Titanium–Sapphire Laser

Abstract

As an example of a laser, we describe the titanium–sapphire laser.

Problems

5.1

Geometrical length of the resonator. Determine the optical length of a resonator (distance between reflector and an output coupling mirror 50 cm) that contains a titanium–sapphire crystal (length 1 cm; refractive index $n =1.76$).

5.2

Photon density. The diameter of a laser beam at the output coupling mirror is 10 cm. The laser generates visible radiation of a power of 1 W and fluorescence radiation of a power of 1 W too.

• (a) Estimate the power of laser radiation from the active medium of the laser passing through an area of 1 cm diameter in a distance 10 m away from a laser that emits radiation into a cone with a cone angle of 0.1 mrad.

• (b) Estimate the power of fluorescence radiation from the active medium of the laser passing through the same area.

5.3

What is the prescription of conversion of the shape of a narrow fluorescence spectrum on the wavelength scale into the shape of the spectrum on the frequency scale? [Hint: for the answer, see Sect. 7.6.]

5.4

Population of the upper laser level. A Ti$^{3+}$:Al$_2$O$_3$ crystal of a length of 1 cm is optically pumped in a cylindrical volume of 0.2 mm diameter.

• (a) Estimate the pump power necessary to excite a tenth of the Ti$^{3+}$ ions into the excited state.

• (b) Determine the absolute number of excited Ti$^{3+}$ ions.

• (c) Determine the energy stored as excitation energy and the corresponding energy density per liter.

• (d) Estimate the pump power necessary to excite a tenth of the Ti$^{3+}$ ions into the excited state in the case that the population disappears every 300 ns. [Why may it be possible that the population disappears regularly?]