‘Nonlinear’ optical phenomena are not part of our everyday experience. Their discovery and development were possible only after the invention of the laser.

In optics we are concerned with the interaction of light with matter. At the relatively low light intensities that normally occur in nature, the optical properties of materials are quite independent of the intensity of illumination. If light waves are able to penetrate and pass through a medium, this occurs without any interaction between the waves. These are the optical properties of matter that are familiar to us through our visual sense. However, if the illumination is made sufficiently intense, the optical properties begin to depend on the intensity and other characteristics of the light. The light waves may then interact with each other as well as with the medium. This is the realm of nonlinear optics. The intensities necessary to observe these effects can be obtained by using the output from a coherent light source such as a laser. Such behaviour provides insight into the structure and properties of matter. It is also utilised to great effect in nonlinear-optical devices and techniques which have important applications in many branches of science and engineering.

Another effect of light on matter can sometimes be to induce changes in the chemical composition; such ‘photochemical’ processes lie outside the subject of this book.

Origins of optical nonlinearity

We now consider in a simple way how nonlinear-optical behaviour might arise.

Introduction

LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. As the name implies, in a laser, the process of stimulated emission is used for amplifying light waves. It was as early as 1917 that Einstein first predicted the existence of two different kinds of processes by which an atom can emit radiation; these are called spontaneous and stimulated emissions. The fact that the stimulated emission process could be used in the construction of coherent optical sources was first put forward by Townes and Schawlow in the USA and Basov and Prochorov in the USSR. And finally in 1960 Maiman demonstrated the first laser. Since then the development of lasers has been extremely rapid and laser action has been demonstrated with gases, solids, liquids, free electrons, semiconductors etc.

The three main components of any laser are the amplifying medium, the pump and the optical resonator. The amplifying medium consists of a collection of atoms, molecules or ions which act as an amplifier for light waves. Under normal conditions, the number of atoms in the lower energy state is always larger than the number in the excited energy state; as such, a light wave passing through such a collection of atoms would cause more absorptions than emissions and therefore the wave will be attenuated. Thus in order to have amplification, it is necessary to have population inversion (between two atomic states) in which there is a large number of atoms in the higher energy state as compared to that in the lower energy state.

Introduction

Integrated optics is a new and exciting field of activity which is primarily based on the fact that light can be guided and confined in very thin films (with dimensions ∼ wavelength of light) of transparent materials on suitable substrates. By a proper choice of substrates and films and a proper configuration of the waveguides, one can perform a wide range of operations such as modulation, switching, multiplexing, filtering or generation of optical waves. Due to the miniature size of these components, it is possible to obtain a high density of optical components in space unlike the case in bulk optics. These devices are expected to be rugged in construction, have good mechanical and thermal stability, be mass producible with high precision and reproducibility, and have a small power consumption.

One of the most promising applications of integrated optics is expected to be in the field of optical fibre communications. As discussed in Chapter 13, the field of optical fibre communication has assumed tremendous importance because of its high information-carrying capacity; it is here that integrated optics is expected to play an important role in optical signal processing at the transmitting and receiving ends and on regeneration at the repeaters. Other important applications of integrated optics are envisaged to be in spectrum analysis (see Chapter 19) and optical signal processing.

In addition to the above, use of integrated optic techniques may lead to the realization of new devices which may be too cumbersome to be fabricated in bulk optics.

Introduction

In all that has been discussed in earlier chapters we have assumed that when a light beam propagates through a material, the properties of the material are not affected by the light beam itself. However, if the intensity of the light beam is large enough, the properties of the medium (such as refractive index etc.) are affected and the study of the propagation of a light beam becomes quite involved. For one thing the principle of superposition does not remain valid. This is the domain of nonlinear optics where many new effects are observed. Basically, the nonlinear effects are due to the dependence of properties such as the refractive index on the electric and magnetic fields associated with light beam. Before the advent of lasers, the electric fields associated with light beams were so weak that nonlinear effects could not easily be observed. With the advent of laser beams, it is now possible to have electric fields which are strong enough for many interesting non-linear effects to be observed. It is of interest to mention that the fact that intense electric and magnetic fields change the properties of a medium has been known for a very long time. In 1845 Faraday discovered that the plane of polarization of a light beam propagating through glass is rotated if a magnetic field is applied along the direction of propagation of the light beam.

Introduction

Since optical frequencies are extremely large (∼ 1015 Hz), as compared to conventional radio waves (∼ 106 Hz) and microwaves (∼ 1010 Hz), a light beam acting as a carrier wave is capable of carrying far more information in comparison to radio waves and microwaves. It is expected that in the not too distant future, the demand for flow of information traffic will be so high that only a light wave will be able to cope with it.

Soon after the discovery of the laser, some preliminary experiments on. the propagation of information-carrying light waves through the open atmosphere were carried out, but it was realized that because of the vagaries of the terrestrial atmosphere – e.g., rain, fog etc. – in order to have an efficient and dependable communication system, one would require a guiding medium in which the information-carrying light waves could be transmitted. This guiding medium, is the optical fibre which is hair thin and guides the light beam from one place to another (see Fig. 13.1). In addition to the capability of carrying a huge amount of information, fibres fabricated with recently developed technology are characterized by extremely low losses (∼ 0.2 dB/km) as a consequence of which the distance between two consecutive repeaters (used for revamping the attenuated signals) can be as large as 250 km.

Introduction

In this chapter we will study the reflection and refraction of electromagnetic waves from an interface separating two media and from a stack of films. Such studies are very important in understanding many practical optical devices such as Fabry–Perot etalons, interference filters, special optical coatings etc. Furthermore, by studying the state of polarization of a light beam reflected from, a medium, one can obtain its optical characteristics; this forms the basis of the field of ellipsometry.

In deriving the reflection and transmission coefficients we will use the following continuity conditions at the interface:

1. (a) continuity of the tangential components of the electric vector E;

2. (b) continuity of the normal components of the displacement vector D;

3. (c) continuity of the tangential components of the magnetic field vector H and

4. (d) continuity of the normal components of the magnetic induction vector B.

We will find that the equations determining the reflection and transmission coefficients fall into two groups: one of the groups contains only the components of E parallel to the plane of incidence (and H perpendicular to the plane) and the other group contains only the components of E perpendicular to the plane of incidence (and H parallel to the plane). Therefore the two cases (being independent of each other) will be considered separately and using them we can study the reflection (and refraction) of electromagnetic waves which have arbitrary states of polarization.

Introduction

A photograph represents a two-dimensional recording of a three-dimensional scene. What is recorded is the intensity distribution that prevailed at the plane of the photograph when it was exposed. The light sensitive medium is sensitive only to the intensity variations and hence while recording a photograph, the phase distribution which prevailed at the plane of the photograph is lost. Since only the intensity pattern has been recorded, the three-dimensional character (e.g., parallax) of the object scene is lost. Thus one cannot change the perspective of the image in the photograph by viewing it from a different angle and one cannot refocus any unfocussed part of the image in the photograph. Holography is a method evolved by Gabor in 1948, in which one not only records the amplitude but also the phase of the light wave. Because of this the image produced by the technique of holography has a true three-dimensional form. Thus, as with the object, one can change one's position and view a different perspective of the image and one can focus at different distances. The capability to produce images as true as the object itself is what is responsible for the wide popularity gained by holography.

The basic technique in holography is the following: in the recording of the hologram, one superimposes on the object wave another wave called the reference wave (which is usually a plane wave) and the photographic plate is made to record the resulting interference pattern (see Fig. 7.1(a)).