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)).

Introduction

The acoustooptic effect is the change in the refractive index of a medium caused by the mechanical strain produced by an acoustic wave. Since the strain varies periodically in the acoustic wave, the refractive index of the medium also varies periodically leading to a refractive index grating. When a light beam is incident on such a refractive index grating, diffraction takes place and this produces either multiple order diffraction or only single order diffraction. The former is referred to as Raman–Nath diffraction and is usually observed at low acoustic frequencies. The latter is analogous to Bragg diffraction of X-rays in crystals and is referred to here also as Bragg diffraction; this is usually observed at high acoustic frequencies.

The interaction between acoustic waves and light waves is used in a number of applications such as in acoustooptic modulators, deflectors, frequency shifters for heterodyning, spectrum analysers, Q-switching and mode locking in lasers. In this chapter we will discuss the basic principle of Raman–Nath diffraction and in the next chapter we will discuss Bragg diffraction.

Raman–Nath and Bragg regimes of diffraction

As discussed in the previous section when an acoustic wave propagates in a medium, the periodic strain associated with the acoustic wave generates a periodic refractive index variation in the medium. This periodic refractive index grating has the same period as the acoustic wave and is also propagating at the same velocity as the acoustic wave.

Ever since the invention of the laser in 1960, there has been a renaissance in the field of optics and the field of optical electronics encompassing generation, modulation, transmission etc. of optical radiation has gained tremendous importance. With optics and optical electronics now finding applications in almost all branches of science and engineering, study of these subjects is becoming extremely important. The present book intended for senior undergraduate and first year graduate students is an attempt at a coherent presentation of the basic physical principles involved in the understanding of some of the important optoelectronic effects and devices.

The book starts with the basic formulation of the study of propagation of electromagnetic waves, reflection and refraction and propagation through anisotropic media. This is followed by diffraction and its application in the study of spatial frequency filtering and holography. Basic physics behind laser operation is treated next with a brief discussion on different laser types. The next four chapters deal with the subject of optical waveguides including fibre and integrated optics which are already revolutionizing the field of information transmission. The next five chapters deal with three very important effects which are used in many opto-electronic devices namely the electrooptic, acoustooptic and nonlinear optical effects.

The various concepts in the book have been derived from first principles and hence it can also be used for self study. A large number of solved and unsolved problems have been scattered throughout the book.

Introduction

In Chapter 1 we discussed wave propagation in isotropic media in, which the velocity of propagation of an electromagnetic wave is independent of the direction of propagation. In this chapter we will discuss wave propagation in anisotropic media in which the velocity of propagation, in general, depends on the propagation direction and also on the state of polarization and one observes the phenomenon of double refraction. Anisotropic media form the basis of a large number of polarization devices such as quarter wave and half wave plates, the Soleil–Babinet compensator, the Wollaston prism, etc. Their study is also very important for understanding various light modulators based on the electrooptic effect (see Chapter 15).

In Sec, 3.2 we will discuss the phenomenon of double refraction and in Sec. 3.3 we will discuss some important polarization devices based on anisotropic media. Sees. 3,4–3.7 will discuss the electromagnetics of anisotropic media. In Sec. 3.8 we will introduce the index ellipsoid and show how from the index ellipsoid one can obtain the velocities of propagation and the polarizations of the two waves which can propagate along any given direction.

Double refraction

If we place a crystal of calcite or quartz on a point marked on a piece of paper, we will, in general, observe two images of the point. This phenomenon is referred to as double refraction or birefringence. This happens because when a ray enters the crystal it splits up, in general, into two rays which propagate along different directions and which are orthogonally polarized.