SHG Simulation with KTP Crystal

This repository provides a Python implementation for simulating Second Harmonic Generation (SHG) using a KTP (Potassium Titanyl Phosphate, KTiOPO₄) crystal. The code calculates optical properties of the KTP crystal (refractive index, group index, group velocity) and performs phase-matching calculations for SHG, including the phase mismatch (Δk) and the phase matching function (Φ).

Features

• KTP Crystal Optical Properties:
  • Refractive index calculation using the Sellmeier equation with coefficients from United Crystals.
  • Group index and group velocity computation.
• SHG Phase Matching:
  • Phase mismatch (Δk) calculation based on group velocity mismatch (GVM).
  • Phase matching function (Φ) using the sinc function.
• Vectorized Computations:
  • Supports NumPy arrays for efficient computation over ranges of frequencies or wavelengths.
• Visualization:
  • Example script to plot phase mismatch and phase matching function using Matplotlib.

Installation

Prerequisites

• Python 3.8 or higher
• Required packages:
  • numpy (for numerical computations)
  • matplotlib (for plotting)

Steps

1. Clone the repository:

   git clone https://github.com/your-username/SHG-and-PDC-simulation.git
   cd simulation-ktp

2. (Optional) Create a virtual environment:

   python -m venv venv
   source venv/bin/activate  # On Windows: venv\Scripts\activate

3. Install the required dependencies:

   pip install numpy matplotlib

Usage

The main classes are KTPCrystal and PhaseMatching, located in the cristal.py and nonlinear_optics.py files. Here's a quick example to get started:

Example: Compute and Plot Phase Mismatch and Phase Matching Function

import numpy as np
import matplotlib.pyplot as plt
from shg_simulation import KTPCrystal, SHGPhaseMatching

# Initialize the KTP crystal and SHG phase matching calculator
ktp = KTPCrystal()
phase_matching = PhaseMatching(ktp, lambda_0_um=0.795)  # Fundamental wavelength: 795 nm

# Define a frequency range around the second harmonic frequency
omega_0 = phase_matching.omega_0
omega_range = np.linspace(0.95 * omega_0, 1.05 * omega_0, 100)

# Calculate phase mismatch (Δk) and phase matching function (Φ)
delta_k = phase_matching.phase_mismatch(omega_range)
L = 1e-3  # Crystal length: 1 mm
phi = phase_matching.phase_matching_function(delta_k, L)

# Plot the results
plt.figure(figsize=(12, 5))
plt.subplot(1, 2, 1)
plt.plot(omega_range / omega_0, delta_k, label='Δk(ω)', color='b')
plt.xlabel('Frequency ω / ω₀')
plt.ylabel('Phase Mismatch Δk (m⁻¹)')
plt.title('Phase Mismatch')
plt.grid(True)
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(omega_range / omega_0, phi, label='Φ(ω)', color='r')
plt.xlabel('Frequency ω / ω₀')
plt.ylabel('Phase Matching Function Φ')
plt.title('Phase Matching Function')
plt.grid(True)
plt.legend()

plt.tight_layout()
plt.savefig('phase_mismatch_and_matching.png')
plt.show()

This will generate a plot (phase_mismatch_and_matching.png) showing the phase mismatch and phase matching function over the specified frequency range.

Technical Details

KTP Crystal Optical Properties

The KTPCrystal class calculates the refractive index of KTP using the Sellmeier equation:

[ n^2 = A + \frac{B}{\lambda^2 - C} - D \lambda^2 ]

• (\lambda) is the wavelength in micrometers (μm).
• Coefficients (A), (B), (C), and (D) are sourced from United Crystals.
• The class also computes the group index ((n_g = n - \lambda \frac{dn}{d\lambda})) and group velocity ((v_g = \frac{c}{n_g})).

SHG Phase Matching

The SHGPhaseMatching class calculates:

1. Phase Mismatch (Δk): [ \Delta k = \left( \frac{1}{v_g(2\omega_0)} - \frac{1}{v_g(\omega_0)} \right) (\omega - 2\omega_0) ] Where (v_g(\omega)) is the group velocity at frequency (\omega), and (\omega_0) is the fundamental frequency.

2. Phase Matching Function (Φ): [ \Phi = \text{sinc} \left( \frac{\Delta k L}{2} \right) ] Where (L) is the crystal length in meters.

Contributing

Contributions are welcome! If you'd like to contribute, please follow these steps:

1. Fork the repository.
2. Create a new branch (git checkout -b feature/your-feature).
3. Make your changes and commit them (git commit -m "Add your feature").
4. Push to your branch (git push origin feature/your-feature).
5. Open a Pull Request.

Please ensure your code follows the PEP 8 style guidelines and includes appropriate documentation.

License

This project is licensed under the MIT License. See the LICENSE file for details.

References

• The Sellmeier coefficients for KTP are sourced from United Crystals.
• Inspired by standard nonlinear optics literature, including Nonlinear Optics by Robert W. Boyd.