I Determination of nonlinear susceptibilities of new materials

I Determination of nonlinear susceptibilities of new
Creation of highly effective converters of laser frequencies allows to solve
numerous tasks of nonlinear crystal optics, laser physics, medical diagnostics,
ecology and so on. On the other hand the task of the analysis of interaction of
intensive radiation with substance is important. It will allow to define material
parameters of substances, first of all nonlinear susceptibilities, for example,
fullerene structures. In the given work it is offered to spend the analysis of process
of conversion in the constant-intensity approximation. The analysis of frequency
conversion process in this aproximation, taking into consideration changes of the
phases of interacting waves, allowed one to suggest a new method of
determination of nonlinear susceptibility of the second and higher orders. As a
result of analysis in this approximation in contrast to the constant-field
approximation the minima of intensity of the second-harmonic dependent on the
nonlinear susceptibility of a substances. This fact allows simple, reliable way with
greater accuracy to define nonlinear susceptibilities of substances.
Areas of application
A measurement technique and skilled installation in which the companies can
become interested, engaged search of new nonlinear materials for development of
effective converters the frequencies. The companies working in the optical
industry, creating devices of management of laser radiation in the optical
communication systems, developing elements of the optical computers, new
coherent sources of optical radiation in UV area of a spectrum, The developed pilot
(skilled) installation will be offered to the industrial enterprises on manufacturing
converters of frequency, optical production, for the decision of problems in
spectroscopy and the optical industry.
The methods of nonlinear optics are successfully used for measuring nonlinear
optical properties of materials. As a rule the results of measuring don't differ with
high accuracy that is connected with the accuracy of registration of power of the
basic wave, second-harmonic and space -time distribution of intensity of laser
beam. That's why as a rule in most cases non absolute but relative value of
nonlinearity is measured.
As a rule the determination of nonlinear susceptibility of a matter was made at
small efficiency of frequency conversion, analytically described by expressions
obtained in the constant-field approximation. However in this approximation the
inverse reaction of the excited wave on the pumping wave is not taken into
consideration, that's why the information about qualitatively important features of
nonlinear process is lost.
The new way of definition of a nonlinear susceptibility of the optical substances,
differing from earlier existing the technique is offered. As to accuracy of spent
measurements comparison of results of calculation of first three zero of a curve of
synchronism in the constant-intensity approximation the constant-field
approximation and the numerical account has been lead. Comparison shows, that
results in the constant-intensity approximation will well be agreed with results of
the numerical account. Hence expected accuracy in measurement should be above,
than in the existing methods of the measurement based on the constant-field
For intensity of the second harmonic it is received
I 2   22 I1(0)  1(sin 2 x  sh2 y)exp ( 2  21) z  ,
  21
 2 ( 2  21 )2
  a  b , a  2  
, b 2
2   1 2 I1 (0) ,
I1 (0)  A1 ( z  0) , x   z cos , y   z sin ,   arctg .
From this it follows that at low absorption coefficients the intensity of a harmonic
is a periodic function of the nonlinear interaction length. As the serial number of
the period increases, the maximum intensity I 2 decreases. Unlike the results of the
constant-field approximation, in the constant-intensity approximation the period of
the spatial beats of the amplitude of a harmonic depends on the nonlinear
susceptibility  . This means that it can be determined by measuring the spatial
position of the minima of the intensity of a harmonic. By measuring this intensity,
it is also possible to determine the absolute value of  for given values of the
parameters of the problem.
Table: Positions of the first three zeros of the synchronism curve obtained in
calculated directly (  c ), in the constant-intensity (  CIA ) and constant-field (  CFA )
Fig. Schematic diagram of the apparatus intended for measuring the relative
quadratic nonlinear susceptibility of materials: (1) crystal with an unknown and (2)
with a known nonlinear susceptibilities; (3) filters, (4) photodetectors; (5) laser
beam; the optic axes of the crystals are parallel to the front face which serves as the
axis of rotation.
Thus the original way of definition of a nonlinear susceptibility of the optical
substances, differing from earlier existing the technique is offered. The offered
method is more exact, simple and reliable. Measurement both relative, and an
absolute susceptibility of substances is expected. And measurement of a relative
susceptibility will be with greater accuracy as thus there is no necessity for
absolute measurements of characteristics of laser radiation.
1. Z.A.Tagiev, and R.J.Kasumova, "Determination of Nonlinear Optical Susceptibility of
Substances“, Patent I 2000 0162, Azerbaijan.
2. Z.A.Tagiev and R.Zh.Kasumova,” Determination of Nonlinear High-Order
Susceptibilities”, Opt.Spectrosk., 1996, v.80, 941-943
[Opt.Spectrosc. 1996, v.80, 848-850].
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