Introduction

In this chapter we shall discuss in some detail the operating principles, characteristics, and design features of solid-state lasers in which the laser medium is an insulating or glassy solid. In many of these lasers the active particles are impurity ions doped into a host matrix. These lasers are pumped optically, with a pulsed or continuous lamp, and most commonly by another laser. Our discussion will build on the brief introduction to one laser of this class, namely the ruby laser, given in Chapter 3. The chapter will conclude with a discussion of the characteristics of the radiation emitted by such lasers and how this radiation can be modified and controlled in time.

Optical pumping in three- and four-level lasers

Optical pumping in an insulating solid-state laser is illustrated schematically in Fig. 7.1. Light from the pumping lamp(s) excites ground-state particles into an absorption band, labeled 3 in the figure. Ideally, particles that reach this state should transfer rapidly into the upper laser level, level 2. If transfer occurs preferentially to level 2 rather than to level 1, a population inversion will result between levels 2 and 1, and laser action can be obtained. The drain transition from level 1 back to the ground state should be fast, in order to keep level 1 from becoming a “bottleneck.” The performance of the laser will be influenced by several factors.

In this chapter we shall discuss both from a ray and from a wave standpoint how light can be guided along by planar and cylindrical dielectric waveguides. We shall explain why optical fibers are important and useful in optical communication systems and discuss briefly how these fibers are manufactured. Some practical details of how fibers are used and how they are integrated with other important optical components will conclude the chapter.

Introduction

We saw in the previous chapter that a Gaussian beam can propagate without beam expansion in an optical medium whose refractive index varies in an appropriate manner in the radial direction. This is a rather specific example of how an optical medium can guide light energy. However, we can discuss this phenomenon in more general terms. By specifying the spatial variation in the refractive index, and through the use of the wave equation with appropriate boundary conditions, we can show that dielectric waveguides will support certain “modes” of propagation. However, it is helpful initially to see what can be learned about this phenomenon from ray optics.

Introduction

All lasers are to some extent tunable. Their output frequency can be varied continuously without discontinuous changes in output power by moving the position of the oscillating modes under the gain profile. However, if the gain profile is not very wide then this range of tunability is limited. For any atomic gas laser, for example, where gain profiles typically have Doppler widths on the order of 1 GHz, tunability of a single axial mode over about a 1 GHz range can be accomplished by changing the optical length nl of the cavity. This can be done by moving one of the mirrors with a piezoelectric transducer and thereby varying the geometric length l, or by adjusting the laser pressure so as to adjust the index n. Although a tunable frequency range of 1 GHz might seem large in absolute terms, it represents a very small fraction of the operating frequency of the laser, 1014−1015 Hz, say. Discontinuous tunability in the infrared can be obtained by using a molecular gas laser, for which several vibrational–rotational transitions have gain. Systems, such as the CO2 laser, can offer many lines over a relatively broad wavelength region, but a graph of output power vs. frequency is not continuous.

To achieve continuous tunable laser operation over a broad wavelength region we must use an amplifying medium with a broad gain profile.

When the laser was first invented, it was described as “a solution looking for a problem.” This comment did not long survive scrutiny, and nowadays lasers are ubiquitous in many aspects of daily life, with many technological, artistic, and educational applications. This chapter highlights some of the important application areas where lasers have become essential.

Optical communication systems

Introduction

Optical communications systems have a long history. Ancient man signaled with smoke and fire, often relaying messages from mountain top to mountain top. However, this optical communication scheme had limited transmission capacity. Such messages could serve as a warning, as Queen Elizabeth the First of England planned when she had a network of bonfires erected to be set in the event of a seaborne invasion from Spain. The smoke signals transmitted by native Americans had the capacity to transmit various messages. Since the end of the eighteenth century,messages have been passed by semaphore – the use of flags to indicate the transmission of one letter at a time. This form of communication could transmit information at a rate of about one letter per second over a direct line of sight, although messages could be relayed over long distances. Such means of communication were not very secure: anyone in the line of sight to the message sender could read the information (if he or she knew the code).

Introduction

Gas lasers operate using a large number of different atomic and molecular gases and gas mixtures. On a macroscopic scale gases are intrinsically uniform, so the properties of the laser medium are immune to the defects and structural issues that affect lasers using solid materials. In addition, continuous variations of the composition and pressure of a gas medium offer a degree of flexibility in laser design. On the other hand, gases must be held in a container and lack the robustness offered by solid materials. Just as vacuum and gas-filled electronic tubes have been largely supplanted by solid-state devices, except in niche applications, gas lasers, especially atomic-gas lasers, have been largely replaced by lasers using solid active media. Even so, some gas lasers remain important in various applications, and the renewed interest in optically pumped gas lasers, which until relatively recently had seemed only of historical interest, suggests that no laser should necessarily be written off as “out-dated” prematurely. In this chapter we shall consider some of the fundamental processes which are used to produce, and maintain, population inversion in atomic gases. We shall see that the technological features of gas lasers, and the efficiency with which they can be made to operate, are intimately connected with the particular mechanism used to excite the upper laser level. Our attention will be concentrated on a consideration of gas lasers in which the laser action involves energy levels of a neutral or ionized atom.

Introduction

To give a little more practical emphasis to some of the ideas we have dealt with so far, let us consider some of the details of the two laser systems in which population inversion and laser oscillation were first demonstrated. One of these lasers uses an amplifying medium that is a crystalline solid – the ruby laser; in the other the amplifying medium is a gas – a mixture of helium and neon. In each case, the amplifying medium is pumped into a state of population inversion by feeding energy into it in an appropriate way. Laser oscillation occurs when the amplifying medium is placed between a pair of suitable aligned mirrors that provide the necessary optical feedback to cause oscillation to occur. The ruby laser was the first operational laser, being demonstrated on May 16, 1960 by Theodore Maiman of the Hughes Aircraft Company in Malibu, California [1].

That the ruby laser was the first laser to be demonstrated surprised many in the scientific community. This is because the ruby laser is a three-level laser, which was expected to be much more difficult to operate than a four-level laser. This is an important distinction, which we will examine before describing the first two lasers in detail.

Three- and four-level lasers

The distinction between three- and four-level lasers can be illustrtated with the aid of Fig. 3.2. Energy is fed into the system to move particles from the ground state, level 0, to a pumping energy level, level 3.

Introduction

In this chapter we discuss wave propagation in anisotropic media. We shall see that in such media the electric vector of a propagating wave is not in general parallel to its polarization direction, which is defined by the direction of its electric displacement vector. Further, for propagation of plane waves in a particular direction through an anisotropic medium two distinct possible polarization directions exist, and waves having these polarization directions propagate with different velocities. We shall discuss an ellipsoidal surface called the indicatrix and show how with its aid the allowed polarization directions and their corresponding refractive indices can be determined for wave propagation in a given direction. Other three-dimensional surfaces related to the indicatrix and their use in describing different optical properties of anisotropic media are also discussed. We shall concentrate our attention primarily on uniaxial crystals, which have optical properties that can be referred to an indicatrix with two equal axes, and will discuss how such crystals can be used to control the polarization characteristics of light.

Important anisotropic optical media are generally crystalline, and their optical properties are closely related to various symmetry properties possessed by crystals. To assist the reader who is not familiar with basic ideas of crystal symmetry, Appendix 8 summarizes a number of aspects of this subject that should be helpful in reading this chapter and some of those succeeding it.

Introduction

Many important laser systems operate using molecular species. The laser transition occurs between energy levels of the molecule, which may be in the gaseous, liquid, or solid state. To understand more about molecular lasers it is important to consider the additional complexity of the energy-level structure of a molecule compared with that of an atom. In this chapter we will explain the three different kinds of energy level – electronic, vibrational, and rotational – which occur for molecular species, and then go on to explain how such a complex energy-level structure allows the possibility of laser oscillation over a very broad wavelength range.

The energy levels of molecules

Electronic energy states

In an atom, the orbiting electrons move in the spherically symmetric potential of the nucleus, and the various energy levels of the system correspond, in a simple sense, to different orbital arrangements of these electrons. For example, an excited electron frequently moves into an orbit that takes it further from the nucleus. In a molecule the electrons travel in orbits that surround all the nuclei of the molecule, although quite often there will be considerable localization of some electrons near a particular nucleus. The electronic energy states of the molecule result from different arrangements of the orbiting electrons about the nuclei. Electrons that move from one electronic energy level of a molecule to another experience changes in energy that are broadly comparable to such jumps in atoms.

Introduction

Practical photonic systems can conveniently be divided into four distinct parts: (a) the optical source (or sources), (b) a passive optical structure, (c) an active optical structure, and (d) a detection system. A good example of such a system is the human eye, which is shown schematically in Fig. 13.1. In this system the source of light is the Sun, or artificial lighting that renders objects visible to the eye. The passive optical structure includes the cornea, the intraocular fluid, and other fixed structures in the eye. The active optical structure includes the deformable eye lens, whose shape is controlled by the ciliary muscles, and the iris, whose diameter is adjusted to control the amount of light entering the eye. The detector in this system is the retina, where photons are absorbed by special molecules, leading to chemical reactions that produce charges and subsequent electrical signals to the brain along the optic nerve.

We have already explored in some detail the fundamental physics, constructional details, and properties of lasers.We have also seen the connection between the amplifying medium and the optical structures that turn the laser amplifier into an oscillator. In this and the following chapters we will further examine the characteristics of various passive and active optical structures that are important in photonic systems. Initially we will discuss the characteristics of important passive optical components and systems. These will include optical materials, lenses, mirrors, prisms, diffraction gratings, interferometers, crystals, polarizers, and optical fibers.

Introduction

In this chapter we shall examine some of the characteristics of laser radiation that distinguish it from ordinary light. Our discussion will include the monochromaticity and directionality of laser beams, and a preliminary discussion of their coherence properties. Coherence is a measure of the temporal and spatial phase relationships which exist for the fields associated with laser radiation.

The special nature of laser radiation is graphically illustrated by the ease with which the important optical phenomena of interference and diffraction are demonstrated using it. This chapter includes a brief discussion of these two phenomena with some examples of how they can be observed with lasers. Interference effects demonstrate the coherence properties of laser radiation, while diffraction effects are intimately connected with the beam-like properties that make this radiation special.

Diffraction

Diffraction of light results whenever a plane wave has its lateral extent restricted by an obstacle. By definition, a plane wave traveling in the z direction has no field variations in planes orthogonal to the z axis, so the derivatives ∂/∂x or ∂/∂y operating on any field component give zero. Clearly this condition cannot be satisfied if the wave strikes an obstacle: at the edge of the obstacle the wave is obstructed, and there must be variations in field amplitude in the lateral direction. In other words, the derivative operations ∂/∂x and ∂/∂y do not give zero, and the wave after passing the obstacle is no longer a plane wave.

Introduction

In this chapter we shall continue our discussion of molecular gas lasers. Many of the lasers to be discussed here provide substantial CW and pulsed power output, or have unusual and innovative technical features. Some of the lasers to be discussed have already been encountered in another context in earlier chapters. For many lasers a change in the method of excitation enhances some important aspects of laser performance, for example providing higher power output or operation in a new wavelength range. Radical departures from traditional methods of gas-discharge excitation have been particularly important in allowing the development of many of the laser systems to be described in the present chapter.

Gas transport lasers

In many laser systems a fundamental limit to the average output power is set by the buildup of waste heat that results from inefficient laser operation. Even in the relatively highefficiency CW CO2 and CO lasers, collisions that destroy vibrationally excited molecules, rather than just leading to energy exchange from one molecule to another, cause the temperature of the laser medium to rise. In these lasers the temperature rise reduces the population inversion through thermal excitation of the lower laser level. The rise in temperature also reduces the gain through an increase in the Doppler width. Waste heat can also produce changes in the optical properties of the laser medium in a spatially inhomogeneous way. This leads to a phenomenon called thermal lensing.

Introduction

In this chapter we shall use a variety of analytic techniques to analyze periodic optical systems and understand their behavior. These are optical systems in which a ray crosses a repeating pattern of interfaces, a so-called stratified medium, or passes through a sequence of optical components that repeat in a periodic fashion along the axis.

These periodic systems include multi-layer structures that have special reflective or transmissive properties and structures whose dielectic properties vary symmetrically in two or three dimensions. Such periodic structures are often called photonic crystals. Periodic lens sequences are axisymmetric arrangements of multiple lenses arranged along an axial direction. They can be described as stable or unstable. Stable lens sequences have the ability to confine a propagating bundle of rays near to the axis in such a way that the rays never deviate by more than a certain finite distance from the axis and remain confined. Periodic lens sequences can also be used to study the paths of light rays bouncing back and forth between pairs of mirrors – optical resonators. This will allow us to deduce the stability condition for such resonators.

Plane waves in media with complex refractive indices

The relative permittivity and the relative permeability characterize a medium in terms of its difference from a vacuum. Most materials that are important in a discussion of lasers and optical devices are not strongly magnetic, and it is generally legitimate to assume that for such materials μr = 1.