Download NON-LINEAR MATERIALS Definition

LECTURE-VI
CONTENTS

NON LINEAR OPTICAL MATERIALS AND ITS
APPLICATIONS
NON-LINEAR MATERIALS
Definition
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 103 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.
P 0  E
NON-LINEAR PHENOMENA
Non-linear phenomena are, higher harmonic generation,
optical mixing, parametric amplification optical phase
conjugation, soliton etc.,
HIGHER HARMONIC GENERATION
In 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.
P   0 ( 1 E   2 E 2   3 E 3  ....)
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
P   0 ( 1 E   2 E 2 )
The electric field passing through the medium can be
represented by E = E0Cos ωt, Hence
(1  cos 2 wt )
P   0 ( 1 E0 cos wt  2 E02 cos 2 wt )   0 1 E0 cos wt  0  2 E02
2
1
1
  0  2 E02   0 1 E0 cos wt   0  2 E02 cos 2 wt
2
2
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
P   0 ( 1 E   2 E 2  3 E 3 )
  0 ( 1 E0 cos wt  2 E02 cos 2 wt   3 E03 cos 3 wt )
1
3
1
1
  0  2 E02  (  0 1 E0   0  3 E03 ) cos wt   0  2 E02 cos 2wt   0  3 E03 cos 3wt
2
4
2
4
The last term in the above equation represents third harmonic
generation at frequency 3ω. Likewise one can account for higher
harmonic generation.
OPTICAL MIXING
The 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 t
Hence
P   0 1 ( E1 cos 1t  E 2 cos  2 t )   0  2 ( E1 cos 2 1t  E 22 cos 2  2 t )  2 0  2 E1 E 2 cos 1t cos  2 t
2
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 + n1I2
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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