Electro-Optic and Acousto-Optic Effects

7.3.2. Electro-Optic and Acousto-Optic Effects

There are systems, which are based on Laser technology that will need a set of extra technical items to the Lasers and wave guides. We can cite examples of devices that modulate, deflect, switch, translate in frequency, and also modify ‘optical signals’ in a manner, which can be controlled and pre- dicted. The requirements in this field have resulted in the development of materials that are capable of ‘optical communicaton’ with a very low loss in transmission. These types of optical properties of a material can be ‘changed’ by various fields interacting with the ‘optical signal’, e.g. by electric field (called electro-optic) or by magnetic field (called magneto-optic), or even by an externally applied stress,

i.e. elasto-optic, which is already discussed above, i.e. birefringence.

7.3.2.1. The Electro-Optic Effect

When an electric field, which may be ‘static’, ‘microwave’ or even an ‘optical electro-magnetic’ field, interacts with the ‘optical signal’ to produce a ‘change’ in the “Optical Dielectric Properties”, then an “electro-optic” effect occurs in the materials. In certain crystalline materials, the electro-optic phe- nomenon arises due to ‘electronic’ effect and in some other materials, it is mainly due to the ‘phonons’,

i.e. the vibrational modes of the atomic system. This kind of effect in certain cases may be due to a variation in linear fashion or in a quadratic manner with the electric field.

In a typical description of the refractive index in terms of a single electron-oscillator, the action of the low frequency electric field (E) is to produce a ‘shift’ of the characteristic frequency from n 1 to n 2 , which can be expressed as :

2 –n 1 = [2e v (ε + 2)E]/3mv 0

where, e and m are the electronic charge and mass, v is the anharmonic force constant, and ε is the low- frequency dielectric constant (since the field is of low-frequency). It is already known that the ‘refrac-

tive index’ n varies as 1/(ν 2 2 2 –ν 1 ), and hence the above equation directly expresses the linear variation of this refractive index with the electric field.

In the above description of a dipolar material, it was tacitly assumed that the dipole strength (µ) was a linear function of the externally applied electric field (E), which is expressed as :

µ =αE

For a dipolar material with N number of dipoles, the polarization (P) is given as :

P = Nµ = N α E

So, the above description is for a linear case. However, for a crystal system lacking a ‘centre of symmetry’, e.g. a ferroelectric crystal like lithium niobate and lithium tantalate, the electric field can be also expressed in non-linear terms by involving the ‘polartizability’ of the atomic system [3, 4], since in

259 this case, the polarization is not a linear function of the applied electric field (see also the section 7.2.3).

OPTICAL PROPERTIES

Hence, it is expressed up to the third order as :

P=α <E> + α <E 2 1 2 >+α 3 <E 3 >

where, α 1 = Nα, and α 2 and α 3 are the coefficients with the non-linear terms, which are basically material constants.

One way to express the ‘principal electro-optic’ effect is to invoke the ‘field-distance’ product at hal-wavelength (λ/2), i.e. <E . L> λ /2 , where L is the ‘optical path length’. This particular ‘field-distance’ product signifies the ‘voltage’ needed in order to produce half-wave retardation effect in a specific geometry of the sample or material, i.e. L/d = 1, where d is the thickness of the crystal through which the signal passes. The optical phase retardation (φ) can be expressed in radians as :

φ = (2πL/λ 0 )[n 1 (E) – n 2 (E)]

where, λ 0 is the wavelength of the light in vacuum, and n 1 (E) and n 2 (E) are the electric field-dependent refractive indices. The form of their difference depends on the following :

(a) Crystal Symmetry, (b) Direction of the Applied Electric Field, and also on (c) Propagation and Polarization Direction of the Optical Beam. As mentioned earlier, there are various important electro-optical materials like lithium niobate,

lithium tantalate, potassium tantalate-niobate, calcium niobate, strontium-barium niobate, barium-so- dium niobate, etc. In many of these crystals, Nb or Ta ion is octahedrally coordinated with six oxygen ions, which form the basic structural unit. The main property of the 'change' in refractive index with an applied electric field is exploited in the electro-optic materials in terms of a variety of applications such as :

(a) Optical Oscillators, (b) Frequency Doublers, (c) Voltage-Controlled Switches in Laser Cavities, and of course (d) Modulators for Optical Communication Systems. Many of these devices or device accessories have been improved in recent years with novel nano

materials. There is a constant search for newer nano-materials.

7.3.2.2. The Acousto-Optic Effect

In the above example of electro-optic materials, the refractive index changes with an applied electric field. Instead of electric field, if a crystal is strained, then also the refractive index can effect a change. This change of refractive index by strain is known as ‘acousto-optic’ effect. The crystal lattice has a potential, which can be changed by the action of strain that changes the shape and size of the molecular orbitals of the weakly-bound electrons. This causes a change in the polarizability and refrac- tive index as well.

In a polarizable crystal, the strains have different values at different spatial directions, which are ultimately expressed as a strain tensor. Hence, the effect of the strain on the indices of refraction of a crystalline lattice depends on the direction of these ‘strain axes’ and also on the direction of the ‘optical polarization’. These spatial dependence eventually guide the acousto-optic properties of the nano crys- talline materials.

NANO MATERIALS

If a plane elastic wave is excited with a given crystal system, a periodic strain effect occurs with

a spatial extent that is equal to the acoustic wavelength. Then, due to this strain effect, an acousto-optic variation of the refractive index occurs in the crystalline lattice, which is equivalent to a ‘volumetric diffraction grating’. Based on this principle of partial diffraction of light incident on an aousto-optic grating at a proper angle, the acousto-optic devices are made. In an acousto-optic device, the use of a particular crystal depends on many factors, such as :

(a) The ‘piezoelectric’ coupling (produced by the strain in the crystal), (b) The ‘ultrasonic’ attenuation, and also on (c) The ‘acousto-optical’ coefficients. The important acousto-optic crystals are lithium tantalate, lithium niobate and some other lead-

based compounds. The refractive index of these material is about 2.2, and they are also transparent in the visible spectrum, i.e. 400 nm to 700 nm of wavelength. There are single domain and multi-domain materials, which have been superbly crafted by means of ‘domain engineering’ in the nano scale, which makes an ‘integrated optical device’ very efficient with precise control. On the application front, there are a variety of uses as components in the laser system, waveguides, couplers, modulators, diffractors and in optical detection (see the section 8.2.1 on nano-optics) [2, 5].