CC BY
9
https://doi.org/10.29013/ESR-21-1.2-44-47
Rasulov Voxob Rustamovich, associate professor of Fergana State University Rasulov Rustam Yavkachovich, professor of Fergana State University E-mail: [email protected] Axmedov Baxodir Baxromovich, doctoral student of Fergana State University Muminov Islombek Arabboyevich, doctoral student of Fergana State University
Niyozov Shoxrux, Undergraduate of Fergana State University
SINGLE-PHOTON LINEAR-CIRCULAR DICHROISM IN NARROW-GAP CRYSTALS. TAKING INTO ACCOUNT THE EFFECT OF COHERENT SATURATION
Abstract. In the paper, from a microscopic point of view, the linear-circular dichroism of one-photon between band absorption of light in the Kane approximation in narrow-gap crystals is investigated.
The linear-circular dichroism of one-photon absorption of polarized light is calculated taking into account the effect of coherent saturation in photoexcited charge carriers. Keywords:
The matrix elements of one-photon interband optical transitions and the corresponding linear-circular dichroism and the spectral dependence of the light absorption coefficient are calculated.
Currently, in practice, nonlinear optical phenomena occurring in crystals are widely used [1-3]. In this context, the research of nonlinear absorption of polarized light is actual both from the physical point of view and from the point of view of application.
Note that in the case of one-photon absorption oflight, optical transitions do not occur through virtual states at all. Therefore, linear-circular dichroism is not observed in single-photon optical transitions in crystals with cubic and tetrahedral symmetry.
One- and multiphoton absorption of polarized light in crystals, caused by optical transitions between the subbands of the valence band, was researched in [4-11], where the contribution to the interband one-photon absorption of light from the effect of coherent saturation [6; 7], caused by the finite lifetime of photoexcited carriers current in the final state, to which this work is devoted.
If we take into account the contribution to the absorption of the effect of coherent saturation, then the coefficient of two-photon absorption of light will be written in the form
K(1) (w,T) = ^ hW X ( ( - fc ) (Ehh - Ec + hw))
4p
M CflvJk )
h
k ;s=±l/2,m=±1/2 ,±3/2
a
1 + 4tWt
h2w2
m £v,m(k )
(i)
where fhh (f ) and Ehh (Ec) - distribution functions and energy spectra of holes (electrons), respectively, sign (...) means averaging over the solid angles of the wave vectors of current carriers, the rest are generally known values.
K (1)(w,T ) =
16e2
3cw h n,
m ■ kW • P2
It can be seen from (10) that the coefficient of interband one-photon absorption of light K(w,T ) consists of partial components that differ from each other in the type of optical transitions. In particular, for an optical transition of the type |V, ±3/2) C, ±1 / 2) it is expressed as
(2)
• F (b,iw)-3(®).[ fhh (EX') - L (S)
here
F (ß,1,w) = [1 - exp (ßhw)) exp [ß(-Ehh (k(*U ))
z = 4-^
^ffl -J-2 2
h w
2 ii(w)
k2,l = %(hw-Ej ,
ch
u(+)
H'c ,L
1 1
-+-
m
L 0
number: 3(Cm = 0) = —, i.e. in this case, one-photon
linear-circular dichroism is not observed. However, if we take into account the effect of coherent saturation, then Cm ^ 0, which means that in this case one-photon linear-circular dichroism arises. This is due to the fact that for linearly polarized light
•+i. 1 -m2
b- = kBT, 3(m) = ^-r
+ Cm \e±1
Also, it can be seen from (13) that the linear-circular dichroism of one-photon absorption of light is determined by the quantity 3(m), which depends on the frequency and degree of polarization of light, the band parameters of the sample, which arises due to the complexity of the band structure of the crystal.
Note that if we disregard the effect of coherent saturation (Cm = 0 ), then K (1)(m,T) does not depend on the quantities mentioned above, in particular on the degree of polarization of light, i.e. is a constant
3lin
f
J_1 dm
1
1+Zw(1 -m2 )
for circularly polarized light
f+1, , 2(1+m'2 )
j_1 dm -¡=
3. =
arc
1 + Zw
2 (1+m'2 ) Pcirc m
(3)
(4)
where Pcirc - degree of circular polarization of light, sign "±" refers to s± of the polarized light f(f') -angle between vectors e and q, m' = cosf', m = cosf, q is the wave vector of a photon.
For example, in the case Pcirc = 1 for linearly polarized light
3,. =z
lin
-5/2
z<3/2 +zw2 • arcsin
Zw
\ 1/2
1+z
Z arcsin
w
Zw
\ 1/2
1+z
w
(5)
for circularly polarized light
2 (Z^-Zwarcsi^VZW)
3circ
Z
5/2
w
(6)
Figure 1 shows the graphs of the functions 3l,n (Cm) and 3arc (Cm) depending on the value
f eA Y
C x —0 I x I. As can be seen from (Fig. 1), with
m I c h 0
increasing light intensity coefficient of interband single-photon linear-circular dichroism
h = 3l,n (Cm)! 3c,rc (Cm) increases and tends to saturation, i.e. at very high intensity values ( Cm >> 1) does
not depend on the intensity and h » 1.1. For quantitative calculations, we used the data from [14].
Thus, one-photon linear-circular dichroism due to interband optical transitions in a narrowgap crystal arises when the effect of coherent saturation is taken into account. However, in the case of interband multiphoton absorption of polarized light, linear-circular dichroism is observed regardless of whether the effect of coherent saturation is taken into account or not. This issue requires separate consideration.
2
2
2
Figure 1. Function graphs 3Un, %circ and h factor of linear-circular dichroism depending on I (on light intensity) in Kane approximation in a narrow-gap crystal
Appedex
According to [12; 13], the effective carrier Ham-iltonian for the three-band Kane model is expressed as follows:
œ " -V2/3Pkz -iPk /43ö
where kz = k =
Eel (k ), Elh (k ),.
k . This equation has three solutions: \0 (k) . From (Ap. 2) we have
k 2(E ) =
1 (Ec - E)(Ev - E)(Ev - E + D)
and with the
Hef (k ) =
Ec
ijmpkz iPk I S
Ev 0
0
E-D
, (Ap.1)
PL (E - Ev + 2D/3) help of the last dependence the graph of k2 (E) is built in (Fig. 2) shows that all energy bands are nonpara-bolic, and the quadratic dependence of the energy
whose eigenvalue is determined by the equation: E - E)(E, - EW, -A-E)-
-P2k2(Ev - E - 2D /3) = 0,
on k =
the wave vector.
observed in the region of small values of
Figure 2. Energy spectra of charge carriers in GaAs ( A / Eg = 2,4 Eg = 1,42 eV , mel = 0,067 • m0 ) and InSb ( A / Eg = 3,4 Eg = 0,18 eV , mel = 0,013 • m0 ) in the three-zone isotropic Kane model, where the range of negative values of the quantity k2(E ) correspond to the band gap and the spin-orbit splitting band
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