optical properties of multilayer thin-film interference

LFNM 2006, 29 June - 1 July 2006, Kharkiv, Ukraine

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OPTICAL PROPERTIES OF MULTILAYER THIN-FILM INTERFERENCE FILTERS Iryna Y. Yaremchuk1, Volodymyr M. Fitio1, Yaroslav V. Bobitski1,2 1

Department of Photonics, Institute of Telecomunications and Radio Engineering Lviv Polytechnic National University 12 Bandera Str., 79013 Lviv, Ukraine Phone: 8-032-2582581, e-mail: [email protected] 2 Institute of Technology Rzeszow Unirsity 16b T. Rejtana St., 35959, Poland Abstract – The spectral properties of multilayer interference systems produced by multiple repeating of symmetric tree-component period, especially, the tree-component construction of dielectric thin films and the types of dielectric – metal – dielectric systems, were investigation. These thin films structures can be used as infrared interference filters as well as a standard for calibration of different spectral devises. The transmission and reflection analysis of these systems using matrix method was conducted. The obtained results allow to select systems with spectral characteristics that fit with applied problems. Keywords: interference, thin-films filter, multilayer system

INTRODUCTION Recently the interference filters are widely applied for the monochromatization of infrared radiation. Among them the most popular ones are multilayer dielectric filters, which are obtained by vacuum condensation on a substrate of many numbers of films with different materials, i.e. dielectrics and semiconductors. Interference phenomena appearing as a result of radiation passing through consecutive series of properly chosen films lead to change of its transmission and reflection coefficients for different radiation wavelengths. The purposeful change of these characteristics can be used for the creation of the filters. The development of the optical industry and laser techniques are closely joined with the development of optic elements covering with different thin films. The elementary system like to a Fabry-Perot standard was the most commonly used as pass-band filters. Behaviors and parameters of such systems were well studied for a long time [1,2]. Lately for the manufacture of pass-band filters are used other systems [3-6]. During last few years the quantum electronics and other directions of science and technique defined the necessity of new problems solving joined with interference coatings. Thus, the one of most important problems of design of thin-films systems arises, especially, narrow-band filters with definitely stabilized and regulated optical characteristics that stimulated a study of influence of different factors on interference coatings optical parameters. The type of coating which consists of metallic layer and dielectric interference system dielectrics is peculiar interesting for practice. For example, metal-dielectric mirrors belong to this type as well as interference filters [7-8]. They perform an important part in lasers optics technologies, that allow to obtain the coatings with practically any transmission and reflection characteristics on a given wavelength. This work covers study of spectral properties of both dielectric tree-component systems and dielectric–metal–dielectric structure with different thicknesses of single layers within certain period. It is important that on the basis of such structures the narrow-band filters of new type can be designed.

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2. MULTILAYER THIN-FILM SYSTEM OF DIELECTRICS For calculation as well as transmission and reflection analysis of the tree-component dielectric system a Ge-BaF2-Ge system was used. Ge was used as material with high refractive index, and BaF2 as material with low refractive index. Such materials are widely used in vacuum technologies of coatings deposition. They are enable to obtain layers of good optical quality, providing a required adhesion of film. They are suitable for design of all the types of filters, especially those, which are appointed for work at hard use conditions [1]. Refractive indices of Ge and BaF2 are defined to be 4.1 and 1.45 for wavelength region 1 μm ÷ 8 μm, respectively. As substrate for researching system KCI with refractive index of 1.47was used, refractive index of air is equal to 1. As a method of research, the matrix method proposed in [9] for the study of optical properties of the two-component pass-band interference systems is used For the calculation the thicknesses of BaF2 layers were used to be λ/4 (λ=8 μm). The thicknesses of layers of Ge were calculated in according to equation [10]: ɰ + 2 ⋅ πm (1) d1 = d 3 = ɥ 3 4ɪ n where: m = 0,1,2,... ; φ3 is the phase change for the reflected wave off the layer, which is situated between two limitless mediums ( Ge - in our cause); n – is the refractive index of the limitless medium. Investigations for s and p polarizations were conducted; thicknesses of layers of Ge were used to be 9.67969 μm. Fig. 1-3 show the dependences of transmission on wavelength of one period system, three periods’ system and four periods’ system for s and p polarizations at incidence angle of plane wave of 20º, respectively.

Figure 1 – The dependence of transmission on wavelength of one period’s system: solid line – ppolarization; diamonds – s-polarization.

Figure 2 – The dependence of transmission on wavelength of three periods’ system: solid line – p-polarization; diamonds – s-polarization.

Fig. 4 shows the dependence of transmission on wavelength of two periods’ system for s polarization at incidence angles of plane wave of 0º, 15º and 30º, respectively The quarter-wavelength systems represented a basis for forming on them of other systems modificating thicknesses of certain layers. Filters, which are based on phenomenon of optical interference, are highly universal and can be designed over optical range.


Figure 3 – The dependence of transmission on wavelength of four periods’ system: solid line – p-the polarization; diamonds – s-the polarization.

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Figure 4 – the dependence of transmission on wavelength of two periods’ system for s-the polarization: solid line – 0 º, crosses – 15 , diamonds – 30º.

3. THIN-FILM SYSTEM OF TYPE OF DIELECTRIC – METAL – DIELECTRIC The analysis of the transmission and reflection spectral dependences of the symmetric structures of type of dielectric – metal – dielectric was conducted for different dielectric constants by matrix method [9]. The calculations were conducted for wavelength of 1,5 μm. Silver and gold thin films were used as metallic films. Silver and gold films thicknesses were used to be 0.03 μm. The calculations were conducted for dielectric with refractive indices of 4.1, 6.7. The refractive index of metal was deduced from n = ε 1 + Im ε 2 . The dielectric permittivity ε 1 ɿ ε 2 , for silver, were calculated using equations [11]: ε 1 = 4.5 − 55λ2 − 0.005λ4 , ε 2 = −0.007λ + 1.1λ3 − 0.08λ5 (2) The dielectric permittivity ε 1 ɿ ε 2 , for gold, were calculated using equations [11]:

ε 1 = 7.5 − 50λ2 − 0.01λ4 , ε 2 = −0.5λ + 3.5λ3 − 0.025λ5

(3) The dielectric layers thicknesses were calculated according to the formula (1). The dependences of transmission on wavelength of the dielectric – metal – dielectric system including silver film with 0,03 μm thickness, the 6.7 refractive index dielectric with 0.59528 μm thickness and the 4.1 refractive index dielectric with 0.98345 μm thickness for both p and s polarizations at incidence angle of 20º are shown in Fig 5 and Fig 6, respectively.

Figure 5 – The dependences of transmission on wavelength of dielectric – the metal (silver) – dielectric structure a) ndielec=6.7; b) ndielec=4.1; solid line – without polarization; crosses – the ppolarization; boxes – the s-polarization.

Figure 6 – The dependences of transmission on wavelength of dielectric – the metal (silver) – the dielectric structure: ndielec=6.7; solid line – without polarization; circles – s-polarization.

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Fig. 7-8 show analogue investigations for system with thin film of gold. For analyses of spectral properties of the system of dielectric – metal –dielectric singly-periodic structure was used.

Figure 7 – The dependences of transmission on wavelength of dielectric – metal (gold) – dielectric structure: a) ndielec=6.7; b) ndielec=4.1; solid line – p-polarization; diamonds – spolarization.

Figure 8 – the dependences of transmission on wavelength of dielectric – metal (gold) – dielectric structure: ndielec=6.7; solid line – ppolarization.

It should be noted, that the structure’s transmission is significant at small changes of wavelength. Some deviations from optimal values lead to abrupt decrease of transmission. Hence, on the basis of such structures we can create polarization-sensitive filters with characteristics like to characteristics of interference filters.

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