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Results in Optics

Non-linear optical properties of excitonic complexes in prolate ellipsoidal quantum dot

Yuri Y. Bleyan, Maxim Ya. Vinnichenko, Nabil Zeiri, C.A. Duque, D.B. Hayrapetyan

Published Feb 1, 2026• 1 citation

Abstract

This study presents a theoretical study of ground-state exciton and biexciton properties in strongly prolate ellipsoidal GaAs quantum dot. Using a variational approach with trial wave functions constructed from single-particle states, we examine the dependence of exciton and biexciton energies on the dot’s geometric parameters. The oscillator strengths of exciton–biexciton transitions are analyzed as functions of the major and minor semiaxes. We further investigate the third-order optical susceptibility near single- and two-photon resonances, elucidating the role of exciton–biexciton interactions. The results show that one-photon resonances dominate the nonlinear response, with contributions exceeding those of two-photon resonances by approximately four orders of magnitude. Absorption coefficients for exciton and biexciton transitions are evaluated for a fixed major semiaxis and varying minor semiaxis, along with the biexciton two-photon absorption coefficient. Finally, we analyze biexciton-induced nonlinear refractive index modulation, which exhibits a sign reversal across resonance and a pronounced peak–dip structure, indicating strong dispersive behavior and significant excitonic phase modulation.

DOI: 10.1016/j.rio.2026.100982

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This study presents a theoretical study of ground-state exciton and biexciton properties in strongly prolate ellipsoidal GaAs quantum dot. Using a variational approach with trial wave functions constructed from single-particle states, we examine the dependence of exciton and biexciton energies on the dot’s geometric parameters. The oscillator strengths of exciton–biexciton transitions are analyzed as functions of the major and minor semiaxes. We further investigate the third-order optical susceptibility near single- and two-photon resonances, elucidating the role of exciton–biexciton interactions. The results show that one-photon resonances dominate the nonlinear response, with contributions exceeding those of two-photon resonances by approximately four orders of magnitude. Absorption coefficients for exciton and biexciton transitions are evaluated for a fixed major semiaxis and varying minor semiaxis, along with the biexciton two-photon absorption coefficient. Finally, we analyze biexciton-induced nonlinear refractive index modulation, which exhibits a sign reversal across resonance and a pronounced peak–dip structure, indicating strong dispersive behavior and significant excitonic phase modulation.

Abstract The biexciton states of the ground and excited levels in a GaAs strongly oblate ellipsoidal quantum dot are studied with the use of the variational method. The trial variational wave function of the biexciton is constructed on single-particle wave functions, obtained within the geometrical adiabatic approximation. The biexciton energies are obtained from the geometric parameters of an ellipsoidal quantum dot for both the ground and excited states. The linear and nonlinear refractive indexes of the biexciton around one- and two-photon resonances are calculated as the real parts of the first- and third-order nonlinear susceptibilities, respectively. The spectra of changes of the biexciton refractive index for transitions between ground states as a function of the photon energy are obtained for different values of the small semiaxis of the ellipsoidal quantum dot.

The optical properties of an exciton trapped by an ionized donor in an ellipsoidal quantum dot (QD) with both oblate and prolate shapes under applied electric field and hydrostatic pressure have been studied. We have calculated the linear and third-order nonlinear absorption coefficients (ACs) and refractive index changes (RICs) by using a variational method within the perturbation theory. The results show that the QD shape and size have a significant influence on the positions and magnitudes of the peaks of the (ACs) and RICs, moreover, the influence of hydrostatic pressure and electric field under different QD shape is also different.

Intersubband optical absorption coefficient and refractive index changes of a weakly prolate ellipsoidal quantum dot, using the compact-density matrix formalism and iterative method, are investigated. In this regard, the linear and nonlinear intersubband optical absorption coefficient and refractive index changes of a GaAs / Al x Ga 1-x As ellipsoidal quantum dot, as functions of the dot radius, ellipticity constant, stoichiometric ratio and incident light intensity are calculated. The results indicate that absorption coefficient and refractive index changes strongly depend on the light intensity, size and geometry of the dot and structure parameters such as aluminium concentration in GaAs / Al x Ga 1-x As structures.

Exciton-biexciton coherent coupling effects are examined in semiconductor quantum dots. The exciton absorption spectrum is measured with the microphotoluminescence excitation technique in a single InGaAs quantum dot. The spectrum changes from a Lorenztian-type line shape to an unusual dip-shaped line shape with increasing excitation intensities in a higher exciton state where there is a large oscillator strength between the exciton and biexciton states. The intensity dependence of the dip energy width clearly indicates that coherent Rabi oscillation occurs between the exciton and biexciton states. The absorption properties with excitation light of different polarizations show that the dip-shaped spectra only appear when there is a large biexciton state population with linear polarization. A theoretical analysis undertaken with the density matrix method agrees well with experimental results. This agreement reveals that exciton-biexciton coherent interactions lead to unusual absorption spectra and contribute crucially to the optical properties of quantum dots. The exciton-biexciton coherent effects provide a scheme for controlling four distinguishable states, which can be applied to a demonstration of quantum gate operations.

In this paper, we study the exciton absorption spectra in InGaAs prolate ellipsoidal quantum dots when a strong pump laser resonant with electron quantized levels is active. Our obtained results by renormalized wavefunction theory show that, under suitable conditions, the initial exciton absorption peak is split into two new peaks as the evidence of the existence of the three-level optical Stark effect of excitons. We have suggested an explanation of the origin of the effect as well as investigating the effect of pump field energy, size, and geometric shape of the quantum dots on effect characteristics. The comparison with the results obtained in the spherical quantum dots implies the important role of geometric shape of the quantum structures when we examine this effect.

The absorption spectra and the refractive index changes are calculated theoretically for an exciton in a core/shell quantum dot. The advantage of our methodology is that one can investigate the influence of the repulsive core by varying two parameters in the confinement potential. The dimensionality effect of exciton quantum dots on the optical absorptions has been studied. It has been found that in the same regime, the optical absorption intensities of excitons are much smaller for the core/shell quantum dots than for the two-dimensional quantum rings. The linear and the nonlinear optical absorption coefficients and refractive index changes have been examined with the change of the confinement potential. The results show that the optical absorptions and the refractive index changes are strongly affected by the repulsive core of core/shell quantum dots. Moreover, the calculated results also reveal that as the inner radius increases, the peak values of the absorption coefficients and the refractive index changes of an exciton will show the optical Aharonov–Bohm oscillation in core/shell quantum dots.