Introduction

Abstract

We will ask and partly answer a few questions. What is the difference between a laser and a light bulb? In which frequency ranges are lasers available? Which are the sizes and the costs of lasers? Why is it necessary to have different types of lasers in the same frequency range? We will also mention some specific lasers and we will discuss the concept of the book.

Problems

1.1

Physical constants. Remember numerical values of physical constants (in units of the international system, SI).

• (a) $c =$ speed of light.

• (b) $h =$ Planck’s constant.

• (c) $\hbar =$ $h/(2 \pi )$.

• (d) $e =$ elementary charge.

• (e) $m_0 =$ electron mass.

• (f) $\mu _0 =$ magnetic field constant.

• (g) $\varepsilon _0 =$ electric field constant.

• (h) $k =$ Boltzmann’s constant.

• (i) $N_\mathrm{A} =$ Avogadro’s number.

• (j) $R =$ gas constant.

• (k) $L_0 =$ Loschmidt’s number.

[Hint: in examples in the text and in the Problems, an accuracy of several percent of a quantity is in most cases sufficient.]

1.2

Frequency , wavelength, wavenumber, and energy scale. It is helpful to characterize a radiation field on different scales: frequency $\nu$; wavelength $\lambda$; wavenumber $\tilde{\nu } = \nu /c {\,=\,} 1/\lambda$ ( = number of wavelengths per unit of length = spatial frequency) ; and photon energy $h \nu$ in units of Joule or eV. Express each of the following quantities by the corresponding quantities on the three other scales.

• (a) $\lambda =$ 1 $\upmu$m.

• (b) $\nu =$ 1 THz.

• (c) $\lambda =$ 1 nm.

• (d) $\tilde{\nu } =$ 1 m$^{-1}$.

• (e) $h \nu =$ 1 eV.

1.3

Express the following values on different scales:

• (a) kT for T = 300 K ($T =$ temperature); (b) 1 meV; (c) 1 cm$^{-1}$; (d) 10 cm$^{-1}$.

1.4

Power of the sun light and of laser radiation. The intensity of the sun light on earth (or slightly outside of the atmosphere of the earth) is 1, 366 W m$^{-2}$.

• (a) Evaluate the power within an area of 1 cm$^2$.

• (b) Estimate the power density ( = intensity) if the radiation incident on a 1 cm$^2$ area is focused to an area of 100 $\upmu$m diameter; focusing to a smaller diameter is not possible because of the divergence (5 mrad) of the radiation from the sun.

• (c) Determine the power density of the radiation of a helium-neon laser (power 1  mW, cross sectional area 1 cm$^2$) focused to an area that has a diameter of $1 \,\upmu$m.

1.5

Determine the time it takes light to propagate

• (a) A distance that corresponds to the diameter of an atom.

• (b) A distance of 1 cm.

• (c) From a point of the surface of the earth to a point on the surface of the moon (at a distance of 174, 000 km).