Multiple Cavity Square Narrow and Broad Band Optical Filters for Infrared Region Application

In this work, theoretically optimization design of wide and narrow band pass filters have been suggested within middleinfrared region (MIR) that ranged from 9000 nm to 12000 nm. For the numerical calculation, use Germanium (Ge) as the substrate, Zinc sulfide (ZnS) and Cryolite (Na3A1F6) as high and low refractive index respectively. The results shows that, for normal incidence yields the transmittance is high ( T ˃ 99.5 ) at the center of Design wavelength (λo). Also, when the angle of incidence increase, The transmittance of electric polarization decreases and that of magnetic polarization increases , As in the case for the proposed design: Air/(LH)4LHHL(HL)4H(LH)4LHHL(HL)4(HL)4(HL)4HH(LH)4 (LH)4/Ge (TE=96.79) and (TM=99.57) at the angle 30 .


Introduction
Thin-film filters as a rule comprise of various limits between different homogeneous media furthermore, it is the impact which these limits will have on an incident wave .A filter which has area of transmission limited on either side by districts of rejection is known as a band-pass filter.For the broadest band-pass filters, the most reasonable development is a mix of long wave-pass and short wave-pass filters [1].Filters in which the essential characteristic is an unexpected change between an area of rejection and a district of transmission are known as edge filters.Edge filters are separated into two main categories , long wave-pass and shortwave pass.Thin-film filter technology gives an ordinary way to deal with delivering narrow-band infrared filters.Interference between light reflecting from each layer will add constructively for a narrow range of wavelengths, yielding a strong narrow-band reflection.Thin-film filters can accomplish highly efficient filtering [2].The most complete data on the execution of a filter is provided by spectral transmittance (T), reflectance (R), absorbance (A), and optical density [3, .The transmittance of a thin-film gathering is independent of the direction of spread of the light [1,5].Dielectric materials are preferred on the metals, because the metals have the absorption property, which increase the temperature of the coating and leads to damage it or decrease the reflectance and transmittance of the coating.While the dielectric materials have very low absorption which do not affect the reflectance and transmittance of the coating [6].
Optical spectral filters are of growing significance in today's world, where they play an important role in different fields, such as communication systems which are moving towards optical wavelengths.There are also used for wavelength separation in optical spectrometers and photometry [7], Many filtering methods are proposed based on film interference, Fabry-Perot(F-P) interference , guide-mode resonance Mach-Zehnder (M-Z) interferometer and photonic crystals etc. [8] .Fiber Bragg gratings, exhibit high reflectance bands Quarter-wave phase-shifted fiber Bragg gratings Serves as narrow-band transmission filters [9].The aim of the work, is to design multiple cavity square narrow and broad band filters for infrared region and study the variation of incidence angle on optical transmittance of designed filters.

Theoretical Part
Assume that a plane electromagnetic wave with wave-vector (K) is incident on a plane surface separating isotropic media with refractive indices n₁ and n₂ as show in Fig. 1 [ 10].
where n r is the relative refractive index between the two media.
The reflectance from aggregation of thin films is ascertained through the idea of optical admittance.we substitute the multilayer by a single surface which provides a admittance (Y) , which is the ratio of the total tangential electric and magnetic fields and is given by [1]: = 2   / , where ( δr ) is the phase shift ,( ) is the wavelength in free space ,( N) is the complex refractive index , ϑ is angle of incidence , (d) is physical thickness of the spacer and ( ηm) substrate admittance.
The order of multiplication is important.If( q) is the layer next to the substrate then the order There are many various methods of describing the performance of optical coatings and filters.
The fundamental equation that all filters performance depend on it is [11] R+T+A=1 ……… (7) For example, transmission and reflection filters intended for visual applications .Referring to Fig .2. at a wavelength λ the normal incidence spectral transmittance T(λ) of a filter placed between two semi-infinite media is equal to: where , T (λ) is the light intensity transmitted at that wavelength by the filter , Io (λ) is the incident intensity of the light at the same wavelength [11] .In this paper ,We design a computer

Fig. 2 .
Fig.2. the incident light on a plane-parallel [11]. ( 1) which using a computer program in MATLAB version 7 to calculate Transmittance within middle-infrared region (MIR) that ranged from 9000nm to 12000 nm. at designed wavelength λₒ=10600 nm.For the numerical calculation ,we used coating consist from Zinc sulfide (ZnS) (n=2.2) , Cryolite (Na3A1F6) (n=1.35) as materials and Germanium (n=4) as the substrate.Fig.0.shows the transmission spectra as the function of wavelength of coating( ZnS, Na3A1F6) and (Ge) as the substrate for three different proposed designs and their results shows in Table(1) .