Journal of Luminescence 132 (2012) 1420–1426

Contents lists available at SciVerse ScienceDirect

Journal of Luminescence

0022-23

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jlumin

Density of states in a cylindrical GaAs/AlxGa1�xAs quantum well wire undertilted laser field

Adrian Radu, Ecaterina Cornelia Niculescu n

Department of Physics, ‘‘Politehnica’’ University of Bucharest, 313 Splaiul Independentei, Bucharest, RO 060042, Romania

a r t i c l e i n f o

Article history:

Received 27 November 2011

Received in revised form

4 January 2012

Accepted 6 January 2012Available online 21 January 2012

Keywords:

Quantum well wire

Tilted laser field

Finite element method

Density of states.

13/$ - see front matter & 2012 Elsevier B.V. A

016/j.jlumin.2012.01.020

esponding author.

ail address: niculescu@physics.pub.ro (E.C. Ni

a b s t r a c t

Within the effective-mass approximation the subband electronic levels and density of states in a

semiconductor quantum well wire under tilted laser field are investigated. The energies and wave

functions are obtained using a finite element method, which accurately takes into account the laser-

dressed confinement potential. The density of states obtained in a Green’s function formalism is

uniformly blueshifted under the laser’s axial field whereas the transverse component induces an

additional non-uniform increase of the subband levels. Our results confirm that the tilted laser field

destroys the cylindrical symmetry of the quantum confinement potential and breaks down the

electronic states’ degeneracy. Axial and transversal effects of the non-resonant laser field on the

density of states compete, bringing the attention to a supplementary degree of freedom for controlling

the optoelectronic properties: the angle between the polarization direction of the laser and the

quantum well wire axis.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

By the advent of artificial semiconductor structures with sizescomparable to the de Broglie wavelength of electron, newopportunities arise for investigating the intense laser field (ILF)effects on quantum nanostructures. It is proved that the electro-nic transport characteristics and optical properties of low-dimen-sional systems irradiated by ILFs are different from those of a bulksemiconductor, more pronouncedly as the carriers’ confinementis increased by dimensionality reduction [1–14]. Since 1D semi-conductor structures are usable for designing ultrafast electronicdevices, there is a strong motivation to study their response tointense external fields such as lasers. Some theoretical studieshave focused on shallow donor states [13,15–19] and intersub-band transitions [20,21] in QWWs dressed by laser fields polar-ized perpendicularly to the wire axis. By making use of anonperturbative method [13,21], a significant laser-induced shiftof the electronic levels was found, more pronounced for thinnerQWWs. For an ILF linearly polarized along the wire axis recentworks [22–24] have predicted an axial localization effect, whichleads to a transition from one-dimensional to zero-dimensionalbehavior of the density of states (DoS). However, the restrictionon the polarization direction such as being along or perpendicularto the wire axis may not be always experimentally feasible.Moreover, due to the strong optical and magnetic anisotropies

ll rights reserved.

culescu).

induced by ILFs [19,21] the question of an optimal interactionsetup (i.e. the relative orientation between a QWW and an opticalfield, which leads to a maximum interaction) becomes technolo-gically important.

The main objective of our study is to settle on the dependenceof the laser-driven electronic DoS in a cylindrical QWW on thelaser’s tilt angle between two limit cases, the first occurring for alaser radiation linearly polarized along the wire, and the last for apolarization in the QWW’s transverse plane. A proper under-standing of the DoS is important for controlling the opticalproperties related to electrons in semiconductor QWWs. There-fore, besides providing a theoretical framework with which tointerpret polarization-dependent absorption-emission spectra ofQWWs, our results can be used for designing novel electronicdevices in which the DoS tuning plays a significant role.

The paper is organized as follows. Section 2 describes thetheoretical framework. Section 3 presents the influence of the tiltedlaser field on the energy levels and DoS for electrons confined in aGaAs/AlGaAs cylindrical QWW. The possibility of tuning such quan-tities by varying the laser polarization direction and frequency waspointed out. Finally, our conclusions are summarized in Section 4.

2. Theory

2.1. Electron states under tilted laser fields

The physical system we consider is the nanostructure formedby surrounding a long cylindrical wire made up of direct bandgap

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–1426 1421

semiconductor material (GaAs) by a coaxial layer material with awider bandgap (AlxGa1�xAs) and practically the same latticeconstant (Fig. 1). The QWW is considered to interact with apolarized single-mode laser beam, non-resonant with the energylevels of the electrons in the wire.

The z-axis is chosen along the wire direction. The quasi-monochromatic laser beam is linearly polarized along an s

direction, which makes an angle y with the z-axis. The orthogonaltransverse axis x and y are chosen so that xC(z,s). The hard-wallconfinement potential has the cylindrically symmetric form

VðrÞ ¼0, rA ½0,RÞ

V0, rA ½R,1Þ,

(ð1Þ

where V0 is the conduction-band offset and r¼(x2þy2)1/2 is the

electron’s radial position in the wire.The electrons have a free movement along the wire but in its

transverse plane (x,y) the quantum confinement effect becomesimportant if radius R is comparable to the electron’s Bohr radiusin the bulk semiconductor. We will demonstrate that the laser’stransverse component dresses the energy levels associated withthe lateral confinement, whereas the axial laser field modifies theelectronic energies related to the movement along the wire.

If there is no laser irradiation on the QWW, the electron’senergy levels can be calculated by solving the atemporalSchrodinger equation in cylindrical coordinates

�_2

2mn

1

r@

@rr @

@r

� �þ

1

r2

@2

@j2þ@2

@z2

" #CðrÞþVðrÞCðrÞ ¼ ECðrÞ ð2Þ

The wave functions of the electronic subbands may be set intothe form

Cp,n,kz ðr,j,zÞ ¼Fp,nðr,jÞexpðikzzÞ ¼Rp,nðrÞexpðipjÞexpðikzzÞ,

ð3Þ

where p is an integer and kz ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mnEz

p=_ is the continuous wave

number in the z direction. Ez is the axial, not quantized, electron’senergy. The radial eigenfunctions Rp,nðrÞ are analytical solutionsof the Bessel equation

r2 @2R

@r2þr @R

@rþ r2 2mn

_2E�VðrÞ� �

�p2

� �R¼ 0 ð4Þ

Fig. 1. Schematic view of a cylindrical GaAs/AlGaAs QWW irradiated by an ILF. R is

the wire’s radius and y is the angle between s, the polarization direction of the

laser and z, the longitudinal axis of the wire.

and have the forms

Rp,nðrÞ ¼Ci

p,nJpðkip,nrÞ, rA ½0,RÞ

Cop,nKpðko

p,nrÞ, rA ½R,1Þ,

8<: ð5Þ

where Jp is the p-order Bessel function, Kp is the modified Besselfunction, ki

p,n ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mnEp,n

p=_ and ko

p,n ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mnðV0�Ep,nÞ

p=_. Ep,n are

the discrete bound-state energy eigenvalues corresponding to thebottoms of 1D subbands. Coefficients Ci

p,n, Cop,n and energies Ep,n

may be obtained by matching the wave functions given by Eq. (5)and their derivates at the wire boundary and by wave functions’normalization. It should be noticed from Eq. (4) that Ep,n¼E�p,n,which means the states described by eigenfunctions Fpa0,n(r,j)are double-degenerated.

Total subband energies corresponding to the eigenfunctionsCp,n,kz ðr,j,zÞ are given by

Ep,nðkzÞ ¼ Ep,nþEz ð6Þ

Under the tilted laser field described by the vector potentialAðtÞ ¼ ðxsinyþ zcosyÞA0 sinðotÞ the quantum states can beobtained from the time-dependent Schrodinger equation in rec-tangular coordinates

ðp?þ xeAxðtÞÞ2

2mnþðpzþ zeAzðtÞÞ

2

2mnþVð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2þy2

qÞ

" #Cðr,tÞ ¼ i_

@Cðr,tÞ

@t,

ð7Þ

where p? (pz) is the electron momentum perpendicular to (along)the wire axis.

When the vector potential has only an x-component (y¼p/2)Eq. (7) implies that

ðp?þ xeAxðtÞÞ2

2mnþVð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2þy2

qÞ

" #Fðx,y,tÞ ¼ i_

@Fðx,y,tÞ

@tð8Þ

By applying the time-dependent translation x-xþððeA0 sinyÞ=ðmnoÞÞsinðotÞ, one has [25]

p?2

2mnþ ~V ðx,y,tÞ

~Fðx,y,tÞ ¼ i_

@ ~Fðx,y,tÞ

@t, ð9Þ

where ~V ðx,y,tÞ ¼ Vðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxþa0xsinðotÞÞ2þy2

qÞ is the laser-dressed

confinement potential with a0x ¼ ððeA0xÞ=ðmnoÞÞ ¼ ððeA0 sinyÞ=

ðmnoÞÞ denoting the laser parameter in the x-direction. In thehigh-frequency limit [26] the laser-dressed bound states for thetransversal motion are solutions of the time-independentSchrodinger equation

�_2

2mn

@2

@x2þ@2

@y2

!þ ~V aðx,yÞ

" #~Fðx,yÞ ¼ ~E ~Fðx,yÞ, ð10Þ

where ~V aðx,yÞ is the zero-order Fourier component of the dressedpotential energy, i.e. its time average over one period

~V aðx:yÞ ¼o2p

Z 2p=o

0

~V ðx,y,tÞdt ð11Þ

For the particular potential function given by Eq. (1), Eq. (11)may be analytically integrated to the closed form

~V aðx,yÞ ¼V0

p Re Yða0x�x�Re

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2�y2

q� �Þarccos

RefffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2�y2

qgþx

a0x

0@

1A

8<:

þYða0xþx�Re

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2�y2

q� �Þarccos

RefffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2�y2

qg�x

a0x

0@

1A9=;,

ð12Þ

where Y is the Heaviside unit-step function. This is the firstanalytical form proposed in the literature for the laser-dressed

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–14261422

confinement potential of a cylindrical QWW, which allows anaccurate calculation of the dressed subband states.

By solving Eq. (10) with a finite element method [27–29], onemay obtain the laser dressed transverse energies ~Ep,n and therelated transverse eigenfunctions ~Fp,nðx,yÞ. The orthogonal states,which degenerate in Fpa0,n(r,j) for a0x¼0 still have x and y asaxis of symmetry, thus their energies and wave functions will bedenoted by ~E

x

p,n, ~Fx

p,nðx,yÞ and ~Ey

p,n, ~Fy

p,nðx,yÞ, respectively.Note that Schrodinger Eq.(8) for the transversal motion is not

affected by the presence of an additional axial componentAzðtÞ ¼ A0cosysinðotÞ of the vecftor potential; thus, the eigenva-lues ~Ep,n and the corresponding eigenfunctions ~Fp,nðx,yÞ obtainedby solving Eq.(10) remain the same. By writing Cðr,tÞ ¼~Fp,nðx,yÞULðz,tÞ [24] in Eq. (7) we obtain two Schrodinger equa-

tions: one related to a motion of electrons perpendicular to thewire axis, which is identical to Eq. (10), and the other for theparallel motion, that is

ðpzþeAzðtÞÞ2

2mnþ ~Ep,n

" #Lðz,tÞ ¼ i_

@Lðz,tÞ

@tð13Þ

Here L(z,t) depends only parametrically on the vector poten-tial component perpendicular to the wire axis, via the energy ~Ep,n.By temporal integration [23,24] of Eq. (13) one finds

Lðz,tÞ ¼Lðz,0Þexp �i ~Ep,nþ_2k2

z

2mnþDEz

!t

_þ2a0zkzsin2 ot

2

� ��DEz

2_osinð2otÞ

" #( ),

ð14Þ

where DEz¼((eA0z)2/(4mn))¼mn((a0zo)/(2))2 is the energy blue-

shift induced by the axial component of the laser field anda0z ¼ ððeA0zÞ=ðm

noÞÞ ¼ ððeA0cosyÞ=ðmnoÞÞ denotes the laser para-meter in the z direction.

Fig. 2. Laser-dressed confinement potential of the cylindrical QWW with R¼75 A.

2.2. Laser-driven density of states

Following the Green’s function approach introduced in[22–24] for quasi-1D electronic systems under ILFs and takinginto account Eq. (14), the retarded propagator (or Green’s func-tion) for non-interacting electrons is written as

Gþ ðp1,n1,kz1; p2,n2,kz2Þ ¼dp1 ,p2

dn1 ,n2dkz1kz2

i_Yðt2�t1Þ

exp i ~Ep,nðkzÞt2�t1

_þ2a0zkz sin2 ot2

2

� ��sin2 ot1

2

� � �

�DEz

2_o sinð2ot2Þ�sin ð2ot1Þ½ �

�ð15Þ

where ~Ep,nðkzÞ ¼~Ep,nþDEzþðð_

2k2z Þ=ð2mnÞÞ.

The laser-driven DoS per unit length in each 1D subband as afunction of electron’s energy can be derived from the imaginarypart of the Green’s function Fourier transform [23,24], so that

dp,nðEÞ ¼Dp,nðEÞ

L¼

gs

2p

ZdðE� ~Ep,nðkzÞÞf 0

2ðkzÞdkz, ð16Þ

where gs¼2 is the spin degeneracy factor and f 0ðkzÞ ¼P

iA2ZJi

ððDEzÞ=ð2_oÞÞJ2iða0zkzÞ, Ji denoting the order i Bessel function. Bymaking use of the Dirac-d function properties, one can obtain [24]the following expression for the overall DoS per unit length

dðEÞ ¼DðEÞ

L¼ gs

ffiffiffiffiffiffiffiffiffiffi2mnp

2p_Xp,n

YðE� ~Ep,n�DEzÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE� ~Ep,n�DEz

q f 02ð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mnðE� ~Ep,n�DEzÞ

q=_Þ

ð17Þ

Due to the term DEz in the denominator and the Y function, anuniform blueshift of the DoS profile as a whole is expected underan axial laser field.

3. Results and discussion

The numerical calculations were performed for a GaAs/Alx-

Ga1�xAs cylindrical QWW with x¼0.3 and R¼75 A. The size ofconsidered GaAs nanostructure is chosen to be slightly smallerthan the electronic Bohr radius in bulk GaAs (ffi100 A). A numberof characteristic features of energy levels are revealed in thisintermediate quantum confinement regime, when the strength ofthe electron-laser field interaction and quantum confinementeffects are comparable.

An isotropic effective mass mn¼(0.0665þ(0.08þ1/300)x)m0

of the electron throughout the nanostructure was assumed (m0

denoting the free electron mass). The conduction-band offsetV0¼228 meV was introduced by taking into account the Miller’srule (V0¼60%DEgapE0.7xþ0.2x2 in eV units). The laser parameteris considered to be a constant a0¼R¼75 A, so that the QWW’sconfinement potential will be significantly modified as the laserpolarization angle y varies from 0 to p/2. In the absence of thelaser filed, there are four bound states in the QWW (the secondand the third being double degenerated): E0,1¼37.22 meV,E1,1¼93.65 meV, E2,1¼164.67 meV and E0,2¼187.96 meV.

3.1. Laser-dressed electronic states

Fig. 2 shows the time-averaged laser dressed confinementpotential given by Eq. (11) for a0x¼75 A (y¼901), when theradiation provokes maximum changes on the potential energy.At high energies the effective potential profile seems to beenlarged along the laser polarization direction, while at thebottom of the well the potential has a sharp profile. The meanwidth of the QWW confinement potential within the y¼0 section,defined as ð2=V0Þ

R V0

0~V a�1ðxþ ,0ÞdV , remains equal with 2R. On the

other hand, the mean width within the x¼0 section has adiminished value with respect to the no-dressing case,ð2=V0Þ

R V0

0~V a�1ð0,yþ ÞdV o2R, because there is no enlargement

in the y direction. These observations clearly suggest a laser-induced strong enhancement of the quantum confinement forlow-energy states.

Fig. 3 illustrates the changes of the transverse probabilitydensity for the electron ground state when rotating the laserfrom axial to transversal polarization. For a0x¼0 (Fig. 3(a))one may observe the angular independence characteristic to

Fig. 3. Cross section of the electron probability density for the ground state, at (a)

y¼0; (b) y¼901.

Fig. 4. Cross section of the electron probability density for the first excited state,

at y¼0 (a) and(c) and y¼901 (b) and (d).

Fig. 5. Cross section of the electron probability density for the second excited

state, at y¼0 (a) and (c) and y¼901 (b) and (d).

Fig. 6. Cross section of the electron probability density for the third excited state,

at (a) y¼0; (b) y¼901.

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–1426 1423

non-degenerate states and a maximum probability density on thewire axis. This on-axis maximum is enhanced for a0x¼75 A and asignificant blueshift of the ground state energy is observed(Fig. 3(b)).

The probability density of the electron in the first excited stateis presented in Fig. 4. As expected, in the absence of the lasercomponent on the x-axis, there are two orthogonal eigenstateswith the same energy E1,1 (Fig. 4(a) and (c)). For both states theprobability density has an on-axis minimum and two identicalmaxima symmetrically positioned with respect to the wire axis.The ILF breaks down the radial symmetry so that two laserdressed orthogonal states with different energies are obtained(Fig. 4(b) and (d)).

Fig. 5(a) and (c) shows the density of probability for the secondexcited state of the electron, also double-degenerated. For bothorthogonal states the localization probability is zero on the wireaxis and has four equal maximums with equidistant angularseparation. Fig. 5(b) and (d) illustrate the laser-induced degen-eracy breaking with an obvious difference between the orthogo-nal states ~F

x

2,1ðx,yÞ and ~Fy

2,1ðx,yÞ. It’s also apparent fromFig. 5(b) and (d), that the electron wave functions spread in thebarrier regions of the dressed QWW. This later feature is a general

characteristic of low-dimensional structures subjected to non-resonant laser fields [19].

The upper subband state is not degenerated because its wavefunction is also angularly independent (Fig. 6(a)). Two radialmaxima can be observed on the density of probability image,one in the middle of the wire (on-axis maximum) and the otherby the form of a circular ring (near-edge maximum). In hightransverse laser fields (Fig. 6(b)), due to the leakage of the wavefunction into the barrier regions, the probability density isstrongly affected, having two symmetrical large peaks outsidethe wire and another two weaker maxima inside.

Fig. 7 offers a better image of the transverse subband levelsdependence on the in-plane component of the laser parameter.One may observe that, although all the energy levels are blue-shifted, the ground level is the most affected by the field,increasing with more than 60 meV. The effect of the radiation isless pronounced for higher energy levels due to a weakerconfinement in the upper part of the dressed QWW potential. Itis clear from Fig. 7 that large field intensity is needed to induceappreciable changes of the upper-lying states. Indeed, E2,1 levelremains degenerated under relatively high transverse laser

Fig. 7. Transverse subband energy levels versus in-plane laser parameter.

Fig. 8. Energy levels blueshift induced by the axial laser filed, as a function of the

laser frequency.

Fig. 9. Electron DoS versus energy for (a) o/2p¼10 THz; (b) o/2p¼25 THz and

three different orientations of the laser field. Dotted line is for the DoS in the

absence of laser radiation. a,b,c,d represent the ground and the three excited

subbands, respectively. Notations x, y stand for different levels originating from

the same electronic state through laser degeneracy breaking.

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–14261424

parameter, a0xffiR/2, and for the highest excited state only a slowvariation with growth of a0x is observed. The coalescence of thesubband energy levels with the increase of the transverse laserparameter is a remarkable aspect, which has been also reportedfor square QWs under ILFs [11].

Fig. 8 depicts the energy blueshift induced by the axialcomponent of the laser field as a function of the laser frequency.All levels present a parabolic increase while keeping the sameenergy separation. For relatively small frequency values(o/2po20 THz), the blueshift DEz brought by an axial orientationof the laser field is observed to be less important than the typicalenergy levels increase induced by the same laser in the transverseorientation case (Fig. 7). By maintaining the same laser parameterat higher values of o, one may notice the opposite situation.

3.2. Laser-driven density of states

Accordingly to previous discussion, we calculated the electronDoS for two different values of the laser frequency.Fig. 9(a) presents the results obtained for o/2p¼10 THz, at threedifferent orientations of the laser field. For y¼0 there is only arelatively small and uniform blueshift of all energy levels, inducedby the axial laser field, as compared with the unperturbed DoS. Inaddition, the DoS profile changes from the characteristic shape foran unperturbed QWW to a set of sharp peaks, which is a sign of anincreased confinement due to the axial field effect on the electron[23]. For y¼p/4 the energy blueshift is the combined effect ofboth radiation components. The level splitting, which is apparentfrom this figure results from degeneracy breaking effect producedby the transverse laser component. For y¼p/2, only the

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–1426 1425

transverse effect remains, the energy spectrum being non-uni-formly blueshifted.

Fig. 9(b) presents the electron DoS for o/2p¼25 THz, at thesame three orientations of the laser field. For y¼0 (axial laserpolarization) there is a large uniform blueshift of the energy levelsand a strong decrease of the DoS profile height. For y¼p/4 theenergy blueshift and the level splitting are the combined effects ofthe axial and transversal laser components. Unlike in Fig. 9(a), theDoS profile is redshifted as compared with y¼0 case. For y¼p/2(transverse laser polarization), there is an even larger redshift ofthe DoS, energies being still blueshifted as compared with theunperturbed DoS profile.

Fig. 10. DoS as a function of the electron energy and the laser field orientation for

(a) o/2p¼10 THz; (b) o/2p¼25 THz.

As a more comprehensive analysis, in Fig. 10(a,b) we presentthe electronic DoS as a function of the energy and the laserpolarization direction. High DoS areas are delimited by singularitylines, where d-N. For a relatively small laser frequency(Fig. 10(a)) the singularity lines are blueshifted by the increase ofthe angle y, starting with a DoS configuration characteristic to theaxial laser (y¼0) and ending up with a configuration typical to thetransverse laser effect (y¼p/2). For higher values of the laserfrequency (Fig. 10(a)) the DoS exhibits a different behavior, thesingularity lines being redshifted by the increase of the angle y.

One may now observe that the question of optimal geometryfor the laser–QWW interaction depends on the electron’s statesinvolved in optical transitions and on the wire size. Since a laserfield polarized along the axis of the wire uniformly shifts thesubband levels (Fig. 9), the intersubband transitions are notaffected. Consequently, geometries with small y values are morelikely to yield efficient tuning of the interband transitions, forwhich there is an uniform and predictable energy blueshift ofððe2A2

0zÞ=ð4ÞÞðð1=mnÞþð1=mn

hhÞÞ, where mn (mn

hh) is the electron(heavy-hole) effective masse. Note that this shift in the jointdensity of states is independent of the quantum wire’s size orshape. One the other hand, at large y values the conductionsubband states are strongly and not uniformly affected by thetransverse laser field (Fig. 10). This effect depends on the sizeand shape of the wire being more pronounced at strongercarrier confinement, i.e. for lowest-lying levels and small R

values. Therefore, the desired energy range for the intersubbandtransitions may be obtained by changing the size and/or compo-sition of the heterostructure as well as the polarizationdirection of the laser field. For GaAs/AlGaAs low-dimensionalstructures the hole states are less sensitive to the transversal laseraction, for two reasons: (i) the mass of the heavy-hole inside theQWW (mn

hh ¼ 0:35m0) is five times larger than the effective massof the electron, so that the laser parameter a0x is five timessmaller for the valence band; (ii) the offset for the heavy-hole isroughly 1.5 times smaller than the conduction band offset, so thatthe THz radiation effect is weakened. Consequently, for thinQWWs in which the electron ground-state subband energy isvery sensitive to the radiation strength, the angle between thepolarization direction of the laser and the wire axis could tune theblueshift of the lowest-energy interband transition (i.e. the band-gap energy).

4. Conclusions

A semiconductor QWW under tilted ILF was investigated in theeffective mass-approximation using a non-perturbative approachand a finite element method. The originality of this work consistsin proposing a new degree of freedom for controlling the electro-nic DoS in 1D nanostructures and the emergent optical proper-ties: the angle between the polarization direction of the laser andthe wire axis. Moreover, an original closed-form expression forthe laser dressed potential of a cylindrical semiconductor QWWwas proposed.

Our results revealed that the effects of the non-resonant laserfield on the electron probability density, reflected in the behaviorof the energy levels, are very dependent on the laser polarizationdirection. An axial laser field induces an uniform blueshift of theenergy levels, which has a parabolic increase with the laserfrequency and is more suitable for interband optical tuning inQWWs. A transverse laser field mostly affects the first conductionsubband level being adequate for tuning the intersubband transi-tions and also the band-gap energy. Any intermediary laserorientation has a combined effect on the energy spectrum andthe DoS, depending on the tilt angle and the frequency.

A. Radu, E.C. Niculescu / Journal of Luminescence 132 (2012) 1420–14261426

Acknowledgment

One of the authors (A.R.) recognizes financial support from theEuropean Social Fund through POSDRU/89/1.5/S/54785 project:‘‘Postdoctoral Program for Advanced Research in the field ofnanomaterials’’.

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