Third-harmonic Generation Susceptibility Research Articles

Linear and nonlinear optical properties in quantum wells

In this paper, the linear and nonlinear optical properties, especially the optical rectification (OR), the second-harmonic generation (SHG) susceptibility, the third-harmonic generation (THG) susceptibility, the optical absorption coefficients (OACs), and the refractive index changes (RICs) of GaAs-AlGaAs semi-parabolic well (SPW) are studied in detail utilizing the compact density matrix approach and iterative procedure. The states of electron in the SPW with electric field are obtained utilizing the techniques of the displacement harmonic-oscillator and the envelope wave-function. Our results reveal that the confinement frequency, the electric field, the relaxation time, and the incident field strength have considerable influences on the optical properties of the SPW. If it is desired to obtain the OR, SHG, THG, OAC, and RIC with large values, then a relatively weaker incident field strength and confinement frequency, as well as a relatively stronger electric field intensity, should be chosen. If the optical strength is relatively large, then the effect of the nonlinear (third-order) term is important and cannot be neglected when investigating the non-linear optical properties in the SPW. The semiparabolic well is a promising candidate for these properties.

Third-harmonic generation in excitonic insulators

We study third-harmonic generation (THG) in an excitonic insulator (EI) described in a two-band correlated electron model. Employing the perturbative expansion with respect to the external electric field, we derive the THG susceptibility taking into account the collective dynamics of the excitonic order parameter. In the inversion-symmetric EI, the collective order parameter motion is activated at second order of the external field and its effects arise in THG. We find three peaks in the THG susceptibility at energies $\hbar \Omega = \Delta_g/3$, $\Delta_g/2$, and $\Delta_g$, where $\Delta_g$ is the band gap. While the THG response at $\Delta_g/3$ is caused by bare three-photon excitation of the independent particle across the band gap, the latter two peaks involve the motion of the order parameter activated at second order. The resulting resonant peaks are prominent in particular in the BCS regime but they become less significant in the BEC regime. We demonstrate that the resonant peak originated by the collective excitation is observable in the temperature profile of the THG intensity. Our study suggests that the THG measurement should be promising for detecting the excitonic collective nature of materials.

Strong Second- and Third-Harmonic Generation in 1D Chiral Hybrid Bismuth Halides.

Breaking the symmetry of a crystal structure can enable even-order nonlinear activities, including second-harmonic generation (SHG). The emerging chiral hybrid organic-inorganic metal halides feature unique optical and electronic properties and flexible crystal structures, making them a class of promising nonlinear optical materials. However, their nonlinear response performances are currently inferior to traditional nonlinear crystals, because of the lack of research on resonant enhancement and third-harmonic generation (THG). Herein, we designed chiral hybrid bismuth halides with naturally nonsymmetrical structure to enable SHG. Simultaneously, these chiral compounds preserve 1D crystal structures to create strong free exciton, broad self-trapped exciton (STE), and discrete band energy levels, which facilitate the resonant enhancement of SHG and THG susceptibilities. These new chiral films showcase superior effective SHG susceptibility (χ(2) ∼ 130.5 pm V-1 at an interesting wavelength of 1550 nm), exceeding that of the reference, a commercial LiNbO3 (χ(2) ∼ 83.4 pm V-1) single-crystal film. Furthermore, their THG intensities are even higher than their SHG intensities, with effective THG susceptibility (χ(3)) being ∼9.0 × 106 pm2 V-2 at 1550 nm (37 times that of the reference monolayer WS2). Their high SHG and THG performances indicate the promising future of these 1D chiral hybrid bismuth halides toward nonlinear optical applications.

Higgs-mode resonance in third harmonic generation in NbN superconductors: Multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence

We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurity scatterings. Using the estimated pairing interactions with multiband impurity scattering rates being varied from clean to dirty regimes, we calculate the THG susceptibility for NbN in a channel-resolved manner by means of the BCS and self-consistent Born approximations. In the dirty regime, which is close to the experimental situation, the leading contribution is given by the paramagnetic channel of the Higgs mode having almost no polarization-angle dependence, while the second leading contribution comes from the paramagnetic channel of quasiparticles generally showing significant polarization-angle dependence. The result is consistent with the recent experimental observation of no polarization-angle dependence of THG, giving firm evidence that the Higgs mode dominantly contributes to the THG resonance in NbN superconductors.

Effect of an Inverse Parabolic Confining Electric Potential on Third Harmonic Generation in Cylindrical Quantum Wires

A theoretical investigation of the effect of an inverse parabolic potential on third harmonic generation in cylindrical quantum wires is presented. The wave functions are obtained as solutions to Schrödinger equation solved within the effective mass approximation. It turns out that peaks of the third harmonic generation susceptibility (THGS) associated with nanowires of small radii occur at larger photon energies as compared to those associated with quantum wires of larger radii. The inverse parabolic potential red-shifts peaks of the THGS, and suppresses the amplitude of the THGS. THGS associated with higher radial quantum numbers is diminished in magnitude and blue-shifted, as a function of the photon energy. As a function of the inverse parabolic potential, the THGS still characterized by peaks, and the peaks shift to lower values of the potential as the photon energy increases.

Nonlinear Refractive Index in Rectangular Graphene Quantum Dots

Alongside its other favorable properties, the large refraction nonlinearity of graphene-related material makes it ideal for use in optoelectronics applications. Numerous experimental studies about nonlinear optical refraction have been conducted, but theoretical verification is lacking. In this paper the nonlinear refractive index for rectangular graphene quantum dots (RGQDs) was calculated using the relationship between nonlinear refractive index and the third-order nonlinear optical susceptibility. The third-order nonlinear optical susceptibility for third harmonic generation was derived employing the electronic states obtained from the Dirac equation around K point in RGQDs under hard wall boundary conditions. Results revealed that the calculated nonlinear refractive index, n 2 , was in the magnitude of 10−14 m2/W in the visible region, which is nearly five orders larger than conventional semiconductor quantum dots, while in the infrared region the nonlinear refractive index reached up to the magnitude of 10−11 m2/W for M = 3M0 sized RGQDs where the resonance enhancement occurred. The nonlinear refractive index could be tuned both by the edges and sizes.

Effect of an Inverse Parabolic Confining Electric Potential on Third Harmonic Generation in Cylindrical Quantum Wires

A theoretical investigation of the effect of an inverse parabolic potential on third harmonic generation in cylindrical quantum wires is presented. The wave functions are obtained as solutions to Schrödinger equation solved within the effective mass approximation. It turns out that peaks of the third harmonic generation susceptibility (THGS) associated with nanowires of small radii occur at larger photon energies as compared to those associated with quantum wires of larger radii. The inverse parabolic potential red-shifts peaks of the THGS, and suppresses the amplitude of the THGS. THGS associated with higher radial quantum numbers is diminished in magnitude and blue-shifted, as a function of the photon energy. As a function of the inverse parabolic potential, the THGS still characterized by peaks, and the peaks shift to lower values of the potential as the photon energy increases.

Effect of an Inverse Parabolic Confining Electric Potential on Third Harmonic Generation in Cylindrical Quantum Wires

A theoretical investigation of the effect of an inverse parabolic potential on third harmonic generation in cylindrical quantum wires is presented. The wave functions are obtained as solutions to Schrödinger equation solved within the effective mass approximation. It turns out that peaks of the third harmonic generation susceptibility (THGS) associated with nanowires of small radii occur at larger photon energies as compared to those associated with quantum wires of larger radii. The inverse parabolic potential red-shifts peaks of the THGS, and suppresses the amplitude of the THGS. THGS associated with higher radial quantum numbers is diminished in magnitude and blue-shifted, as a function of the photon energy. As a function of the inverse parabolic potential, the THGS still characterized by peaks, and the peaks shift to lower values of the potential as the photon energy increases.

Optical third harmonic generation in black phosphorus

We present a calculation of Third Harmonic Generation (THG) for two-band systems using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the third order current density response. The calculation is applied to bulk and monolayer black Phosphorus (bP) using a non-orthogonal tight-binding model. Results show that the low energy response is dominated by mixed inter-intraband processes and estimates of the magnitude of THG susceptibility are comparable to recent experimental reports for bulk bP samples.

Energy spectra and the third-order nonlinear optical properties in GaAs/AlGaAs core/shell quantum dots with a hydrogenic impurity

The energy levels and binding energies of hydrogenic impurity associated with the ground state and some low-lying states in GaAs/AlGaAs core/shell quantum dots are theoretically studied by using the finite difference method. It is shown that energy levels and binding energies are depended dramatically on the size of the quantum dot due to quantum size effect. The change of the level ordering for hydrogenic impurity can be found and then to cause the corresponding changes in the binding energies, which can be adjusted by the radius of the quantum dot. Based on the analysis of these energy levels, the third-harmonic generation susceptibility in this quantum dot with (or without) impurity is investigated by using the compact-density-matrix approach. The results show that the third harmonic generation susceptibility obtained in the two cases can reach the magnitude of ∼10−7 m2 V−2 by choosing a large radius of quantum dot. For the large quantum dot with impurity, it is found that the third-harmonic generation susceptibility can be effectively enhanced about 1.3 ∼ 1.5 times than the case regardless of the impurity. Finally, the resonant peak and its corresponding to resonant energy are also taken into account.

Frequency dependence of optical third-harmonic generation from doped graphene

In connection with the controversial question about the frequency dependence of the optical third-harmonic generation (THG) from doped graphene, which has recently been discussed in the literature, we develop an analytical theory for the THG susceptibility of doped graphene by using the original Genkin–Mednis nonlinear-conductivity-theory formalism including mixed intra- and interband terms. The theory is free of any nonphysical divergences at zero frequency, and it predicts the main resonant peak in the THG spectrum to be located at the photon energy ħω equal to two thirds of the Fermi energy EF of charge carriers in doped graphene.

Third-harmonic generation susceptibility spectroscopy in free fatty acids.

Lipid-correlated disease such as atherosclerosis has been an important medical research topic for decades. Many new microscopic imaging techniques such as coherent anti-Stokes Raman scattering and third-harmonic generation (THG) microscopy were verified to have the capability to target lipids in vivo. In the case of THG microscopy, biological cell membranes and lipid bodies in cells and tissues have been shown as good sources of contrast with a laser excitation wavelength around 1200 nm. We report the THG excitation spectroscopy study of two pure free fatty acids including oleic acid and linoleic acid from 1090 to 1330 nm. Different pure fatty acids presented slightly-different THG χ(3) spectra. The measured peak values of THG third-order susceptibility χ(3) in both fatty acids were surprisingly found not to match completely with the resonant absorption wavelengths around 1190 to 1210 nm, suggesting possible wavelengths selection for enhanced THG imaging of lipids while avoiding laser light absorption. Along with the recent advancement in THG imaging, this new window between 1240 to 1290 nm may offer tremendous new opportunities for sensitive label-free lipid imaging in biological tissues.

Theory of Anderson pseudospin resonance with Higgs mode in superconductors

A superconductor illuminated by an ac electric field with frequency $\Omega$ is theoretically found to generate a collective precession of Anderson's pseudospins, and hence a coherent amplitude oscillation of the order parameter, with a doubled frequency $2\Omega$ through a nonlinear light-matter coupling. We provide a fundamental theory, based on the mean-field formalism, to show that the induced pseudospin precession resonates with the Higgs amplitude mode of the superconductor at $2\Omega=2\Delta$ with $2\Delta$ being the superconducting gap. The resonant precession is accompanied by a divergent enhancement of the third-harmonic generation (THG). By decomposing the THG susceptibility into the bare one and vertex correction, we find that the enhancement of the THG cannot be explained by individual quasiparticle excitations (pair breaking), so that the THG serves as a smoking gun for an identification of the collective Higgs mode. We further explore the effect of electron-electron scattering on the pseudospin resonance by applying the nonequilibrium dynamical mean-field theory to the attractive Hubbard model driven by ac electric fields. The result indicates that the pseudospin resonance is robust against electron correlations, although the resonance width is broadened due to electron scattering, which determines the lifetime of the Higgs mode.

Highly efficient third-harmonic generation from resonant intersubband transitions in core/shell spherical quantum dots

The efficient third-harmonic generation related to intersubband transitions in GaAs/AlGaAs core/shell spherical quantum dots is studied in detail. An analytic formula for the third-harmonic-generation susceptibility under the condition of the triple resonance is derived by the compact density matrix approach and the iterative procedure. The numerical results show that a very large third-harmonic generation susceptibility of the order of magnitude of 10−12(m/V)2 can be obtained by choosing properly the radius of the spherical quantum dot and the angular frequency of incident light to satisfy the triple resonance condition. In addition, the influence of the relaxation time on the third-harmonic generation susceptibility is clarified. These properties make spherical core/shell quantum dots be potential candidates for extensive applications in optical information storage and nanophotonic devices.

Photoionization and third-order susceptibility of a neutral donor in ZnS/InP/ZnSe core/shell spherical quantum dots

The optical properties of a neutral donor in a ZnS/InP/ZnSe core/shell spherical quantum dot have been investigated using the variational method and the compact density-matrix approach. Two parametric potential is chosen as a confinement potential for the shell. Considering the band structure of the system it is assumed that electron is localized in InP shell. It is assumed that the impurity is located in the center of quantum dot core (ZnS). The photoionization cross section as well as the third-order nonlinear optical susceptibility of third harmonic generation has been calculated. The results show that the photoionization and the third-order nonlinear optical susceptibility of a donor in a core/shell spherical quantum dot are strongly affected by the shell thickness. We found that small applied shell thickness will lead to a significant blue shift of the peak positions in the optical spectrum. This kind of structure gives an opportunity to tune and control the photoionization and the third-order nonlinear optical susceptibility of third harmonic generation of a donor impurity by changing the shell thickness.

Effects of Polaron and Quantum Confinement on the Nonlinear Optical Properties in a GaAs/Ga1−xAlxAs Quantum Well Wire

The binding energy of a polaron confined in a GaAs/Ga1−xAlxAs quantum well wire is calculated within the framework of the variational technique and Lee‐Low Pines approach. The polaron‐induced photoionization cross section as a function of normalized photon energy for a on‐centre donor impurity in the quantum wire is investigated. The oscillator strength with the geometrical effect is studied taking into account the polaron effects in a GaAs/Ga0.8Al0.2As quantum well wire. The effect of polaron on the third‐order susceptibility of third harmonic generation is studied. Our theoretical results are shown to be in good agreement with previous investigations.

Effects of magnetic field and hydrostatic pressure on a confined exciton in a strained GaAs<SUB align="right">0.9P<SUB align="right">0.1/GaAs<SUB align="right">0.6P<SUB align="right">0.4 quantum dot

Simultaneous effects of magnetic field and the hydrostatic pressure on the confined exciton in a cylindrical GaAs0.9P0.1/GaAs0.6P0.4 strained quantum dot are investigated taking into account the geometrical confinement effect. Calculations are done using variational formulism within the single band effective mass approximation numerically. The oscillator strength as a function of dot radius is computed in the influence of magnetic field strength and pressure effect. Second order nonlinear coefficient, second order harmonic generation and the third-order nonlinear optical susceptibility of third order harmonic generation as a function of dot radius, are carried out in the presence of magnetic field strength and the hydrostatic pressure. Our results show that the optical properties strongly depend on the spatial confinement, the hydrostatic pressure and magnetic field strength.

Third-order nonlinear optical susceptibility and photoionization of an exciton in quantum dots

In this study, an investigation of an exciton in a disk-like quantum dot has been carried out by using the matrix diagonalization method and the compact density-matrix approach. The dependences of binding energies of excitons for the light and heavy hole masses on the size of the confining potential are analyzed explicitly. The third-order nonlinear optical susceptibility of third harmonic generation as well as the photoionization cross section has been calculated for the light-hole and heavy-hole excitons. The results are presented as a function of the incident photon energy. The results show that the third-order nonlinear optical susceptibility and the photoionization cross section of an exciton in a quantum dot are strongly affected by the dot size and the hole mass.

Third-order nonlinear optical susceptibility of a donor in elliptical quantum dots

The optical properties of a donor in anisotropic quantum dots with elliptical shape are investigated. Calculations are performed by using the variational method and the compact-density–matrix approach within the effective mass approximation. We have investigated the effects of the geometrical size and the degree of anisotropy on the oscillator strength and the third-order susceptibility of third harmonic generation. The results show that the dot anisotropy and the dot size play a fundamental role in determining the nonlinear optical properties of quantum dots.

The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot

The combined effects of the hydrostatic pressure and temperature on the binding energy, ΔE (transition energy), the oscillator strength and the third-order susceptibility of third harmonic generation (THG) of a hydrogenic impurity in a spherical QD, in the presence of the external electric field, have been investigated by means of the perturbation approach within the framework of effective-mass approximation. It is found that the binding energy, ΔE (transition energy), the oscillator strength and the third-order susceptibility of third harmonic generation (THG) of the hydrogenic impurity are affected by the confinement strength, the electric field, pressure and temperature.