The computed results show that the proposed design has the advantages of achieving the larger CPBGs compared to the other three configurations. The influences of geometric parameters of filled unit cell and plasma frequency on the properties of CPBGs are studied in detail. The calculated results demonstrate that CPBGs of the proposed 2D PPCs can be easily engineered by changing those parameters, and the larger CPBGs also can be obtained by optimization. The self-collimation in such 2D PPCs also is discussed in theory under TM wave. The theoretical simulations reveal that the self-collimation phenomena can be found in the TM bands, and both the frequency range of self-collimation and the equifrequency surface contours can be tuned by the parameters as mentioned above. It means that the frequency range and direction of electromagnetic wave can be manipulated by designing, as it propagates in the proposed PPCs without diffraction. Those results can hold promise for designing the tunable applications based on the proposed PPCs.

An approach to achieve all-angle, polarization-insensitive and broad-band self-collimation in 2D square-lattice photonic crystals

We have investigated the possibility for achieving (in the same structure), an all-angle, polarization-insensitive and broad-band self-collimation (SC), one of...

Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator

We propose a simple and straightforward method to generate spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90° bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable, and could be extended to other kind of lattices as well.