The Birss App

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.

Live Demo

Features

• 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.
• 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.
• 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.
• Help & Documentation:
  • Comprehensive physics background, mathematics behind the intensity calculations, and usage instructions.

Conventions & References

The tensor component output follows the conventions of Birss, Symmetry and Magnetism (1966): the y-axis secondary convention for trigonal and hexagonal groups (σ(2)=[2_y], σ(4)=[-2_y]), and the z-unique monoclinic setting. The app's rank-3 polar tensor output has been verified against all 21 rows of Birss Table 4e. Point group names use Hermann–Mauguin notation with ITC-style rendering (overbars for roto-inversions, primes for time-reversed operations).

• Birss, R. R. (1966). Symmetry and Magnetism: Authoritative source for magnetic point groups and tensor component calculation. Reference tables typeset in manganite/birss-tables.
• International Tables for Crystallography: General crystal symmetry aspects. See DISCREPANCIES.md for a detailed comparison of Birss vs ITC conventions.
• 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.

Validation & Testing

The tensor-calculation engine (src/services/) is covered by a Vitest suite of 490+ tests, organized in tiers of increasing specificity:

• Tier 1 — group order: for all 122 magnetic point groups, getSymmetryOperations returns a group of the expected order.
• Tier 1b — true closure: for all 122 groups, every pairwise product of elements in the closed group is itself a member, independently verifying the floating-point-hardened closure algorithm in symmetryGroups.ts.
• Tier 2 — parity invariants: for all 122 groups, structural invariants such as "ED vanishes for centrosymmetric groups", "EQ never vanishes", and "grey groups G1' reproduce G for i-type tensors".
• Tier 3 — golden component relations: 40+ fixtures pinning down the exact independent-component relations for specific (group, tensor type, time-reversal) combinations. Includes all 21 Birss Table 4e symbol classes (A3–U3) at rank 3, every Type-III crystal family, c-type ED (e.g. the canonical Cr₂O₃ -3'm' magnetoelectric tensor), axial (MD) tensors, and rank-4 EQ. See src/services/goldenTensors.fixtures.ts for sources and citations.

Tech Stack

• 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

Running Locally

1. Clone the repo: git clone https://github.com/manganite/birss-app.git
2. Install dependencies: npm install
3. Start development server: npm run dev
4. Build for production: npm run build

Project History

This repository was originally bootstrapped from a Google AI Studio app export; the application has since been fully rewritten and no scaffold code remains.

Changelog

See CHANGELOG.md for release history.

License

This project is licensed under the MIT License.