Optimization Analysis

Dispersion Analysis

Phase, GD, GDD, DGD analysis for pulse broadening and chromatic dispersion

This page covers the dispersion detector group: Phase, GD (Group Delay), GDD (Group Delay Dispersion), and DGD (Differential Group Delay). These detectors are used for pulse broadening evaluation, chirp compensation coating design, PMD (Polarization Mode Dispersion) assessment, and chromatic dispersion budget analysis. The current software does not expose Phase / GD / GDD / DGD as direct optimization targets. The standard workflow is Run -> Sweep -> Results.

Relevant result pages:

Dispersion results: Phase, GD, GDD, DGD
Basic Optical Results

Example Setup

The following screenshots show the structure and optics configuration used for dispersion analysis:

Dispersion Analysis Structure Setup

Dispersion Analysis Optics Setup

Prerequisites

Condition	Current requirement
Detector activation	Enable one or more of `Phase`, `GD`, `GDD`, `DGD` in `Optics > Dispersion`
Wavelength mode	`Sweep` mode required; `Single` and `Average` modes do not produce dispersion spectra
Structural coherence	Fully coherent stack recommended; incoherent layers may degrade the physical meaning of phase-based quantities
Cone Angle	Not supported for dispersion detectors
Analysis entry	`Run` and `Run Sweep`
Optimization entry	No direct `Phase / GD / GDD / DGD` target is currently available

Physical Definitions

Detector	Definition	Unit
Phase (φ)	Spectral phase of the transmitted or reflected complex amplitude	rad
GD	Group Delay: first derivative of phase with respect to angular frequency, GD = −dφ/dω	fs or ps
GDD	Group Delay Dispersion: second derivative of phase, GDD = d²φ/dω²	fs² or ps²
DGD	Differential Group Delay: difference in group delay between s- and p-polarization components	fs or ps

GD describes the delay experienced by a pulse envelope. GDD describes how different frequency components experience different delays, leading to pulse broadening. DGD quantifies polarization-dependent delay differences relevant to PMD.

Application Scope

Scenario	Main question	Recommended detectors	Recommended sweeps
Pulse broadening in ultrafast optics	Does the coating introduce excessive GDD that broadens femtosecond pulses?	`GDD`, `Phase`	`structure layer thickness`, wavelength range
GDD compensation coating design	Can the layer thicknesses be tuned to produce a target GDD profile?	`GDD`, `GD`	`structure layer thickness`
PMD evaluation in telecom coatings	Is the DGD within acceptable bounds across the operating band?	`DGD`, `GD`	`optics/incidentAngle`, `structure layer thickness`
Chromatic dispersion budget	What is the total GDD contribution of this coating in the system?	`GDD`, `Phase`	wavelength range extension
Phase ripple analysis	Are there rapid phase oscillations that degrade pulse fidelity?	`Phase`, `GD`	wavelength step refinement

Common Problems and Diagnostics

Problem	Symptom	Recommended action
Excessive GDD	Pulse broadening beyond tolerance in the target band	Sweep layer thicknesses to find a GDD minimum; verify with `Phase` continuity
Uncontrolled DGD	Polarization-dependent pulse distortion	Sweep `incidentAngle` and `pRatio` to isolate the angular sensitivity; check at normal incidence first
Phase ripple	Rapid oscillations in `Phase` or `GD` spectra	Reduce wavelength step for finer sampling; check whether ripple correlates with thin-layer interference
Low confidence at spectral edges	GD and GDD values show large fluctuations near the wavelength range boundaries	Extend the wavelength range beyond the region of interest; edge artifacts from numerical differentiation are expected
GDD sign ambiguity	Confusion between positive and negative chirp	Verify the sign convention by comparing with a known dispersive substrate

GD and GDD are computed from numerical differentiation of the spectral phase. Results near the edges of the wavelength range may exhibit increased noise. Extend the wavelength range beyond the region of interest to reduce edge artifacts.

Recommended Sweep Strategy

Goal	Sweep parameter	Expected output
GDD sensitivity to layer thickness	`structure/{layer}/thickness`	GDD spectrum family; identify thickness values that flatten or invert GDD
Phase continuity check	Wavelength step refinement (decrease step size)	Smoother `Phase` curve; confirm absence of phase jumps
Angular dependence of DGD	`optics/incidentAngle`	DGD vs. angle; identify the angular range with minimal PMD
Multi-layer GDD optimization preparation	Multiple layer thicknesses	Parameter sensitivity map for downstream manual or R/T/A-based optimization

Result Review Order

Start by checking the Phase page to verify phase continuity:

Phase φ(λ) Result Page

Then focus on the GDD page to quantify the pulse broadening contribution:

GDD Result Page

Step	Detector	Purpose
1	`Phase`	Verify phase continuity; identify spectral regions with smooth vs. rapid phase variation
2	`GD`	Confirm group delay profile; identify delay peaks and flat regions
3	`GDD`	Quantify pulse broadening contribution; locate GDD zero-crossings and sign changes
4	`DGD`	Evaluate polarization mode dispersion; confirm acceptable DGD across the operating band
5	`Reflectance` / `Transmittance`	Back-check energy performance; confirm that dispersion optimization does not degrade spectral targets

Relation to the Optimizer

Item	Current status
Direct `Phase / GD / GDD / DGD` optimization	Not supported
Indirect approach	Use `Sweep` to identify parameter sensitivity, then optimize `R / T / A` with Curve Fit or Scalar goals to achieve the spectral profile that corresponds to acceptable dispersion
`optics` variables as optimization variables	Not exposed in the current UI
`R / T / A` back-check	Recommended after any dispersion-driven parameter adjustment

Although dispersion detectors cannot be used as direct optimization targets, the Sweep analysis identifies which structural parameters most strongly affect GDD. Use that information to define the optimization variable set and constrain the R/T/A optimization to a parameter region with acceptable dispersion.

Conclusion Boundaries

The current software supports Phase, GD, GDD, and DGD prediction and sweep-based parameter sensitivity analysis.
The current software does not support direct optimization toward a target GDD or DGD value.
Dispersion results require wavelength Sweep mode; they are not produced in Single or Average mode.
Cone Angle averaging is not applied to dispersion detectors.

Case Study Entry

For full structures and workflows, see Case Studies. Future cases will cover GDD compensation for ultrafast mirror coatings, PMD evaluation for telecom filter stacks, and chirped mirror design.

Next Step

If the problem involves system-level reflectance or transmittance targets, return to RTA and Layer Absorption Analysis. For full application workflows, proceed to Case Studies.

Depth Detector Analysis

Depth distribution, local absorption, and field enhancement analysis

Case Studies

Application cases, reproductions, and the entry point for future expansions