# Training Videos

## Nonlinear Optical Interactions

This is a continuation from the previous tutorial - nonlinear optical susceptibilities. Optical susceptibilities in the frequency domain are, in general, complex quantities. Following the same convention, used in the linear optical susceptibility tutorial and the material dispersion tutorial for complex linear susceptibility in the frequency domain, complex nonlinear susceptibilities in the frequency domain can be expressed as $$\boldsymbol{\chi}^{(2)}=\boldsymbol{\chi}^{(2)'}+\text{i}\boldsymbol{\chi}^{(2)''}$$ and $$\boldsymbol{\chi}^{(3)}=\boldsymbol{\chi}^{(3)'}+\text{i}\boldsymbol{\chi}^{(3)''}$$ to define their real and imaginary parts clearly. Similarly to the case of linear susceptibility discussed in the material dispersion tutorial, the imaginary part of a nonlinear susceptibility is always associated with the intrinsic resonances of a material. Such resonances signify...

## Nonlinear Optical Susceptibilities

This is a continuation from the previous tutorial - optical nonlinearity. The nonlinear optical properties of a material are characterized by its nonlinear optical susceptibilities. In this tutorial, the general properties of nonlinear optical susceptibilities are discussed. It can be seen from (9-3) and (9-4) [refer to the optical nonlinearity tutorial] that the space- and time-dependent nonlinear susceptibilities $$\boldsymbol{\chi}^{(n)}(\mathbf{r}-\mathbf{r}_1,t-t_1;\mathbf{r}-\mathbf{r}_2,t-t_2;\ldots;\mathbf{r}-\mathbf{r}_n,t-t_n)$$ are real tensors because both $$\pmb{P}^{(n)}(\mathbf{r},t)$$ and $$\pmb{E}(\mathbf{r},t)$$ are real vectors. Though $$\boldsymbol{\chi}^{(n)}(\mathbf{r}_1,t_1;\mathbf{r}_2,t_2;\ldots;\mathbf{r}_n,t_n)$$ is always a real function of space and time, its Fourier transform is generally complex. Therefore, the frequency-dependent nonlinear susceptibilities $$\boldsymbol{\chi}^{(n)}(\omega_q=\omega_1+\omega_2+\cdots+\omega_n)$$ defined in the frequency domain are generally...

## Optical Nonlinearity

This is a continuation from the previous tutorial - guided-wave acousto-optic devices. The functioning of electro-optic, magneto-optic, and acousto-optic devices discussed in the earlier tutorials is based on the fact that the optical properties of a material depend on the strength of an electric, magnetic, or acoustic field that is present in an optical medium. At a sufficiently high optical intensity, the optical properties of a material also become a function of the optical field. Such nonlinear response to the strength of the optical field results in various nonlinear optical effects. Nonlinear optics is an established broad field with applications...