LECTURE-VI

CONTENTS

NON LINEAR OPTICAL MATERIALS AND ITS

APPLICATIONS

NON-LINEAR MATERIALSDefinition If the physical properties of optical materials depend on the

intensity of light, such materials are known as non-linear materials.

Explanation

The light is an electro-magnetic radiation in the frequency range 1015 Hz. When it passes through any optical material, due to the oscillating electric and magnetic fields, the atoms or molecules of the material experience oscillating force.

Since the magnitude of the magnetic field is small it may be ignored. With the conventional light sources

the electric field strength is of the order 1033 V/cm. Since the inter atomic field strength is in the range 107 to

1010 V/cm, the field due to the light does not affect the atoms.The material behaves linearly.

Instead of light, when intense laser radiation which generates field of strength 108 to 109 V/cm passes through the material, the atoms are influenced by this high field. This results in induced dipoles oscillating with higher amplitudes. Only when the amplitude of oscillation is small linear effect is observed.

☆ Owing to this concept, let us take the case of oscillations of a simple pendulum. The oscillations are simple harmonic only when the amplitude is small (i.e., we equate the sine[Sin] of the angle swept by the pendulum to the angle itself that is sin ≈,since it is small). When amplitude is large, higher harmonic terms come into play. Under this condition nonlinear effects originate. At such high fields, the optical properties depend on intensity.

NON-LINEAR PHENOMENANon-linear phenomena are, higher harmonic generation,

optical mixing, parametric amplification optical phase conjugation, soliton etc.,

HIGHER HARMONIC GENERATIONIn a linear medium, polarization P is proportional to the

electric filed E that induces it. P=χε0E where χ is the electric susceptibility.

In nonlinear medium, for higher fields, i.e., higher intensities of light.

....)( 33

2210 EEEP

where χ1 is the linear susceptibility and χ2, χ3 …….. are higher order nonlinear susceptibilities. With increase of filed higher order terms come into play. Let us assume that the field is strong enough to give rise to χ2, then

EP 0

)( 2210 EEP

The electric field passing through the medium can be represented by E = E0Cos ωt, Hence

)coscos( 2202010 wtEwtEP

2

)2cos1(cos 2

020010

wtEwtE

wtEwtEE 2cos2

1cos

2

1 2020010

2020

The nonlinear polarization indicates that it contains the second harmonic of ω (third term) as well as an average (d.c.) term (first term) called optical rectification. It can be shown that only in the crystals lacking inversion symmetry, second harmonic generation (SHG) is possible. SHG crystals are Quartz, Potassium dihydrogen phosphate (KDP), Ammonium dihydrogen phosphate (ADP), Barium titanate (BaTiO3) and Lithium Iodate (LiIO3).

The fundamental radiation from a laser is pass through SHG crystal, due to SHG, it converts into double the frequency i.e., half the wavelength takes place. For example 1.064μm radiation from Nd:YAG laser gets converted to 0.532μm on passing through crystals like KDP, ADP etc.

If the incident radiation from the laser is intense enough such that the polarization needs to be represented by three terms, then

)( 33

2210 EEEP

wtcosEwtcosEwtcos)EE(E 34

12

2

1

4

3

2

1 3030

2020

3030010

2020

The last term in the above equation represents third harmonic generation at frequency 3ω. Likewise one can account for higher harmonic generation.

)coscoscos( 3303

2202010 wtEwtEwtE

OPTICAL MIXINGThe generation of new frequencies with help of nonlinear

phenomena is called optical mixing. Suppose two coherent waves of unequal frequencies, ω1 and ω2 are traversing the material,

then E = E1 cos ω1 t + E2 cos ω2 tHence

ttEEtEtEtEtEP 212120222

2122

120221110 coscos2)coscos()coscos(

The second term gives rise to 2ω2. The last term can be expressed as 2ε0 χ2 E1 E2 cos ω1t = ε0 χ2 E1 E2 [cos (ω1 + ω2) t + cos (ω1 – ω2) t]

Thus waves of frequencies ω1, 2ω1, ω2, 2ω2, (ω1+ω2) and (ω1–ω2) are generated. Using proper optical arrangement it is possible to get sufficiently intense output at any one of these frequencies.

The generation of (ω1+ ω2) is called frequency-up conversion and (ω1–ω2) is called frequency-down conversion Crystals like KDP, ADP are used for up conversion while LiNbO3, quartz are used for down conversion.

Arrangement for generating a new frequency by optical mixing

PARAMETRIC AMPLIFICATION

The amplification of a weak signal frequency ω1is mixing with a strong pump beam of frequency ω2 inside a nonlinear crystal is possible. Then photon of pump beam at frequency ω3 is converted into two photons.

(a) Signal wave photon ω1

(b) Idler wave photon ω2

i.e. ω3 = ω1 + ω2

Signal is thus amplified. Crystal like KDP, LiNbO3, LiIO3 are used for this purpose.

OPTICAL PHASE CONJUCTION Let us consider a diverging beam, conjugate of the beam is

nothing but a converging beam. i.e., if we give time or wave front reversal to a beam, we can get conjugate beam.

Nonlinear media which are capable of reversing the incident optical beam to produce its phase conjugate beam are called Phase Conjugate Mirrors (PCM). To understand the property of PCM, let us compare the reflection of a plane wave front and diverging spherical wave front at ordinary mirror with these at a PCM [Shown in below fig].

Reflection of plane wave front and spherical wave front at (a) ordinary mirror and (b) PCM.

Thus in PCM, wave front reversal takes place. Another interesting property of PCM is distortion correction.

When a plane wave front (i) passes through a distorting medium the wave front is distorted (ii). If this distorted wave front is reflected at the ordinary mirror and the reflected distorted wave (iii) is allowed to pass through the distorting medium again further distortion takes place (iv) as shown in Fig below (a).

Instead if it is reflecting by PCM phase reversal takes place (iii) and when it again passes through the distorting medium, distortion correction takes place and plane wave front is obtained (iv) as shown in Fig below (b).

Stages of distortion from(i) to(iv) in (a) indicates enhanced distortion of a plane wave front after passing through distorting medium twice; once before reflection and another after reflection at a plane mirror. In (b) the role of distortion correction by a PCM is indicated.

Optical phase conjugation has very interesting applications such as distortion correction in optical fibres, optical image processing, optical neural network etc.

SOLITONS• In fibre optic communication, the light signal is sent in the form of light pulses. Since the ligh source is not hundred percent monochromatic and also the signal travels through very long distance, due to chromatic dispersion, pulse broadening takes place. This limits the bit rate or transmission capacity of the fibre. Also due to absorption and scattering, the energy of the pulse reduces and pulse loose its height. During this propagation of the optical pulse through the fibre, there is change in pulse shape, height and width. In order to compensate for the loss and reshape the pulses repeaters have to be installed at regular intervals.

This problem can be overcome by making use of some nonlinear effects. Since the diameter of the fibre is very small (of the order of few microns), even for a modest input optical power, the field inside the fibre can be large enough to cause nonlinear effects. The refractive index of the fibre core becomes intensity dependent. n = n0 + n1I

2

Where n1 is the nonlinear component of refractive index and I-is the intensity of light.

(we must remember that intensity of light I E2, Here E is the strength of the applied electric field).

When a light pulse is launched, for the leading edge of the pulse where intensity(I) is increasing, there is an increase in refractive index and hence velocity of the wave decreases. At the trailing edge refractive index decreases and hence velocity of the wave increases. This phenomenon is called self phase modulation (SPM). This SPM results in compression of the pulse in time. With proper choice, it is possible to cancel or compensate for the pulse broadening due to chromatic dispersion.

Next ONE how to overcome the problem of energy loss due to absorption and scattering when the light pulse propagates through the fibre.

It is, now-a-days, possible to fabricate fibres which amplify the light signal propagating through it. They are called fibre amplifiers. By pumping the atoms inside the fibre by sending a pump beam, population inversion is created in the fibre core.

When the signal pulse is sent amplification takes place which compensates for the loss. Thus the signal pulses can be made to travel for very long distances without any change in their shape and pulse width. The concept of pulse propagation without change of shape and loss of energy for any long distance is referred to as solitons. It has been found that such a pulse must have sech distribution in intensity for propagation.

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