feat: Add EMEInterfaceSMatrixMonitor (FXC-4275)

[caseyflex]

This PR:

• Adds a new monitor and data classes to record cell interface s matrix data. This is normally used in the EME solver, but is sometimes needed for optimizing structures
• Fixes the documentation a bit for frequency interpolation in EME
• Changes the EME num_freqs validation to use sampling points, with a larger limit for the overall interpolated freqs
• Changes default num_sweep from 1 to None for EMECoefficientMonitor

Note: the interface s matrices are not currently normalized. To normalize S21 for example, you need to multiply by sqrt(abs(real(flux2)/real(flux1))), where flux1 and flux2 are the flux in cell 1 and cell 2, respectively. In the future, we can add a flag normalize to this monitor and EMECoefficientMonitor, and maybe make it default to True.

Greptile Overview

Greptile Summary

This PR adds EMEInterfaceSMatrixMonitor to record cell-interface S-matrices in the EME solver, which is useful for structure optimization. The implementation follows established patterns in the codebase by creating the full class hierarchy (monitor, data array, dataset, and monitor data classes) and properly exporting them in the public API.

Key changes:

• Added EMEInterfaceSMatrixMonitor with appropriate field overrides for interval_space, eme_cell_interval_space, and num_sweep
• Created corresponding data classes: EMEInterfaceSMatrixDataArray (5D with dimensions for f, sweep_index, eme_cell_index, mode_index_out, mode_index_in), EMEInterfaceSMatrixDataset, and EMEInterfaceSMatrixData
• Changed default num_sweep from 1 to None in EMECoefficientMonitor to record all sweep indices by default
• Improved EME frequency validation to distinguish between sampling points (for mode solving) and total interpolated frequencies, raising the limit for the latter from 500 to 2000
• Updated documentation to clarify frequency interpolation behavior in EME simulations
• Added comprehensive tests for the new monitor and data classes

Confidence Score: 5/5

• This PR is safe to merge with minimal risk
• The implementation follows established patterns consistently, includes comprehensive tests, and all previous review comments have been addressed. The changes are well-structured with proper inheritance hierarchy, documentation, and API exports.
• No files require special attention

Important Files Changed

File Analysis

Filename	Score	Overview
tidy3d/components/eme/monitor.py	5/5	Added EMEInterfaceSMatrixMonitor class with fields and storage size calculation; moved num_sweep from base EMEMonitor to specific monitor classes
tidy3d/components/eme/data/monitor_data.py	5/5	Added EMEInterfaceSMatrixData class that combines monitor with dataset, following standard pattern
tidy3d/components/data/data_array.py	5/5	Added EMEInterfaceSMatrixDataArray class with 5-dimensional structure for interface S-matrix data
tidy3d/components/eme/data/dataset.py	5/5	Added EMEInterfaceSMatrixDataset with S11, S12, S21, S22 fields mirroring EMESMatrixDataset structure
tidy3d/components/eme/simulation.py	5/5	Updated frequency validation to use sampling points with higher limits for interpolated frequencies; improved documentation

Sequence Diagram

sequenceDiagram
    participant User
    participant EMESimulation
    participant EMEInterfaceSMatrixMonitor
    participant EMEInterfaceSMatrixData
    participant EMEInterfaceSMatrixDataset
    participant EMEInterfaceSMatrixDataArray

    User->>EMESimulation: Create simulation with EMEInterfaceSMatrixMonitor
    EMESimulation->>EMEInterfaceSMatrixMonitor: Validate monitor configuration
    EMEInterfaceSMatrixMonitor->>EMEInterfaceSMatrixMonitor: Check num_modes, freqs, num_sweep
    EMEInterfaceSMatrixMonitor->>EMESimulation: Calculate storage_size()
    
    User->>EMESimulation: Run simulation
    EMESimulation->>EMESimulation: Solve EME cells and compute interface S-matrices
    EMESimulation->>EMEInterfaceSMatrixDataArray: Create data arrays for S11, S12, S21, S22
    Note over EMEInterfaceSMatrixDataArray: Dimensions: (f, sweep_index, eme_cell_index, mode_index_out, mode_index_in)
    
    EMEInterfaceSMatrixDataArray->>EMEInterfaceSMatrixDataset: Populate S11, S12, S21, S22 fields
    EMEInterfaceSMatrixDataset->>EMEInterfaceSMatrixData: Combine with monitor reference
    EMEInterfaceSMatrixData->>User: Return simulation data
    
    User->>EMEInterfaceSMatrixData: Access interface S-matrices
    Note over User,EMEInterfaceSMatrixData: S-matrix at eme_cell_index=i<br/>is between cells i and i+1

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[caseyflex]

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[caseyflex]

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Diff Coverage

Diff: origin/develop...HEAD, staged and unstaged changes

• tidy3d/init.py (100%)
• tidy3d/components/data/data_array.py (100%)
• tidy3d/components/eme/data/dataset.py (100%)
• tidy3d/components/eme/data/monitor_data.py (100%)
• tidy3d/components/eme/monitor.py (100%)
• tidy3d/components/eme/simulation.py (100%)

Summary

• Total: 37 lines
• Missing: 0 lines
• Coverage: 100%

[yaugenst-flex]

Thanks @caseyflex just some minor comments!

[yaugenst-flex]

I guess we should capitalize "S-matrix" here? I noticed the spelling is a bit inconsistent and I think capital S is most common.

[yaugenst-flex]

Inconsistent spelling here too

[caseyflex]

Thanks @caseyflex just some minor comments!

Thanks! Will incorporate these, but I’m going to change the api significantly after some discussions so will close this in favor of a new PR

[caseyflex]

Partially subsumed by #3032 (just the easy stuff)

The actual interface S matrices will come in a separate PR