Optical specifications of laser-induced Rosen-Morse quantum well

Optical Materials 90 (2019) 231–237

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Optical Materials journal homepage: www.elsevier.com/locate/optmat

Optical specifications of laser-induced Rosen-Morse quantum well a,∗

b

F. Ungan , M.K. Bahar a b

T

Faculty of Technology, Department of Optical Engineering, Sivas Cumhuriyet University, 58140, Sivas, Turkey Department of Energy Systems Engineering, Faculty of Engineering, Karamanoğlu Mehmetbey University, 70100, Karaman, Turkey

ARTICLE INFO

ABSTRACT

Keywords: Nonlinear optical properties Quantum well Rosen-Morse confinement Intense laser field

In this study, for the first time, the influences of a monochromatic linearly polarized laser field on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of quantum well (QW) with the Rosen-Morse potential confinement by constituting GaAs/GaAlAs heterostructure are considered. Time-dependent in the Schrödinger equation is modified through the Kramers-Henneberger (KH) transformation and the dipole approximation, and then the laser-dressed counterpart of well potential is generated by using the Ehlotzky approximation. The bound state energy values and the wave functions of the Rosen-Morse quantum well (RMQW) under the influence of the intense laser field (ILF) are obtained by using the diagonalization method in the framework of the effective mass approach and the parabolic band approximation. The effects of structure parameters on TRICs and TACs of RMQW are also explained in detail, as well as the ILF's ones. In addition to these, the alternativeness to each other of the structure parameters and the ILF on the optical specifications is also discussed. The results of the present work are necessary and crucial in optimization of the optical specifications of RMQW to be fabricated for devices applications.

1. Introduction The quantum confinement occurs in case of sufficiently small structure sizes in which the encompassing energy is greater than the thermal energy at the same temperature. The semiconductor quantum wells (QWs) that have restriction with one-dimensional (1D) are manufactured by epitaxial growth of the superfine layers [1]. However, advanced fabrication techniques at the present time make possible to produce QW with various confinement geometries [2]. But, the experimental data suggest well-like shape potentials to encompass electrons [3]. The manufacturing of QWs which have different confinement geometries has significant advantages in controlling of the electronic and optical specifications in devices applications, for special purposes. The determination clearly of this control mechanism plays a crucial role in designing and fabricating of devices such as semiconductor lasers [4], optical memories [5], and ultra-fast infrared photodetectors [6,7]. Because, the restricted quantum structures and their operating mechanism form the essence of devices mentioned above. More recently, some researches have taken into consideration structures such as quantum wells, wires, dots, disk and ring shaped have parabolic [8], Smorodinsky-Winternitz [9], Gaussian [10], pyramidal [11], diskshaped [12], ring-shape elliptical [13], Manning-Rosen [14], and pseudoharmonic [15] confinements, and then examining their

∗

electronic and/or optical properties. All these examinations and the corresponding results are very important due to the fact that the different QWs (or wires, dots, rings, disks) exhibit different electronic or optical specifications. Such diversities on quantum structures can be a required specification for special aims in devices applications. The welllike shape potential suggestions of experimental studies to encompass electrons, and the importance of various confinement geometries for devices applications have caused us to focus Rosen-Morse confinement potential [16]. Because, RMQW displays a parabolic confinement, and to the best of our knowledge as result of our literature researches, it has been considered within ILF in the present study, for the first time. RMQW is given by

VRMQW (z ) =

V1 sec 2 ( z ) + V2 tanh2 ( z ),

(1)

where, while V1 and V2 are the depth parameters of RMQW, η is the width parameter with 1/length dimension. The linear and nonlinear optical properties of a spherical quantum dot with Rosen-Morse potential have been investigated by solving analytically the Schrödinger equation using Nikiforov-Uvarov method within Pekeris-type approximation [17]. The electronic and optical specifications of QWs correlate with, closely, their intersubband transitions (ISBTs). When considering the relation directly between the ISBTs and the overlapping of bound states, the functionality of the external fields shines out. Because, the

Corresponding author. E-mail addresses: [email protected] (F. Ungan), [email protected] (M.K. Bahar).

https://doi.org/10.1016/j.optmat.2019.02.040 Received 11 January 2019; Received in revised form 22 February 2019; Accepted 24 February 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

external electric field break the symmetry of confinement potential. More clearly, while the external electric field leads to change confinement profile by bending to the left or the right QW profile, the external laser field can affect QW profile unevenly. The corresponding symmetry change causes to even-order nonlinear optical specifications by changing overlapping of bound states. This operating of the external fields can be alternative to growths implemented by fabrication techniques. In this context, applying electric and magnetic field on QWs has been examined in detail in many works: the investigation of, the external field effects on optical ACs of inversely parabolic QW via the potential morphing method [18], the effect of static electric field and permanent dipoles on the intensity-dependent nonlinear optical properties in a symmetric coupled QWs via the density matrix equations [19], the external magnetic field effect on linear and nonlinear optical absorption features of finite symmetric parabolic QW through one- and two-photon processes [20], the combined effect of the electric and magnetic field on optical properties of semi-parabolic QWs via the compact density matrix method [21], and the comparison of the external electric and magnetic field effects on binding energy of hydrogenic donor impurity in the square, V-shaped and parabolic QWs [22] are some of considerable currently works that consider the electric and magnetic field effects on QWs. In addition to these studies, it is important to note that the magnetic field influences on the linear and nonlinear optical specifications have also been investigated for monolayer MoS2, graphene, and monolayer phosphorene [23–25]. The most important common result of these studies is that the electric and magnetic fields lead to various optical properties by shifting bound states localizations of QWs, forming a functional mechanism in tunability of corresponding optical properties. In addition to shifting effect, it has been observed for only the external electric field in such studies that the external electric field causes to even-order optical features by breaking of the symmetry of QWs. If the considerable effects of the external electric and magnetic field on QWs are taken into consideration, it can be said that the ILF can be alternative to the electric and magnetic field in order to become more attractive or repulsive QW profile. The ILF can therefore exhibit a similar behavior on overlapping of the localizations compared to that of the electric and magnetic field. But, there are two different features of ILF compared to the electric and magnetic field: First one, the ILF depends on the time, and the solution of the time-dependent wave equation is be discussed. However, this solution is much more difficult compared to one with the electric and magnetic field. Second one relates with the strength of ILF. The investigation of second-order optical properties called as also nonlinear properties is possible thanks to applying a laser with high-power. In addition to these, the increment of ILF strength can be converted the parabolic QWs to double-well type, in which converting can be used, in consideration of the linear and nonlinear optical properties for devices applications, for special purposes. Here it should also be noted that ILF is more functional, compared to the electric and magnetic field, to encompass electrons in QWs (wires, dots) [26]. The examination theoretically of quantum systems with ILF is more complicated compared to ones with other external fields. Therefore, in order to be able to make theoretical analysis, approximations such as the Keldysh approximation [27], the space translation [28], the momentum translation method [29], and some perturbation and variational methods [30,31] are used. In this study, we have obtained the laser-dressed potential for RMQW by using the Ehlotzky approximation [34,35] within the Kramers-Henneberger (KH) unitary translation transformation [32,33]. Some of important works performed on optical specifications of the ILF-QW system can be outlined as follows: Karimi et al. have examined the laser field effect on the optical rectification and second harmonic generation coefficients of strained InGaN/AlGaN QW via the fourth-order Runge-Kutta method [36]. Panda et al. have investigated the ILF effects on optical properties such as optical rectification, second harmonic generation, third-order nonlinear susceptibility of symmetric and asymmetric Pöschl-Teller

QWs using the density matrix method [37]. In addition, the combined effect of the electric field and ILF on nonlinear optical features of a square QW through effective mass approach and density matrix formalism has been probed by Karabulut [38]. There are also one including ILF influences and optical specifications of quantum dot [39], wire [40], ring [41] and disk [42]. In this manner, the investigation of firstorder nonlinear optical properties of RMQW will be provided significant data to examine theoretically and experimentally electronic features and first-order and higher-order optical specifications of quantum wire, ring, disk and dot, as well as the importance of RMQW in devices applications. By the by, it is significant to note for QWs in devices applications that, QWs that have various confinement geometries, and tunability of their electronic and optical properties are building stone of devices semiconductor lasers [43], optical memories [44], and ultra-fast photodetectors [45,46].The work is organized as follows: In Section II, theoretical model is outlined. In Section III, the results and detailed discussions about them are carried out. Section IV is allocated to a brief summary and conclusions of work. 2. Theoretical model The Schrödinger equation for an electron with the effective mass in a QW under the influence of a monochromatic linearly polarized (along the z direction) ILF is stated in the following form:

( p + A)

2

q c 2m *

+ VQW (z )

(z , t ) = i

(z , t ) , t

(2)

where the electromagnetic radiation field depends on A (z, t ) through A F = t , due to . A = 0 and (z) = 0 in the Coulomb gauge. The timedependent resulting from the kinetic energy term in Eq. (2) has been counterchanged into the potential energy term through KH transformation [32,33] and the dipole approximation [47]. In that case, Eq. (2) becomes 2

2

2m *

˜ (z , t ) + (VPD [z + (t )]) ˜ (z, t ) = i

˜ (z , t ) , t

(3)

where ˜ (z , t ) results from acting the KH operator on (z , t ) . It is (t ) = 0 sin ( t ) where 0 = eF0/ m* 2 , and while F0 designates the amplitude of the electromagnetic field strength, ω designates the angular frequency of the electromagnetic field. 0 is allowed as the parameter that specifies the ILF strength, calling as the laser-dressing parameter. When considering Eq. (2), it is clear that the Hamiltonian for an electron in RMQW under the influence of ILF polarized along the z direction can be written using the Ehlotzky approximation [34,35] and the Fourier-Floquet series [48] in the following form:

H=

2

2

2m *

z2

+ V ( 0, z )

(4)

where V ( 0, z ) is the laser-dressed RMQW confinement potential, expressing as

V ( 0, z ) = (1/2)(VRMQW (z +

0)

+ VRMQW (z

0 )).

(5)

Then, the time-independent wave equation with 1D to be solved is H (z ) = E (z ) where (z ) and E are the wave function and the bound state energy of electron, respectively. The wave functions and energy values are obtained by using diagonalization method within the framework the effective mass and parabolic band approximations. To solve the equation (4), we take as base the eigenfunctions of the infinite potential well of width L. These bases are given at following: n (z )

=

2 n z cos L L

where n is; 232

n

(6)

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

0, n is odd , n is even 2

n=

(7)

cn

n (z )

(1)

t

˜ + Ee

(3) ( , I ) =

P (t ) =

0

˜ ( ) Ee

i t

+

0

˜ i ) Ee

(

t

( , I) =

0

(1)

(3)

( )=

|M12 |2 i

E21

(10)

( )=

E21

,

~ |M12 |2 |E |2 i

(E21

i

× 21

4|M12 |2 )2 + (

(E21

(M22 M11 ) 2 21)(E21

i

21)

21)

(12)

where is the carrier density, E2,1 is the energy separation between the initial (1) and final (2) energy state, Mfi is the dipole matrix elements specified by Mfi = < f |z|i> where f is the final state, and i is the initial state, = 1/ is the relaxation rate for 1,2 states. Then, the refractive index change is presented as, being nr the refractive index,

n( ) = Re nr

( ) . 2nr2

(13)

When considering Eqs.11–13, the linear and the third-order nonlinear RICs are obtained by Ref. [50].

n(1) ( ) |M12 |2 = nr 2nr2 0

E21 )2 + (

(E21

µc|M12 |2 4nr3 0 [(E21

n(3) ( , I ) = nr

I )2 + (

4(E21

)|M12 |2

× [(E21 )(E21

)

×

21)

,

2

21)

(14) 2]2

(M22 M11 ) 2 {(E21 (E21 ) 2 + ( 21) 2 (

21)

2]

(

21)

2 (2(E

21)

) )} , (15)

where μ is the permeability of the system, c is the velocity of light in vacuum, I is the incident optical intensity with the definition

I=2

R

µ

|E ( )|2 =

2nr |E ( )|2 . µc

(16)

is the real part of the permittivity. The TRIC is figure where R = out by considering the linear and nonlinear contributions [50]:

nr2 0

n ( , I) = nr

n(1) ( ) + nr

n(3) ( , I ) . nr

(E21

µ

I

R

0 nr c

)2

×

21)

|M12 |4 [(E21

2

, 21

(19) 2

)2 + ( 21)2]

( 21) 2 + 2(E21 )(E21 (E21 )2 + ( 21)2

)

1

|M22 M11 |2 |2M12 |2

(20)

(1)

( )+

(3)

( , I ).

(21)

In this study, for RMQW constituted by GaAs/GaAlAs heterostructure, the effects of the ILF on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) have been probed. There are four parameters on optical specifications of RMQW under the influence of ILF as follows: RMQW confinement parameters (V1, V2 and η), and the laser dressing parameter ( 0 ) that characterizes the ILF strength. In Fig. 1a, in absence of laser field ( 0 = 0 ), TRICs of RMQW with V1 = 100,300 meV, V2 = 228 meV and = 0.01, 0.02 cm 1 are shown. Here it should be pointed out that, for V2 = 100,300 meV and V1 = 228 meV, the total depth of the quantum well is the same as when V1 = 100,300 meV, V2 = 228 meV. In both cases, the structure exhibits the same optical properties as the depth of the total QW does not change. Therefore, we did not examine the effect of V2 on the optical properties of the system. When = 0.01 cm 1, the increment of V1 parameter from 100 meV to 300 meV leads to a blue-shift in resonance energies of TRICs (See Fig. 1a), in which case is also true for = 0.02 cm 1 (See Fig. 1a). The reason of this blue-shift can be understood by examining the profile of QW. In this manner, when 0 = 0 , the profile of RMQW with V1 = 100,300 meV, V2 = 228 meV and = 0.01 cm 1 has been shown in Fig. 3a. As seen, the increase of V1 leads to a more attractive potential. The bound states in a more attractive potential localize to create greater energy gaps. In Fig. 3a, the localizations of the ground state and the first excited state are shown when V1 = 100 meV and 300 meV, in which case the energy gap between localizations for V1 = 300 meV is greater than that for V1 = 100 meV. This result arising from a more attractive potential well has been caused blue-shift in resonance energies of TRICs. In that case, it can be predicted that a blueshift case will come true for further V1 values. As seen in Fig. 4a, for = 0.01 and 0.02 cm 1 when 0 = 0 , V1 = 100 300 meV, V2 = 228 meV, the energy gap between the first two bound states increases linearly (with increasing V1), which case confirms the localizations in Fig. 3a and blue-shift in Fig. 1a. Also, the deepening of QW leads to decrease TRICs amplitudes (See Fig. 1a). When considering Eq. (17), it is clear that RICs amplitude depends on matrix elements in the linear and nonlinear contributions. If the dominance of the linear contribution in TRICs is considered, the dependence to |M12 | of TRICs amplitude is understood more clearly. In Fig. 5a, when 0 = 0 , the behavior of |M12 | is shown for V1 = 100 300 meV, V2 = 228 meV and = 0.01, 0.02 cm 1 parameter set. As seen, |M12 | decreases linearly as a result of the increase of V1, which leads to decrease TRICs amplitudes (See Fig. 1a). The considerable effects on optical specifications of η the width

2

,

(E21

|M12 |2 21 )2 + (

(t ) . The linear and the third-order

3. Result and discussions

(11)

21

(18)

Finally, it should be pointed out that we have used the following parameters that are suitable for GaAs/GaAlAs heterostructures [51] * mGaAs = 0.067m 0 (m 0 is mass of the free electron), GaAs = 12.58, nr = 3.2 , I = 0.05 mW/cm2 , = 3 × 10 22m 3, Hm 1 and = 0.14 ps.

The linear and nonlinear susceptibilities are determined within the framework of same density-matrix formalism, their analytical forms are given by 0

( )),

0

The TAC is given by considering the linear and nonlinear contributions [50]:

However, the electronic polarization P (t ) and susceptibility (t ) are presented via the dipole operator M and the density matrix ρ: being V, ρ and 0 are the volume of system, the one-electron density-matrix of the system, the dielectric constant of vacuum, respectively.

1 = Tr ( M ) V

2 ×

(9)

i t.

µ

( )=

r

where cn is the coefficient of the expansion. Applying a linearly polarized electromagnetic (EM) field with ω frequency on RMQW is considered, and this time-dependent EM field is given by Ref. [50].

˜ i E (t ) = E0 cos ( t ) = Ee

Im (

( ) is the Fourier component of nonlinear ACs are obtained by

(8)

n=1

1/2

R

and the wave function described the system is formed from a complete set as [49].

(z ) =

µ

( )=

(17)

However, the AC change is stated as 233

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

Fig. 1. The TRICs as a function of the incident photon energy versus a) V1 = 100,300 meV for = 0.01 and 0.02cm 1 when 0 = 0 and V2 = 228 meV b) 100A0 when = 0.01 cm 1, V1 = 100 meV and V2 = 228 meV, c) 0 = 0 , 50A0 and 100A0 when = 0.02 cm 1, V1 = 100 meV and V2 = 228 meV.

parameter have also been determined. As seen in Fig. 1a, the increments of η from 0.01 to 0.02 cm 1 lead to a blue-shift in resonance energies of TRICs. Because, η parameter does not affect the depth of RMQW, but affecting drastically the width of well (See Fig. 3b). As seen in Fig. 3b, the increment of η decreases the width of well, and this decrease impresses significantly bound state localizations. The narrowing QW causes to increase the energy gap between the first two bound states (See Fig. 3b), which case ends up a blue-shift in TRICs. Also, the increment of η from 0.01 to 0.02 cm 1 decreases TRICs amplitudes (See Fig. 1a), which case is also confirmed in Fig. 5a, because |M12 | values for = 0.02 cm 1 are always less than ones for = 0.01 cm 1 (See Fig. 5a). Fig. 2a is same with Fig. 1a but it shows TACs. As seen, converging of localizations in RMQW deepened by increasing V1 has also been led to a blue-shift in resonance energies of TACs, as in TRICs. Similarly, a blue-shift has been observed as a result of diverging of localizations in RMQW narrowed by increasing η. However, the increase of V1 and η does not create a noteworthy effect on TACs amplitudes (See Fig. 2a). Because, the nonlinear contribution on TACs is proportional to |M12 |4 (See Eq. (20)), suppressing by reducing the contribution arising from |M12 |2 in the linear contribution (See Eq. (19)). In Fig. 1b, the influence of ILF on TRICs of RMQW with V1 = 100 meV, V2 = 228 meV and = 0.01 cm 1 has been analyzed by considering 0 0 = 0,50,100A . Here, the increment of 0 increases the repulsive of QW potential (See Fig. 3c), and then decreasing the energy gaps between bound states, in which cases are also verified by Fig. 4b. As seen in

0

= 0 , 50A0 and

Fig. 4b, the increase of 0 decreases the energy gap between the first two bound states of both RMQW (with = 0.01 cm 1 and = 0.02 cm 1 when V1 = 100 meV, V2 = 228 meV), which means a red-shift in TRICs. However, as seen in Fig. 1b, the increase of 0 leads to increase TRICs amplitudes. As also mentioned before, the linear and nonlinear contributions to TRICs are proportional to |M12 |2 (See Eq. (14)), and the linear one is more dominant. It is observed the increment of M12 as result of increasing 0 in Fig. 5b. The increment of 0 causes to increase TRICs amplitude, as the linear and nonlinear contribution are proportional to |M12 |2 , and due to dominance of the linear one. Fig. 1c is same with Fig. 1b but = 0.02 cm 1. TRICs specifications of RMQW with = 0.02 cm 1 are similar to ones of QW with = 0.01 cm 1. Namely, the increase of ILF in the case with = 0.02 cm 1 increases also the amplitudes, leading to red-shift. Because, as also seen in Fig. 3d, the increment of ILF strength ( 0 ) becomes more repulsive it by decreasing the depth of QW potential. Also, it is evident that the energy gap in QW with 0 = 100A0 is less than that in QW with 0 = 0 (See Fig. 3d), which is the reason of corresponding red-shift. But, here it should be pointed out that while, when 0 = 0 , the increment of η from 0.01 to 0.02 cm 1 causes to decrease TRICs amplitude (See Fig. 1a), when 0 0 (for example, 0 = 100A0 ), same increment of η increases TRICs amplitude (See Fig. 1b and c). More clearly, while the positive peak point is around 0.038 for 0 = 100A0 in Fig. 1b ( = 0.01 cm 1), one is around 0.065 for 0 = 100A0 in Fig. 1c ( = 0.02 cm 1). That case arises from the presence of a critic value of ILF for = 0.01 cm 1 and = 0.02 cm 1. 234

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

Fig. 2. The TACs as a function of the incident photon energy versus a) V1 = 100,300 meV for = 0.01 and 0.02cm 1 when 0 = 0 and V2 = 228 meV b) 100A0 when = 0.01 cm 1, V1 = 100 meV and V2 = 228 meV, c) 0 = 0 , 50A0 and 100A0 when = 0.02 cm 1, V1 = 100 meV and V2 = 228 meV.

As seen in Fig. 5b, it is clear that while the matrix elements in case with = 0.01 cm 1 are greater compared to ones with = 0.02 cm 1 up to around 0 = 50A0 , the matrix elements in case with = 0.02 cm 1 are greater for values greater than 0 = 50A0 . This case is the reason for higher TRICs amplitude of RMQW with = 0.02 cm 1, 0 = 100A0 . The matrix elements for = 0.01 cm 1 and 0.02 cm 1 around 0 = 50A0 are equal to each other (See Fig. 5b), which causes nearly same TRICs amplitudes (See Fig. 1b and c). The remarkable influences of ILF on TACs have also been found out. In Fig. 2b, the effects of ILF on TACs of RMQW with = 0.01 cm 1, V1 = 100 meV, V2 = 228 meV have been examined within 0 = 0,50,100A0 . As seen, since the increase of 0 makes more repulsive QW, and so decreasing the energy gap between localizations (See Fig. 3c), it leads to a red-shift in TACs. This red-shift in resonance energies is also valid for RMQW with = 0.02 cm 1 (See Fig. 2c). As seen in Fig. 2b and c, the increase of 0 causes to decrease also TACs amplitudes for cases with = 0.01 cm 1 and 0.02 cm 1 due to the fact that the nonlinear contribution is proportional to |M12 |4 , suppressing the linear contribution (is proportional to |M12 |2 ). As seen in Fig. 2b and c, there is an explicit diminishment in TACs amplitudes in case with = 0.02 cm 1 because of more explicit response of = 0.02 cm 1 case versus the increase of 0 (See Fig. 5b). Here there is a point that should be specified in particular for η: the increment of η parameter doesn't affect the depth of RMQW but decreases its width, as can be sen in Fig. 3c and d. The ILF tends to convert RMQW profile to double-well type, and this tend is more obvious for a narrower RMQW. When

0

= 0 , 50A0 and

considering also overlapping cases of wave functions in a double-well type RMQW, it is clear that the combined effect of η and 0 parameters constitutes an important mechanism for TRICs and TACs. As seen in Fig. 3d, the ILF effect shows up more explicitly in RMQW narrowed by increasing η from 0.01 to 0.02 cm 1, and RMQW starts to transform into double-well type. In this manner, the increment of 0 for a given η (here = 0.02 cm 1) or the increment of η for a given 0 converts to RMQW potential into double-well type. The ILF has a critical value for TRICs and TACs of RMQW. The results of confinement provided by η at this critical value start to change. More clearly, as seen in Fig. 4b, the energy gaps ( E ) are same for = 0.01 and 0.02 cm 1 around 0 = 65A0 , and after for further 0 values, E s of RMQW with = 0.01 cm 1 are greater compared to ones in RMQW with = 0.02 cm 1. Also, around 0 = 0.02 cm 1 are greater 0 = 55A , the matrix elements in case with than ones in case with = 0.01 cm 1 (See Fig. 5b). The determination of critical value of the ILF is important for the optimum of the optical specifications of RMQW. Because, the dominance to each other of different η values on magnitudes of TRICs and TACs resonance energies and amplitudes can change, as confirmed from Figs. 4b and 5b. 4. Conclusion In this work, the effects of ILF and structure parameters on TRICs and TACs of RMQW generated by GAaS/GaAlAs heterostructure have been examined in detail. The influences of V1, η and 0 parameters on 235

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

Fig. 3. The plot of RMQW potential profile and in which the first two bound states localizations for a) V1 = 100 and 300 meV when 0 = 0 , = 0.01 cm 1, V2 = 228 meV, b) = 0.01 and 0.02cm 1 when 0 = 0 , V1 = 100 meV, V2 = 228 meV, c) 0 = 0 and 100A0 when = 0.01 cm 1, V1 = 100 meV, V2 = 228 meV, d) 0 = 0 and 100A0 when = 0.02 cm 1, V1 = 100 meV, V2 = 228 meV.

QW profile and overlapping of the wave functions have been shown clearly. As the effect of V2 on the depth of well is the same as V1, the investigations about V2 have not been done. V1 parameter is very functional in adjusting of overlapping of bound states due to its influence on QW depth. In this manner, the increase of V1 enables blue-shift

of resonance energies for TRICs and TACs. The effect of V1 on TRICs amplitudes is more obvious compared to that on TACs ones. Therefore, while, the adjustment of the optimum of RMQW for TACs is unlikely through V1 parameter, RMQW for TRICs is optimum in smaller values of V1. The increase of η parameter is narrowed RMQW profile, and causing

Fig. 4. The energy gap ( E ) between the ground state (E1) and the first excited state (E2 ) a) as function of V1 for as function of 0 for = 0.01 and 0.02cm 1 when V1 = 100 meV, V2 = 228 meV. 236

= 0.01 and 0.02cm

1

when

0

= 0 , V2 = 228 meV, b)

Optical Materials 90 (2019) 231–237

F. Ungan and M.K. Bahar

Fig. 5. The matrix elements a) as function of V1 for meV, V2 = 228 meV.

= 0.01 and 0.02cm

1

when

0

= 0 , V2 = 228 meV, b) as function of

rise localizations of bound states. Corresponding shift in localizations leads to red-shift in resonance energies of TRICs and TACs by increasing overlapping of wave functions. Also, η parameter on TACs amplitudes is not functional. But, for TRICs, that case is not same, because RMQW is more optimum in small values of η. Then, it is important to note that η and V1 are alternative parameters to each other in adjusting of resonance energies of TRICs and TACs. However, this alternativeness is only valid in TRICs for amplitudes. The increase of ILF strength ( 0 ) decreases the depth of RMQW, but it increases the width of RMQW, which causes to increase the overlapping of the wave functions. This overlapping is major reason of red-shift in TRICs and TACs. While, RMQW for TRICs is optimum in the strong regimes of the ILF, it is optimum in the weak ILF regimes for TACs. The tendency of 0 to create double-well type confinement is more explicit for a narrower well structure. Therefore, combining of ILF influence and decreasing effect of η on well width lead to a double-well type confinement. Then, it can be said that ILF which has certain range of 0 can be applied for special purposes. In addition to these, there is a critical value of ILF for the effects of η parameter on magnitudes of resonance energies and amplitudes of TRICs and TACs. How to use the structure parameters and ILF in adjusting of firstorder optical properties of RMQW in devices applications has been presented clearly. We think that the present detailed analysis will be a significant manual for fabrication and operating of RMQW.

0

for

= 0.01 and 0.02cm

1

when V1 = 100

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