# Extraction of Bend-Resolved Modal Basis in Deformed Multimode Fiber

This dataset accompanies the manuscript: _Extraction of Bend-Resolved Modal Basis in Deformed Multimode Fiber_ 

This record provides the processed **subset** of off-axis digital holography data underlying the figures presented in the publication, corresponding to excitation with Gaussian spot-like foci. The complete dataset, including excitations with orbital angular momentum (OAM) modes or the original interferograms, is available upon request due to size limitations.

## Data:

All data are stored in MATLAB `rawData.mat` format as a single struct `rD` with the following fields:

### 1. `rD.info`
General information about the dataset:
- `created` — date of creation (MATLAB `datetime`)
- `license` — usage license (e.g. `"CC-BY-4.0"`)
- `matlab` — MATLAB version used for saving

### 2. `rD.data`
Main experimental dataset:
- `fields` — complex output fields at the fiber output (dimensionless)
- `dtype` — MATLAB data type (e.g. `'single'`)
- `shape` — size of the data array _Shape:_ `[Nx, Ny, Nd, Nb]` 
- `order` — axis ordering string  _Order of dimensions:_ `"x-axis, y-axis, displacement, bend"`  

### 3. `rD.axes`
Coordinate vectors and control parameters:
- `dx`, `dy` — pixel size (stored in meters, typically interpreted in µm)
- `x`, `y` — spatial coordinate vectors (stored in meters, typically interpreted in µm)  
- `displacement.idx`, `displacement.idy` — excitation displacement indices (dimensionless)  
- `bend` — bend displacement vector (stored in meters, typically interpreted in mm)  

### 4. `rD.fiber`
Fiber and laser parameters:
- `lambda` — laser wavelength (stored in meters, typically interpreted in nm)  
- `rCore` — fiber core radius (stored in meters, typically interpreted in µm)  
- `rCladd` — fiber cladding radius (stored in meters, typically interpreted in µm)  
- `NA` — numerical aperture (dimensionless)

#### Units

All numerical values are stored in SI units (meters) for consistency.  
For interpretation in the context of the manuscript:

- Multiply by **1e3** to obtain mm (e.g. `bend`).  
- Multiply by **1e6** to obtain µm (e.g. `x`, `y`, `dx`, `dy`, `rCore`, `rCladd`).  
- Multiply by **1e9** to obtain nm (e.g. `lambda`).  

## Figures:

- **Figure 1a** can be constructed from `rd.data.fields` in MATLAB by applying a transparency threshold of $e^{-2}$.
  
- **Figure 1b** can be generated by summing intensities from `rd.data.fields` according to the equations provided in the figure caption.

- **Figures 2 and 3** are based on simulations using the software described in Ref. 42, with parameters set according to those specified in the respective figure captions.

- **Figure 4b** can be reproduced in MATLAB using **Eq (E1 & E2)**.

- **Figure 5a** can be generated from the first three dimensions of `rd.data.fields` by:  
  1. Evaluate the overlap integrals for each deformation state, as specified in **Eq. (1)**. 
  2. Apply singular value decomposition (SVD) to the resulting matrices, following the formulation in **Eq. (2)**.
  3. Derive the per-deformation modal bases in accordance with **Eq. (3)**.
Each singular mode $\eta$ corresponding to bend state $(p)$ is expressed as a linear combination of speckle patterns $\mu$, weighted by the entries of the associated singular vector and normalized by the reciprocal square root of the corresponding singular value $\sigma$.

- **Figure 5b** all three plots for $\mathrm{LG}_{00}$ can be generated by plotting the singular values according to the equations shown next to each curve.

- **Figure 6b & 6c** correlations as well as the cross-sections through singular modes can be constructed by following the equations provided in the figure caption.

- **Figure 7b** the deformation-resolved global basis can be constructed from unified correlation super-matrix following **Eq. (4)**.

- **Figure 8a & 8b** can be reproduced by applying the previously described procedure, with the bent dataset subsampled according to the specific deformation indices indicated in the figure caption.  

- **Figure 9a – 9d** can be reconstructed using the same methodology, restricted to a selected subset of deformation states drawn from the complete dataset.

- **Figure 10b** can be reproduced by following the procedure described in **Appendix B:** Correlative Analysis.

- **Figure 11a** can be reproduced by projecting the bend-resolved singular basis onto the theoretically computed linearly polarized (LP) modes, obtained by solving the eigenvalue equation for a step-index fiber with parameters specified in **Appendix C:** Aligment with Theoretical Eigensolutions.

- **Figure 11b** the top and bottom panels are constructed from the inner products between the corresponding modal bases, while the middle panel displays the propagation constants derived from the theoretical solution of the fiber eigenvalue equation.

- **Figure 12a & 12b** can be reproduced in MATLAB using **Eq (E1 & E2)**.