Optical Absorption

The absorption limit of 8.73 eV in Table 23 is close to the band gap of 8.8 eV for alu­mina. At energies lower than 8.73 eV, trace impurities and defects in the alumina lead to absorption tails as described in [49]. Values of n and к at higher energies than

8.73 eV are given in Table 23 to three or four significant figures. Values from different research groups can vary substantially [49]; those in Table 23 are from [50]. See [49] for n and к values at many more energies (wavelengths).

The values of к in Table 23 show a maximum at about 13 eV, which can be attributed to exitonic absorption [49]; other electronic processes in the ultra-violet spectral range are also described in [49].

Appreciable absorption begins in the infrared spectral range above a wavelength of 4.0 pm, as shown in Table 24; there are absorption peaks at 17.24 pm (580 cm-1) and

22.73 pm (440 cm-1), which result from lattice vibrations. For more details see [49]. The optical anisotropy of alumina results in slightly different n and к values for the

ordinary and extraordinary ray, as shown in detail in [49] (see Table 22). This anisot­ropy is related to the hexagonal (rhombohedral) structure of the alumina.

Table 21 Refractive Index of sapphire at 25°C in the spectral range where к < 10 6, from [49, 50]

Wavelength, X, (|im)

Refractive index, n

Wavelength, X (pm)

Refractive index, n

0.1464

2.231

1.367

1.749

0.1603

2.070

1.530

1.747

0.1802

1.947

1.709

1.743

0.200

1.913

1.960

1.738

0.220

1.878

2.153

1.734

0.240

1.854

2.325

1.731

0.260

1.838

3.244

1.704

0.280

1.824

3.507

1.695

0.300

1.815

3.707

1.687

0.330

1.804

4.000

1.675

0.361

1.794

0.405

1.786

0.436

1.781

0.486

1.775

0.546

1.771

0.579

1.769

0.644

1.765

0.707

1.763

0.852

1.759

0.894

1.758

1.014

1.755

Table 22 Refractive index [16], constants at 20°C from 0.2 to 5.5 mm, from [49, 50]

Term

Ordinary ray

Extraordinary ray

*1

0.0726631

0.0740298

*2

0.1193242

0.1216529

*3

18.028251

20.072248

A

1.4313493

1.5039759

0.65054713

0.5506141

A3

5.3414021

6.5927379

The refractive index of alumina increases slightly with increasing temperature T in the visible and near-visible spectral range. The value of the temperature coefficient dnl dT of the refractive index from wavelengths 0.4-0.8 pm is about 13(10)-6°K-1 [49].