In this report we present an investigation of the optical properties and band
structure calculations for the photonic structures based on the functional
materials- ferroelectrics. A theoretical approach to the optical properties of
the 2D and 3D photonic crystals which yields further insight in the phenomenon
of the reflection from different families of lattice planes in relation to the
presence of photonic gaps or photonic bands. We calculate the photonic bands
and optical properties of LiNbO3 based photonic crystals. Calculations of
reflection and transmission spectra show the features correspond to the onset
of diffraction, as well as to additional reflectance structures at large values
of the angle of incidence.Comment: 10 pages, 4 figures, 1 table, This paper were presented at 21 st
  International Symposium on Applications of Ferroelectrics (ISAF ECAPD PFM
  2012 Averio, Portugal) and accepted for publication in Ferroelectrics (2013

Mamedov, Amirullah M.

Ozbay, Ekmel

Simsek, Sevket

English

arXiv

Sevket Simsek

Amirullah M. Mamedov

Ekmel Ozbay

Crossref

Ferroelectrics

Two-Dimensional Ferroelectric Photonic Crystals: Optics and Band Structure

In this report we present an investigation of the optical properties and band structure calculations for the photonic structures based on the functional materials- ferroelectrics. A theoretical approach to the optical properties of the 2D and 3D photonic crystals which yields further insight in the phenomenon of the reflection from different families of lattice planes in relation to the presence of photonic gaps or photonic bands. We calculate the photonic bands and optical properties of LiNbO3 based photonic crystals. Calculations of reflection and transmission spectra show the features correspond to the onset of diffraction, as well as to additional reflectance structures at large values of the angle of incidence. © 2013 Copyright Taylor and Francis Group, LLC

Simsek, ŞEVKET

Hakkari Üniversitesi Akademik Veri Yönetim Sistemi

Two-dimensional ferroelectric photonic crystals: Optics and band structure

Simsek S.

Mamedov, A. M.

Özbay, Ekmel

Bilkent University Institutional Repository

Full Terms & Conditions of access and use can be found athttp://www.tandfonline.com/action/journalInformation?journalCode=gfer20Download by: [Bilkent University] Date: 13 November 2017, At: 03:53FerroelectricsISSN: 0015-0193 (Print) 1563-5112 (Online) Journal homepage: http://www.tandfonline.com/loi/gfer20Two-Dimensional Ferroelectric Photonic Crystals:Optics and Band StructureSevket Simsek , Amirullah M. Mamedov & Ekmel OzbayTo cite this article: Sevket Simsek , Amirullah M. Mamedov & Ekmel Ozbay (2013) Two-Dimensional Ferroelectric Photonic Crystals: Optics and Band Structure, Ferroelectrics, 448:1,23-28, DOI: 10.1080/00150193.2013.822272To link to this article:  http://dx.doi.org/10.1080/00150193.2013.822272Published online: 20 Sep 2013.Submit your article to this journal Article views: 92View related articles Citing articles: 1 View citing articles Ferroelectrics, 448:23–28, 2013Copyright © Taylor & Francis Group, LLCISSN: 0015-0193 print / 1563-5112 onlineDOI: 10.1080/00150193.2013.822272Two-Dimensional Ferroelectric Photonic Crystals:Optics and Band StructureSEVKET SIMSEK∗, AMIRULLAH M. MAMEDOV,AND EKMEL OZBAYBilkent University, Nanotechnology Research Center (NANOTAM),Ankara, TurkeyIn this report we present an investigation of the optical properties and band structurecalculations for the photonic structures based on the functional materials- ferroelectrics.A theoretical approach to the optical properties of the 2D and 3D photonic crystalswhich yields further insight in the phenomenon of the reflection from different familiesof lattice planes in relation to the presence of photonic gaps or photonic bands. Wecalculate the photonic bands and optical properties of LiNbO3 based photonic crystals.Calculations of reflection and transmission spectra show the features correspond to theonset of diffraction, as well as to additional reflectance structures at large values of theangle of incidence.Keywords Photonic band gap; transmission spectrumI. IntroductionOver the past ten years, there has been great interest in photonic crystal lattices (PCLs)due to their ability to manipulate light and great potential for technological applicationsin nanophotonics and integrated optoelectronic devices [1–3]. PCLs are artificial materi-als; optical and electronic properties of two (2D)- and three (3D)-dimensional PCLs areintensively studied with the goal of achieving control of electromagnetic propogation, and,especially, a complete photonic band gap in all directions [2].The properties of PCLs strongly depend on the configuration of the selected materials,which cannot be modified after fabrication. Also, photonic band gap (PBG) structuredepends on the refractive indices of the selected materials. If the PBG structure of the PCLscan be externally modulated by some other means, the PCLs can be applicable as activeelements of many optoelectronic devices. Therefore, as photonic crystalline material weused LiNbO3-ferroelectric material, that has interesting properties for the implementationof active PCLs.In this paper, we study the electronic band structure and optical properties ofthe 2D and 3D LiNbO3 based PCLs with square lattices by using FDTD technique,that based on computing eigenstates of Maxwell’s equations for periodical dielectricsystems [4].Received September 29, 2012; in final form March 4, 2013.∗Corresponding author. Email: ssimsek 001@hotmail.com[293]/23Downloaded by [Bilkent University] at 03:53 13 November 2017 24/[294] S. Simsek et al.II. Method of CalculationIn our simulation, we employed the finite-difference time domain (FDTD) technique whichimplies the solution of Maxwell equations with centered finite-difference expressions forthe space and time derivatives. FDTD schemes are especially promising for the investiga-tion of PBG structures, as they provide an opportunity of analyzing the spatial distributionof the electromagnetic field in PBG structure. All calculations in this work were performedusing OptiFDTD package [5]. OptiFDTD enables to design, analyze and test modernpassive and nonlinear photonic components for wave propagation, scattering, reflection,diffraction, polarization and nonlinear phenomena. The core program of OptiFDTD isbased on the Finite-Difference Time-Domain (FDTD) algorithm with second-order numer-ical accuracy and the most advanced boundary conditions—Uniaxial Perfectly MatchedLayer (UPML).The algorithm solves both electric and magnetic fields in temporal and spatial domainusing the full-vector differential form of Maxwell’s coupled curl equations. This allowsfor arbitrary model geometries and places no restriction on the material properties of thedevices.The FDTD is characterized by the solution of Maxwell’s curl equations in the timedomain after replacement of the derivatives in them by finite differences. Since it is atime-domain method, FDTD solutions can cover a wide frequency range with a singlesimulation run, and treat nonlinear material properties in a natural way. The time-dependentMaxwell’s equations (in partial differential form) are discretized using central-differenceapproximations to the space and time partial derivatives. The resulting finite-differenceequations are solved in either software or hardware in a leapfrog manner: the electricfield vector components in a volume of space are solved at a given instant in time; thenthe magnetic field vector components in the same spatial volume are solved at the nextinstant in time; and the process is repeated over and over again until the desired transientor steady-state electromagnetic field behavior is fully evolved [4].It is well known that LiNbO3 is an important material because of showing nonlinearbehavior. Here, a rectangle lattice with various types scatterer in a dielectric backgroundhas been considered at the effect of various parameters on a complete band gap has beeninvestigated. The permittivities of air and LiNbO3 are taken 1 and 5, respectively. We useLorentz Drude model for the permittivity of Al and we consider first five resonance terms[6]. Resonance frequency, plasma frequency, strength and damping frequency for Al isgiven Table 1. The LiNbO3 cylinders and spheres are 0.04 μm in diameter and cylindersTable 1Strengths, plasma frequencies, resonant frequencies and damping frequencies for AlsubstrateResonance Plasma Resonant Dampingterms Strength Frequency(rad/s) Frequency(rad/s) Frequency(rad/s)1 5.23 × 10−1 2.2758 × 1016 0 7.14 × 10132 2.27 × 10−1 2.2758 × 1016 2.461 × 1014 5.059 × 10143 5.23 × 10−2 2.2758 × 1016 2.346 × 1015 4.74 × 10144 1.66 × 10−1 2.2758 × 1016 2.747 × 1015 2.053 × 10155 3.0 × 10−2 2.2758 × 1016 5.276 × 1015 5.138 × 1015Downloaded by [Bilkent University] at 03:53 13 November 2017 Two-Dimensional Ferroelectric Photonic Crystals [295]/25Figure 1. Unit cell and associated Brillouin zone for square lattice (Color figure available online).are 0.06 μm in height. They are arranged in square mesh with a lattice constant of a =0.1 μm.III. Results and DiscussionPhotonic Band Gap CalculationThe goal of photonic band structure calculation is the solution of the wave equation for thePCLs, i.e., for a strictly periodic array of ferroelectric material. The resulting dispersionrelation and associated mode structure may then be further processed to derive somephysical quantities such as optical properties and imagine map of electric field in x and ydireciton.Figures 1 and 2 show the unit cell and associated Brillouin zone for LiNbO3 basedPCLs, and the geometry of calculated structures in PCLs. In Fig. 3, we show the hybridband structures for TE- and TM polarized radiations in 2D PCLs consisting of a squarelattice (lattice constant a) of the spheres and cylindirical dielectric rods. These strcuturesexhibit three complete bandgaps in the X-M and M- high symmetry directions.Figure 2. Geometry of the calculation for LiNbO3 based structures on Al substrate: cylinders (a)and spheres (b) (Color figure available online).Downloaded by [Bilkent University] at 03:53 13 November 2017 26/[296] S. Simsek et al.Figure 3. Hybrid photonic band structure of LiNbO3 based PCLs on Al substrate: cylinders (a) andspheres (b).Transmission and Reflection in Ferroelectric Based PCLLet us consider a photonic crystal structure in the form described in Fig. 1 and 2. Thisstructure is characterized by the dielectric permittivities of the layers of the medium ε. Thethicknesses of the layers are d1 and d2 and the structure period is a = d1 + d2. In the Lorentz-Drude approximation we study the transmission and reflection spectra of polarized wavesDownloaded by [Bilkent University] at 03:53 13 November 2017 Two-Dimensional Ferroelectric Photonic Crystals [297]/27Figure 4. Transmitted power spectrum of LiNbO3 PCLs on Al substrate: cylinders (a) and spheres(b).propagating in the xz-plane. For the structure unders study, the electric field distribution inthe layers has the formEx(n, t) =[Aneiαn(z−zn) + Bneiαn(z−zn)]e−iωtDownloaded by [Bilkent University] at 03:53 13 November 2017 28/[298] S. Simsek et al.Where An and Bn are the amplitudes of the incident and reflected waves in the nth layer,αn = (ω/c)√εn − sin2 θ , and θ is the angle of incidence of the radiation. The magnetic fielddistribution in the layers has the same classical expresseion.From the continuity of the electric and magnetic fields at the interface zn = zn+1between layers, we can obtain the system of equations which can be represented as thematrix equation. Let us now study particular features of the transmission and reflectionspectra of PCL by using FDTD software.Fig. 4 shows a typical seed band structure of the transmission spectrum of PCL withε1 = 1.0 (air), ε2 = 5 (LiNbO3) in the case of normal incidence of radiation on the structure.The first band gap of this PCL (rods) lies in the wavelength region between 125.6 nm and135.6 nm and the frequency ω0 lies in the center of this region (130 nm), the next bandgap lies in the wavelength between 180 nm and 199.4 nm and the frequency ω0 lies inthe center of this region (189.7 nm) and the last band gap lies in the wavelength between269.7 nm and 303.1 nm and the frequency ω0 lies in the center of this region (286.4 nm).For the PCL (sphere) the first band gap of this PCL (rods) lies in the wavelength regionbetween 116.4 nm and 128.1 nm and the frequency ω0 lies in the center of this region(122.3 nm), the second band gap lies in the wavelength between 159.1 nm and 181.6 nmand the frequency ω0 lies in the center of this region (170.4 nm) and the last band gap liesin the wavelength between 245.3 nm and 268.7 nm and the frequency ω0 lies in the centerof this region (257 nm).IV. ConclusionIn this paper a study of the photonic band structure for LiNbO3 based artificial PCLswith square primitive lattice is reported. The reduce photonic bands and reflectance andtransmittance spectra of LiNbO3 based PCLs with two different geometrical configuration(rods and spheres) are calculated by using FDTD scheme.References1. K. Sakoda, Optical properties of Photonic Crystals. Springer Berlin Heidlberg, New York 2005.2. K. Busch, M. Frank, A. Garcia-Martin, D. Hermann, S. F. Mingaleev, M. Schillinger, and L.Tkeshelashvili, A solid state theoretical approach to the optical properties of photonic crystals.Phys. Stat. sol. (a) 197(3), 637–647 (2003).3. C. Denz, S. Flach, and Y. S. Kivshar, Nonlinearities in Periodic Structures and Metamaterials.Springer Heidelberg Dordrecth, Nev York 2010.4. http://en.wikipedia.org/wiki/Finite-difference time-domain method5. http://www.optiwave.com/6. A. D. Rakic, A. B. Djurisic, J. M. Elazer, and M. L. Majewski, Optical properties of metallicfilms for vertical-cavity optoelectronic dvices. Applied Optics. 37, 5271 (1998).Downloaded by [Bilkent University] at 03:53 13 November 2017 

http://repository.bilkent.edu.tr/bitstream/11693/26716/1/Two-dimensional%20ferroelectric%20photonic%20crystals%20Optics%20and%20band%20structure.pdf

Two-Dimensional Ferroelectric Photonic Crystals: Optics and Band
  Structure

Two-Dimensional Ferroelectric Photonic Crystals: Optics and Band Structure

Abstract

Similar works

Full text

Available Versions

Crossref

Hakkari Üniversitesi Akademik Veri Yönetim Sistemi

Bilkent University Institutional Repository