toftul / tensors-in-curvilinear-coordinates

In various curvilinear coordinates

Done in SymPy. General formula is $$\chi^{(2)}_{(\ell n m)_{\text{curv}}}= R_{\ell i} R_{n j} R_{m k} \chi^{(2)}_{(ijk)_{\text{cart}}}$$ where rotation matrix $\hat{R}$ is defined as $$\mathbf{A}^{\text{curv}} = \hat{R}^{-1} \mathbf{A}^{\text{cart}}$$

In literature

This code was used in:

• Toftul, I., Fedorovich, G., Kislov, D., Frizyuk, K., Koshelev, K., Kivshar, Y., & Petrov, M. (2023). Nonlinearity-Induced Optical Torque. Phys. Rev. Lett., 130(24), 243802. doi: 10.1103/PhysRevLett.130.243802