13.1 Fundamental Physical Constants

Physical constants useful in optics are listed in Table 13.1. The values of these constants are those listed by the National Institute of Science and Technology (NIST) available at the time of publication.

13.2 Conversion Quantities

Conversion quantities often used in optics are listed in Table 13.2. The conversion values for the electron volt and the atomic mass unit are the values listed by the NIST available at the time of publication.

In narrow-linewidth tunable laser design and spectroscopy, the units on linewidth and linewidth conversion units are important. From the approach to the uncertainty principle, given in Chapter 3, the following linewidth expressions are obtained:

given in meters (m), and its equivalent in the frequency domain

given in hertz (Hz). In spectroscopy, a widely used unit for linewidth is the reciprocal centimeter (cm⁻¹) (Herzberg 1950), as indicated in Table 13.2. This spectroscopist’s linewidth follows from Equation 13.2 since

where:

the units of Δx are in meters (m)

Conversion of the linewidth to units of cm⁻¹ can be done via the identity

so that the equivalent of Δν ≈ 30 GHz, which is (1/Δx) ≈ 100 m⁻¹, becomes (1/Δ x c) ≈ 1 cm⁻¹. A more specific example for the conversion of Δν ≈ 350 MHz, at λ ≈ 590 nm, is given in Table 13.3.

TABLE 13.2
Laser Optics Conversion Quantities

The conversion between photon energy in eV units and wavelength is carried out using the identity

This equivalence is given in Table 13.4 for the energy range 1 ≤E ≤ 10,000 eV.

13.3 Units of Optical Quantities

The units of optical quantities used throughout this book are listed in Table 13.5.

13.4 Dispersion Constants of Optical Materials

The Sellmeier dispersion equation applicable to various optical materials is given by

where:

λ is the wavelength at which the refractive index n is to be calculated

The constants for fused silica, SF10, calcium fluoride, and zinc selenide are given in Table 13.6. For the constants given in this table, λ is in μm units.

An important parameter is the dispersion of the prism material, or ∂n/∂λ (see Chapter 4), that can be obtained by differentiating Equation 13.6 so that

TABLE 13.6
Fundamental Physical Constants

which can be expressed more succinctly as

where:

Thus, the second derivative can be written as

The values for n(λ), λ_λn, and ${\mathrm{\nabla }}_{\mathit{\lambda }}^{\mathrm{2}}\mathit{n}$, for various materials of interest, are given in Table 4.1.

13.5 ∂N/∂T of Laser and Optical Materials

An important parameter in the design of solid-state lasers, tunable laser oscillators, and optical systems is the ∂n/∂T factor. This is given in Table 13.7 for a collection of optical materials and gain media.

Problems

13.1 For a tunable laser emitting at the wavelength of λ = 510.00, with a line-width of Δν = 300 MHz, express this linewidth in the wavelength domain (Δλ) and also in the spatial domain (1/Δx′).

13.2 Discuss the advantages and disadvantages of expressing the laser line-width in the wavelength domain (Δλ), the frequency domain (Δν), and the spatial domain (1/Δx′).

13.3 Find the wavelength equivalence, in nanometers, of 300 keV.

13.4 Starting from Equation 13.8 show that ${\mathrm{\nabla }}_{\mathit{\lambda }}^{\mathrm{2}}\mathit{n}$ is given by Equation 13.11.

13.5 Calculate for fused silica: n(λ), ∇_λn, and ${\mathrm{\nabla }}_{\mathit{\lambda }}^{\mathrm{2}}\mathit{n}$, at λ = 510.554 nm.

13.6 Calculate for fused silica: n(λ), ∇_λn, and ${\mathrm{\nabla }}_{\mathit{\lambda }}^{\mathrm{2}}\mathit{n}$, at λ = 308 nm.