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Timestamp: 2019-04-18 17:12:53+00:00

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We have measured and characterized, over a wide range of doping levels, the UV-near-IR (190-2000-nm) absorption properties of Ti:sapphire crystals. We find that the strengths of absorption centered around 400-450 and 268 nm depend on the square of the Ti3+ doping level, suggesting an origin from pairs of Ti3+ ions. In addition, we have identified an absorption feature below 210 nm due to Ti3+, rather than Ti4+ charge-transfer transitions. Finally, our data on 800-nm-peak, near-IR absorption shows a complex lineshape, with a lower limit set by Ti3+ pair absorption. Thus the maximum possible Figure-of-Merit for Ti:sapphire reduces as the doping level increases.
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Fig. 1. Absorption spectra vs. wavelength from three samples. Note different scales for regions above and below 300 nm, and scale magnification for wavelengths above 700 nm. Data is pi-polarized for wavelengths greater than 300 nm and unpolarized at shorter wavelengths. Data below 300 nm is from CT2b, with data from CT2a plotted at longer wavelengths.
Fig. 2. Absorption spectra vs. wavenumber and energy from three samples also shown in Fig. 1. Three different absorption regions are indicated for discussion. Note the different scale (on the right) for Region 3, and scale magnification for Region 1.
Fig. 3. (a) Region 2 pi-polarized absorption spectra vs. wavelength from eight samples. (b) Same data as for (a) but normalized to absorption at 490 nm.
Fig. 4. (a) Region 2 sigma-polarized absorption spectra vs. wavelength from five samples. (b) Same data as for (a) but normalized to absorption at 490 nm.
Fig. 5. (a) Region 3 unpolarized absorption spectra vs. wavelength from seven samples. (b) Same data as for (a) but plotted with a logarithmic scale for absorption.
Fig. 6. (a) Region 3 pi-polarized absorption spectra vs. wavelength from eight samples. (b) Same data as for (a) but plotted with a logarithmic scale for absorption.
Fig. 7. (a) Region 3 sigma-polarized absorption spectra vs. wavelength from seven samples. (b) Same data as for (a) but plotted with a logarithmic scale for absorption. The data for samples SY7d and CT2b cuts off at 80 cm-1, the practical limit for our measurement instrument given the sample thicknesses.
Fig. 8. Region 3 pi- and sigma-polarized absorption spectra vs. wavelength from two samples, plotted together to provide a comparison.
Fig. 9. (a) Region 1 sigma- and pi-polarized and absorption spectra from three samples with relatively high absorption. (b) Same data as for (a) but for four samples with lower absorption.
Fig. 10. Pi-polarized absorption for sample UC1a, along with a two-Gaussian fit, with each Gaussian band shown, as well as the difference between data and fit plotted on the expanded right-hand axis.
Fig. 11. Sigma-polarized absorption for sample UC1a, along with a two-Gaussian fit, with each Gaussian band shown, as well as the difference between data and fit plotted on the expanded right-hand axis.
Fig. 12. (a) Region 2 pi-polarized residual absorption spectra from ten samples. (b) Same data as for (a) but plotted on logarithmic scale.
Fig. 13. (a) Region 2 sigma-polarized residual absorption spectra from seven samples. (b) Same data as for (a) but plotted on logarithmic scale.
Fig. 14. Plots of pi-and sigma-polarized residual absorption for three samples, for comparison of the two polarizations. Note expanded scale for sample UC1a, on the right-hand vertical axis.
Fig. 15. The ratio of pi-polarized absorption for the residual absorption at 400 nm to that of the peak absorption of the high band as a function of the high-band peak absorption coefficient. Data is for 17 samples, sorted and color coded for high-FOM samples from Synoptics (SY) and for all other samples, with the latter further sorted into low and high FOMs. We include linear fits (forced zero origin) to the high-FOM sets of samples, along with fitting parameters and associated R-squared values.
Fig. 16. (a) UC1a, Region-3 absorption, scaled Ti4+ absorption, and Ti4+-corrected absorption derived by subtracting the scaled absorption from the data (b) Same data as for (a) but for sample SY7d.
Fig. 17. The scaling factor for sample SY1a Ti4+-related absorption, versus the samples’ high-band peak absorption coefficient for both unpolarized and pi-polarized data.
Fig. 18. (a) Sample UC1a, Region-3 absorption, Ti4+-corrected absorption, Gaussian fitting to the E-Band peak and the difference between the Ti4+-corrected absorption and the fit. (b) Same data as for (a) but for sample SY7d.
Fig. 19. Plot of the percentage difference from unpolarized Ti4+-corrected data and Gaussian fit for E band around the peak, for three samples.
Fig. 20. Plot of ratio of the E-band peak absorption coefficient, determined by Gaussian fit, to the high-band peak absorption coefficient. We plot unpolarized, pi-, and sigma-polarized data, along with the characteristics of zero-intercept linear fits.
Fig. 21. Log plot of Ti4+-corrected, pi-polarized absorption (solid lines), along with fitted Urbach tails (dashed lines) and one dotted line showing our Gaussian fit (SY7d Gn) to the data for sample SY7d. Also included is data, without a fit, for Ti4+-related absorption in SY1b.
Fig. 22. (a) Pi-polarized, Region 2 residual absorption from five samples, with absorption from the tail of the E band subtracted. (b) Same data as for (a) but plotted on a log scale.
Fig. 23. (a) and (b). Similar to Fig. 22 but for sigma-polarized data.
Fig. 24. Log plot of Ti4+-corrected, unpolarized absorption (solid lines) at wavelengths below 210 nm (deep-UV absorption), along with fitted Urbach tails (dashed lines).
Fig. 25. (a) Pi-polarized, 820-nm absorption from samples listed in Table 5 as a function of high-band peak absorption coefficient. Blue solid line is square-law fit to data for all but the labeled sample points. (b) Same as for (a) but with FOM plotted. Blue solid line is inverse-law fit to all but labeled sample points.
Fig. 26. FOM vs. the inverse of the Ti4+ scaling factor, for the samples or sample sets indicated. The dotted line is a linear, zero-origin fit to the data for samples CT1a, CT2a, SY2a,d, and SY7b.
Fig. 27. (a) Pi-polarized, IR absorption from sample SY2b, with three-Gaussian fit, fit components and difference between data and fit plotted, all as function of frequency. (b) Same data as for (a) but with for sigma-polarized absorption from sample SY7c.
Fig. 28. (a) Pi-polarized, IR and visible-wavelength absorption from sample UC3, with fitted low- and high-band spectra, and an IR band determined by subtraction from the data of the fitted bands. Also shown is the difference between sum of the bands and the data. (b) Fitting of IR band to four Gaussian function bands (IR1-IR4) and difference from the fit.
Fig. 29. (a) Peak frequencies for IR1-IR3 bands as a function of IR3-band peak absorption, the latter on a logarithmic scale. Data is shown for both polarizations. Solid-fill data points are for Synoptics samples, while no-fill points are for all other sample. (b) Same as for (a) but showing fraction of fitting strength (see text).
Fig. 30. (a) Same as for Fig. 29(a) but for linewidth (FWHM). (b) Same as for 29(a) but showing polarization ratio for each band (see text).
Fig. 31. (a) Pi-polarized, IR absorption from sample SY1b, with plotted three-Gaussian fit, fit components and the difference between data and fit, all as function of frequency. (b) Same data as for (a) but with for sigma-polarized data, with only two Gaussians needed for fitting.
Fig. 32. Simplified energy-level diagrams for isolated and pairs of Ti3+ ions in sapphire. Two calculated energy levels for pairs are shown (a) from Ref.  and (b) from Ref. .
Table 2. Wavelength ranges for bands or regions discussed in paper.
Table 3. Two-Gaussian fitting parameters for pump band.
Table 4. Gaussian fitting parameters for E band, different polarizations.
Table 5. Absorption at 820 nm and FOM for selected samples.
Table 6. IR3 band (pi polarized) peak absorption for selected samples.
Table 7. Comparison of IR band properties, sample SY1b and others.
Table 8. Al3+-ion spacings in Al2O3 and calculated results on Ti3+ pairs.
Table 9. Oscillator strengths (f) for Ti:sapphire absorption features.
Wavelength ranges for bands or regions discussed in paper.
Two-Gaussian fitting parameters for pump band.
Gaussian fitting parameters for E band, different polarizations.
Absorption at 820 nm and FOM for selected samples.
IR3 band (pi polarized) peak absorption for selected samples.
Comparison of IR band properties, sample SY1b and others.
Al3+-ion spacings in Al2O3 and calculated results on Ti3+ pairs.
Oscillator strengths (f) for Ti:sapphire absorption features.

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