Optical Vortex BEMD Processing

Numerical analysis of optical vortex generation with helical filter using empirical mode decomposition

A complete framework for processing optical vortex electromagnetic field data using BEMD (Bidimensional Empirical Mode Decomposition) for noise reduction and signal enhancement.

Figure 1: FDTD electromagnetic simulation showing l=1 right-handed optical vortex at 84GHz frequency

Overview

This project demonstrates the application of BEMD to optical vortex analysis, specifically processing FDTD (Finite-Difference Time-Domain) electromagnetic simulation data. The framework separates high-frequency noise from the main optical vortex structure, enabling cleaner analysis and visualization of vortex characteristics.

Features

• Complete Pipeline: From raw FDTD data to processed visualization
• BEMD Integration: Sophisticated noise reduction using empirical mode decomposition
• Component-wise Processing: Separate analysis of E, V1, V2, V3 field components
• Intelligent Visualization: Comparative analysis showing original, noise, and denoised fields
• Error Handling: Robust processing with fallback mechanisms

Method

BEMD Processing Logic

1. Component Separation: Process E, V1, V2, V3 components separately
2. IMF Extraction: Extract 3 Intrinsic Mode Functions (IMFs) for each component
   • IMF1: High-frequency noise component
   • IMF2 + Residual: Main optical vortex structure
3. Field Reconstruction: Combine components to reconstruct field intensity
4. Visualization: Generate comparative analysis plots

Physical Significance

• Original Field: Complete electromagnetic field including noise
• IMF1 (Noise): High-frequency computational artifacts and noise
• Denoised Field: Clean optical vortex structure with preserved physics

Quick Start

Prerequisites

• Python 3.7+ with numpy, matplotlib, scipy, pandas, opencv-python
• MATLAB with Signal Processing Toolbox
• 4GB+ RAM for processing

Installation

git clone https://github.com/yourusername/optical_vortex_BEMD.git
cd optical_vortex_BEMD/example
pip install -r requirements.txt

Running the Example

python run_example.py

The example processes a single time step (1005) from l=1 right-handed optical vortex simulation at 84GHz.

Example Results

The processing generates a comprehensive 2×3 visualization showing the BEMD decomposition:

Figure 2: BEMD analysis results showing (top row) field intensities and (bottom row) vector fields

Top Row (Field Intensities):

• Left: Original electromagnetic field with noise
• Center: IMF1 component (extracted high-frequency noise)
• Right: Denoised field showing clean optical vortex structure

Bottom Row (Vector Fields):

• Vector field visualizations corresponding to each intensity map
• Clear vortex rotation pattern visible in original and denoised fields
• Noise component shows random/chaotic vector patterns

Energy Analysis Results

• Original Energy: 2.15×10¹⁵
• IMF1 (Noise): 4.97×10¹³ (2.3% of total energy)
• Denoised Signal: 9.92×10¹⁴ (46.1% of total energy)

This demonstrates that BEMD successfully separates a small but significant noise component while preserving the main optical vortex structure.

Processing Steps

Step 1: Data Processing (step1_data_processing.py)

• Reads FDTD simulation data from CSV format
• Extracts Ex, Ey, Ez field components
• Calculates field intensity and vector components
• Crops data to focus on optical vortex region (560×560)
• Saves data in MATLAB format

Step 2: BEMD Processing (step2_bemd_processing.m)

• Applies BEMD to each component (E, V1, V2, V3) separately
• Extracts 3 IMFs (Intrinsic Mode Functions) per component
• Saves BEMD results in compatible format
• Generates verification plots

Step 3: Visualization (step3_visualization.py)

• Loads original data and BEMD results
• Generates 2×3 comparative visualization
• Calculates energy analysis and statistics
• Saves analysis summary

Data Format

Input Data

• Format: CSV files with FDTD simulation results
• Structure: x, y, z, Ex, Ey, Ez columns
• Example: loam1/exy/exy1005.csv (24MB, single time step)

Output Files

• Data Files: loam1*.mat (MATLAB format data)
• BEMD Results: loam1data_BIMF0_*.mat (decomposition results)
• Visualization: bemd_analysis_1005.png (main analysis plot)
• Summary: bemd_analysis_summary_1005.txt (statistics)

Technical Details

BEMD Algorithm

• Uses bidimensional empirical mode decomposition
• Extracts 3 IMFs per component
• Processes spatial data in 2D domain
• Preserves local characteristics of optical vortex

Performance

• Processing Time: ~5 minutes for single time step
• Memory Usage: ~4GB peak
• Data Size: 44MB output for single step
• Spatial Resolution: 560×560 grid points

File Structure

optical_vortex_BEMD/
├── README.md                    # This documentation
├── LICENSE                      # MIT License
├── .gitignore                   # Git ignore rules
├── example/                     # Complete working example
│   ├── requirements.txt         # Python dependencies
│   ├── run_example.py          # Main execution script
│   ├── step1_data_processing.py # Data processing
│   ├── step2_bemd_processing.m  # BEMD decomposition
│   ├── step3_visualization.py   # Analysis and plots
│   └── output/                  # Results directory
├── bemd/                        # BEMD algorithm library
│   ├── bemd.m                  # Core BEMD algorithm
│   └── license.txt             # Algorithm license
└── loam1/                       # Sample simulation data
    ├── simulation_info.md       # Simulation parameters
    ├── tmp.png                 # Example simulation image
    └── exy/exy1005.csv         # FDTD data (time step 1005)

Validation

The processing has been validated against reference implementations:

✅ Data Structure: Correct (height, width, nimfs) format
✅ Component Processing: Separate E, V1, V2, V3 processing
✅ IMF Extraction: Proper IMF1 (noise) and IMF2+Residual (signal)
✅ Field Reconstruction: Accurate intensity calculations
✅ Visualization: Consistent 2×3 layout and scientific presentation

Troubleshooting

Common Issues

1. MATLAB not found: Ensure MATLAB is installed and in PATH
2. Missing data file: Check loam1/exy/exy1005.csv exists
3. Memory issues: Ensure sufficient RAM (4GB+)
4. Package errors: Run pip install -r requirements.txt

Parameter Adjustment

• Modify crop_size in step1 for different region sizes
• Adjust nimfs in step2 for different IMF counts
• Change step_viz and alpha in step3 for vector field visualization

Applications

• Optical Vortex Analysis: Clean extraction of vortex characteristics
• Noise Reduction: Removal of computational artifacts from simulations
• Signal Enhancement: Improved visualization of electromagnetic phenomena
• Research Tool: Framework for optical vortex beam analysis
• Educational: Demonstration of advanced signal processing techniques

Extension

To process multiple time steps:

1. Modify target_step parameter in each script
2. Update file paths and loops accordingly
3. Consider memory and processing time requirements

Citation

If you use this framework in your research, please cite the following paper:

@article{dong2025numerical,
  title={Numerical analysis of optical vortex generation with helical filter using empirical mode decomposition},
  author={Dong, Ran and Fujita, Yoshihisa and Nakamura, Hiroaki and Kawaguchi, Hideki and Ikuno, Soichiro},
  journal={International Journal of Applied Electromagnetics and Mechanics},
  pages={13835416251330972},
  year={2025},
  publisher={SAGE Publications Sage UK: London, England}
}

License

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