Second Harmonic generation in non-centro symmetric materials

1. 1
Nonlinear optics
Presented
by
R. Gandhimathi
Second Harmonic Generation

2. 2
➢ Overview on Lasers
➢ Symmetry operations of crystals
➢ Introduction to nonlinear optics
➢ Maxwell’s Equation for EM waves
➢ Second Harmonic generation
Outline

3. 3
Laser - A source of coherent monochromatic radiation (0.2 m - 20m)
Components of Laser
1.Gain medium or active medium
2.Pump or power supply
3.Optical feed back unit (resonator)
Changing the color of laser light on the fs time scale
➢ Done by second harmonic generation (SHG)
➢ Inserting a nonlinear optical (NLO) element within the laser cavity makes possible a diversity
of new lasers and applications e.g. gain media crystals or glasses- solid state laser generation
Laser Applications
Laser devices are used in innumerable areas like manufacturing, medicine, data storage, communications,
military and various areas of modern science.
Overview on Lasers
Mechanism
Whenever gain exceeds loss, net
amplification is achieved and the
laser can start oscillating

4. 4
Inversion centre
➢ A point through which an inversion
operation is performed
➢ e.g. if there is an atom at a distance
(a, b, c) relative to the inversion
centre, there must also be another
atom at (-a,-b,-c)
SYMMETRY OPERATIONS OF CRYSTAL
1.Rotation operation- produces patterns where the original basis is sustained()
2.Reflection operation- Reflection of an object occurs across a plane(m)
3.Inversion operation - produces an inverted object through an inversion center (i)
Centrosymmetric Noncentrosymmetric
➢ A structure with an inversion
centre is called
centrosymmetric
➢ In centrosymmetric materials
the second order dipole
response is zero
➢ A structure with no inversion
centre is called
Noncentrosymmetric
➢ In Noncentrosymmetric
media, nonlinear polarization
contains a component that
radiates at twice the
frequency of the input light
With inversion centre
Without inversion centre

5. 5
➢Branch of Physics deals about interaction of high intensity laser light with matter in which the
polarization density P responds non-linearly to the electric field E of the light
➢The interaction and behavior of laser light within materials aids to understand refractive index and
absorption ability of the materials and extends their applications in fabrication of various optical
elements like filters, polarizers and electro-optical devices
➢Propagation of laser beam through nonlinear media (lacking inversion symmetry) gives rise to
vibrations at harmonics of the fundamental frequency and it halves the wavelength () and doubles
the frequency of incident light. This is called frequency doubling
➢E.g. Potassium dihydrogen Phosphate (KDP) crystals convert invisible light (-1064nm) into visible
green light (532nm)
Introduction to Nonlinear optics

6. 6
Nonlinear optical effects
2nd order nonlinear optical effects 3rd order nonlinear optical effects
➢ Pockels/electro optic effect
➢ Second harmonic generation (SHG)
➢ Sum/difference frequency generation
➢ Optical parametric
amplification/oscillation/generation
➢ Optical rectification
➢ Optical kerr /quadratic pockels effect
➢ Third harmonic generation
➢ Self focusing
➢ Four wave mixing
➢ Two photon absorption
➢ Stimulated Raman/Brillion scattering
Nonlinearity leads to the generation of new frequency components i.e. Generation of
light with doubled, tripled or higher order frequency, i.e. multiplies fundamental
frequency to second, third order and even higher harmonics depending upon the
symmetry of the media

7. 7
0 0 0
0
. 0
. 0
D
B
B
E
t
E
B J
t
or
E
H J
t
  

 =
 =

  = −


  = +


  = +

Vacuum -a linear, homogeneous, isotropic and non-dispersion
medium in which no charge or no current exists
In Medium
Describes presence of electromagnetic field in a
medium. when an atom is placed in an electric field,
the electron cloud shifts in opposite direction with
respect to the nucleus. Thus, a dipole is constituted.
i i
i
d rq= 
Due to the application of Electric field the material is polarized
and the Maxwell’s equations are modified for polarized and
magnetized materials
0
0
D E P
B
H M


= +
= −
Where
P -polarization and M-magnetization.
External field induces charges and current.
The current and charge densities due to the polarization of the material
.
. 0
ext
ext
D
B
B
E
t
D
H j
t
 =
 =
−
 =


 = +

Maxwell’s Equation in Vacuum And in A Medium
In Vacuum
·
pol
pol
P
J
t
P

=

= −

8. 8
Wave Equation in A Linear Medium (One Dimension)
(1)
B
E
t

 = − − − − −

0 0 0 (2)
E
B J
t
P
J
t
  

 = + − − −


=

( )
( ) (3)
B
E
t
 
  = − − − − −

0 0 0
2
0 0 0 2
2 2
0 0 02 2
0 0
2 2
02 2 2
( )
( )
( )
1
1
( ) ( )
E
J
t
t
E P
t t t
E P
t t
c
E P
E
c t t
  
  
  
 


 +
= −

  
= − +
  
 
= − +
 
=
 
  = − +
 
In equation (1) take curl on both side
Substitute equation (2) in (3)
Ampere’s law
2
2 2
2
02 2 2
2 2 2
2
2 2 2
2 2 2
02 2 2 2
22 2
02 2 2 2
( . ) ( )
. 0
1
1
1 linear
E E E
E
E P
E
c t t
E E E
E
x y z
E E P
x c t t
PE E
x c t t



 =   −    
 =
 
 = +
 
  
 = + +
  
  
= +
  
 
− =
  
(1)
0linearP E =
The linear polarization P is
Faraday’s law
We know that
The wave equation becomes
22 2
0
02 2 2 2
2 2 2
0 02 2 2 2
2 2
2 2 2
1
1
0
1
(1 ) 0
EE E
x c t t
E E E
x c t t
E E
x c t
 

  

 
− =
  
  
− − =
  
 
− + =
 
Where -gives refractive index(1 )+
-describes the linear
optical effects

9. 9
(1) (2) 2 (3) 3
0 0 0 ......linear nonlinearP P P E E E     = + = + + +
22 2 2
02 2 2 2
nonlinearPE n E
x c t t

 
− =
  
2 2 2 2 2 2 3
(2) (3)
0 0 0 02 2 2 2 3
.....
E n E E E
x c t t t
     
   
− = + +
   
( ) *( )
0 0
2 2 (2 ) 2 *2 ( 2 )
0 0 0
( )
( ) 2
j t j t
j t j t
E t E e E
E t E e E E e
 
 
−
−
= +
= + +
2nd harmonic term, frequency
doubled component (2)
And the wave equations turn into
In the case of nonlinear medium, the polarization P is
The electric field of EM wave
Thus, the medium which lacks inversion symmetry is polarized nonlinearly and radiates an EM wave with
twice the incident light frequency and this effect is called Second Harmonic Generation (SHG)

10. 10
A nonlinear optical process in which two photons of high
intensity light interacting with a nonlinear material are
combined to form a new photon with twice the energy, and
therefore twice the frequency and half the wavelength of the
initial photons. The second order polarization from equation can
be written as
2 (2)(2)
0P E = + −−−
In order to realize an efficient device with second-order
nonlinear optical (NLO) effects, such as SHG, it is necessary
to obtain phase-matching within a material with high
nonlinearity
Second Harmonic Generation
the quadratic term which describes second harmonic
generation in noncentro-symmetric materials
where k1 and k2 are the wave numbers of the fundamental and second-
harmonic beam.
Ammonium dihydrogen phosphate(ADP)
β-barium borate(BBO)
gallium selenide(GaSe)
lithium iodate(LiIO3)
lithium niobate (LiNBO3)
lithium triborate (LBO)
potassium niobate (KNBO3)
monopotassium phosphate
potassium titanyl phosphate(KTP)
Examples for some SHG materials

11. 11
1. Robert Boyd, Nonlinear Optics, 3rd Edition,2008
2. Ming-Rung Tsai, Chiu Yu-Wei, Men-Tzung Lo, Chi-Kuang Sun, “Second
harmonic generation imaging of the collagen in myocardium for atrial
fibrillation diagnosis”, 2010, Journal of Biomedical Optics 15(2):026002
3. J. E. Conrad, Electromagnetic Waves and Radiating Systems, 2nd ed., Prentice
Hall, Englewood Cliffs, NJ (1968).
4. J. Aukong, Electromagnetic Wave Theory, John Wiley & Sons, New York
(1986)
5. Nannapaneni Narayana Rao, Fundamentals of Electromagnetics for
Engineering, Edward C. Jordan Professor Emeritus of Electrical and Computer
Engineering, University of Illinois at Urbana–Champaign, USA
References

12. 12
Thank you