Tuning a conventional quantum well laser by nonresonant laser field dressing of the active layer

Physics Letters A 378 (2014) 3308–3314

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Physics Letters A www.elsevier.com/locate/pla

Tuning a conventional quantum well laser by nonresonant laser field dressing of the active layer Adrian Radu, Nicoleta Eseanu ∗ , Ana Spandonide Department of Physics, “Politehnica” University, 313 Splaiul Independentei, RO-060042 Bucharest, Romania

a r t i c l e

i n f o

Article history: Received 5 July 2014 Accepted 9 September 2014 Available online 16 September 2014 Communicated by R. Wu Keywords: Semiconductor Quantum well Laser field Threshold current Characteristic temperature

a b s t r a c t Tunable semiconductor lasers may be considered as a critical technology for optical communications. We investigate the theoretical feasibility of tuning a conventional GaAs/Al0.2 Ga0.8 As quantum well laser emitting at 825 nm by non-resonant laser-dressing of the active layer. Conduction and valence subbands are sensitive to the intense dressing field and this effect can be used to blueshift the active interband transition. The laser-dressed electron and hole states are calculated in the effective mass approximation by using the finite difference method. Emitted wavelength, threshold current and characteristic temperature are discussed as functions of the dressing laser parameter and cavity length. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Achieving frequency tuning in semiconductor laser systems is not a trivial task [1]. In the last decades, several types of tunable semiconductor lasers (TSLs) have been designed and commercialized, such as the selectable distributed-feedback (DFB) array, grating-coupled external-cavity (GCEC) laser, vertical-cavity surface-emitting laser with external micro-electromechanical mirror (MEMs/VCSEL), grating-coupled sampled-reflector (GCSR), sampled-grating distributed-Bragg-reflector (SGDBR) [2] or integrated ring mode-locked lasers [3]. All these lasers are based on some additional mode selection systems, therefore being less suitable for a high-speed tuning of the frequency. Instead of selecting a single frequency from a multimodal emission spectra, one may imagine a method for actively changing the band gap of the semiconductor. Generally the band gap depends on the chemistry of the composed semiconductor, and much less on various physical conditions, such as temperature, pressure and external static or dynamic fields. However, in low-dimensional materials, such as semiconductor quantum wells (QWs), wires (QWWs) and dots (QDs), the effective bandgap exceeds the bandgap of the bulk semiconductor by some quantity much more susceptible to be changed by the structure geometry and external factors [4]. This extra energy is due to the quantization of the carrier dynamics in the nanostructures. For example, the single mode quantum laser diodes operate

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http://dx.doi.org/10.1016/j.physleta.2014.09.017 0375-9601/© 2014 Elsevier B.V. All rights reserved.

at a precise frequency and the emission wavelength is determined by the effective bandgap of the quantum well [5]. The effective bandgap depends on the discreet energy levels of the carriers in the QW and can be modified by changing the quantum well width in the fabrication process or actively by using external fields. The electrons and holes energy levels may be shifted by intense fields, for example by quantum confined Stark effect [6]. There are other interesting processes as well, involving not static but dynamical fields and our work will make use of such an effect, known as the laser-dressing of the quantum wells. The dressing of the electronic states in a quantum structure means a modification of the energies and wave functions of the confined electrons under a non-resonant intense laser radiation [7–9]. We will demonstrate that in a QW laser’s active layer the effective band gap could be actively modified by a non-resonant laser-dressing of the subband states. This implies the possibility of tuning the emission wavelength of the QW laser in real time by changing the intensity of the dressing radiation. Such an optoelectronic system would lead to very interesting applications, such as accordable semiconductor laser sources and fast optical modulators capable to “translate” an intensity-modulated optical signal into a frequency-modulated one. We consider a conventional QW laser grown by an epitaxial method on a GaAs substrate. The cladding layers are made of Al0.4 Ga0.6 As, the optical confinement layer (OCL) material is Al0.2 Ga0.8 As and the active layer is a GaAs square quantum well (SQW) [10] (Fig. 1). In the absence of external fields, the confinement potentials for electrons and holes have the typical square shape (black curves). If the semiconductor heterostructure is irradiated with a THz non-resonant intense laser field (ILF), it has

A. Radu et al. / Physics Letters A 378 (2014) 3308–3314

 −



h¯ 2

3309

e A z (t ) ∂ ±i ∂z h¯

2me∗(h)

2

 ∂ + V e(h) ( z) ψ( z, t ) = ih¯ ψ( z, t ), ∂t (2)

the temporal dependence may be transferred from the kinetic energy operator to the potential energy term [13]:

 −

h¯ 2

2me∗(h)

   ∂2 ∂ 0 + V e(h) z ± αe(h) sin(Ω t ) ψ( z, t ) = ih¯ ψ( z, t ), ∂t ∂ z2 (3)

Fig. 1. (Color online) Schematic of a GaAs/Al0.2 Ga0.8 As quantum well structure under intense laser field. QW denotes the active layer and OCL is the optical confinement layer. Dressed confinement potentials of the electron (red line) and hole (blue line) are illustrated.

been stated [11] that the electrons and holes will “see” different time-averaged laser-dressed confinement potentials (red and blue curves, respectively). The conduction subbands of the QW will be raised in energy by the increase of the laser dressing parameter α0e (see theory section), while the valence subbands will be lowered. As a direct consequence, the effective band-gap of the nanoheterostructure will be increased by the ILF and the active optical interband transition (IBT) of the QW laser will be blue-shifted: h¯ ω(α0e ) > h¯ ω(0). Since the dressing laser parameter depends not only on the frequency Ω but also on the intensity I d of the driving laser, one may obtain a significant tunability of the QW laser by modulating the amplitude of the ILF. We will calculate/discuss the wavelength range of tunability, saturation modal gain, radiative recombination inside and outside the active region, lasing condition and lasing threshold density of carriers. We will present threshold current density and characteristic temperature of the QW laser as functions of the emitted wavelength and laser cavity length. It should be mentioned that our work is based on a very simple prototype of QW laser since its aim is not to discuss the efficient design of semiconductor lasers but to propose a method for achieving tunability of such devices. Conventional QW lasers may be significantly improved by bandedge-engineering as it was shown by several authors [10,12]. Therefore the principle exposed in the current study is expected to be further extended and generalized for more complex and efficient laser devices. The paper is organized as follows. In Section 2 the theoretical framework is described. Section 3 is dedicated to the results and discussion, and finally, our conclusions are summarized in Section 4.

2.1. Laser-dressed electronic states in the QW We assume an electron (e ) or a heavy hole (h) subjected to the confinement potential of a square quantum well (SQW):

V e(h) ( z) =



 | z | − l i /2 ,

 −

h¯ 2

2me∗(h)

 ∂2 d + V ( z ) φ( z) = E φ( z), e (h) ∂ z2

(4)

where V ed(h) ( z) is the laser-dressed confining potential, with the general form [16]:

V ed(h) ( z)

=

Ω

2π





V e(h) z ± αe0(h) sin ϕ dϕ .

2π

(5)

0

For the SQW potential given by Eq. (1), it was shown that the integral in Eq. (5) can be analytically solved [17] to:

V ed(h) ( z)

=

V c0( v ) 2π

e



 Θ 2αe0(h)

σ =±1





+ 2σ z − li arccos

l i − 2σ z 2αe0(h)

 (6)

.

In order to solve Eq. (4) with the potential given by Eq. (6), a finite difference method (FDM) will be used. We will denote by e (h) E1 the energies of the lowest electron (hole) subband edges in the QW, which will be functions of the laser dressing parameter. By noting that α0h = α0e me∗ /mh∗ , we may use a single, more convenient dependence on α0e , for all quantities which are dependent on the laser dressing. Therefore, the IBT energy in the QW will be written as:

Ei













α0e = E ig + E 1e α0e + E h1 α0e ,

(7)

where E ig is the bandgap of the QW material (we will further denote by E og = E ig + V c0 + V v0 the bandgap of the barrier material). It is known that the laser-dressing of the confinement potential of a QW induces a delocalization of the carriers [18]. Thus, the probability of finding the electron (hole) inside the QW:

2. Theoretical framework

V c0( v ) Θ

where αe0(h) = e A 0 /(me∗(h) Ω) is the laser-dressing parameter for the electron (hole). In the high-frequency limit [14,15] the laserdressed eigenstates are solutions of the time-independent Schrödinger equation:

(1)

where V c0( v ) is the conduction (valence) band off-set, Θ is the Heaviside step function and li is the QW width (Fig. 1). The carrier is also under the action of a nonresonant laser field of frequency Ω , linearly polarized on the growing direction of the QW, described by the vector potential A z (t ) = A 0 cos(Ω t ). We will further denote by ∓e and me∗(h) the electric charge and the effective mass of the electron (hole), respectively. By using the translations z → z ± e A z (t )/(me∗(h) Ω) in the time-dependent Schrödinger equation describing the interaction dynamics:

+ lQW /2

e (h)  e  P1 o

α =

e(h) 2 φ ( z) dz 1

(8)

−lQW /2 e (h)

will depend on the laser parameter. Here, by φ1 ( z) we denote the first subband wave functions of the electron (hole). The overlap integral of the ground state wave functions of the electron and hole [19,20] will also be an implicit function of αoe :

I eh





αoe =

+∞ φ1e ( z)φ1h ( z)dz.

−∞

(9)

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2.2. Threshold characteristics of the QW laser

recombination current densities in the QW and OCL materials, respectively [19,21]:

In this paragraph we briefly discuss several aspects related to the lasing condition in a quantum well laser. The most important concepts of gain and loss in the laser cavity, threshold carrier density and characteristic temperature are recalled. These quantities will be dependent on the laser dressing parameter, as we shall prove. The presentation of the theoretical concepts and mathematical formulas in this paragraph are based on the valuable works of Asryan et al. [19,21]. Further use of subscripts or superscripts i (o) will make reference to the values of the concerned physical quantities inside the QW material or outside (in the OCL material) respectively. The peak value of the modal gain spectrum of the QW laser is [19,21]:









g nei , nhi = g 0 1 − exp

nei − 2D Nc



− exp

e (h)

where g 0 is the saturation gain, ni N c2D (v )

nhi − 2D Nv

 ,

(10)

is the 2D density of electrons

= me∗(ih)k B T /(π h¯ 2 ) is the 2D effective

(holes) in the QW and density of states for the conduction (valence) band in the QW [19]. Here k B is the Boltzmann constant and T is the temperature. By using the expression of N c2D ( v ) and the condition of charge neutrality in the QW (nei = nhi ), Eq. (10) may be rewritten as:



 



g nei = g 0 1 − exp −

nei



N c2D

 m∗i nei − exp − e∗i 2D . mh N c

(11)

By K i (o) we will further denote the Kane’s parameter for the QW (OCL) material [21,22]:

( K i (o) )2 =

3h¯ 2 2



1 ∗i (o)

me

−

1 m0



i (o)

i (o)

E g (E g i (o)

3E g

+ 0i (o) ) i (o)

+ 2 0

,

(12)

i (o)

where m0 is the free-electron mass and 0 is the spin–orbit splitting energy in the QW (OCL) material. The saturation modal gain in Eqs. (10)–(11) can be expressed [19,21] as:

g0 = π

i 2 ( K i /h¯ )2 I eh α 2μeh

no

lc E i

(13)

,

 

g nei L c + ln( R ) = 0,

(14)

where L c is cavity length and R is the reflectivity of the interfaces [23]. We will further denote by nlti the solution of Eq. (14). The threshold carrier densities in the OCL are given [21] by: e (h)

4π e αno E i ( K i nlti )2

3h¯ c 2 k B T (me∗i + mh∗i )

√

+

4 2π 3/2 e αno L o E og ( K o )2 noe nho 3c 2 [k B T (me∗o + mh∗o )]3/2

,

(16)

where L o is the thickness of the OCL material (Fig. 1). The characteristic temperature of the QW laser which is an indication of the temperature stability of the threshold current is given [10,21] by:

Tc =

j lt T



j lt + j o

1 2

+

E og − E ig − E 1e − E h1 kB T

−1 .

(17)

3. Numerical results and discussion For numerical calculations of the subband energy levels and wave functions in the QW, the following values of the involved parameters have been used: li = 50 Å, me∗ = (0.0665 + 0.0835x)m0 [25–27], mh∗ = (0.3497 + 0.122x)m0 [26,27] (where x denotes the concentration of Al in the structure), V c0 = 130 meV, V v0 = 118 meV [10]. Other material parameters further used in lasing characteristics calculation are also little different in QW and OCL materials. The bandgap of Alx Ga1−x As at room temperature T = 293 K is taken as a function of Al concentration [25]: E g = (1.424 + 1.247x) eV. The spin–orbit splitting energy in Alx Ga1−x As is 0 = (0.34 − 0.04x) eV [28]. The relative dielectric permittivity of Alx Ga1−x As under high-frequency fields was taken as εr = 10.89 − 2.73x [29]. The as-cleaved facet reflectivity of the QW laser cavity was considered to be R = 0.32 as in Ref. [21]. In all calculations we have used the same geometrical parameters of the QW laser structure, excepting the cavity length: a characteristic length of the light confinement in the transverse direction of the optical resonator lc = 0.7 μm [19] and a thickness of the OCL material L o = 0.4 μm [10,21]. The cavity length L c was considered to have different values, as in Refs. [10,19,21]. 3.1. Laser-dressed energies, localization probabilities and overlap integral

√

where α is the fine structure constant, no = εr is the refractive i index of the OCL, μeh = me∗i mh∗i /(me∗i + mh∗i ) is the reduced mass of an electron and a hole in the QW, lc is the characteristic length of the light confinement in the transverse direction of the optical resonator, and E i , I eh are given by Eq. (7) and Eq. (9), respectively. At the lasing threshold, the peak value of the modal gain spectrum g (nei ) given by Eq. (11) equals the loss from the resonant cavity by reflections on cavity-end interfaces (as-cleaved facets). This condition leads to:

no

jlt = j i + j o =



lt   e (h) e (h)  ni V 0 − E1 − − , = N c3D exp exp 1 (v ) 2D kB T

N c(v )

(15)

∗o where N c3D ¯ 2 )]3/2 is the 3D effective density of ( v ) = 2[me (h) k B T /(2π h states for the conduction (valence) band in the OCL material [24]. The threshold current density defines the lower limit of the current from which the lasing will occur theoretically. This quantity may be calculated as the sum of the spontaneous radiative

Eq. (4) was numerically solved by using the one-dimensional FDM for different values of the laser dressing parameter (on which the effective confinement potential given by Eq. (6) directly depends). The method allows us to obtain all the eigenvalues and corresponding eigenfunctions of the electron and hole energies in the QW. For this paper purposes, only the first conduction and valence subbands dependences on the laser parameter are of interest, since we will further investigate only the IBT from the ground electron level to the ground hole level. The maximum electron laser parameter is generally chosen to be of the same order of magnitude as the size of the quantum structure [16,18]. Some authors [17] use a maximal value of α0e two times bigger than the QW width. In this work we take a limit value of 75 Å for the electron laser parameter in GaAs. Larger values which could provide a wider wavelength tunability of the QW laser are theoretically possible but we observed that further increasing α0e would be not practical for two main reasons: (i) the increase of the electron energy with the laser parameter slows down at high values of α0e , due to a behavior known as the coalescence of the laser-dressed subbands [17,30], while the hole energy absolute variation remains small, no matter of the dressing parameter; (ii) the electron is strongly delocalized by the intense laser dressing which will be an additional disadvantage from the QW lasing threshold perspective.

A. Radu et al. / Physics Letters A 378 (2014) 3308–3314

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Fig. 2. (Color online) (a) Laser-dressed confinement potential V ed ( z) of the electron and first conduction subband density of probability |φ1e |2 ( z) for three values of the laser parameter α0e ; (b) first energy level of the electron (solid red line) and probability of finding the electron inside the QW (dashed black line) as functions of the electron laser parameter.

Fig. 3. (Color online) (a) Laser-dressed confinement potential V hd ( z) of the heavy hole and first valence subband density of probability |φ1h |2 ( z) for three values of the laser parameter α0e ; (b) first energy level of the hole (solid blue line) and probability of finding the hole inside the QW (dashed black line) as functions of the electron laser parameter.

Fig. 2(a) presents the obtained results concerning the laserdressed confinement potential of the electron (black curves) and the first conduction subband density of localization probability (red curves) for three values of the laser parameter, α0e = 5, 35, 65 Å. Each probability function has its zero located on the energy scale at the corresponding eigenvalue of the electron energy. One may observe that the dressed confinement potential has its bottom “raised” by the laser field from zero (for α0e = 5 Å) to ≈ 50 meV (for α0e = 35 Å) and up to ≈ 80 meV (for α0e = 65 Å), with the characteristic formation of a hill-like median barrier as already reported in literature [17,31]. The dressed effective quantum well also becomes wider in its upper part, proportionally with the laser parameter. The dressed potential behavior directly affects the localization of the electron. Under small laser fields the electronic cloud is almost entirely confined in the QW GaAs layer. As the laser parameter increases, the wave function of the electron expands in the lateral AlGaAs barriers leading to a delocalization of the particle, which is clearly visible in the figure. The most important feature of the electron laser dressing is the blueshift of the energy level which increases from ∼58 meV at zero laser field up to ∼104 meV for α0e = 75 Å. Fig. 2(b) better illustrates the dependence of the first energy level of the electron on the laser parameter and also the variation with α0e of the QW in-layer localization probability given by Eq. (8). One may notice that the

monotonic increase of E 1e with the laser parameter tends to saturate at high α0e values. The QW electron localization probability decreases monotonically from ∼ 76% for the undressed quantum down to ∼ 32% at maximum laser field parameter. Equivalent information concerning the heavy hole in the QW is contained in Fig. 3. Fig. 3(a) presents the laser-dressed confinement potential of the hole (black curves) and the first valence subband density of probability (blue curves) for the same three values of the electron laser parameter, α0e = 5, 35, 65 Å (which correspond to much smaller values of the hole laser parameter, as discussed in the theory section). It should be noticed that the effective confinement potential of the hole is weakly affected by the laser field, the reason for this behavior being its larger value of the effective mass, as compared to electron. As a consequence, the delocalization of the hole is reduced, as we may observe in the same figure. Even under large dressing laser fields, the hole wave function is almost entirely confined in the QW layer and very little in the OCL material. The blueshift of the hole energy level is also reduced, with an increase from ∼21 meV at zero laser field up to ∼29 meV for α0e = 75 Å. Fig. 3(b) presents the first energy level of the heavy hole and the hole localization probability given by Eq. (8) as functions of the electron laser parameter. E h1 increases quasi-quadratically with the laser parameter in the entire range of α0e values but it has a total variation under 8 meV. The decreasing of the hole localization probability is very reduced, remaining in

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A. Radu et al. / Physics Letters A 378 (2014) 3308–3314

Fig. 4. Interband transition energy E i (solid line) and squared overlap integral of the electron and hole wave functions I eh (dashed line) versus the electron laser parameter α0e .

Fig. 5. Lasing threshold 2D density of electron-hole pairs in the QW, as a function of the electron laser dressing parameter α0e , for three values of the cavity length [10]. The inset presents the lasing wavelength λi as a function of dressing parameter.

the range (94, 95)% for all interesting values of the electron laser parameter. By summing-up the results above, Fig. 4 shows the active IBT energy given by Eq. (7) and the electron–hole overlap integral defined by Eq. (9) as functions of the electron laser parameter. One may observe a global increase of almost 55 meV of the transition energy as α0e raises from zero up to 75 Å. This increase will determine the wavelength range of tunability of the QW laser. It is also apparent from Fig. 4 that the laser dressing of the QW will reduce the squared overlapping integral of the electron and hole by a factor 2, this being mainly due to the behavior of the electron 2 wave function. Both quantities (E i and I eh ) have a straight influence on the saturation modal gain of the QW laser, as defined by 2 Eq. (13). The gain g 0 decreases direct proportionally with I eh and varies inverse proportionally with E i , thus it will have a monotonically decrease with the raise of the electron laser parameter. These results have an obvious physical interpretation, related to the possible functioning of an intense field tunable QW laser: the accordability of the semiconductor laser (decreasing of the lasing wavelength) comes with the price of a reducing modal gain which will have to be compensated by increasing the current density in order to maintain the threshold condition.

length λi , for several values of the cavity length. It becomes clear that obtaining accordability of the semiconductor QW laser with relatively short cavities (under 0.5 mm) will be particularly difficult since it may imply variations of the threshold current of up to 3 orders of magnitude. It also may be deduced that for a fixed current density, the wavelength range of tunability will have a shortwavelength limit depending on both the particular value of the current and the cavity length. From the tunability viewpoint, it will be more convenient to have long cavities and to provide high values of the current density. Moreover, for a constant current density not only the wavelength of the QW laser will be dependent on the laser dressing field but also the optical output power of the laser (at higher emitted photon energies, output laser intensities will be smaller). Fig. 6(b) presents the characteristic temperature of the QW laser as a function of the lasing wavelength, for the same three values of the cavity length. Here again we see that longer cavities are a better option, because they allow a higher temperature stability of the threshold current density. The characteristic temperature is modified by laser-dressing of the QW such that at smaller emitted wavelengths the temperature stability of the threshold current is lower. Figs. 7(a) and (b) present the dependence of the same two quantities (threshold current density and characteristic temperature, respectively) as functions of the cavity length, for several values of the electron laser parameter. One may observe on the logarithmic scale in Fig. 7(a) that the threshold current has a very fast increase with the diminution of L c , which may be an important limitative argument for choosing practical cavity lengths. However, this limitation holds mostly for conventional QW lasers, for which carriers recombination occurs in the QW layer and also in the OCL. The threshold currents may be much reduced by a more complex structural design of the QW laser, including supplementary potential barriers to inhibit the OCL recombination of the electrons and holes [21]. It is also observable that for a given threshold current density the minimal allowed cavity length will depend on the maximal laser parameter which is intended to be used for tuning the QW laser. Fig. 7(b) illustrates the saturation of the characteristic temperature augmentation with the cavity length. This means that from the viewpoint of the temperature stability of the threshold current density, increasing of L c may be useful only up to a point, which particularly depends on the laser dressing parameter. For example, at zero dressing field the characteristic temperature of the QW laser has practically no significant increase for cavity lengths beyond 1 mm. With the laser parameter increasing,

3.2. Threshold current density and characteristic temperature We will first discuss the dependence of the lasing threshold 2D density of electrons (holes) in the QW as a function of the laser dressing parameter. Fig. 5 presents the numerical solution of algebraic equation (14) for several values of the cavity length. For a particular cavity, nlti is monotonically augmented by the increase of the laser parameter, the growth rate being dependent on the cavity length. In shorter cavity cases, larger values of the threshold density of carriers will be demanded for lasing to occur, this behavior being more and more apparent as the laser parameter increases. For example, reducing cavity length from 1.5 mm to 0.5 mm increases nlti by a factor 1.5 at zero dressing field and by a factor 2.8 at maximum laser parameter. The inset of Fig. 5 displays the dependence of the emitted laser wavelength λi = hc / E i on the laser dressing parameter. One may notice that the QW laser would emit in near infrared spectrum with an accordability range of 28 nm. Since discussing the tuning of the QW laser and related lasing concepts is the main objective of this paper, we prefer to further presents some of our results as functions of the emitted wavelength of the laser. Fig. 6(a) shows on a logarithmic scale the threshold current density j lt as a function of the QW lasing wave-

A. Radu et al. / Physics Letters A 378 (2014) 3308–3314

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Fig. 6. Threshold current density j lt (a) and characteristic temperature T c (b) as functions of the QW lasing wavelength λi , for three values of the cavity length.

Fig. 7. Threshold current density j lt (a) and characteristic temperature T c (b) as functions of the cavity length L c , for several values of the electron laser parameter.

the “saturation” value of T c is lowering from ∼170 K (at α0e = 0) to ∼80 K (at α0e = 75 Å). The results displayed in Figs. 6 and 7 may serve as a starting point for designing the basic types of semiconductor quantum well laser tuned by nonresonant laser field dressing of the active layer. Further improvements/generalizations of this theoretical model are expected in several possible directions: analyzing the dressing-induced spectral linewidth broadening of the conventional QW laser emission, studies of tunable multiple QW lasers, laser-dressed bandedge-engineered QW structures, quantum cascade lasers, QWW and QD lasers. 4. Conclusions We have investigated the possibility of tuning a semiconductor QW laser by using a non-resonant laser-dressing field. We have considered as a prototype a conventional GaAs/AlGaAs SQW laser grown by an epitaxial method, with a single mode optical emission at 825 nm. When the semiconductor heterostructure is irradiated with a non-resonant ILF, the effective confinement potentials of the electrons and holes are modified. By solving the Schrödinger equation for the electron and hole in the laser-dressed confinement potential, we calculated the eigenvalues and eigenfunctions of their energies as functions of the laser parameter. The finite difference method in the effective mass approximation was used for numerical calculation of the laser-dressed electron and hole states. We obtained that the conduction subbands of the QW are augmented in energy by the increase of the laser dressing parameter, while the valence subbands are lowered. Since the conduction and

valence subbands are sensitive to the intense dressing field, this effect leads to an increase of the effective bandgap of the semiconductor nanostructure and to a subsequent optical blueshift of the active IBT. Since the dressing laser parameter depends on the intensity of the driving laser, a significant tunability of the QW laser can be achieved by modulating the amplitude of the ILF. The calculated wavelength range of tunability was (797–825) nm for a maximal value of the laser parameter 1.5 times larger than the QW width. We have also discussed the lasing condition and the dependence of the threshold density of electrons/holes on the laser dressing parameter of the electron. The threshold current density and characteristic temperature of the QW laser were represented as functions of the emission wavelength and laser cavity length. It was emphasized that tunable semiconductor lasers could be significantly improved by bandedge-engineering as it was already shown in the literature for conventional QW lasers. Therefore the ideas presented in the current study are expected to be further extended and generalized for more complex and efficient tunable laser designs. References [1] B. Mroziewicz, Opto-Electron. Rev. 16 (4) (2008) 347. [2] L.A. Coldren, G.A. Fish, Y. Akulova, J.S. Barton, L. Johansson, C.W. Coldren, J. Lightwave Technol. 22 (1) (2004) 193. [3] J.S. Parker, P.R.A. Binetti, Y. Hung, L.A. Coldren, J. Lightwave Technol. 30 (9) (2012) 1278. [4] J.H. Davies, The Physics of Low-dimensional Semiconductors: An Introduction, Cambridge University Press, 1998. [5] F.T. Vasko, A.V. Kuznestow, Electronic States and Optical Transitions in Semiconductor Heterostructures, Springer, New York, 1999.

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