We propose an arbitrary vector beam (VB) generation scheme in a thin disk-shaped quantum dot (QD) medium considering phonon interaction. The QD biexciton system exhibits the interplay between first- and third-order nonlinear susceptibility between two orthogonal circular polarization transitions. Three QD transitions are coupled with one applied weak and two strong control orbital angular momentum (OAM) carrying fields. Therefore, the applied field experiences absorption, and a new field with the desired OAM is generated via four-wave mixing (FWM). These two orthogonal field superpositions produce VB at the QD medium end. We also demonstrate the polarization rotation of a VB by changing only the relative control field phase. Additionally, we analyze the effect of temperature on the VB generation.
We propose an arbitrary vector beam (VB) generation scheme in a thin disk-shaped quantum dot (QD) medium considering phonon interaction. The QD biexciton system exhibits the interplay between first- and third-order nonlinear susceptibility between two orthogonal circular polarization transitions. Three QD transitions are coupled with one applied weak and two strong control orbital angular momentum (OAM) carrying fields. Therefore, the applied field experiences absorption, and a new field with the desired OAM is generated via four-wave mixing (FWM). These two orthogonal field superpositions produce VB at the QD medium end. We also demonstrate the polarization rotation of a VB by changing only the relative control field phase. Additionally, we analyze the effect of temperature on the VB generation.
We propose a scheme to generate structured light using a medium consisting of semiconductor quantum dots via four-wave mixing (FWM). We consider a four-level quantum-dot structure where two strong electromagnetic fields couple upper-level biexciton transitions, whereas a weak field is applied to one of the ground-level exciton transitions. A weak signal field is generated, corresponding to a second ground-level exciton transition; thus the overall configuration transforms into a closed-loop diamond-type shape. To realize a spatially dependent modulating quantum-dot medium, we consider strong coupling fields as structured lights and investigate different regions of spatially structured electromagnetically induced transparency via absorption of the generated signal field. The azimuthal phase-dependent modulation of the absorption profile of the generated signal field is the key factor behind the creation of structured light. In addition, we also demonstrate transfer of orbital angular momentum (OAM) of the control beam to the generated beam through the FWM process and study the effect of phase mismatch on efficiency of the OAM transfer.
In the past few years, many interesting optical phenomena, such as electromagnetically induced transparency, coherent optical control of a biexciton, slow light and optical solitons, have been investigated in single quantum dot (QD). However, in an actual semiconductor device there exist many quantum dots (QDs). Recently, QD molecule, which is comprised of double semiconductor QDs coupled by tunneling coupling, has been proposed. In this new semiconductor structure, many complex but interesting phenomena have been discovered. In fact, three QD molecules may also be composed of three QDs, which can be coupled by interdot tunneling coupling. For the three semiconductor QDs molecules, the influence of the interdot tunneling coupling strength must be considered. So, in this paper, with considering that a weak, -linear-polarized probe field can form left- and right-polarized components under the control of the parallel magnetic field, and when they are combined with the tunneling coupling among the QDs, an electromagnetically induced transparency medium of a five-level M configuration semiconductor three QDs is proposed. Subsequently, the nonlinear Faraday rotation in the semiconductor three QDs is analytically studied. For the linear case, the linear dispersion relation is driven by a method of multiple scales. Then, by studying the linear optical properties, it is found that the system exhibits a single tunneling induced transparency window due to the quantum destructive interference effect driven by the interdot tunneling coupling under appropriate conditions, and the width of the tunneling induced transparency window can be effectively controlled by the strength of the interdot tunneling coupling. Meanwhile, the switch regulatory effect, which changes from the anomalous dispersion regime to the normal dispersion regime, is likely to be achieved by changing the strength of the interdot tunneling coupling. For the nonlinear case, two coupled nonlinear Schrdinger equations, which govern the evolutions of left- and right-polarized components of the weak, -linear-polarized probe field under the applied longitudinal magnetic field, are derived. By studying the nonlinear properties, it is shown that a large nonlinear Faraday rotation angle can be obtained due to the quantum interference effect which is induced by the interdot tunneling coupling with a very low absorption of the weak, -linear-polarized probe field. In addition, it is also found that the nonlinear Faraday rotation direction is opposite to line Faraday rotation for the same magnetic field. What is more, the nonlinear Faraday rotation angle grows bigger than the linear Faraday rotation. These results mean that the Faraday rotation of the three semiconductor QDs with the electromagnetically induced transparency can be more effectively controlled by the nonlinear effect.
In recent years,the subject of optical nonlinearity in semiconductor quantum confined structures such as quantum wires and quantum dots has attracted a considerable attention because of their relevance for studying practical applications and as a probe for the electronic structure of media.It has been shown that the low dimensional quantum systems present very large nonlinear optical susceptibilities .Theoretically,most of the studies on quantum dots are focused on spherical quantum dots for simplicity.The shape of quantum dot depends on growth conditions.In fact,quantum dots are better described as thin disk or cylinder.In the present work third order nonlinear optical susceptibilities in disk shaped quantum dots due to resonant intersubband transition are analyzed by a compact density matrix approach.It has rarely been discussed in literatures.Firstly,we consider an electron moving in a quantum disk whose radius R is very large compared to its thickness d .For simplicity,we assume that the isotropic effective mass approximation is valid within the disk and that the inner potential is null while the outer confining potential is approximately infinite.Using the adiabatic approximation we solve the three dimensional Schrdinger equation and obtain the analytical expressions of wave functions and energy levels in cylindrical coordinates.Secondly,we consider the system is excited by an electromagnetic field with frequency ω. The electromagnetic field is incident with a polarization vector normal to the disk.We treat H′=ezE(t) as a perturbation term.By using the compact density matrix method,we derive a general formula for third order nonlinear optical susceptibilites employing a four level model in quantum disk.Finally,numerical results are illustrated for a typical GaAs quantum disk.We calculate the third order nonlinear optical susceptibilities as a function of the disk thickness.It is shown that the third order nonlinear optical susceptibilities in quantum disk are 10～100 times larger than that in quantum well for various disk thickness.Furthermore,if we choose an optimized thickness of quantum disk,we could obtain a quite large refractive index with a comparatively small absorption coefficient.Therefore,we suggest that the quantum dots would be an excellent system in the field of optical communications and optical switching.
With the presence of the signal pulse, a quantum dot (QD) four-level structure interacting with four fields forms a double-cascade configuration. The linear optical properties for amplification, absorption, and dispersion of two weak near-infrared (NIR) lights in this scheme are investigated. It shows that the amplification, transparency, normal and anomalous dispersion of the probe and signal fields, i.e., the two NIR waves, can be achieved by adjusting the relative phase of the applied lasers, the probe detuning, and the two pump Rabi energies appropriately, while when the signal pulse is removed, the nonlinear optical phenomenon four-wave mixing (FWM) originating from quantum interference is demonstrated. A highly efficient FWM process with a NIR mixing field generated can be realized in this system. Such investigation in a semiconductor QD system with flexible design and widely adjustable parameters may provide new possibilities for realizing the efficient generation and gain of NIR waves and manipulating light propagation between subluminal and superluminal in the solid-state materials.
Laguerre-Gaussian (LG) beams contain a helical phase front with a doughnut-like intensity profile. We use the LG beam to introduce a rather simple method for generation of a vector beam (VB), a beam with spatially-dependent polarization in the beam cross section, via the nonlinear magneto-optical rotation (NMOR). We consider the NMOR of the polarization of a linearly polarized probe field passing through an inverted Y-type four-level quantum system interacting with a LG control field and a static magnetic field. It is shown that the polarization of the transmitted field is spatially distributed by the orbital angular momentum (OAM) of the LG control field, leading to generation of the VB with azimuthally symmetric polarization distribution. We show that the polarization and intensity distributions of the VB spatially vary by changing the OAMs of the LG control field. Moreover, the radial index of the LG control field has a major role in more spatially polarization distributing of the VB. It is shown that the intensity of the generated VBs in different points of the beam cross section can be controlled by the OAM as well as the radial index of the LG control field. However, the VB with highly spatially distributed can be generated for higher values of the radial index of LG control field. The analytical calculations determine the contribution of the different nonlinear (cross-Kerr effect) phenomena on the generation of the VB. We show that the VB is mainly generated via birefringence induced by the applied fields. Finally, we use asymmetric LG (aLG) beams for making the VBs with asymmetric polarization distribution. It is shown that by applying aLG beams, the azimuthal symmetry of the polarization distribution breaks and the asymmetric polarization distribution can be controlled by OAM and radial index of the aLG control field. The obtained results may find more interesting applications in fiber/free space optical communication to enhance the capacity of the information transmission.
Abstract In this paper, we study the spatially structured optical effects that occur when weak laser lights interact with coherently prepared semiconductor quantum dots (SQDs). Initially, the SQD is prepared in a coherent superposition of the lower exciton states. By utilizing two weak optical vortex fields that couple to a biexciton state, we observe spatially dependent effects of the absorption of probe fields. Using the well-established Maxwell–Bloch equations, we analyze the generation of composite optical vortex beams within this system. Our investigation revolves around the formation of different types of spatially dependent beams, exploring their properties and characteristics. Additionally, the transfer of optical vortices through the parametric generation process is examined, for the case where only one vortex beam is present at the beginning of the medium. This study provides insights into the spatially structured optical phenomena in coherently prepared SQDs and contributes to the understanding of light–matter interactions in such systems.