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Home / Issues / № 2, 2013

Materials of the conference "EDUCATION AND SCIENCE WITHOUT BORDERS"

METHODS OF FOURIER OPTICS IN NONLINEAR SPECTROSCOPY
Dubnishcheva Tatyana

In nonlinear laser spectroscopy absorption of the trial (weak) wave (frequency , wave vector ) at presence strong wave (k), saturating the resonant transition (frequencies ) in a gas [1-3] is studied. The opposite or unidirectional waves are usually investigated. At carrying out of experiments it is necessary to scan frequency of the trial field. There are narrow failures on the nonlinear absorption counter near the resonance () . The failures depend on power of the strong field and characteristics of the investigated fluid.

Any light beam can be considered as superposition of plane waves. As the wave equation linearly for it the principle of superposition is just. Its decision will be the sum of plane waves with any parameters. Such solution write down as integral from function

E(x, y, z) = A exp (ij) exp(i), (1)

where k2 = kx2 + ky2 + kz2, and kx = k sin α, ky = k cos α· sin j, k=2π/λ.

Integral Fourier for the decision of the wave equation has a following appearance [1]:

(2)

where g (kx, ky) - the complex function describing an amplitude and phase of the separate plane wave with the direction of propagation determined by the valid variables kx, ky.

Coordinates x, y have dimension of length. Spatial frequencies kx, ky have dimension reciprocal to length. The phase of any plane wave is represented the sum of temporary and spatial terms:. Therefore changes of characteristics of a field in the nonlinear flluid can naturally be considered both on temporary and on spatial parameters. Research of the contour on spatial frequencies is possible do by methods of Fourier-optics.

The solution (2) of wave equations allows to solve many tasks given boundary conditions in a plane z = 0. Let this condition is the assigned function

(3)

Then for a finding of function g (kx, ky) it is necessary to execute inverce Fourier-transformation:

(4)

Function g (kx, ky) describes distribution of amplitudes and phases of plane waves on directions. It named a spatially-frequency spectrum or an angular spectrum of a light field. Narrow failures on the contour of the nonlinear absorption depend on mutual orientation light waves resonance interacting in the fluid under investigation.

For two-level gas in a field of two plane light waves propagating under the ungle φ to each other factors of absorption η and refraction n under condition of , and will look like [2]:

(5)

(6)

where ; η0 - nonsaturated factor of absorption; Г - half with of the line; ω12 - frequency of transition; γ2 - return time of a life of the second level; - parameter of saturation.

Fig. 1 Dependence of factor of absorption ( a) and factor of refraction (b ) from φ.

In figure 1 dependence of factor of absorption and factor of refraction from φ for parameters of saturation: = 1 (curves 1-4), = 0,5 - (a curve 5) is shown at = 0.01 and j0 = 7° [2]. From expression (5) follows, that at small values α the greater contribution to factor of absorption is given with a term describing coherent effects of interaction of fields. It depends on spatial frequency . The contour of absorption thus becomes narrow-band on spatial frequencies with resonant frequency w0 = 0 for the motionless fluid.

The steepness and the form of a contour of absorption on spatial frequencies depends on parameter of saturation, also carries the information on physical characteristics of fluid. Its research expands opportunities of nonlinear spectroscopy and simplifies experiment as disappears necessity of scanning of temporary frequency.



References:
1. Dubnishchev Yu. N., Popova T.Ya. //Technical Physics Letters. 1978. No. 9, pp.526-529

2. Kurbatov A.A., Popova T. Ya. //Optics and spectroscopy. 1980. Vol. 49, pp. 402-404.

3. Letohov V.S., Chebotaev V.P. Nonlinear laser spectroscopy of the ultrahigh resolution.-Moscow: Nauka, 1990. - 512 p. (in Russian)



Bibliographic reference

Dubnishcheva Tatyana METHODS OF FOURIER OPTICS IN NONLINEAR SPECTROSCOPY. International Journal Of Applied And Fundamental Research. – 2013. – № 2 –
URL: www.science-sd.com/455-24309 (28.03.2024).