Nonlinear optics (NLO), the branch of optics, refers to light behavior (the dielectric polarization ** P** responds non-linearly to the electric field strength

**) in media with nonlinear phenomena. The relationship between dielectric polarization**

*E***and field strength**

*P***can be written as follows,**

*E*Figure 1. Second-order nonlinear optical properties

(Pike, N.A. and Pachter R., 2021)

The nonlinear effect is the result of ** E** to the first power and higher power terms working together. In NLO, the superposition principle is no longer valid. With regard to the mechanisms of the optical constants variation, there are some notable types such as electronic optical nonlinearity, thermally induced optical nonlinearity, and external field-induced optical nonlinearity.

Nonlinear optical materials are widely used in energy, quantum communication, health care, and industrial manufacturing. Design of new high-performance functional materials with targeted properties is imperative, while the diversity of potential structures in chemical synthesis and design makes it full of challenges. In order to quickly address the difficulties, nonlinear optical properties analysis services provide a powerful approach to the efficient prediction of functional materials properties. Compared with traditional material design, nonlinear optical properties analysis services employ first-principles calculation, material high-throughput screening, and material properties prediction, shortening the research cycle of material preparation and improving the successful possibility of desirable materials.

### Scope of Analysis

- Optical rectification

The optical rectification effect is a special nonlinear optical effect. It is a process of generating low-frequency electric polarization field (THz) by the interaction of pulsed laser and nonlinear medium. This low-frequency electric polarization field can generate ultra-fast electromagnetic wave radiation. Optical rectification can be used as a non-contact detection approach to study the electro-optic effect of nonlinear materials, and measure the ratio between the second-order nonlinear polarization tensor elements of nonlinear materials.

- High-order harmonic generation

After the fundamental frequency wave of a single frequency is incident on the nonlinear medium, a light wave radiation wave with a frequency three times, four times or even higher than that of the incident light wave (fundamental frequency wave) is generated due to the coupling effect of the high-order nonlinear electrical polarization coefficient. This kind of nonlinear optical phenomenon is called high-order harmonic effect, and the generated light waves are called high-order harmonics. As a coherent broad-spectrum high-energy light source, it can be used to generate attosecond pulses. It can also replace the synchrotron radiation source in the band near and below one hundred electron volts, and is even better than the synchrotron radiation source to a certain extent.

- Frequency mixing

When a beam of strong light and a beam of weak light enter the nonlinear medium at the same time, a three-wave mixing effect can be formed resulting in a frequency mixing phenomenon including sum-frequency generation, difference-frequency generation, optical parametric oscillation and so on. These typical second-order nonlinear phenomena are one of the most mature means to produce optical frequency conversion, which provide new effective approaches for studying physical structure, molecular transition relaxation and condensed matter physical formation.

- Stimulated Raman scattering

Stimulated Raman scattering refers to the strong interaction between high-intensity laser and material molecules, so that the scattering process has the nature of stimulated emission. This kind of scattered light is Raman scattered light and this nonlinear optical effect is called Stimulated Raman scattering. Fiber Raman lasers and fiber Raman amplifiers made by using the Raman effect have gained widespread attention due to their unique characteristics. In addition, the Raman scattering effect and its application in the fiber field have become a hot research topic in the nonlinear optics.

- Optical Kerr effect

An an instantaneous nonlinear effect of light in a medium, optical Kerr effect is related to nonlinear electronic polarization. When there is a strong light propagating in glass and crystals (and some gases), there will be a non-linear optical effect such as the Kerr effect. The Kerr effect is an instantaneous nonlinear response, which can be simply described as the effect on the refractive index. Optical Kerr effect contain the following effect: self-focusing, Kerr-lens modelocking, self-phase modulation, optical solitons, and self-diffraction.

- Optical phase conjugation

Optical phase conjugation is a common technique to overcome the scattering and aberration of inhomogeneous media. This method is also called optical time reversal and has been widely used in the field of microscopic imaging. In recent years, optical phase conjugation technique has also received abroad attention in the application of multimode fiber.

- Multi-photon absorption

In the multi-photon absorption theory, substance may absorb several or even dozens of photons at the same time under the irradiation of a high-intensity laser beam. In the process of multi-photon absorption, the material transitions from the initial state to the final state only through an imaginary intermediate state. Multi-photon absorption is a very common nonlinear physical phenomenon in the interaction between laser and matter. It is an important experimental technique for studying the energy level structure of the excited state of matter, laser-induced fluorescence, chemical reaction control, and various other nonlinear optical processes.

### Common methods

NLO study is of great significance for the development of laser technology, spectroscopy, and material structure analysis. At Alfa Chemistry, we have experienced methods for NLO properties analysis.

- Frequency-domain methods

In a frequency domain method, the unsteady flow is assumed to be composed of a steady and a fluctuating part: where is the steady part of the flow variables while is the fluctuating part. The fluctuating part is harmonic in time for many flows of engineering interest, and the unsteady perturbation flow can be expressed as a Fourier series. Our teams have designed algorithms based on a finite element method which is newly formulated in the frequency domain for the analysis of nonlinear optical waveguide discontinuities. The nonlinear field solutions can be simply obtained by iterating the calculation of linear problem.

- Time-domain numerical modeling

At Alfa Chemistry, we have developed numerical methodologies based on the finite-dif-ference time-domain (FDTD) technique and applied to model optical structures with Raman and Kerr type nonlinearities. Our methods include the alternating-direc-tion implicit finite-difference time-domain (ADI-FDTD) and FDTD based on a recently introduced spatially filtered method. Both of them are able to extend FDTD time steps beyond the conventional Courant-Friedrichs-Lewy stability limit. We use the well-designed time-domain numerical modeling to design and analyze the nonlinear periodic structures. Moreover, we are capable of solving various problems including numerical stability, optical propagation in nonlinear media, peri-odic structures while maintaining a high level of calculation accuracy.

- First-principles calculations

Our nonlinear optical properties analysis platforms support first-principles approaches based on density functional theory with the generalized gradient approximation. We provide several structural parameters, the imaginary and real parts of the frequency-dependent linear optical response, optical functions such as the spectral reflectivity, the absorption coefficient and the electron energy-loss spectrum. In addition, we also study the NLO susceptibilities and calculate the NLO susceptibility tensor.

### Advantages and Features

- Wide applicability
- High accuracy
- High-throughput screening

Our NLO properties analysis includes a very wide scope of NLO to meet your needs in NLO materials.

NLO properties analysis services focus on accuracy to give effective and useful data.

Screening excellent-performance functional materials is our highlight of high-throughput quantum chemistry.

### Customer Notice

### Customers provide

- Specific requirements of nonlinear optical properties analysis services
- Analysis cycle

### We deliver

- Calculation algorithms and methods
- Raw data and analysis results

Alfa Chemistry provides various services of nonlinear optical properties analysis to facilitate your materials research. Our analysis service for accurate prediction of NLO properties is helpful to evaluate the material performance, which reduces the time and cost of later experiments. Our clients have direct access to our staff and instant feedback on their inquiries. If you are interested in our services, please contact us for more details.

References

- Pike, N.A. and Pachter R. Second-order nonlinear optical properties of monolayer transition-metal dichalcogenides by computational analysis.
*J. Phys. Chem. C*2021, 125: 11075-11084. - You, J.W.;
*et al*. Nonlinear optical properties and applications of 2D materials: theoretical and experimental aspects.*Nanophotonics*2019, 8(1): 63-97. - Lei, B.-H.;
*et al*. A module-guided design scheme for deep-ultraviolet nonlinear optical materials.*J. Am. Chem. Soc*. 2018, 140: 10726-10733.