Excitonic effects in nonlinear optical rectification in small semi‐parabolic quantum dots

Abstract

We study the effects of excitons in nonlinear optical rectification in one-dimensional semi-parabolic quantum dots. We consider the case that the electron and the hole are confined in semi-parabolic potential with the same oscillator frequency. We present approximate analytical results in the strong confinement regime and find a closed-form relation between the nonlinear optical rectification coefficient of an exciton in the structure and the corresponding coefficient when only one electron exists in the structure. These results are also verified by numerical calculations performed with the potential morphing method.1 Introduction Recently, Yu et al. studied the effects of an exciton on the nonlinear optical rectification (OR) in an one-dimensional quantum dot that is strongly confined in the x and y directions. They also assumed that the electron and the hole in the z direction are confined in semi-parabolic potentials with the same oscillator frequency [1]. They showed that the existence of an exciton enhances the nonlinear OR coefficient in comparison to the case that only one electron exists in the structure. In the present work we extend the results of Yu et al.[1] and present approximate analytical results in the strong confinement regime. With the use of these results we find a closed-form relation between the nonlinear OR coefficient in the case that one exciton is confined in the quantum dot structure and the corresponding coefficient when only one electron exists in the structure. It is found that the two coefficients are related only by formula that contains the effective masses of the electron and the hole. These results are also verified by numerical calculations performed with the potential morphing method (PMM) [2][3][4].

Nonlinear optical rectification and optical absorption in GaAs–Ga1–xAlxAs asymmetric double quantum wells: Combined effects of applied electric and magnetic fields and hydrostatic pressure

“…Indeed, very large second-order nonlinear optical properties associated with ISBT such as the second harmonic generation (SHG) [3], the nonlinear optical rectification [4], and frequency down conversion [5], and third-order nonlinear optical properties such as the dc Kerr effect [6], third harmonic generation (THG) [7], and four-wave mixing [8] have been observed experimentally. Following these experimental observations, many theoretical studies related to the optical nonlinearities have also been performed [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Excitonic effects on the second-order nonlinear optical properties of semi-spherical quantum dots

“…The second-order nonlinear optical coefficients can be obtained by density matrix approach and perturbation expansion method [ 12 , 13 ]. The expression for the OR coefficient, within a two-level system approach, is given by [ 5 , 6 ] …”

“…Recently, several authors [ 5 , 6 , 8 ] studied the effects of an exciton on the second-order nonlinear properties in one-dimensional semi-parabolic quantum dots. Using analytical approximate results, they showed that the excitonic effects enhance significantly the OR and SHG coefficients.…”

Second-order nonlinear optical properties in a strained InGaN/AlGaN quantum well under the intense laser field

“…Among the nonlinear optical properties, more attention had been paid to the second-harmonic generation (SHG) [17][18][19][20][21][22][23][24][25][26] and optical rectification (OR) [23][24][25][26][27][28][29][30][31][32][33] coefficients. It is well known that these even-order nonlinear optical properties are only non-zero in asymmetric quantum systems.…”