Theory

Depth-Resolved Quantities

Energy flux, absorption, and electric fields versus depth

Depth-resolved quantities describe how energy flux, absorption, and fields are distributed through the thickness of the stack. They are used to locate standing waves, local absorption peaks, and field-enhancement regions.

Scope of this chapter

QuantityFocusResult page
Poynting VectorNet energy-flow distribution through depthDepth-Distribution Results
Absorption DensityLocation of local dissipationDepth-Distribution Results
Electric FieldMagnitude, phase, and component variation through depthDepth-Distribution Results
Data structureOrganization of wavelength-depth matricesDepth-Distribution Results

Shared data structure of depth outputs

The app stores depth outputs as matrices over a globally expanded depth axis.

Data itemCurrent structurePhysical meaning
depth_point_list1D arrayGlobal depth coordinates in nm
layer_info_listPer-layer start and end depth metadataUsed to mark layer boundaries in plots
Depth matricesTypically [wavelength_index][depth_index]Distribution versus depth at each wavelength
Complex electric-field valuesEx / Ey / Ez stored as [real, imag]Used to derive magnitude and phase displays

When reading these plots or tables, separate the two axes:

  1. the wavelength dimension;
  2. the depth dimension through the stack.

Heatmaps and tables are different views of the same matrix data. Sweep views add the parameter-combination dimension on top of that matrix.

Poynting Vector: energy flow through the stack

The Poynting Vector page shows the normalized normal (z-direction) component of the energy flux.

Reading pointPractical use
Higher values indicate stronger net forward energy flow at that depthDetermine the main energy-transport path
A continuous decay with depth usually indicates absorptionQuickly identify the loss location
Strong variation near interfaces usually indicates interference or standing-wave redistributionJudge whether interface reflections are dominating the field pattern

Use this quantity to check:

  1. whether optical power reaches the target region;
  2. whether power is mainly reflected or dissipated near the front of the stack.

Absorption Density: local dissipation

Absorption Density measures local energy dissipation per unit volume. For total absorption by layer, compare it with Layer Absorption in Basic Optical Results.

Reading pointPractical use
Peak regions correspond to the strongest local absorptionLocate the active absorber or parasitic loss layer
If strong absorption appears in a layer that should be nearly transparent, the material model is likely wrongCheck index files and stack ordering
Compared together with Poynting Vector, it separates “energy passing through” from “energy being consumed”Distinguish transport-limited behavior from absorption-limited behavior

For absorbing devices, this directly shows whether the absorption occurs in the intended layer.

Electric Field: magnitude, phase, and components

The Electric Field page includes component, magnitude, and phase information.

ViewCurrent dataMain information
ComponentsEx, Ey, EzDominant field direction
MagnitudeDerived Magnitude viewField-enhancement locations
PhaseEx_phase, Ey_phase, Ez_phaseNodes, phase jumps, and standing-wave structure

The three views expose different information:

  1. Magnitude: location of field enhancement;
  2. Component: dominant field component;
  3. Phase: nodes, phase flips, and standing-wave structure.

Resolution and data-volume limits

The most common failure mode in depth-resolved analysis is excessive data volume. The frontend applies explicit thresholds to keep rendering stable.

ItemCurrent thresholdPurpose
Maximum table rows500,000Above this, table rendering is blocked
Maximum 2D chart points500,000Above this, chart rendering is blocked or downgraded
Maximum scatter3D points80,000Stricter 3D limit because GPU and memory load are higher
Maximum bar3D points50,0003D bar geometry is more expensive than scatter
Chart optimization threshold100,000Above this, smoothing, animations, and dense point markers are reduced
Single-request TMM solve count50,000Backend safety limit to prevent timeout or memory exhaustion

As Depth Resolution becomes smaller, the number of depth points increases. As total thickness increases, it also increases. Therefore:

  1. a finer resolution is denser, not automatically better;
  2. a thick substrate kept coherent can create very large datasets;
  3. in sweep mode, total data size also scales with the number of parameter combinations.

Field-related detectors depend on coherent field solutions. Refractive Index only expands the structure itself and does not require a fully coherent stack.

DetectorRequires a fully coherent stackReason
Poynting VectorYesIt depends on the coherent field solution
Absorption DensityYesIt depends on coherent fields and local dissipation
Electric FieldYesIt directly uses field components and phase
Refractive IndexNoIt is only a depth expansion of the structure, not a coherent field result

Use Refractive Index when you only need to verify the expanded structure. Use field and energy-flow detectors only with a fully coherent stack.

Analysis order

Use the depth outputs in this order:

  1. Poynting Vector: confirm whether energy reaches the region of interest.
  2. Absorption Density: locate where that energy is dissipated.
  3. Electric Field: explain enhancement, nodes, and component-dependent behavior.
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