Self-collimation Phenomenon Research Articles

Spatially resolved x-ray detection with photonic crystal scintillators

We study the self-collimation phenomenon in photonic crystals (PhC) of wide bandgap materials for ultra-fast and high spatial resolution x-ray detection. We work on various heavy inorganic scintillators: BaF2, GaN, ZnO, CsI:Tl, NaI:Tl, LYSO, WO4 compounds, and plastic scintillators. Conventional scintillator detectors do not rely on a direct detection mechanism; hence, they require intricate design and fabrication processes. We offer a PhC design to observe self-collimation phenomena and overcome the ongoing spatial resolution challenges with these types of materials. We investigate the photonic band diagrams and iso-frequency contours. Fourier transforms based on finite-difference time-domain and frequency domain simulations are done for verifying and analyzing the self-collimation with the selected material. Light extraction efficiency at the PhC–air interface, depending on the truncation distance from the excitation point, is measured. Beam divergence values are calculated at 1 mm propagation distance. The vertical field profiles are obtained to observe the confinement. For the spatial resolution analysis, cross-sectional beam profiles have been examined. Gaussian envelopes are fitted to beam profiles for a consistent data analysis, and full-width-at-half-maximum values are considered. As a result, we theoretically prove and demonstrate the spatially resolved x-ray detection at the sub-micrometer level for a wide range of scintillator materials.

All-angle polarization insensitive cloaking in 2D photonic crystals

In this article, a 2D hole-type square lattice photonic crystal is considered to achieve all-angle polarization insensitive cloaking using self-collimation phenomenon. The regarded structure is composed of air holes in a high dielectric background of PbTe (nPbTe˜6) and is applicable for Mid-IR range. The bandwidth achieved for the maximum deviation angle of self-collimation of 2o is Δω/ωc=0.55% corresponding to Δλ=22.6nm at central wavelength of λc=4.1175μm. The presented structure is capable of cloaking of any structure in any size and shape since the propagating wave is not interacting with the cloaking region. To reduce the reflections from interfaces an optimized one-layer antireflection has been designed to reduce the reflections caused due to index mismatch. The structure and its functionality have been investigated by the PWE and the FDTD methods.

Wide-band low cross-talk photonic crystal waveguide intersections using self-collimation phenomenon

Abstract In this paper, wide-bandwidth low cross-talk W1 photonic crystal waveguide intersections are proposed based on self-collimation effect. The waveguides are realized using a 2D square lattice of GaAs rods in an air background. A second photonic crystal lattice is inserted in the intersection region which provides the self-collimation effect and eliminates the cross-talk. The region between the two lattices is optimized in this paper to produce the highest transmittance and widest bandwidth. Consequently, several waveguide intersections are designed based on the proposed method. Each has a different bandwidth and central wavelength. Due to their unique features such as the wide bandwidth, the low cross-talk value and having high transmittances, such structures have a variety of applications in highly integrated optical circuits which are realized based on photonic crystals. Plane wave expansion and finite difference time domain methods are used to analyze the structures. Simulation results show that a bandwidth of 124 nm and a maximum transmission value of 99% can be obtained using the proposed method.

Self-collimation in PT -symmetric crystals

We predict the self-collimation phenomena (or equivalently, dynamical localization) in two-dimensional $\mathcal{P}\mathcal{T}$-symmetric complex potentials, where the complex modulation is considered in the transverse, longitudinal, or simultaneously in both directions. Nondiffractive propagation is analytically predicted and further confirmed by numerical integration of a paraxial model. The parameter space is explored to identify the self-collimation regime in crystals with different $\mathcal{P}\mathcal{T}$ symmetries. In addition, we also analyze how the $\mathcal{P}\mathcal{T}$-symmetric potentials determine the energy distribution between spatial modes of the self-collimated beams.

Self-collimation-based photonic crystal notch filters

We introduce a design concept of an optical notch filter (NF) utilizing two perfectly reflecting mirrors and a beam splitter. Based on the new design concept, a photonic crystal (PC)-NF based on the self-collimation phenomenon in a two-dimensional PC is proposed and studied through finite-difference time-domain simulations and experimental measurements in a microwave region. The transmission properties of the self-collimation-based PC-NF were demonstrated to be controlled by adjusting the values of parameters such as the radius of rods in the line-defect beam splitter, distance between the two perfectly reflecting mirrors, and radius of rods on the outermost surface of the perfectly reflecting mirrors. Our results indicate that the proposed design concept could provide a new approach to manipulate light propagation, and the PC-NF could increase the applicability of the self-collimation phenomenon in a PC.

Design of highly efficient polarization beam splitter based on self-collimation on Si platform

A highly efficient polarization beam splitter based on self-collimation phenomenon in 2D square array of air holes in Si background is presented. For the presented structural parameters, a broad bandwidth of Δω/ωc = 1.3% for the incidence angle of |θin| < 80° is obtained. Here, a maximum deviation angle of |θp|max < 5° from ideal self-collimation is considered. The extinction ratios for TE and TM polarizations exceed 70 and 12 dB, respectively, in the whole frequency range through applying optimized anti-reflections at input and output ports. Structural simplicity and its compatibility with existing fabrication technologies along with the flexibility of the design to match for desired central frequency in IR range using scalability rule of Maxwell equations are outstanding features of the design.

Self-collimation-based photonic crystal Mach–Zehnder demultiplexer

A photonic crystal Mach–Zehnder demultiplexer (PC-MZDmux) with four output ports based on the self-collimation phenomenon in a two-dimensional (2D) PC is proposed and numerically studied using finite-difference time-domain simulations. The PC-MZDmux is composed of three Mach–Zehnder interferometers (MZIs) and each MZI consists of two 50:50 beam splitters and two perfect mirrors. Employed as the design parameters to achieve the demultiplexing functionality are the radius of phase control rods (PCRs) in the mirrors and the distance between the beam spitter and the mirror in the three MZIs. From spatial electric field distributions and transmission spectra, it is demonstrated that an incident self-collimated beam with four different frequencies can be demultiplexed to four output ports of the PC-MZDmux with proper design parameters. Our results indicate that this device design may constitute an efficient approach to light propagation manipulation and increase the application range of self-collimated beams.

The manipulation of self-collimated beam in phononic crystals composed of orientated rectangular inclusions

Self-collimation is wave propagation in straight path without diffraction. The performance is evaluated by bandwidth, angular collimating range and straightness of equi-frequency contours. The present study aims to manipulate the self-collimated beam in square-array phononic crystals by means of orientated rectangular inclusions. Finite element simulations are performed to investigate the effects of the aspect ratio and orientation angle of rectangular inclusions on the self-collimated beam. The simulation results show that the proposed design successfully achieves all-angle self-collimation phenomenon. In addition, it also shows that the propagation direction of a self-collimated beam can be effectively manipulated by varying the orientation angle of inclusions. Numerical simulation result of the S-shaped bend demonstrates that acoustic collimated beam can be steered with negligible diffraction. Overall, the proposed design has significant potential for the realization of applications such as collimators, acoustic waveguides and other phononic crystals-based systems.

Self-collimation-based photonic crystal Mach–Zehnder add-drop filters

Photonic crystal Mach–Zehnder add-drop filters (PC-MZADFs) based on the self-collimation phenomenon in a two-dimensional (2D) PC are proposed and numerically studied using finite-difference time-domain (FDTD) simulations. Each PC-MZADF is composed of a symmetric Mach–Zehnder interferometer (MZI) with an identical filter in each of its two different optical paths. Zizag-box resonators (ZBRs) and Fano resonators (FRs) are employed as the optical filters in rod-type and hole-type PCs, respectively. It is shown that self-collimated beams with the ZBR and FR resonant frequencies can be dropped or added using multiple-beam interference. We also show that the resonant frequencies of the resonators can be adjusted by varying the radii of their rods or holes. Our results indicate that this device design may constitute an efficient approach to light propagation manipulation and increase the application range of self-collimated beams.

A comprehensive comparison of photonic band gap and self-collimation based 2D square array waveguides

In this paper, one of the most recently introduced phenomena in Photonic Crystal structures was investigated to design self-collimation based waveguides. The advantages of using self-collimation property to design waveguides are discussed and the idea is thoroughly compared with conventional band gap engineered waveguides made by defects. The 2D square lattice waveguides presented in this article, guide the 1.55μm wavelength, most commonly used in telecommunication applications. Results indicate the high coupling efficiency enhancement in Self-Collimation based waveguides due to using low index contrast materials. The simulations are done using Plane Wave Expansion (PWE) and Finite Difference Time Domain (FDTD) methods and results confirm the value of using self-collimation phenomena in waveguide design.

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.

Photonic crystal logic gates: an overview

Photonic crystals are considered as the suitable structures for creating all-optical processors because of low loss and high capability in guiding and controlling the light. This paper contains a comprehensive review of the principles, different types of designing methods and operational improvements of optical logic gates. The presented designs are investigated and categorized into three groups of all-optical photonic crystal logic gates based on interference waveguides, resonator structures and self-collimation phenomenon. Two former structures can be designed by utilizing linear or nonlinear materials while the later one performs just in linear regime and is independent from the input beam intensity. In general, the main purpose of previously accomplished studies has been presenting the designs to be resulted in broad operational bandwidth, low power consumption, high switching speed, high contrast ratio and excellent integration capability by trading off between different parameters. Also a comprehensive study has been done on the advantages and disadvantages of different design methods.

Observation of valley-dependent beams in photonic graphene.

Valley-dependent propagation of light in an artificial photonic hexagonal lattice, akin to electrons in graphene, is investigated in microwave regime. Both numerical and experimental results show that the valley degeneracy in the photonic graphene is broken when the frequency is away from the Dirac point. The peculiar anisotropic wave transport property due to distinct valleys is analyzed using the equifrequency contours. More interestingly, the valley-dependent self-collimation and beam splitting phenomena are experimentally demonstrated with the armchair and zigzag interfaces, respectively. Our results confirm that there are two inequivalent Dirac points that lead to two distinct valleys in photonic graphene, which could be used to control the flow of light and might be used to carry information in valley polarized beam splitter, collimator or guiding device.

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.

Collimating emission from photonic crystals based on the quasi-zero-effective-index

Transmission of light waves at the frequency near the edge of the band gap in two-dimensional square lattice photonic crystals is studied by using the plane wave expansion method (PWM) and finite difference in time domain (FDTD) method. It is found that, directional emission from two-dimensional photonic crystals can be realized if the effective refractive index is nearly zero. Moreover, the direction of the emitting beam is independent of the orientation of the crystal lattice, but dependent on the direction of the crystal surface. This is quite different from the self-collimation phenomenon in photonic crystals.

Beam splitting using self-collimation phenomenon in photonic crystal

In this paper, we propose an in-plane beam splitter for self-collimated beams in a two-dimensional photonic crystal. An optical filter inserted on the propagation path of the input self-collimated beam divides this beam into two parallel equi-power self-collimated beams. The optical filter has a multistage configuration designed using well-known techniques. The proposed beam splitter has a compact configuration appropriate for integrated optics. Design procedure and the numerical results obtained using the finite-difference time-domain method, as well as a method for extraction of the S parameters of the beam splitter, are presented.

Millimeter-Scale and Large-Angle Self-Collimation in a Photonic Crystal Composed of Silicon Nanorods

We report the observation of a large-angle self-collimation phenomenon occurring in photonic crystals (PCs) composed of nanorods. Electromagnetic waves incident onto such PCs from directions covering a wide range of incident angles become highly localized along a single array of rods, which results in the narrow-beam propagation without divergence. A propagation length of 0.4 mm is experimentally observed over the wavelength ranging from 1540 nm to 1570 nm even in the large incident angle case, which is a very considerable length scale for on-chip optical interconnection.

Compact design of all-optical logic gates based on self-collimation phenomenon in two-dimensional photonic crystal

Optical logic gates are a basic and fundamental component for optical networks and optical computing. The authors propose a structure for AND, NAND, XNOR, and NOR logic gates in two-dimensional photonic crystal, which utilizes dispersion-based self-collimation effect. The self-collimated beam is split by the line defect and interferes with other self-collimated beams. This interference may be constructive or destructive based on its phase difference. This phenomenon is employed to realize all optical logic gates. The gates are demonstrated numerically by computing electromagnetic field distribution using finite difference time domain (FDTD) method. The results ensure that this design could function as AND, NAND, XNOR, and NOR logic gates. The size of the structure is about 10 µm × 10 µm, which, in turn, results in increasing the speed, and all the gates are realized in the same configuration. On-off contrast ratios of the gates are about 6 dB.

Self-Collimation in Square Lattice Two Dimensional Photonic Crystals with Ring-Shaped Holes

We demonstrate self-collimation phenomena based on a new type of photonic crystals made of square lattice with ring shaped holes. The plane wave expansion (PWE) method is used to get the three dimensional band diagram and equi-frequency of the second band which displays the self-collimation phenomena for the structure we proposed in this paper. The collimation angle is mainly depending on the maximum flatness half width (MFHW) of the equi-frequency. The FDTD method is employed to demonstrate the electric field amplitude distributions for the collimation phenomena. Partly, in order to achieve high efficient coupling of the input and output port, we modify both surface structures to modulate the wave-front to obtain desired effect. The parameter of the input surface is modified which will prevent the production of surface modes which takes away the EM power and enhance the transmittance. For a square lattice with the modified parameters at each side of the input surface, the surface modes are suppressed to couple with the continuum of the dielectric waveguide modes. More importantly, they might have potential application in integrated optical circuits.

Ring-type Fabry-Pérot filter based on the self-collimation effect in a 2D photonic crystal

We propose a ring-type Fabry-Pérot filter (RFPF) based on the self-collimation effect in photonic crystals. The transmission characteristics of self-collimated beams are experimentally measured in this structure and compared with the results obtained with the simulations. Bending and splitting mechanisms of light beams by the line defects introduced into the RFPF are used to control the self-collimated beam. Antireflection structures are also employed at the input and output photonic crystal interfaces in order to minimize the coupling loss. Reflectance of the line-defect beam splitters can be controlled by adjusting the radius of defect rods. As the reflectance of the line-defect beam splitters increases, the transmission peaks become sharper and the filter provides a Q-factor as high as 1037. Proposed RFPF can be used as a sharply tuned optical filter or as a spectrum analyzer based on the self-collimation phenomena of photonic crystals. Furthermore, it is suitable for a building block of photonic integrated circuits, as it does not back reflect any of the incoming self-collimated beams owing to the antireflection structure applied.