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https ://doi.org/10.29013/ESR-20-1.2-97-100
Rasulov Voxob Rustamovich, PhD, assistant professor Rasulov Rustam Yavkachovich, DSc, Professor of Fergana State University E-mail: [email protected].
Sultonov Ravshan Rustamovich, Researcher of Fergana State Universityr Eshboltaev Ikbol Mamirjonovich, PhD, lecturer at the Kokand Pedagogical Institute Akhmedov Bahodir Bahromovich, Researcher of Fergana State University
PHENOMENOLOGY OF TWO AND THREE PHOTON LINEAR-CIRCULAR DICHROISM OF LIGHT ABSORPTION IN p-GaAs
Аbsract. a phenomenological analysis of the matrix elements of two and three photon absorption of polarized radiation due to optical transitions between the subbands of the valence band of a semiconductor of cubic symmetry was carried out.
The mechanism of two, three, and four-photon linear circular dichroism of light absorption in a p-GaAs semiconductor is revealed.
Keywords: phenomenological analysis, matrix elements, two and three photon absorption of light, optical transitions, semiconductor.
The advent of lasers and masers made it possible toresearch nonlinear optical phenomena and the multiphoton linear circular dichroism of light absorption in a semiconductor [1-2].
At present, multiphoton linear-circular and circular-circular dichroism has been researched in semiconductors by absorbing light of different frequencies and polarization [3-6], due to interband optical transitions, i.e. Two and three photon absorption of polarized light, due to optical transitions between the valence band and the conduction band of the semiconductor, are researched.
In the above researches, the processes of light absorption due to multiphoton optical transitions between subbands of one, for example, valence or conduction band of a semiconductor, remained open, and the simultaneous absorption of two
photons was not taken into account [7-11]. In particular, the theory of linear circular dichroism of multiphoton light absorption in semiconductors with a complex band structure in the developed nonlinearity region was constructed in [9], i.e. in the field of intensity, when the condition is not satisfied —I^epcv I— /n , where e and I are the po-2 2/*. \2 U r cnmm m0 (nm)
larization vector and light intensity, pcv = pk = epk k is the interband matrix element of the operator momentum, nc is the refractive index of medium light at a frequency ca , and m0 is the mass of a free electron. To fill this research gap, we first discuss the phenomenology of two and three-photon linearly circular dichroism in cubic symmetry semiconductors.
When linearly and circularly polarized light is absorbed, multi-quantum optical transitions through virtual electronic states are allowed, which are found both in the valence and conduction bands and in the zones located far from them. According to the law of conservation of the angular momentum of current carriers, the physical nature of optical transitions depends on the degree of polarization of light. In particular, with photon absorption of circularly polarized light, photoexcited carriers will have non-zero angular momentum. So that the following photons will interact with optically oriented current carriers. According to the rule of choosing the optical transition under consideration for the projection of the moments of current carriers relative to the wave vector of the photon, the probability of two and three-photon optical transitions will depend on both the frequency and the degree of polarization of light. The latter leads to the identification of linearly circular dichroism of light absorption. This is true when the dependence of the absorption of polarized radiation
on the anisotropy of the semiconductor crystal is not taken into account.
As a result, we find that in crystals of cubic symmetry, when the absorbed light propagates along the principal axis of symmetry, a linearly circular dichroism of two- and three-photon absorption of light should be observed. We note here that in the spherical approximation in the energy spectrum of current carriers, the linearly circular dichroism of single-photon absorption of light can be observed when taking into account coherent saturation of the final state of photoexcited current carriers.
In the future, we will calculate then N photon absorption coefficient of polarized radiation K(N) ((o,e ) using the golden rule of quantum mechanics [12] under the condition_0ne I\epcvI_
cnaa>2m20 (ha) Then the probability of N photonic interband optical transitions in a semiconductor is determined by the expression
W
(N )
(k ) =
On
One 0I
\0
V Cna® m0 y
X M(N) (k)0 {(()[l - fv (k)] - fv (()[l - f (()]} x5 \ec (e) - Ev (() - NTm
c ,V ;k
with the help of which the spectral and temperature dependences are determined K(N) (<o,e ), where fc (k ), fv (k ) are the electron distribution function in the conduction band (valence band, M(N) (( ) is the composite matrix element of the transition), 5 Ec (k )- Ev (k )- Nhœ describes the energy conservation law of the optical transition under consideration.
Note that the polarization dependence of the probability of two (three and four) photon interband optical transitions is determined by the tensor of the fourth (sixth and eighth) rank, i.e. W^=0) (e) =
= ~(N=0)e e e*e* (W(NW ie)—^-3) e 1 e*e*e e*
and WcvN=4) ) = WpWeX ), where
summation over repeated indices is implied;
a, P,y,n, X = x, y, z. For example, for tetrahe-
dral symmetric semiconductors, the tensor has three
linearly independent components. Therefore
Wc(vN=2) (e )=»(=2) |ee|2 + s(N=2)|ee* f + + =2)(|el4 + \e I4 + lei4
3 I | x | y I z I
where parameter z[N=2) (and e^X is proportional to the square (cubic and fourth degree) of the light intensity and it was believed that the axes Ox,Oy,Oz are directed along the principal axes of symmetry of the semiconductor. If light propagates along the axis [111], then for semiconductors of tet-rahedral and cubic symmetry we have
WiN-2)(e,q TT[m]) = (£iN
1
0
°)+ i 0)) I eel
+
+ (
?(N=0)
1,
+
3
ee
Here q is the wave vector of the photon, whence for linear polarization the quantity W(N=2) (e,q tt [111]) does not depend on the light polarization vector. Then the coefficient of two photon linear-circular dichroism &<(N=2) =
= WV 2'lm) / W'N 2'arc) is determined by the relation
(2s2N=2'Hn 5 + S(3N=2'Un )) / (3S 2N-2'circ ) + S [N=2'circ )), where
it is taken into account that for linear polarization \e • e\ = 1, e x e* = 0 (for circular polarization, conversely) and for an arbitrary complex vector a, the
I |2 I |2
relation holds a • al + a x a* = (a x a* )2.
Thus, a similar argument can be made for the quantities acN=3) = W^=3,lm5 / W^=3,circ5, a(N—4) =
— W(N=4,lln) /w(N=4, circ) V*cV ' cV .
We also note the probability of the interband optical transition occurring by the absorption of two photons with different frequencies (co1, c2 ) and polarization ( e1, e2 ), then the spectral and polarization dependence of the probability of two photonic optical transitions is determined by the relation
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Similarly, one can make for reasoning for multiphoton optical transitions, taking into account the symmetry of the crystal.
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