Calculates non-zero susceptibility tensor components (Electric Dipole, Magnetic Dipole, Electric Quadrupole) and induced transverse Second Harmonic Generation (SHG) source terms for all 32 crystallographic and 122 magnetic point groups.
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Calculator:
- Automatic determination of non-zero and independent components for Electric Dipole (ED,
$\chi^{(2)}$ ), Magnetic Dipole (MD), and Electric Quadrupole (EQ) tensors. - Supports Time-Reversal symmetry toggles (i-type, c-type).
- Real-time calculation of induced nonlinear response in the Lab Frame (
$S_X, S_Y, S_Z$ ) with incoming light propagating along the Z-axis ($E_Z = 0$ ). - Includes crystal rotation controls (
$\theta_X$ ,$\theta_Y$ ) to simulate experimental setups.
- Automatic determination of non-zero and independent components for Electric Dipole (ED,
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Explorer:
- Browse all 122 crystallographic magnetic point groups.
- Filter by crystal system and group type (Ordinary, Gray, Black & White).
- View symmetry operations and properties for each group.
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Simulator:
- Visualize expected SHG intensity polarimetry patterns.
- Adjust crystal orientation, tensor component amplitudes, and phases to simulate parallel and crossed polarization configurations.
- Interactive radar charts displaying SHG intensity as the analyzer angle is rotated.
- Mathematically simplified and summarized expanded formulas using harmonic Fourier series representation (power reduction and multiple-angle formulas).
- Smart grouping algorithm to automatically pick the most elegant representation (power vs harmonic) and minimize unnecessary minus signs.
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Help & Documentation:
- Comprehensive physics background, mathematics behind the intensity calculations, and usage instructions.
The symmetry relations and calculations presented in this app follow the conventions established in the following literature:
- International Tables for Crystallography: General crystal symmetry aspects.
- Birss, R. R. (1966). Symmetry and Magnetism: Magnetic point groups and tensor component calculation.
- Pershan, P. S. (1963). Nonlinear Optical Properties of Solids: Nonlinear optical multipole contributions.
- Fröhlich, D., et al. (1999). Nonlinear spectroscopy of antiferromagnetics: Source term calculation.
- Developed with Google AI Studio Build — Built, iterated, and deployed using natural language prompting.
- React 19 + Vite
- Tailwind CSS for styling
- Lucide React for iconography
- KaTeX (
react-katex) for mathematical rendering - Recharts for radar chart visualizations
- Framer Motion for smooth animations
- GitHub Actions for automated deployment to GitHub Pages
- Clone the repo:
git clone https://github.com/manganite/birss-app.git - Install dependencies:
npm install - Start development server:
npm run dev - Build for production:
npm run build