Graded Index Materials Research Articles

DESIGN OF A PYRAMIDAL HORN ANTENNA WITH LOW E-PLANE SIDELOBES USING TRANSFORMATION OPTICS

Transformation optics is a convenient way to control the pattern of electromagnetic fields. In this paper, using a novel transformation, we propose the design procedure of a horn antenna having low backlobe and sidelobe levels in its E-plane. By applying conformal transformation, the rectangular horn proposed in this paper can be realized with isotropic materials. This proposed antenna can be easily implemented by both ordinary dielectric materials and isotropic graded refractive index (GRIN) materials. In the first proposed design, in addition to the isotropy, homogeneity is furthermore introduced into the horn, and only four kinds of isotropic materials are required throughout. In the second design, it is demonstrated that the designed structure can also be implemented by graded photonic crystals (GPCs) operating in metamaterial regime. They have low loss as well as broad frequency band and are easy to implement. Simulation results are presented to validate the design approach.

Tunable photonic band-gaps in one-dimensional photonic crystals containing linear graded index material

We have demonstrated control of the photonic band gaps (PBGs) in 1-D photonic crystals using linear graded index material. The analysis of PBG has been done in THz region by considering photonic crystals in the form of ten periods of second, third and fourth generation of the Fibonacci sequence as unit cell. The unit cells are constituted of two kinds of layers; one is taken of linear graded index material and other of normal dielectric material. For this investigation, we used a theoretical model based on transfer matrix method. We have obtained a large number of PBGs and their bandwidths can be tuned by changing the grading profile and thicknesses of linear graded index layers. The number of PBGs increases with increase in the thicknesses of layers and their bandwidths can be controlled by the contrast of initial and final refractive index of the graded layers. In this way, we provide more design freedom for photonic devices such as reflectors, filters, optical sensors, couplers, etc.

Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Mosre and Double-Periodic) photonic crystals

In this paper, we present the investigation on the photonic localization and band gaps in quasi-periodic photonic crystals containing graded index materials using a transfer matrix method in region 150–750THz of the electromagnetic spectrum. The graded layers have a space dispersive refractive index, which vary in a linear and exponential fashion as a function of the depth of layer. The considered quasiperiodic structures are taken in the form of Thue–Morse and Double-Periodic sequences. The grading profile in the layers affects the position of reflection dips and forbidden bands, and frequency region of the bands. We observed that vast number of forbidden band gaps and dips are developed in its reflection spectra by increasing the number of quasi-periodic generation. Moreover, we compare the total forbidden bandwidths with increasing the generation of the quasi-periodic sequences for the structures with linear and exponential graded layer. Results show that the different graded profiles with same boundary refractive index can change the position of localization modes, number of photonic bands and change the frequency region of the bands. Therefore, we can achieve suitable photonic band gaps and modes by choosing the different gradation profiles of the refractive index and generation of the quasi-periodic sequences.

Optical reflectance and omnidirectional bandgaps in Fibonacci quasicrystals type 1-D multilayer structures containing exponentially graded material

A theoretical study of optical reflectance and reflection bands of 1-D photonic quasi-crystals (Fibonacci type arrangement) composed of exponentially graded material is presented. The proposed structures consist of two different layers, one of them is of constant refractive index (L) and the other one is of exponentially graded refractive index (S) dielectric materials. Four different generations (2nd, 3rd, 4th and 5th) of the Fibonacci sequence for 10 periods in one dimension (1-D) are considered and compared in view of their optical reflectance and bandgaps for both TE and TM polarisations. Also, we proposed some heterostructures made by the combination of different Fibonacci generations and their periods to obtain suitable omnidirectional reflection band. We used the transfer matrix method (TMM) to obtain the reflectance, bandgaps and omnidirectional reflectional bandgaps (ODR) of such structures in near infrared spectrum (800–2200nm) at different angles of incidence. We show that ODR exists in these types of structures. The number of ODRs and total bandgap depend on the Fibonacci generations. Extraordinary ODR bandgaps are obtained in the case of heterostructures formed by the combination of different generations of the Fibonacci sequence. The ODR for these structures is similar to the ODR of photonic crystals containing left-handed materials. This work would be useful to study the Fibonacci type photonic crystals having graded index materials and also it will open new window to design several photonic crystal devices like sensors, reflectors, etc. in the infrared region.

Design of High-Gain Lens Antenna by Gradient-Index Metamaterials Using Transformation Optics

Transformation of space coordinates can be used as a convenient tool for producing a controlled electromagnetic field pattern. In this paper, using a conformal transformation, the design procedure of a lens antenna with high gain and low sidelobes is presented which can be realized by isotropic graded refractive index (GRIN) materials. Applying proper simplifying techniques, the designed lens can be made by non-resonant metamaterials or non-magnetic dielectrics having wide frequency band and low loss. A graded photonic crystal (GPC) operating in metamaterial regime is used for this purpose. By placing the lens in a horn antenna, a highly directive beam is achieved. It is also shown that by lateral displacement of the lens medium, the beam direction can be controlled to some extent. A multibeam antenna in which each beam can be controlled independently is also presented. Simulation results are used to justify the design approach.

Reduction of astigmatism in progressive addition lenses by employment of graded-index materials

Reduction of astigmatism in progressive addition lenses by employment of graded-index materials

Copolymer-Based Progressive Addition Lens with Graded Index Designed for Astigmatism and Distortion Correction

In this research, we propose to reduce astigmatism and distortion in a progressive addition lens (PAL) by employing a polymer-based graded-index (GRIN) material. We adopted the diffusion copolymerization method for the GRIN-PAL fabrication. The GRIN material was prepared by partial diffusion of methyl methacrylate (MMA) and 2,2,2-trifluoroethyl methacrylate (3FMA) monomers into the cross-linked benzyl methacrylate polymer gel. GRIN-PAL was prepared by polymerization of the GRIN material in a mold of commercially available PAL. As a result, methods to control Deltan, the diffusion length, and the order of the GRIN profile in polymeric GRIN materials were demonstrated. In a combination of the PBzMA gel and the MMA/3FMA diffusion monomer, 50/50 in volume provides the highest Deltan. The diffusion period mainly affects the diffusion length. These two parameters consequently determine the order of the GRIN profile and the focusing power that the GRIN provides. The difference in the ease of diffusion caused by the difference in the cross-linking density provides a method for positional control of the GRIN profile. Furthermore, GRIN-PAL using a polymeric material was successfully fabricated. Improvement in astigmatism and distortion was demonstrated using GRIN. Therefore, the GRIN material is suggested to be applicable for the further modification of the PAL with low astigmatism and distortion.

Off-axial pulse propagation in graded-index materials with Kerr nonlinearity — a variational approach

We analyze off-axial, self-focused pulse propagation in graded-index Kerr materials with the variational method. Equations which determine the characteristics of the beam, namely the optical path, the wavefront curvature, the beam width, and the pulse duration are derived and solved. We show that continuously adjustable negative group-velocity dispersion can be generated by off-axial propagation, and for pulse energy smaller than a critical value, negative group-velocity dispersion and Kerr nonlinearity warrant the existence of stable spatio-temporal solitary pulses.

Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity

We analyze spatio-temporal pulse propagation in graded-index Kerr materials with the variational method, and find that if the path of propagation provides negative group-velocity dispersion, stable solitary pulses exist for pulse energy smaller than a critical value. Spatial and temporal degrees of freedom cannot be analyzed separately due to their coupling through the Kerr nonlinarity. Our unified analysis not only elucidates the hidden coupling, but also clarifies relations between parameters of the solitary pulse. The analysis is verified by direct numerical simulation of the paraxial wave equation.

Generalized rate equations and modulation characteristics of external-cavity semiconductor lasers

Modulation characteristics such as the power response and the dynamic frequency shift (chirp) of an external-cavity semiconductor laser are analyzed using a set of generalized rate equations for a single longitudinal mode selected by the coupled-cavity device. The general formalism is applied to the specific case where the external cavity consists of a rod of graded-index material (GRINROD cavity). Particular attention is paid to the chirp reduction and its optimization in the presence of intercavity coupling. The results are in reasonable agreement with the recent experimental observations.