Graded Photonic Crystal Research Articles

A tunable flat terahertz lens using Dirac semimetals: a simulation study

We propose and design a flat and tunable terahertz lens achieved through a two-dimensional photonic crystal composed of an array of rods made of a Dirac semimetal placed in air as the background medium. The structure of interest is a graded index photonic crystal, made possible by the slight variations in the rods’ radii in a direction perpendicular to the direction of the light propagation. Dirac semimetals' ability to respond to variations in their Fermi energy level manifested as a change in the refractive index provides the tunability of our proposed lens. The interaction of electromagnetic waves with the designed structure is investigated for both transverse magnetic and transverse electric polarizations using two-dimensional finite-difference time-domain method.

High pass filter based on one-dimensional graded photonic crystal

In this study, a graded thickness photonic crystal is studied containing metamaterial and air multilayers. Transmission spectra are calculated using the transfer matrix method. The transmission values of proposed structure increases with frequency and attain values as unity, which can show an application as optical high pass filter. The frequency corresponding to half transmission value i.e. cut-off frequency of proposed optical high pass filter can be tuned with the graded index parameter.

Study on Focusing Characteristics of Double-Period Graded Photonic Crystal Lens Based on Biconical Interferometry

Study on Focusing Characteristics of Double-Period Graded Photonic Crystal Lens Based on Biconical Interferometry

Focusing characteristics of graded photonic crystal waveguide lens based on interference lithography

Using multi-beam interferometry, a photonic structure with a graded intensity distribution is designed and obtained experimentally. Based on the structure, we choose different exposure thresholds and background materials to design a graded photonic crystal (GPC) lens with a graded air hole diameter. The transmission and focusing characteristics of the GPC lens with bismuth silicate crystal (BSO) and polymethyl methacrylate (PMMA) as background materials are investigated in the visible-light band. Comparatively speaking, the graded photonic crystal lens of BSO with a large refractive index had better performance. In addition, the focal intensity does not decrease significantly with increasing the angle of incidence. The focus point intensity remains above 93% of parallel incidence for both lenses.

Photonic band gap consequences in one-dimensional exponential graded index photonic crystals

We have investigated the photonic bandgap characteristics in one-dimensional (1-D) exponential graded photonic crystals (GPCs) in the microwave region. Proposed 1-D GPC structures are the stacked of the exponential graded index layers. In an exponential graded index layer, the refractive index between the boundaries of the layer modulates in an exponential fashion in terms of the layer's depth. We observe that the number of photonic bands increases with an increase in the graded layer's thicknesses. When the graded layer's thicknesses are proportional to one-quarter of the optical wavelength relative to the mean refractive index, observed photonic bands increase with an integral multiple of λ0/4 (λ0 represents the optical wavelength of the selected frequency). The bandwidth of photonic band gaps can be tuned with the modulations of the initial and final refractive index of the graded layer. Therefore, the desirable photonic bands can be controlled and achieved in a selected frequency range by choosing the GPC structure's convenient parameters. This work will facilitate the design of filters and multi-channel filters and provide more design freedom for other photonic devices. This work may also provide the basis for understanding the effect of exponentially graded material on photonic band gap characteristics in 1-D GPCs.

Multi-channel photonic bandgap consequences in one-dimensional linear, exponential, and hyperbolic graded-index photonic crystals

We present the structuring of different graded-index materials in the form of one-dimensional (1D) photonic crystals (PCs) for highly efficient light trapping and controlling photonic devices in terms of tuned and controlled photonic bandgap (PBG) performance. We consider hyperbolic, exponential, and linear refractive index variation in the graded-index layer. We systematically study the influence of structural and grading parameters on the bandgap performance for two different graded photonic crystal (GPC) structures formed by stacking different graded-index layers. Compared with conventional PCs, the GPC bandgaps can be changed and tuned by the refractive index profile of the graded-index layer. We show that the number of bandgaps increases with the graded-index layer thickness and the bandgap frequencies can be tuned by the grading profiles. We observe the sequential increment in bandwidth for the complete PBGs in the GPC structures with linear, exponential, and hyperbolic graded-index materials. We also study the influence of the stacking pattern and grading profiles on the bandgap, phase shift, group velocity, delay time, and field distribution. The proposed GPC configurations facilitate the design of reflectors, multi-channel filters, detectors, and other photonic devices. The study may also provide the basis of understanding of the influence of graded-index materials on the PBG characteristics in the GPCs.

Photonic bandgaps engineering in double graded hyperbolic, exponential and linear index materials embedded one-dimensional photonic crystals

We present the structuring of different double graded-index materials in the form of one-dimensional (1D) photonic crystals (PCs) for highly efficient light trapping and controlling photonic devices in terms of tuned and controlled photonic bandgap (PBG) performances. Considered 1D graded photonic crystal (GPC) structures are stacked of hyperbolic, exponential, and linear double graded index layers. In the graded index layers, the refractive indices vary in hyperbolic, exponential, and linear fashions as a function of the layer thickness. These configurations show that the operating frequencies and the number of PBGs can be tuned by controlling layer thickness, grading profiles, and grading parameters of the constituted graded layers. The changes in the grading profiles of the graded layers modulate the operation frequencies and also the number of PBGs. We also found that the operating frequencies and bandwidth of PBGs can be tuned by changing the values of initial and final refractive indices of the graded layer. Therefore, the desirable PBG regions and bandwidths can be achieved and controlled by selecting appropriate parameters of the systems. Results can be implemented to design tunable reflectors, multi-channel filters, sensors, and optical detectors. Also, this work may provide an understanding of the effect of different double graded-index materials on PBG characteristics in the GPCs.

Tunable filter properties in 1D linear graded magnetized cold plasma photonic crystals based on Octonacci quasi-periodic structure

Using the transfer matrix method (TMM), we study the transmission properties in Octonacci one-dimensional linear graded photonic crystals compressing a dielectric material and a magnetized cold plasma material. We found that the frequency and the quality factor of filters can be easily manipulated by tuning the external magnetic field (B). In addition, a linear gradation of the thickness allows to enhance the filter’s performance, such as the optimization of the system sensitivity and the increasing of the filtering quality factor. Finally, this study ends by discussing the influences which come from the incident angle for both transverse electric (TE) and transverse magnetic (TM). All of these above parameters are optimized to obtain a tunable filter with high quality factor. These filters may be of interest to design satellite transponders and weather radars.

Design of double-period graded photonic structure by multi-fiber interferometer

Based on the extension of Young’s interfering experiment, we propose a method for designing double-period graded photonic crystal (GPCs) structure and validate the experiment using multi-fiber interferometry. First, we extend the Young’s double-beam interfering theory to multi-beam interference. According to the simplified multi-beam interference theory and using multi-fiber interfering method, GPCs structures can be designed. Designed patterns can be controlled by positioning of fibers, number of fibers and interference distance. Second, a simple experimental system is built to validate the proposed theoretical model. GPCs structures are observed from the experiment. If we record the structure by using photo-sensitive medium, we will obtain GPCs lens. A good consistence is gotten between the theoretical and experimental results. This method has an important guidance for the design and fabrication of GPCs cylindrical lens and arrays.

Ripple suppression of third-order dispersion by using graded index one-dimensional photonic crystals

ABSTRACTA novel one-dimensional photonic crystal design for ripple suppression of third-order dispersion in ultrafast laser systems has been introduced. We investigated and compared the compensation behaviour of a simple photonic crystal and the proposed graded index structure with the same total thicknesses and periodicity at the near infrared region by the transfer matrix method. The results reveal that implementing the proposed graded index structure removes the pulse wings, produces clean pulses without the use of additional optical elements and also results in a dramatic reduction in the fluctuations of the group delay and third-order dispersion curves.

Maxwell’s fisheye lens as efficient power coupler between dissimilar photonic crystal waveguides

The imaging properties of the Maxwell’s fisheye (MFE) lens makes it a viable candidate to implement power coupling between different types of waveguides. A coupler based on the MFE lens is designed to couple a square lattice photonic crystal to a triangular lattice one. The MFE lens is implemented as ring-based multilayer and graded photonic crystal (GPC) structures. The performance of the ring-based MFE lens is better than the GPC-based one in the C-band of optical communication. The proposed ring-based MFE coupler has a footprint of 3.62×3.62μm and covers the entire C and U bands. The S and L bands are partially covered. The average insertion loss of 0.1dB and the maximum return loss of -11dB in the C-band is achieved.

Photonic crystal waveguide intersection design based on Maxwell’s fish-eye lens

The number of waveguides crossing an intersection increases with the development of complex photonic integrated circuits. Numerical simulations are presented to demonstrate that Maxwell’s fish-eye (MFE) lens can be used as a multiband crossing medium. In previous designs of waveguide intersection, bends are needed before and after the intersection to adjust the crossing angle resulting in a larger footprint. The presented design incorporates the waveguide bends into the intersection which saves footprint. In this paper, 4 × 4 and 6 × 6 intersections based on ideal and graded photonic crystal (GPC) MFE lenses are investigated, where 4 and 6 waveguides intersect, respectively. The intersection based on ideal MFE lens partially covers the O, E, S, C, L, and U bands of optical communication, while the intersection based on GPC-MFE lens is optimized to cover the entire C-band. For 4 × 4 and 6 × 6 intersections based on GPC-MFE lens, crosstalk levels are below -24 dB and -18 dB, and the average insertion losses are 0.60 dB and 0.85 dB in the C-band with lenses’ radii of 7×a and 10×a, respectively, where a is the lattice constant of the photonic crystal.

Design of an Electrically Tunable Micro-Lens Based on Graded Photonic Crystal

A micro-lens with an adjustable focal length (FL) is designed by using Graded Photonic Crystal (GPC) structures and a Polymer Dispersed Liquid Crystal (PDLC) material. The GPCs are formed by gradually changing the radius of the polymer rods in the Photonic Crystal (PC) with square lattices of polymer rods in the background of Liquid Crystals (LCs). The electrically tunable focusing characteristics of the micro-lens are investigated by loading a continuous voltage source to change the LC rotation angle. The sensitivity of the focal shift in terms of LCs tilting angle is 0.152 λ(nm/deg). Moreover, the effect of the defects and deviations on the focusing characteristics are also analyzed. This research is crucial for future applications of the proposed device in the integrated photonics and adaptive optics.

Maxwell Fish-Eye and Half-Maxwell Fish-Eye Based on Graded Photonic Crystals

We report on the design of the Maxwell fish-eye based on graded photonic crystals. It is a radially graded refractive index structure, whose remarkable property is to form perfect images in the sense of geometrical optics. The half-Maxwell fish-eye, which takes advantage of the symmetry of the previous, provides directive emission, which applies, amongst others, to wireless communications. The continuous gradient index is nevertheless difficult to practically realize. We show that graded photonic crystals make it possible to get the radially graded index of the Maxwell fish-eye and that the designed graded photonic crystals exhibit the expected properties. Graded photonic crystals fit the requirements of graded index optics. Moreover, they can be scaled with the wavelength.

Polarization-independent and tunable flat lenses based on graded index two-dimensional photonic crystals

In this paper, we perform numerical analyses on polarization-independent and tunable graded index lenses based on two-dimensional graded photonic crystals and utilizing liquid crystals. A simple triangular lattice is used for the graded lens, in which the refractive index profile in the transverse direction varies in such a way that the modulus of the refractive index is biggest at the centre and decreases towards the edges. Three variation functions of linear, parabolic and hyperbolic are implemented for creating graded structures and investigating focusing characteristics of the designed lenses, using plane wave expansion and finite-difference time-domain methods. Finally, we study the variation of the lenses properties by changing the optical axis orientation of liquid crystals. Our numerical results show that, through an appropriate set of design geometrical parameters, polarization-independent and tunable lenses can be achieved.

Study of one-dimensional nanolayered graded photonic crystal consisting of birefringent and dielectric materials

In the present paper, we have studied a comparison between dielectric-dielectric photonic crystal (PhC) and birefringent-dielectric PhC structure with, and without, gradation in the thickness of the layers of the proposed structure. Graded birefringent-dielectric PhC has a linear change in the thickness of the layers. With the help of the transfer matrix method, the proposed structures have been extensively investigated. It is found that photonic band gap (PBG) width and omnidirectional reflection band width has been widely enhanced, in graded birefringent-dielectric PhC structure as compared to the non-graded birefringent-dielectric PhC structure, for both TE and TM polarizations. We have also found that the gradation in the thickness of the birefringent layer is more effective, as compare the gradation in the thickness of the dielectric layer, for enhancement of reflection band width. The results obtained are quite good and thus, it may be widely used as broad band optical and omnidirectional reflector.

Controlling ultrashort pulses shape using one-dimensional graded index photonic crystals

In this study, we analyze the characteristics of a one dimensional coupled cavity-waveguide composed of SiO2/TiO2 layers in which three defects are located symmetrically in structure, using finite-time domain-method and transfer matrix method. Then we introduced a new structure based on mentioned one-dimensional structure in which the higher refractive index material is maintained constant, while lower refractive index slightly increases with a constant step value from the beginning to the end of the structure. Simulation results reveal that the graded structure represents unique features in comparison with the conventional structure.

Investigation of the 1D symmetrical linear graded superconductor-dielectric photonic crystals and its potential applications as an optimized low temperature sensors

Based on the Transfer Matrix Method (TMM) and the two fluid model for a superconductor and by taking account of the thermal expansion effect and thermo optical effects, we theoretically investigates the transmittance spectra of a one dimensional superconductor –dielectric photonic crystal (PC) designed as ((HLS)5/(SLH)5) made up of a BiGeO12(H), SiO2(L) and YaBO2CuO7 (S). The transmittance spectra shows that the system realizes a tunable filter which depends on a nonlinear relation with temperature. It's found that the symmetrical application of a linear deformation d(m) = d0+(m-1).δd(m) where d0 is the initial thickness of the layer m, δd(m) is the elementary added thickness at each layer. This linear gradation of the thickness permits to improve the temperature sensitivity of the system which acts as an optimized low temperature sensor.

Adaptive Graded Index Photonic Crystal Lens Design via Nematic Liquid Crystals

An adaptive graded index photonic crystal (GRIN PC) lens system is designed by using liquid crystal (LC) infiltration. LCs have the property to change their refractive indices when an external voltage is applied. This feature allows for the modulation on the effective index profile of the low-index contrast GRIN PC lens. Alongside this property, without changing the length of the designed 2D GRIN PC, the corresponding focal distance can be adapted from infinity to a certain positive or negative focal point by controlling the applied voltage. The effects of random perturbations and intentional line defects on the focal tuning capability of proposed 2D GRIN PC are also studied. Moreover, due to the scalability of PC’s dispersion relations, the sizes of the proposed devices can be adapted so that it may operate in either infrared or microwave regimes. Consequently, the proposed tunable polymeric GRIN PC can be implemented in various optical applications, such as near-field imaging and scanning systems, vision correction, and auto-focusing.

Tuning light focusing with liquid crystal infiltrated graded index photonic crystals

We perform numerical analyses of tunable graded index photonic crystals based on liquid crystals. Light manipulation with such a photonic medium is explored and a new approach for active tuning of the focal distance is proposed. The graded index photonic crystal is realized using the symmetry reduced unit element in two-dimensional photonic crystals without modifying the dielectric filling fraction or cell size dimensions. By applying an external static electric field to liquid crystals, their refractive indices and thus, the effective refractive index of the whole graded index photonic crystal will be changed. Setting the lattice constant to a=400nm yields a tuning of 680nm for focal point position. This property can be used for designing an electro–optic graded index photonic crystal-based flat lens with a tunable focal point. Future optical systems may have benefit from such tunable graded index lenses.