Study of Optical Specifications of HfO2/Y2O3, Sc2O3 + MgO, and Ta2O5 + TiO2 Used as Resonator Reflector for Nd:YAG Laser (1064 nm)

A theoretical design of a multi-layer for Nd:YAG mirrors resonator is described in this work. An output coupler was designed and fabricated by successive thin layers to achieve very high transmittance at optical wavelengths around 1064 nm for Nd:YAG mirrors resonator. The different film optical filters were used to control the transmittance and reflectance. The three samples of dielectric materials composed of HfO2/Y2O3, Sc2O3 + MgO, and Ta2O5 + TiO2 were used and compared with each other in transmittance, reflectance, full width at half maximum (FWHM), physical thickness, optical thickness, geometric thickness, and incident angles by the software [1].


Introduction
Nd:YAG crystal is the most widely used solid-state laser medium due to its excellent optical and mechanical properties. Generally, most of the researches on Nd:YAG lasers focused on 4 F 3/2 -4 I 11/2 transition at the 1064 nm wavelength and also focused on how to develop the Nd:YAG resonator in this wavelength [2].

Theory
The design of the thin film reflectors for 1064 nm are Air/(HL) 45 /substrate where n is a real number. These reflectors consist of layers of two different materials alternately deposited on a substrate. Each layer has a thickness of one-quarter of the reference wavelength (1064 nm) [3]. The large difference between the refractive indices of the materials can improve the optical characteristics of the filters.
The materials used here were HfO 2 /Y 2 O 3 , Sc 2 O 3 + MgO, and Ta 2 O 5 + TiO 2 . Table 1 gives full details of the transmittance spectrum for different materials with varying thickness and the results of the different reflectors which were designed by alternating dielectric multilayer films using H for a high index and L for a low index, to meet the requirements of the high reflection for 1064 nm, for full information of these dielectric materials [4].      Also, Table 1 gives the full details of the reflectance spectra for the different materials chosen to design good reflectors for 1064 nm. The optimal design, with certain optical parameters, of the components using admittance loci analysis is simple, easy, and promising [5]. By using the thin-film account and the help of the program one can get good results for the reflector with various thicknesses. The results showed that the majority of these multi-layered dielectric materials are suitable for Nd-YAG back mirrors.

Titrations and Results of Three Dielectric Materials HfO2 + Y2O3, Sc2O3 + MgO, and Ta2O5 + TiO2
To examine the performance of the other oxides, different samples composed of HfO 2 /Y 2 O 3 , Sc 2 O 3 + MgO and Ta 2 O 5 + TiO 2 were used to design high reflectance and low transmittance mirrors for Nd-YAG laser (1064 nm) and titration them with each other in reflectance, Full width at half maximum (FWHM), physical thicknesses, optical thickness, geometric thickness, and incident angles.
The first titration: the reflectance (%) for materials. Figure 4 shows the reflectance (%) for each dielectric material to the 1064 nm.
The value of reflectance (%) is almost the same for all-dielectric materials with no clear difference [6]. Because of this, we need other standards for choosing the best dielectric materials, which have better properties. The second titration: the different dielectric materials with full width at half maximum (FWHM). Figure 5 shows a Full width at half maximum (FWHM) for each dielectric material to the 1064 nm. The value of Full width at half maximum (FWHM) is nearly the same for all-dielectric materials with no difference. Because of this, we need other standards for choosing the best dielectric materials, which have better properties for Nd-YAG back mirrors [7]. The third titration: the physical thickness (nm) for the materials.
The relationship between the total physical thickness [8] for thin-film coating and the types of material is shown in Figure 6. The thin film with the lowest physical thickness is Ta   The fourth titration: the geometric thickness for different oxides material. Figure 7 shows the geometric thickness for different oxides material.
The smallest value of geometric thickness is for Ta 2 O 5 + TiO 2 which equals 8.2 then for Sc 2 O 3 + MgO which equals 10.2 and finally is for HfO 2 /Y 2 O 3 , which equals 13.3. In thin-film coating, the smallest geometric thickness provides better coating [9]. Therefore, Ta 2 O 5 + TiO 2 material is the best to act as a back mirror for 1064 nm.  90. In thin-film coating, the smallest optical thickness (depth thickness) provide better coating [10]. Therefore, Ta 2 O 5 + TiO 2 material is the best to act as a back Nd-YAG Laser mirror.
The sixth titration: the relationship between the incidence angles and reflectance (%) for the oxides.
The materials Ta 2 O 3 + TiO 2 , Sc 2 O 3 + MgO, and HfO 2 + Y 2 O 3 with refractive indices 2.10000/2.25000, 1.85000/1.70000 and 1.88867/1.77300, respectively, were titrated with incidence angle. The filters designed of these oxides are ((LH) n ) the wavelength reference was 1064 nm. Previous analyses showed that the reflectance (%), physical thickness, optical thickness, geometric thickness and Full width at half maximum (FWHM) of these three materials were almost similar in this demand. Therefore, the titration between the incidence angle and reflectance of oxide materials Ta 2 O 3 + TiO 2 , Sc 2 O 3 + MgO and HfO 2 + Y 2 O 3 are needed. The results are listed in Table 2 and Table 3.  From the two figures (Figure 9 and Figure 10), we can see that the oxide materials Ta 2 O 3 + TiO 2 have reflectance changed slightly with the incidence angle compared with the rest of the dielectric materials in P and S-polarized light.
When we take into account all previous analyses and titrations of all oxide materials [11], we find that Ta 2 O 3 + TiO 2 is the best compared to the rest of the dielectric materials. The results proved that this material is the best to be used as a back mirror for Nd:YAG Laser (1064). Journal of Applied Mathematics and Physics

Conclusions
From the obtained results, one can conclude that: 1) The best reflector among the chosen materials was Ta 2 O 3 + TiO 2 with reflectivity for 1064 nm equal to 99.9%.
2) Among the chosen materials one can build Nd-YAG resonator composed of Ta 2 O 3 + TiO 2 with 66 Layers as the back mirror.
3) By applying the one-quarter of the reference wavelength (1064 nm) in the calculations for thin film, the best results for Nd-YAG mirrors resonator were achieved.