Solid State Lasers

Abstract

We discuss solid state lasers that make use of electronic states of impurity ions in a dielectric crystals or in glasses—other types of solid state lasers, namely semiconductor lasers that are based on electrons in energy bands of semiconductors, will be treated in later chapters.

Problems

15.1

Ruby laser .

• (a) The crystal of a Q-switched ruby laser is optically pumped by the use of a flash lamp so that almost all Cr$^{3+}$ ions are excited. Estimate the energy and the power of a laser pulse of 100 ns duration. [Hint: ignore oscillations that could cause a temporal structure in the pulse shape].

• (b) Laser oscillation is possible with a ruby crystal cooled to low temperature (4 K) with two plane parallel surfaces as reflectors (refractive index of ruby $n=1.76$). Estimate the threshold pump power of a laser with a ruby crystal (length 1 cm) pumped in a volume of 0.2 mm diameter by another laser (pump wavelength 530 nm); at low crystal temperature, the R$_1$ and R$_2$ lines are 100 times narrower than at room temperature.

15.2

Gain cross sections. Determine, by use of the data of linewidths and spontaneous lifetimes, the ratio of the gain cross section of the 1.06 $\upmu$m line of Nd$^{3+}$:YAG and of the gain cross section at the line center of Ti$^{3+}$:Al$_2$O$_3$.

15.3

Titanium–sapphire laser. Why is the energy distribution of vibronic energy levels of Ti$^{3+}$ in Al$_2$O$_3$ continuous while the vibronic energy levels of N$_2$ are discrete?

15.4

Laser tandem pumping. A femtosecond titanium–sapphire laser can be pumped with the frequency-doubled radiation of a Nd$^{3+}$:YVO$_4$ laser, which itself is pumped by use of a semiconductor laser.

• (a) Estimate the quantum efficiency of such an arrangement if the frequency doubling has a power conversion of 50%.

• (b) What is the advantage of the tandem pumping in comparison with the direct pumping of the titanium–sapphire laser with a semiconductor laser?

15.5

Fiber laser. Estimate the efficiency of an erbium-doped fiber laser pumped with a pump power twice the threshold pump power.

15.6

Explain the nomenclature ($^4$I$_{9/2}$, $^4$I$_{11/2}$, $^7$F$_{7/2}$ etc.) used for characterization of atomic states.