Intersubband and Interband Absorptions in Near-Surface Quantum Wells Under Intense Laser Field

The intersubband transitions in quantum wells have attracted much interest due to their unique characteristics: a large dipole moment, an ultra-fast relaxation time, and an outstanding tunability of the transition wavelengths (Asano et al., 1998; Elsaesser, 2006; Helm, 2000). These phenomena are not only important by the fundamental physics point of view, but novel technological applications are expected to be designed. Many important devices based on intersubband transitions in quantum well heterostructures have been reported. For example: farand near-infrared photodetectors (Alves et al., 2007; Levine, 1993; Li, S.S. 2002; Liu, 2000; Schneider & Liu, 2007; West & Eglash, 1985), ultrafast all-optical modulators (Ahn & Chuang, 1987; Carter et al., 2004; Li, Y. et al., 2007), all optical switches (Iizuka et al., 2006; Noda et al., 1990), and quantum cascade lasers (Belkin et al., 2008; Chakraborty & Apalkov, 2003; Faist et al., 1994). It is well-known that the optical properties of the quantum wells mainly depend on the asymmetry of the confining potential experienced by the carriers. Such an asymmetry in potential profile can be obtained either by applying an electric/laser field to a symmetric quantum well (QW) or by compositionally grading the QW. In these structures the changes in the absorption coefficients were theoretically predicted and experimentally confirmed to be larger than those occurred in conventional square QW (Karabulut et al., 2007; Miller, D.A.B. et al., 1986; Ozturk, 2010; Ozturk & Sokmen, 2010). In recent years, with the availability of intense THz laser sources, a large number of strongly laser-driven semiconductor heterostructures were investigated (Brandi et al., 2001; Diniz Neto & Qu, 2004; Duque, 2011; Eseanu et al., 2009; Eseanu, 2010; Kasapoglu & Sokmen, 2008; Lima, F. M. S. et al., 2009; Niculescu & Burileanu, 2010b; Ozturk et al., 2004; Ozturk et al., 2005; Sari et al., 2003; Xie, 2010). These works have revealed important laser-induced effects: i) the confinement potential is dramatically modified; ii) the energy levels of the electrons and, to a lesser extent, those of the holes are enhanced; iii) the linear and nonlinear absorption coefficients can be easily controlled by the confinement parameters in competition with the laser field intensity. The intersubband transitions (ISBTs) have been observed in many different material systems. In recent years, apart from GaAs/AlGaAs, the InGaAs/GaAs QW structures have


Introduction
The intersubband transitions in quantum wells have attracted much interest due to their unique characteristics: a large dipole moment, an ultra-fast relaxation time, and an outstanding tunability of the transition wavelengths (Asano et al., 1998;Elsaesser, 2006;Helm, 2000). These phenomena are not only important by the fundamental physics point of view, but novel technological applications are expected to be designed. Many important devices based on intersubband transitions in quantum well heterostructures have been reported. For example: far-and near-infrared photodetectors (Alves et al., 2007;Levine, 1993;Li, S.S. 2002;Liu, 2000;Schneider & Liu, 2007;West & Eglash, 1985), ultrafast all-optical modulators (Ahn & Chuang, 1987;Carter et al., 2004;Li, Y. et al., 2007), all optical switches (Iizuka et al., 2006;Noda et al., 1990), and quantum cascade lasers (Belkin et al., 2008;Chakraborty & Apalkov, 2003;Faist et al., 1994). It is well-known that the optical properties of the quantum wells mainly depend on the asymmetry of the confining potential experienced by the carriers. Such an asymmetry in potential profile can be obtained either by applying an electric/laser field to a symmetric quantum well (QW) or by compositionally grading the QW. In these structures the changes in the absorption coefficients were theoretically predicted and experimentally confirmed to be larger than those occurred in conventional square QW (Karabulut et al., 2007;Miller, D.A.B. et al., 1986;Ozturk, 2010;Ozturk & Sökmen, 2010). In recent years, with the availability of intense THz laser sources, a large number of strongly laser-driven semiconductor heterostructures were investigated (Brandi et al., 2001;Diniz Neto & Qu, 2004;Duque, 2011;Eseanu et al., 2009;Eseanu, 2010;Kasapoglu & Sokmen, 2008;Lima, F. M. S. et al., 2009;Niculescu & Burileanu, 2010b;Ozturk et al., 2004;Ozturk et al., 2005;Sari et al., 2003;. These works have revealed important laser-induced effects: i) the confinement potential is dramatically modified; ii) the energy levels of the electrons and, to a lesser extent, those of the holes are enhanced; iii) the linear and nonlinear absorption coefficients can be easily controlled by the confinement parameters in competition with the laser field intensity. The intersubband transitions (ISBTs) have been observed in many different material systems. In recent years, apart from GaAs/AlGaAs, the InGaAs/GaAs QW structures have www.intechopen.com attracted much interest because of their promising applications in optoelectronic and microelectronic devices: multiple-quantum-well modulators and switches (Stohr et al., 1993), broadband photodetectors (Gunapala et al., 1994;Li J. et al., 2010, Passmore, et al., 2007, superluminescent diodes used for optical coherence tomography (Li Z. et al., 2010) and metal-oxide-semiconductor field-effect-transistors, i. e. MOSFETs (Zhao et al., 2010). The optical absorption associated with the excitons in semiconductor QWs have been the subject of a considerable amount of work for the reason that the exciton binding energy and oscillator strength in QWs are considerably enhanced due to quantum confinement effect (Andreani & Pasquarello, 1990;Jho et al., 2010;Miller, R. C. et al., 1981;Turner et al., 2009;Zheng & Matsuura, 1998). As a distinctive type of dielectric quantum wells, the near-surface quantum wells (n-sQWs) have involved increasing attention due to their potential to sustain electro-optic operations under a wide range of applied electric fields. In these heterostructures the QW is located close to vacuum and, as a consequence, the semiconductor-vacuum interface which is parallel to the well plane introduces a remarkable discrepancy in the dielectric constant (Chang & Peeters, 2000). This dielectric mismatch leads to a significant enhancement of the exciton binding energy (Gippius et al., 1998;Kulik et al., 1996;Niculescu & Eseanu, 2010a) and, consequently, it changes the exciton absorption spectra as some experimental (Gippius et al., 1998;Kulik et al., 1996;Li, Z. et al., 2010;Yablonskii et al., 1996) and theoretical (Niculescu & Eseanu, 2011a;Yu et al., 2004) studies have demonstrated. The rapid advances in modern growth techniques and researches for InGaAs/GaAs QWs (Schowalter et al., 2006;Wu, S. et al., 2009) create the possibility to fabricate such heterostructures with well-controlled dimensions and compositions. Therefore, the differently shaped InGaAs/GaAs near-surface QWs become interesting and worth studying systems. We expect that the capped layer of these n-sQWs induces considerable modifications on the intersubband absorption as it did on the interband excitonic transitions (Niculescu & Eseanu, 2011). To the best of our knowledge this is the first research concerning the intense laser field effect on the ISBTs in InGaAs/GaAs differently shaped near-surface QWs. In this chapter we are concerned about the intersubband and interband optical transitions in differently shaped n-sQWs with symmetrical/asymmetrical barriers subjected to intense high-frequency laser fields. We took into account an accurate form for the laser-dressing confinement potential as well as the occurrence of the image-charges. Within the framework of a simple two-band model the consequences of the laser field intensity and carriers-surface interaction on the absorption spectra have been investigated. The organization of this work is as follows. In Section 2 the theoretical model for the intense laser field (ILF) effect on the intersubband absorption in differently shaped n-sQWs is described together with numerical results for the electronic energy levels and absorption coefficients (linear and nonlinear). In Section 3 we explain the ILF effect on the exciton ground energy and interband transitions in the same QWs, taking into account the repulsive interaction between carriers and their image-charges. Also, numerical results for the 1Sexciton binding energy and interband linear absorption coefficient are discussed. Finally, our conclusions are summarized in Section 4.

Intersubband transitions in near-surface QWs under intense laser field
The intersubband transitions (ISBTs) are optical transitions between quasi-two-dimensional electronic states ("subbands") in semiconductors which are formed due to the confinement of the electron wave function in one dimension. The conceptually simplest band-structure engineered system that can be fabricated is a quantum well (QW), which consists of a thin semiconductor layer embedded in another semiconductor with a larger bandgap. Depending on the relative band offsets of the two semiconductor materials, both electrons and holes can be confined in one direction in the conduction band (CB) and the valence band (VB), respectively. Thus, allowed energy levels which are quantized along the growth direction of the heterostructure appear (Yang, 1995). These levels can be tailored by changing the QW geometry (shape, width, barrier heights) or by applying external perturbations (hydrostatic pressure, electric, magnetic and laser fields). Whereas, of course, optical transitions can take place between VB and CB states, in this Section we are concerning only with ISBTs between quantized levels within the CB.

Theory
Let us consider an InGaAs n-sQW embedded between symmetrical/asymmetrical GaAs barriers. It is convention to define the QW growth as the z-axis. According to the effective mass approximation, in the absence of the laser field, the time-independent Schrödinger equation is where  m is the electron effective mass,   (2) Here  is the semiconductor dielectric constant, 22 0 /4  ee  , and 0 d is the distance between the electron and its image-charge without laser field. For the three differently shaped n-sQWs studied in this work the potential   Vz reads as follows. For a square n-sQW,   Vz has the well-known form For a graded n-sQW, the confinement potential is For a semiparabolic n-sQW,   Vz is given by The quantities w L and c L are the well width and capped layer thicknesses, respectively; 0 V is the GaAs barrier height in the QW left side (with cap layer); r V is the barrier height in the QW right side and  is the barrier asymmetry parameter. Under the action of a non-resonant intense laser field (ILF) represented by a monochromatic plane wave of frequency LF  having the vector potential , the Schrödinger equation to be solved becomes a time-dependent one due to the timedependent nature of the radiation field. Here  u is the unit vector of the polarization direction (chosen as z-axis). By applying the translation the equation describing the electron-field interaction dynamics was transformed by Kramers (Kramers, 1956) as The expression describes the quiver motion of the electron under laser field action. 0  is known as the laser-dressing parameter, i. e. a laser-dependent quantity which contains both the laser frequency and intensity, Thus, in the presence of the laser field linearly polarized along the z-axis, the confinement potential is a time-periodic function for a given z and it can be expanded in a Fourier series, where k V is the k-th Fourier component of   Vz and v J is the Bessel function of order v. In the high-frequency limit, i.e. 1  LF   , with τ being the transit time of the electron in the QW region (Marinescu & Gavrila, 1995) the electron "sees" a laser-dressed potential which is obtained by averaging the potential Note that this approximation remains valid provided that the laser is tuned far from any resonance so that only photon absorption was taken into account and photon emission was disregarded. Following some basic works (Gavrila & Kaminski, 1984;Lima, C.A.S. & Miranda, 1981;Marinescu & Gavrila, 1995) the laser-dressed electronic eigenstates in the QW are the solutions of a time-independent Schrödinger equation, Here  z  is the laser-dressed wave function of the electron. The envelope wave functions and subband energies in this modified potential can be obtained by using a transfer matrix method (Ando & Ytoh, 1987;Tsu & Esaki, 1973). In order to characterize the intersubband transitions in laser-dressed n-sQWs the 12  EE transition energy, Here I is the optical intensity of the incident electromagnetic wave (with the angular frequency ex  ) that excites the semiconductor nanostructure and leads to the intersubband optical transition,  is the permeability, 2 0  r n  with r n being the refractive index,  ex  is the pump photon energy produced by a tunable laser source, F E represents the Fermi energy, 1 E and 2 E denote the quantized energy levels for the initial and final states, respectively; B k and T are the Boltzmann constant and temperature, respectively, c is the speed of light in free space, eff L is the effective spatial extent of the electrons and in  is the intersubband relaxation time.
The total absorption coefficient is given by The absorbtion coefficients in n-sQWs under laser field depend on both laser-dressing parameter and QW geometry (well shape, barrier asymmetry, cap layer thickness).

Electronic properties 2.2.1 Laser-dressed confinement potential and energy levels
Within the framework of effective-mass approximation the ground and the first excited energetic levels for an electron confined in differently shaped In 0.18 Ga 0.82 As/GaAs nearsurface QWs: square (SQW), graded (GQW), and semiparabolic (sPQW) under high-frequency laser field were calculated. We used various QW widths L = 100 Å, 150 Å, and 200 Å, different cap layer thicknesses, c L , between 5 Å and 200 Å, for n-sQWs with symmetrical ( = 1) or asymmetrical ( = 0.6 and 0.8) barriers. The small In atoms concentration in the QW layer allowed us to take the same value of the electron effective mass in all regions (barriers, QW), i. e. 0 0.0665   mm . Also, we used F E = 6.49 meV which corresponds to about 1.6 × 10 17 electrons/cm 3 in GaAs, and in  = 0.14 ps (Ahn & Chuang, 1987). Fig. 1 displays the "dressed" potential profiles of the conduction band (CB) for three differently shaped n-sQWs (SQW, GQW and sPQW) with QW width w L = 150 Å, identical barriers ( = 1) and cap layer thickness c L = 20 Å, under various laser intensities described by the laser parameter values 0  = 0; 40; 80 and 100 Å. Only two energy levels have been taken into account for all the n-sQWs investigated in this work: 1 E (ground state) and 2 E (first excited state). They are are plotted in Fig. 1, too. We see that for all studied n-sQWs the increasing of the laser parameter dramatically modifies the potential shape which is responsible for quantum confinement of the electrons. Up to 0 /2  w L  two effects are noticeable: i) while the effective "dressed" well width (i. e. the lower part of the confinement potential) decreases with the laser intensity, the width of the upper part of this "dressed" QW increases; ii) a reduction of the effective well height at the interface between the capped layer and the QW (z = 0). Therefore, under an intense laser field a distinctive blue-shift of the electronic energy levels occurs, as expected (Brandi et al., 2001;Diniz Neto & Qu, 2004;Eseanu, 2010;Kasapoglu & Sökmen, 2008;Lima, F. M. S. et al., 2009;Niculescu & Burileanu, 2010b;Ozturk et al., 2004;Ozturk et al., 2005). This laser-induced push-up effect is more pronounced in the semiparabolic QW due to the stronger geometric confinement.
a supplementary barrier having a "hill"-form appears into the well region and, as a consequence, the formation of a double well potential in the InGaAs layer is predicted. Similar laser-induced phenomena were reported for a GaAs/AlGaAs square QW (Lima, F. M. S. et al., 2009) and for coaxial quantum wires (Niculescu & Radu, 2010c). The two energy levels 1 E (ground state) and 2 E (first excited state) depend on both laser field characteristics (frequency and intensity, combined in the laser parameter) and QW confining geometry (shape, width, cap layer thickness and barrier asymmetry). In Figs. 2 A-C the energy levels 1 E and 2 E are plotted as functions of laser parameter in three differently shaped n-sQWs (SQW, GQW and sPQW) with w L = 200 Å for various cap layer thicknesses. We observed that: i. the laser-induced increasing of the ground level energy 1 E is more pronounced for   0 40 Å in all three differently shaped n-sQWs with the same w L ; ii. the first excited level energy 2 E is almost unaltered by the laser field in the GQW and sPQW for   0 40 Å; instead, in the SQW, 2 E has a significant rising.
The reasons are as follows: i) the ground level 1 E is localized in the lower part of the laserdressed QW and it is significantly moved up only by an intense laser field; ii) in the GQW and sPQW the stronger geometric confinement competes with the laser-induced push-up of the energy levels. As a consequence, the excited level which is localized in the upper part becomes less sensitive to the laser action.    www.intechopen.com Also, in the range of thin cap layers, the energy levels 1 E and 2 E depend on the capped layer thickness ( c L ). Fig. 3 displays the energies 1 E , 2 E and transition energy, L in a near-surface SQW with w L = 150 Å for several values of the laser parameter. This variation is similar in GQW and sPQW. We note that, up to c L  40 Å, the energies 1 E , 2 E and, consequently, the transition energy first rapidly decrease with cap layer thickness and, for further large c L values, these three quantities turn out to be insensitive to the dielectric effect afforded by the cap layer. The reason for this behavior is that the effect of the image-charge is reduced by a thicker cap layer. , increases up to a certain value of the laser parameter,  0M , and then it begin to decrease. The critical laser parameter,  0M , increases for larger QWs (Table 1). A similar behavior have been reported for regular (i.e. uncapped) GaAs/AlGaAs SQW and PQW (Eseanu, 2010;Ozturk et al., 2004). As suggested by Ozturk et al. (2004), for  0 <  0M the transition energy tr E increases due to reduction of the effective "dressed" well width. Instead, for  0 >  0M the subbands levels E 1 and E 2 tends to localize in the upper part of the laser-dressed well (which has a larger width) and thus they become closer to each other. Our calculations show a difference between the increasing rates of E 1 and E 2 values in SQW and GQW under laser field action. Therefore, tr E may have a maximum for a certain value  0M . This critical value of the laser parameter seems to have a weak dependence on the cap layer thickness (Table 1).   The variation of

The
is modulated by the laser field. In the absence of radiation ( 0 0   ) or in a low laser field (   0 40 Å) tr E diminishes in large QWs, as expected, because the levels E 1 and E 2 move down and become closer to each other. For uncapped QW-heterostructures this result is a customary one, for example: in a GaAs/Al 0.3 Ga 0.7 As SQW with w L = 50 -65 Å (Helm, 2000), in GaAs/Al 0.3 Ga 0.7 As SQW and sPQW with w L = 100 -200 Å (Eseanu, 2010) and in a In 0.5 Ga 0.5 As/AlAs SQW with w L = 20 -100 Å (Chui, 1994). By applying an intense laser field the reduction of tr E (as function of w L ) becomes weaker, but for high laser parameter values (   0 80 Å), tr E turn to rise with w L , especially in the presence of a thick cap layer. The reason for this behavior is the competition between the geometric quantum confinement and laser-induced increasing of the energy levels. In the asymmetrical n-sQWs (GQW and sPQW) another factor modifiying the transition energy appears. This is the asymmetry parameter of the QW barriers, , (see Eqs. 2b and 2c). In Fig. 6 the transition energy, tr E , as a function of the barrier asymmetry is plotted for GQW and sPQW with w L = 200 Å and a thin cap layer (20 Å). As seen in this figure tr E is enhanced by the increasing . The dependence is also modulated by the laser field and, to a lesser extent, by the QW shape. In the GQW the increasing of tr E is almost linear for all laser parameter values, but the rising slope is higher under intense laser field (   0 80 Å) due to the laser-induced push-up effect on the energy levels. Instead, the stronger geometric confinement leads to a deviation from linearity of the curve     f E tr in the sPQW. Now we should emphasize an important issue. As a consequence of the laser-induced shift in the subband transition energy it clearly appears the possibility that tr E can be tuned by the joint action of the laser field and a supplementary external perturbation such as: electric www.intechopen.com field (Ozturk et al., 2004;Ozturk et al., 2005) or hydrostatic pressure (Eseanu, 2010), these two cases refering to uncapped QWs. The last case was named "laser-and pressure-driven optical absorption" (LPDOA). The variable cap layer thickness, especially in the range of thin films, in simultaneous action with an intense laser field could be a new method (suggested by the present study) to adjust the transition energy, tr E .  In the symmetrical structure SQW (Fig. 4 A) 2 21 M has a relative minimum at a critical value m 0  of the laser parameter. This value is very close to that for which the transition energy tr E has its maximum. A similar behavior have been reported for regular (i.e. uncapped) GaAs/AlGaAs SQWs (Eseanu, 2010). The explanation for the minimum of . In the presence of laser field, the SQW shape is dramatically modified: as 0  increases the lower part of the confinement potential becomes more and more narrow while the upper part becomes wider. Therefore, the energy subbands will be pushed up to the top of the well. We may identify two regimes: i. for  M monotonically increases with laser parameter (Figs. 4 B, C). This effect is determined by the strong electron localization in the graded barriers. Therefore, the two wave functions is enhanced.

Linear and nonlinear optical absorption
The intersubband linear and nonlinear absorption coefficients given by the Eqs. (11) M . In the n-sQWs under our investigation these quantities are strongly modified by the laser field parameter, but in a different manner (Fig. 4). As a consequence, the absorption coefficients    , cap layer thickness, c L , asymmetry parameter of the QW barriers, , and QW potential shape. In Fig. 7  4. in SQW the absorption peaks are red-shifted for w L = 100 Å, but for w L = 200 Å they are blue-shifted (Fig. 8).

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For SQW and GQW these effects can be connected with the different laser-dependence of the two energy levels 1 E and 2 E (Fig. 2). For sPQW the stronger geometric confinement competes with the laser-induced change of the transition energy. The explanation used for the results plotted in Fig. 4 remains valid for the absorption peak positions too. In all n-sQWs under our study the peak magnitude of the   1  is diminuted by the laser field. The reason for this reduction is the laser-induced spreading of the carriers wave functions in the laser-dressed QW barriers. Concerning the effect of the cap layer on the absorption peak position an obvious red-shift occurs for thicker cap layers, especially in sPQW (Fig. 7). The broadening of the effective n-sQW width for large cap layer thickness leading to a reduction of tr E is the reason for this "dielectric effect".  In Fig. 9 the total absorption coefficient, , as a function of the photon energy for different values of the incident optical intensity I, with and without applied laser field, in differently shaped n-sQWs having w L = 150 Å and symmetrical barriers, is plotted. The cap layer thickness is c L = 20 Å. i. there is no shift of the resonant peak positions with incident optical intensity, as expected; ii. the total absorption coefficient  is significantly diminuted by the increasing optical intensity due to the negative nonlinear term,     3 , ex I  . Therefore, both linear and nonlinear contributions should be taken into account in the calculated absorption coefficient  near the resonance frequency ( tr ex E    ), especially for high exciting intensities.
iii. the magnitude peak of the total absorption coefficient is dramatically reduced by the intense laser field; iv. the resonant peak of  can be bleached at sufficiently high incident optical intensities; the bleaching effect generates a split up of the resonant peak into two peaks. For our n-sQW structures the bleaching intensities depend on the confining potential shape, laserdressing parameter, and cap layer thickness. Similar results were reported for GaAs/AlGaAs uncapped QWs having different shapes: inverse V-type (Niculescu & Burileanu, 2010b) or graded-type (Ozturk, 2010). In the particular case of a relatively low exciting intensity, I = 0.4 MW/cm 2 , the dependence of the total absorption coefficient  on the laser-dressing parameter (Fig. 10) is similar with that for    ex   1 (see Fig. 7). Therefore, the exciting intensity may be used to modulate the intersubband absorption. Concluding, we note that the optical properties of the differently shaped n-sQWs could be tuned by proper tailoring of the heterostructure parameters (well shape and width, cap layer thickness, barrier asymmetry) and/or by varying the laser field intensity. The switch between the strong absorption and induced laser transparency regimes can be suitable for good performance optical modulators.

Interband transitions in near-surface QWs under intense laser field
Excitons play an important role in the optical properties of quantum wells. Compared to those in three-dimensional bulk semiconductors, the exciton binding energy and oscillator strength in QWs are considerably enhanced due to quantum confinement effect, so excitons in QWs are more stable. The electronic and optical properties of the semiconductor QWs are significantly modified by applying intense high-frequency laser fields and this effect provides new degrees of freedom for technological applications.

Theory
Let us consider again the n-sQW structure described in the Section 2.1. According to the effective mass approximation, in the absence of the laser field, the exciton Hamiltonian is Here are the single-particle 1D Hamiltonians. The symbol h e j ,  denotes the electron (hole) and j V is the confinement potential in the growth direction (z-axis). The forms of j V for the three n-sQWs are given by the Eqs. (3 a, b, and c), but 0 V must be replaced by e V (for electron) and h V (for hole). The last term in Eq. (15) represents the electrostatic energy of the repulsive interaction between the carriers and their image-charges Here  is the semiconductor dielectric constant, , and j d 0 is the distance between the electron (hole) and its image-charge. The third and fourth terms of Eq. (14) are the kinetic operators of the mass-center motion and relative motion of an exciton, respectively, in the (x-y) plane.

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The last term in Eq. (14) describes the total electron-hole Coulomb interaction (Chang & Peeters, 2000) where  denotes the in-plane relative coordinate eh   ρρ ; eh d  is the distance between the electron (hole) and hole-image (electron-image) along the z-axis. For the sake of simplicity, in Eqs. (14-17) we have assumed that the electron and hole effective masses as well as the dielectric constant do not vary inside the whole heterostructure. By applying a non-resonant intense laser field (ILF) which has the polarization direction parallel to the QW growth direction (z-axis), in the high-frequency limit (Marinescu & Gavrila, 1995), the electron (hole) "sees" a laser-dressed potential which is obtained by averaging the confining potential    . The laser-dressed repulsive interaction between the carriers and their self-image charges can be approximated by a soft-core potential (Lima, C.A.S. & Miranda, 1981)  Following some important studies (Gavrila & Kaminski, 1984;Lima, C.A.S. & Miranda, 1981;Marinescu & Gavrila, 1995) In order to obtain the envelope wave functions and subband energies of both electron and hole in these modified potentials we have used a transfer matrix method (Ando & Ytoh, 1987;Tsu & Esaki, 1973 (Miller, R.C. et al., 1981) where e E and h E are the single-particle energies of the electron and hole, respectively.
In order to systematically investigate the ILF effects on the optical n-sQW properties, the linear absorption coefficient of the excitonic transitions induced by an exciting light which is polarized along the z-direction have been calculated. We denote by ex  the angular frequency of the light from a tunable source. Assuming the dipole approximation, the absorption coefficient (Bassani & Parravicini, 1975 On the other hand, the oscillator strength per unit area is connected to the excitonic wave function (Bassani & Parravicini, 1975) where M is the optical transition matrix element between the valence and conduction bands,  are the single-particle wave functions under applied laser field, and  2 0  denotes the probability of finding the electron and hole at the same position. For the allowed optical transitions between the hh1 and e1 subbands we obtain where the quantity B is almost frequency-independent in the frequency range of the interband transitions (Bastard, 1981). So, B was taken as a constant. www.intechopen.com

Electronic properties
The numerical calculations were carried out for In 0.18 Ga 0.82 As/GaAs differently shaped n-sQWs with the well width w L = 50 Å or 80 Å and various cap layer thicknesses, c L = 40 Ǻ, 80 Ǻ, 120 Ǻ, by using the material parameters (Gippius et al., 1998) Table 2 and a broadening parameter Г = 1 meV (Sari et al., 2003). The chosen values for w L and c L allowed us to validate the calculation results by the reported experimental data (Gippius et al., 1998;Kulik et al., 1996;Li, Z. et al., 2010;Yablonskii et al., 1996).

Material
GaAs For two nanostructures, GQW and sPQW, one of the GaAs barriers (the cap layer) has an unchanged height, e V (electron) or h V (hole), and the other barrier is variable, The following values for the asymmetry parameter have been used:  = 0.6, 0.8, and 1. The SQW structure is a symmetrical one ( = 1). The laser parameter was chosen in the range of ILF, i. e. 0   [0, 120 Ǻ].

Single-particle energies
The strong laser effect on the potential profile and on energy levels of the conduction band (CB) for SQW, GQW and sPQW with w L = 150 Å was discussed in the Section 2.2.1. For narrower n-sQWs with w L = 50 Å or 80 Å the main laser-induced properties of the CB are very similar (Eseanu, 2011;Niculescu & Eseanu, 2011). In contrast, the laser parameter augmentation has little effect on the heavy-hole potential (not plotted here) because 0   1/ * m (see Eq. (20) and Table 2). In Figs. 11A and 11B the single-particle electron and hole energies, respectively, are plotted as functions of the laser intensity, 0  , in three differently shaped n-sQWs with c L = 40 Å, for several values of the asymmetry parameter:  = 0.6, 0.8, and 1. We can see that the ground state energy in the conduction band first rapidly raises with the laser parameter up to 0   40 Å, i. e. 2 0 / w L   , and for further large laser intensities the e E -level becomes less sensitive to the laser field (Fig. 11A). This is a typical behavior for low-dimensional systems under ILFs, as mentioned in Section 2.2.1. Instead, the valence band states (Fig. 11B) are less affected by the radiation field because of the weaker change of the laser-dressed confinement potential, in comparison with the electronic potential. The values of the single-particle energies are greater in sPQW than in GQW due to the stronger geometric confinement. Also, the increasing of the barrier asymmetry, , generates an enhancement of the energy levels of both electrons and holes in GQW and sPQW (Figs. 11 A,B), as expected. For example, the electronic energies increase almost linearly with , as the inset of Fig. 11A shows. for two types of n-sQWs with w L = 50 Å and identical barriers.
It can be seen that the ground state energy in the conduction band first rapidly decreases with cap layer up to c L  50 Å, and for further thick cap layers it becomes insensitive to the dielectric enhancement. For thin cap layers, the stronger geometric confinement of the www.intechopen.com electron in the sPQW comparing with SQW leads to an enhanced shift of the e E -level toward higher energies. Also, the electron energy presents a significant laser-induced augmentation which is more pronounced for sPQWs with thicker cap layer. There are two reasons for this behavior: i. as the cap layer thickness increases the contribution of the image-charge is weakened and the ILF effect becomes dominant; ii. under laser field action, the potential profile of SQW changes faster than in sPQW, so that the ground state of square structure are faster moved up in the upper part of the dressed QW. In contrast, the valence band states are less affected by the radiation field. With the decrease of c L the contribution of dielectric confinement to the hole energy becomes dominant leading to a pronounced blueshift. This result are in good agreement with the previous theoretical and experimental data in the absence of the laser field (Gippius, 1998;Tran Thoai, 1990).

Exciton binding energy
A noticeable dependence of the electron-hole interaction on the laser parameter, 0  , is expected as a consequence of the obvious laser-induced modification in the electronic structure of the CB. Fig. 13 displays the 1S-exciton binding energy as a function of the laser parameter for SQW, GQW and sPQW with L c = 40 Ǻ and different barrier asymmetries. We observe that for all the heterostructures under our study the exciton binding energy, b E , first increases with 0  , reaches a maximum value at 0   6 Å, and then it experiences a pronounced diminution. Finally, for large enough laser amplitudes b E drops to the In 0.18 Ga 0.82 As bulk characteristic value, 4.45 meV (Chang & Peeters, 2000). In the range of our calculations this value is reached for the sPQW with  = 0.6 under intense laser field, 0  = 120 Å.  Fig. 11).
The explanation of this behavior may be the following: under a low laser field ( 0   10 Å) the electronic ground level is localized in the lower part of the dressed QW which has a narrow width; therefore, the small distance between the electron and hole leads to a considerable exciton binding energy. By increasing the laser field intensity the geometric confinement of the carriers is reduced and thus, they can easily penetrate into the QW barriers. This "travel" results in a pronounced diminution of b E . As the barrier asymmetry parameter, , increases the exciton binding energy is enhanced due to the higher right barrier ( ) which moderates the spreading of the carriers wavefunctions in the QW barriers. Therefore, under intense laser field a competition between the laser intensity and barrier asymmetry in "tailoring" the exciton binding energy occurs. In Figs. 14 A-C the exciton binding energy is plotted as a function of the cap layer thickness, c L , in three differently shaped n-sQWs under various laser field intensities. For the www.intechopen.com asymmetrical structures GQW and sPQW two values of the asymmetry parameter,  = 0.6 and 1, were used. We observe that for c L  40 Å and for all laser parameter values used in this work, the exciton binding energy in the three differently shaped n-sQWs is reduced as c L increases. A similar behavior has been reported for a square n-sQW with w L = 50 Å in two cases: i) under various laser intensities (Niculescu & Eseanu, 2010a) and ii) in the absence of the laser field . This dielectric enhancement of b E obtained by using narrow capped layers, which are experimentally available, could be exploited in new optoelectronic devices. The exciton binding energy properties (presented above) reveal the transition from two-dimensional confinement effect produced by the wave function squeezing in a symmetrical/asymmetrical InGaAs quantum well to the three-dimensional behavior of the exciton, as 0  increases. A similar variation of the ground state binding energy has been reported for excitons in quantum well wires (Sari et al., 2003) and in n-sQWs with symmetrical barriers (Niculescu & Eseanu, 2011), under intense laser field.

Exciton absorption spectra
The exciton absorption coefficient given by the Eq. (27) depends on the exciton transition energy, ex E , whose components have been discussed in Section 3.2 and on the overlap integral  We can also observe that, if 0  is kept unchanged, there is an optimal range of the cap layer thickness corresponding to a broad maximum of the overlap integral. As 0  increases this www.intechopen.com optimal range is shifted to larger c L values in SQW, whereas it remains practically unchanged in the stronger confining structure sPQW. Moreover, since in the sPQW the particles are mostly localized in the QW region, the average electron-hole distance is less sensitive to the laser amplitude leading to an overlap integral nearly independent on the 0  values. Fig. 16 displays the overlap dependence on the barrier asymmetry parameter and laser field intensity in an asymmetrical n-sQW, namely GQW with c L = 80 Ǻ. The intense laser field reduces the overlap, as discussed before. Instead, the overlap integral is enhanced by the increasing barrier asymmetry (), particularly in low laser fields ( 0   40 Å). A similar variation was obtained for sPQW having the same c L = 80 Ǻ (not plotted here). Fig. 16. The dependence of the overlap integral on the barrier asymmetry parameter, , and laser field intensity, 0  in an asymmetrical n-sQW, namely GQW with L c = 80 Ǻ.
This asymmetry effect can be explained by the spreading effect of the wave functions in a QW with reduced barriers. The increasing of the height barrier in the QW right side ( ) in joint action with a low laser field lead to a stronger localization of the wave functions inside the well. Again, the intense laser field action competes with the asymmetry parameter, in the present case on the overlap integral. This effect could be used for particular applications. The exciton absorption coefficient (EAC) is modified by several parameters: pump photon energy, capped layer thickness c L , laser intensity 0  , and barrier asymmetry . In Figs. 17 A, B the dependence of this quantity vs. the pump photon energy in differently shaped n-sQWs with w L = 80 Å, under various laser intensities 0  = 0, 20 Å , 40 Å, and 60 Å, is plotted as follows: a) for SQW with identical barrier heigths and different c L (Fig. 17A); b) for GQW and sPQW having two asymmetry parameter values (Fig. 17 B). Firstly, one can see that the increasing laser intensity generates a significant shift of the absorption peak position to the high photon energies (blue-shift) and a simultaneous reduction of the exciton absorption coefficient magnitude, for all the cases under our study.

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A similar effect was observed for square and semiparabolic n-sQWs of the same width w L = 50 Å, having identical barrier heights and variable cap layer thickness (Niculescu & Eseanu, 2011). As expected, the shifts of the EAC peaks are more pronounced in the SQW (Fig. 17A) due to the weaker quantum confinement afforded by this structure in comparison with GQW and sPQW. The reason for the EAC laser-induced reduction is two-fold: i. the overlap integral diminution under intense laser fields (Figs. 15, 16); ii. the typical laser-induced blue-shift of the E e -levels. Secondly, we observe that the EAC peak positions show a red-shift for thicker cap layers (in the range 40 Å -80 Å) whereas for c L  80 Ǻ these positions are insensitive to the cap layer variation. Thirdly, we note that in the asymmetrical n-sQWs (GQW and sPQW) the blue-shift of the exciton absorption peak positions for  = 1 (identical barriers) is more pronounced comparing with the case  = 0.6.

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For the In 0.18 Ga 0.82 As/GaAs near-surface SQW with w L = 50 Å and variable c L , in the absence of the laser field, our results (Niculescu & Eseanu, 2010a) agree with the photoluminescence excitation measurements (Gippius et al., 1998;Kulik et al., 1996;Li, Z. et al., 2010;Yablonskii et al., 1996) and with theoretical normal-incidence reflectivity spectra (Yu et al., 2004). It is important to emphasize that the red-shift induced by the increasing c L or by the decreasing  can be effectively compensated using the blue-shift caused by the enhanced laser parameter. The changes induced by the joint action of the laser intensity and capped layer thickness or barrier asymmetry parameter in differently shaped QWs can be exploited to design new optoelectronic devices.

Conclusion
Summarizing, we note that the optical properties of the In 0.18 Ga 0.82 As/GaAs differently shaped near-surface quantum wells under intense laser fields could be tuned by proper tailoring of the heterostructure parameters (well shape and width, cap layer thickness, barrier asymmetry) and/or by varying the laser field intensity. This characteristics holds for both intersubband and interband absorptions. For example, in the exciton spectra of narrow In 0.18 Ga 0.82 As/GaAs n-sQWs, our calculations show that the red-shift of the absorption peaks induced by the rising cap layer thickness or by barrier asymmetry diminution can be effectively compensated using the blue-shift caused by enhancing laser parameter. These phenomena could be exploited for particular applications. Also, for both intersubband and interband transitions, the switch between the strong absorption and induced laser transparency regimes can be suitable for good performance optical modulators. To the best of our knowledge this is the first investigation on the intersubband absorption in symmetrical/asymmetrical InGaAs/GaAs n-sQWs under intense laser fields. We expect that these results will be of help for experimental works focused on innovative optoelectronic devices.