High Order Nonlinear Susceptibility Research Articles

Conical diffraction in atomic vapor: Mathematical models and numerical calculations

This study investigated the conical diffraction characteristics in the honeycomb lattice of a Λ-type three-level energy system for rubidium atomic configuration. Its band structure incorporates Dirac cones in accordance with the plane wave expansion method. We determined that the rotation angle θ of the three vectors strongly impacted the cone diffraction profile. For θ=0° and 60°, in the reciprocal lattice space, the Dirac cone states were excited, and symmetric cone diffraction was supported. When 0<θ<60°, an asymmetric cone diffraction with a dark notch appeared on the outer edge of the conical ring. The results indicate that the frequency detuning of the coupling field and high-order nonlinear susceptibilities in the medium are effective and concise approaches to manipulate the occurrence of cone diffraction. The findings of this study enhance the understanding of the cone diffraction phenomena and broaden the practical applicability of atomic configuration.

Influence of the asymmetric excited state decay on coherent population trapping

Electromagnetically induced transparency (EIT) is an optical phenomenon which allows a drastic modification of the optical properties of an atomic system by applying a control field. It has been largely studied in the last decades and nowadays we can find a huge number of experimental and theoretical related studies. Recently a similar phenomenon was also shown in quantum dot molecules (QDM), where the control field is replaced by the tunneling rate between quantum dots. Our results show that in the EIT regime, the optical properties of QDM and the atomic system are identical. However, here we show that in the strong probe field regime, i.e., “coherent population trapping” (CPT) regime, it appears a strong discrepancy on the optical properties of both systems. We show that the origin of such difference relies on the different decay rates of the excited state of the two systems, implying in a strong difference on their higher order nonlinear susceptibilities. Finally, we investigate the optical response of atom/QDM strongly coupled to a cavity mode. In particular, the QDM-cavity system has the advantage of allowing a better narrowing of the width of the dark state resonance in the CPT regime when compared with atom-cavity system.

Giant parabolic nonlinearities at infrared in [formula omitted]-type three level multiple quantum wells

Higher order nonlinear susceptibilities have been investigated in a three level asymmetric multiple quantum well nanostructure wherein a probe pulse and a control laser beam are interacting in Λ-type configuration in the regime of electromagnetically induced transparency. We have identified the existence of giant fifth order susceptibility as large as ∼10−24m4/V4 at a pump wavelength 5.128μm. By changing the value of the Rabi frequency or the pump detuning the peak value of the susceptibility can be obtained at different pump frequency. With the introduction of detuning of the control field, the antisymmetric property of the fifth order susceptibility disappears. The group velocity of the probe field is reported to be slowed down by three order of magnitude in comparison to that of the speed of light in vacuum. These results may have potential applications in optoelectronic devices.

High-Order Nonlinearities of Gold Nanoparticles: The Influence of Size, Filling Factor, and Host

High-order nonlinearities of gold nanoparticles embedded in a nonlinear host were studied using the Maxwell-Garnett model and the degenerate electron gas model. From the nonlinear response, the dependence of the effective third-, fifth-, seventh-, and ninth-order nonlinear optical susceptibilities of gold nanoparticles on the filling factor, the nanoparticle size, and refraction index of the host was calculated. The predicted high-order nonlinear response arose from the enhanced local field factor and was attributed only to the cascaded contribution coming from the third-order nonlinear susceptibility of the nanoparticles. From the calculations, the reversal signal on the high-order nonlinear susceptibilities varying the host refractive index was observed. In addition, tuning the filling factor or the nanoparticle (NP) size, the cancelation of the real part of the third-order susceptibility of the composite material was proposed in order to obtain a refractive macroscopic nonlinear response due only to the real part of the fifth-, seventh-, and ninth-order nonlinearities. It shows a new way to manage the high-order nonlinear optical response of composite materials containing metallic nanoparticles.

Kramers-Kronig relations and high-order nonlinear susceptibilities

As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index ${n}_{2}$ in the near infrared. It was shown that this method allows reproduction of recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of ${n}_{2}$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect (HOKE) dominates in the long-wavelength regime.

Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics

We demonstrate that laser beam collapse in highly nonlinear media can be described, for a large number of experimental conditions, by the geometrical optics approximation within high accuracy. Taking into account this fact we succeed in constructing analytical solutions of the eikonal equation, which are exact on the beam axis and provide (i) a first-principles determination of the self-focusing position, thus replacing the widely used empirical Marburger formula, (ii) a mathematical condition for obtaining the filament intensity, (iii) a benchmark solution for numerical simulations, and (iv) a tool for the experimental determination of the high-order nonlinear susceptibility. Successful comparison with experiment is presented.

Third harmonic autocorrelation and wave mixing in a thin film of poly(p-phenylenevinylene)

We show here that a thin film of a nonlinear conjugated polymer: poly(p-phenylenevinylene) (PPV) is capable of efficiently generating the third harmonic of femtosecond pulses of light at the near infrared (including telecommunication bands) wavelengths, giving coherent, low divergence beams in the visible range. By using more than one fundamental beam overlapping in space and in time on the PPV film, autocorrelation signals are observed as well as higher order mixing signals due to X(5) and higherorder nonlinear susceptibilities. These signals can be used for applications such as short laser pulse diagnostics and photonic signal processing and they provide information about the nonlinear properties of the material itself.

Ionization-induced high-order nonlinear susceptibility

The nonlinear susceptibility of atomic hydrogen interacting with an intense laser field has been investigated using a numerical solution of the time-dependent Schr\"odinger equation. It was shown that the behavior of the nonlinear susceptibility strongly depends on the intensity; it increases linearly in the low-intensity regime (Kerr regime), then saturates at a higher intensity. Furthermore, it was also shown that the nonlinear susceptibility is substantially induced by the ionization, whose magnitude is simply related to the density of the ionized electrons. By analyzing the calculated refractive index, it was found that the refractive index induced by ionization is 7--20 % smaller than that derived from the plasma frequency.

High-order nonlinear susceptibilities of helium

With the goal of providing critically evaluated atomic data for modeling high harmonic generation processes in noble gases, we present calculations of frequency-dependent nonlinear susceptibilities of the ground state of helium, within the framework of Rayleigh-Schr\"odinger perturbation theory at lowest applicable order. The nonrelativistic, infinite-nuclear-mass, atomic Hamiltonian is decomposed in terms of Hylleraas coordinates and spherical harmonics, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. The mixed Hylleraas and Frankowski basis functions are employed to represent accurately the ground-state and perturbed wave functions. We believe our results for nonlinear susceptibilities of helium are the most accurate (and in many cases, the only) available to date, and they are offered as benchmark data for design of future multiphoton experiments.

Nonlinear Response of Granular Composite Medium11The project partly supported by National Natural Science Foundation of China

In this paper, the linear and nonlinear responses of granular composite medium consisting of spherical grains with coating shells embedded in a host medium are studied. We assume that the shell and the host medium are linear (the dielectric constants of which are and respectively), while the spherical grain is nonlinear (the dielectric constant of which is ). Starting from the definition and taking in to account the corrections to the local field within the spherical grains, expressions for the linear and high-order nonlinear susceptibilities are presented.

High order nonlinear susceptibilities of composite medium

We propose an approximate general method for calculating the effective high-order nonlinear susceptibilities of a weakly nonlinear dielectric composite system. General expressions for effective high-order nonlinear susceptibilities are derived. These results are strictly valid if the electric field in each component is uniform. The approximation is applied to two different cases: Low Density Limit, Maxwell-Garnett Approximation, our results are comparable with those of other methods, such as T-matrix approach, perturbation expansion approach.