Reflectance Profile of BaTiO 3 on Multilayer Antireflection Coating Systems Filiz Karaomerlioglu  Department of Electronic and Computer Education, Faculty of Tarsus Technical Education, Mersin University, 33400 Mersin, Turkey Received September 26, 2010; accepted February 25, 2011; published online May 20, 2011 Antireflection (AR) coating systems are very important technology for optoelectronic devices. The optical characteristics of the system can be regulated by external electric or thermal field, and designed broadband ultra low reflection coating systems. It is investigated optical properties of multilayer AR coatings based on different ferroelectric materials to reduce reflectance in other studies. In this study, reflectance profile of BaTiO 3 on multilayer AR coating systems has been developed in the visible region. It has been used ZnSe and ZrO 2 as multilayer AR coatings, and BaTiO 3 as the substrate. Fortran program has been simulated on Fresnell equations base. # 2011 The Japan Society of Applied Physics AR coatings still exceed all the other types of coatings. In some applications AR coatings are required for the reduction of surface reflections. In other words, not only reflection is reduced but also transmittance is increased greatly. As it is a known fact that radiations incident upon the surface of an optical material is separated into reflected, transmitted, absorbed and scattered fractions. The fraction of available energy that is distributed among these is determined by the refraction indices. AR coatings can range from a single layer having almost zero reflectance at just one wavelength, to a multilayer system of many layers having nearly zero reflectance over a wide spectral range. 1) Many hundreds of papers for the design of multilayer, AR coatings, its computer programming, and industrial applications have been investigated in the past. 2–22) In many researches it was used generally glass as a substrate, thick films for multilayer systems, different types of techniques and methods in infrared or ultraviolet region of electromagnetic spectrum. Systematic method can not be applied for AR coatings. Computer simulation by trial and error which is assisted on a vector method or admittance loci 23) is used. Generally, the design of broadband AR coating is achieved by the use of gradient-index layers 22) or multilayers consisting of the different materials combinations of various thick- nesses. 1,2,6–10,17,18,20,21) Lee et al. 5) and Liou 11,12) have also presented a flip-flop method for realizing AR coating in which very thin high and low-index layers are used. Recently attention has been focused on characteristics of the ferroelectric based multilayered AR coating systems in the visible region of electromagnetic spectrum to reduce reflectance. 24–28) It has been developed a software program to simulate the performance of multilayer AR coatings based on the matrix theory. It is used ZnSe and ZrO 2 as different types of layers for multilayer AR coatings, and used LiNbO 3 as the substrate in these papers. The present paper is a continuation of my efforts to determine to what extent it might be possible to produce multilayers that approach the performance of ideal ‘‘perfect AR coatings’’ that would have zero reflection. Following this, the study on this subject is enhanced. In this paper, it is not disrupted characteristics of optical system. It is selected more sensitive materials like BaTiO 3 as a ferroelectric materials to external effects, like temperature and/or external electrical field; and these selected materials is easily found and cheap technologically. I 25,27) used the matrix theory to design an AR coating suited for LiNbO 3 with refractive index 2.28 in the visible region. The minimum reflectance curve of 10-layer coating has 0.0003% in the band between 515 and 590 nm. I 26) used different types of layers which are three-different materials like ZnSe, ZrO 2 , and Ag 2 AsS 3 , and LiNbO 3 as a substrate. The reflectance curves in the visible region for three, six, nine, and twelve layers have been simulated by the matrix theory. In order to a-(LHM) n -s configuration the minimum reflection curve of three-layer is just about 0.0085% in the range from 475 to 655 nm. For a-(MHL) n -s configurations, the minimum reflection curve of three-layer is just about 0.00042% in the range from 475 to 650 nm. In this study, in order to achieve high-performance visible AR coating designs, it is shown that by using n L ¼ 2:05 (ZrO 2 ), n H ¼ 2:39 (ZnSe), and n s ¼ 2:4334 (BaTiO 3 ). In case of two layer configuration, the reflection curve stays almost from 0.27 to 1.44%; for four-layer about 0.0612– 2.972%; and for six-layer nearly 0.00446–2.52%. The characteristic matrix for the jth sublayer with index n j and thickness d at normal incidence is given by M j ¼ cos 0 j i n j sin 0 j in j sin 0 j cos 0 j 2 4 3 5 ; ð1Þ where 0 j ¼ 2%n j d j cos  j =! is the optical phase thickness of the jth sublayer and ! is the wavelength of the light beam. On the other hand, we know that in ferroelectric materials temperature and polarization dependences of refractive index show nonlinear characters as 4) nð pÞ¼ nð0Þþ 1 2! @ 2 n @p 2 p 2 þ ; ð2Þ where nð pÞ is the refractive index depend on spontaneous polarization in ferroelectric phase, nð0Þ is refractive index in nonpolar phase, p is the polarization difference in ferro- electric phase. It can also be written the same expansion for temperature dependence of refractive index. Designs are often specified in terms of fractions of quarter-waves ! 0 =4 at a reference wavelength ! 0 because of the simplicity of assemblies involving quarter- and half- wave optical thicknesses. Usually only two or possibly three different materials are involved in designs and a convenient shorthand notation for quarter-wave optical thicknesses is H, M, or L; where H refers to the highest of the three indices, M the intermediate and L the lowest. 23) Based on the matrix theory 23) at normal incidence, it has been developed a Fortran program to design and simulate the performance of multilayer AR coatings that are consisted of insulator thin films for ferroelectric substrate in which are  E-mail address: filizkrm@mersin.edu.tr Japanese Journal of Applied Physics 50 (2011) 05FH05 05FH05-1 # 2011 The Japan Society of Applied Physics BRIEF NOTE DOI: 10.1143/JJAP.50.05FH05