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The optical absorption of Ti:Al2O3 single crystal has been measured at room temperature, in the wavelength region between 200 nm to 800 nm. The main absorption peaks at 491 nm and 562 nm, the weak infrared absorption band with a peak at 650 nm and the strong UV absorption band below 300 nm were observed. The refractive index is discussed using Fresnel's equation. In particular, the Sellmeier equation was determined in the visible region by means on non-conventional method based on the measurement of refraction by using UV-visible spectroscopy. The refractive indices decreased from 3.71 to 1.28 with wavelength in the range 400 - 800 nm.
Aluminum oxide (Al2O3) is a technological and industrial material of great interest, both for fundamental studies and for application, because of its hardness, good electrical insulation, useful optical properties, high surface area, and catalytic surface activity . Aluminum oxide (sapphire) being an important technological material is used as lasing material in solid state lasers, substrate for micro-electronics ceramic, radiation dosimeter, an insulator for the wall of nuclear fusion reactors and so on . Pure Al2O3 is a durable material with optical transmission spanning the range from UV to IR. Discovery of lasing action in Cr doped Al2O3 has created a basis of modern laser technologies. This role has been taken over more recently by Al2O3 doped Ti that is now successfully used as tunable laser material . Ti: Al2O3 (Ti: sapphire) is useful tunable laser material in the near infrared spectra region of 0.7 nm - 1.1 µm. Crystal of Ti: Al2O3 exhibit a broad absorption band, located in the blue-green region of the visible spectrum that is associated with phonon-coupled excitation of the 3d electron of the Ti3+ ions .
Optical properties of Ti: Al2O3 crystals have been studied [3-7]. The measurement of the optical absorption coefficient near the fundamental absorption edge is a standard method for the investigation of optically induced electronic transition in many materials. Generally, two types of optical transition i.e. direct and indirect occur at the absorption edge . Both of these transitions occur when an electromagnetic wave interacts with a valence electron and raises it across the energy gap to the conduction band.
In this paper, a detailed investigation on the optical absorption of Ti: Al2O3 in the visible and UV region is presented. The room temperature reflectance and transmittance data is analyzed to identity the refractive index of the single crystal Ti: Al2O3. The refractive index of a material depended on the crystal structure . Atoms which are easily polarisable, (i.e. easily displaced), electrons, give rise to a high refractive index, while those with tightly bound electron give rise to a low refractive index.
In this study, we examined Ti: Al2O3 single crystal doped with 0.1 wt. % Ti. The sample was obtained from RODITI International (England). The sample for measurement was polished at both of the large faces to an optical quality. The optical absorption, transmittance and refractivity spectrum was obtained using a Perkin Elmer UV-3101 PC UV-VIS-IR spectrophotometer in the range 200-800 nm at room temperature.
Result and Discussion
The absorption spectra of the Ti: Al2O3 single crystal at room temperature is shown in Figure 1. The spectra exhibit two wide bands in the range 400 - 600 nm, associated with the transitions within different d-levels of the Ti3+ ions (t2g àeg transition) [10,11]. The main absorption is a double structured band with overlapping peaks at 491 nm and 562 nm, due to transitions from the 2T2 ground state of Ti3+ to the 2E excited state. The results are similar as reported by Yamaga et.al . The visible band at 491 nm is the crystal filed absorption band and corresponds to intra-configurationally transition t2g àeg of the d1 configuration in the octahedral field approximation. The blue-green absorption band of Ti: Al2O3 is due to the vibronically broadened 2T2 à 2E transition . The weak infrared absorption band with the peak at 650 nm and the strong UV absorption band below 300 nm are observed in sample. In the absorption spectrum of Ti: Al2O3 is the strong charge transfer absorption which appears below 300 nm. Due to the charge transfer absorption which satisfies both spin and parity selection rules, it is strongly electric dipole allowed, with oscillator strength . This strong absorption makes the observation of structure within the band using crystal of moderate dopant concentration and seasonable thickness very difficult. Tippins reported in Lacovara  has studied the charge transfer bands of titanium (and other transition metals) in Al2O3, using low concentrations and thin samples. Tippins's spectrum of Ti: Al2O3 assigns a hump in the UV absorption energies are between 5.5 eV and 8 eV due to the charge transfer
Ti3+ + O2- à Ti2+ + O-
This is in good agreement with a simple theory. A weakened hump appears approximately between 4.5 eV and 5 eV is attributed to the charge transfer
Fe3+ + O2 à Fe2+ + O-.
Fig. 1 Absorption spectra observed at room temperature for Ti: Al2O3 single crystal
In the UV part of the spectra two strong absorption bands centered at 234 nm (5.30 eV) and 216 nm (5.74 eV). This observation indicates that the two bands are of different origins. As a matter of fact, the so-called E-band centered at 5.30 eV in the absorption spectrum of Al2O3-Ti3+ band was attributed to a bound excited of Ti3+, whereas the 5.74 eV band is attributed to 2pO2 à 3dTi4+ charge transfer transitions .
Determination of Refractive Index
The refractive index of Ti:Al2O3 single crystal can be calculated from the transmission spectrum in the wavelength region of 300 - 800 nm using the Fresnel equation  :
where R is the reflectance and n is the refractive index. The reflectivity can be calculated from the transmittance spectrum using the following equation:
The transmission spectrum of Ti:Al2O3 single crystal was measured as shown in Figure 2. The refractive index was calculated using Fresnel's equation from measurement refraction by using UV-visible spectroscopy. The dispersion relations were calculated using Sellmeier's refractive index dispersion distribution .
where n is the refractive index, is the wavelength, and A, B, C, D, and E are known Sellmeier parameters. The Sellmeier formula is selected since it facilitates a more compact expression for the fitting equation than would generally be expected from a completely empirical formulation. Also, this formula often provides at least a rough guide to the values of the other physical parameters of the optical material. Two terms in the Sellmeier equation, as in Eq (3), was used to fit the data consisting of the ordinary and extraordinary refractive index values measured at given wavelengths.
In the measured range, the Sellmeier equation fitted very well with the experimental values. The fitting parameters are shown in Table 1. The extrapolation to the short wavelength region showed, the Sellmeier fit is realistic, because the latter implied that the material is transparent at wavelength shorter than that at the absorption edge, as can be observed in Figure 3. The Sellmeier equation, with double resonance frequencies (B, D) is accurate enough at short wavelengths. The refractive index for the extraordinary wave is much larger than that of the ordinary wave, therefore, Ti:Al2O3 is an optically uniaxial positive crystal.
Fig. 2 The transmittance spectrum of Ti: Al2O3 single crystal
Table 1. Table of Sellmeier coefficients from the fitting of measured refractive indices using Sellmeier equation. The corresponding curves are shown in Figure 3
Fig.3 Extraordinary and ordinary refractive indices of Ti: Al2O3, ne and no, respectively, and the calculated curve fit with the Sellmeier equation. The corresponding fitting coefficients are given in Table 1
A typical result of refractive index obtained by using Sellmeier fitting methods is shown in Figure 3. The refractive index depends on the wavelength. That is clear the refractive index decreased with wavelength. It can be seen too, that the accuracy of the reconstructed curve is very good, which showed a very small absolute difference between the experimental and interpolated values.
The Ti:Al2O3 single crystal exhibited double-structured absorption peaks at 491 nm and 562 nm, the weak infrared absorption band with a peak at 650 nm and a strong UV absorption band at 234 nm. The optical results indicated that the main absorption is due to isolated Ti3+ ion, whereas the parasitic infrared band is due to Ti3+ - Ti4+ pairs. The refractive indices of Ti: Al2O3 single crystal as a function of the wavelength has been determined by the Fresnel equation and the dispersion relations were calculated using Sellmeier's equation. The extraordinary refractive index is much larger than the ordinary one, therefore Ti: Al2O3 is an optically uniaxial positive crystal.