Features

Dispersion Formulas

FilmOptima provides a range of dispersion models for both the real and imaginary parts of the refractive index. If none of the analytical models are suitable, tabulated data can be used instead, with intermediate values interpolated using cubic splines.

Real

Constant: $n=A_0$
Cauchy: $n(\lambda_0)=A_0+\sum_{i=1}^nB_i\lambda_0^{Ci}$
Conrady: $n(\lambda_0)=A_0+\frac{A_1}{\lambda_0}+\frac{A_2}{\lambda_0^{3.5}}$
Exotic: $n^2(\lambda_0)=A_0+\frac{A_1}{\lambda_0^2-A_2}+\frac{A_3(\lambda_0-A_4)}{(\lambda_0-A_4)^2+A_5}$
Gases: $n(\lambda_0)-1=A_0+\sum_{i=0}^n\frac{B_i}{C_i-\lambda_0^{-2}}$
Lorentz-Drude: $\operatorname{Re}(\epsilon_r(\omega))=\epsilon_r(\infty)+\omega_p^2\sum_{i=1}^M\frac{f_i}{\omega_{0,i}^2-\omega^2+\jmath\omega\Gamma_i}$
Hartmann: $n(\lambda_0)=A_0+\frac{A_1}{\lambda_0-A_2}$
Hartmann-Modified: $n(\lambda_0)=A_0+\frac{A_1}{(\lambda_0-A_2)^2}$
Herzberger: $n(\lambda_0)=A_0+\frac{A_1}{\lambda_0^2-0.028}+A_2\left(\frac{1}{\lambda_0^2-0.028}\right)^2+A_3\lambda_0^2+A_4\lambda_0^4+A_5\lambda_0^6$
Schoitt-Briot: $n^2(\lambda_0)=A_0+A_1\lambda_0^2+\sum_{i=1}^n\frac{B_i}{\lambda_0^{2i}}$
Sellmeier: $n^2(\lambda_0)=A_0+\sum_{i=0}^n\frac{B_i\lambda_0^2}{\lambda_0^2-C_i}$
Sellmeier-Modified: $n^2(\lambda_0)=A_0+\sum_{i=0}^n\frac{B_i\lambda_0^2}{\lambda_0^2-C_i^2}$
Polynomial: $n^2(\lambda_0)=A_0+\sum_{i=1}^nB_i\lambda_0^{C_i}$
RefractiveIndexInfo: $n^2(\lambda_0)=A_0+\frac{B_1\lambda_0^{C_1}}{\lambda_0^2-B_2^{C_2}}+\frac{B_3\lambda_0^{C_3}}{\lambda_0^2-B_4^{C_4}}+B_5\lambda_0^{C_5}+B_6\lambda_0^{C_6}+B_7\lambda_0^{C_7}+B_8\lambda_0^{C_8}$
Datatable: $\text{cubic-spline interpolated}$

Imaginary

Non-Absorptive: $k=0$
Constant: $k=A_0$
Cauchy: $k(\lambda_0)=A_0e^{A_1(\frac{1}{\lambda_0}-\frac{1}{A_2})}$
Exponential: $k(\lambda_0)=A_0e^{\frac{A_1}{\lambda_0}+A_2\lambda_0}$
Lorentz-Drude: $\operatorname{Im}(\epsilon_r(\omega))=\epsilon_r(\infty)+\omega_p^2\sum_{i=1}^M\frac{f_i}{\omega_{0,i}^2-\omega^2+\jmath\omega\Gamma_i}$
Polynomial: $k(\lambda_0)=A_0+\sum_{i=1}^nB_i\lambda_0^{Ci}$
Sellmeier: $k(\lambda_0)=\frac{A_0}{A_1A_2+\frac{A_3}{\lambda_0}+\frac{1}{\lambda_0^3}}$
Datatable: $\text{cubic-spline interpolated}$

Optical Characteristics

Conventional, phase, and layer-specific outputs available during optimization and analysis.

Conventional

R - Reflectance (s-pol, p-pol, avg)
T - Transmittance (s-pol, p-pol, avg)
A - Absorptance (s-pol, p-pol, avg)

Phase

pR / pT - Phase Shift (s-pol, p-pol)
GDR / GDT - Group Delay
GDDR / GDDT - Group Delay Dispersion

Layer-Specific

LA - Layer Absorptance
LOA - Local Absorption
E - Electric Field

Coherence Models

Select the propagation model that matches your stack's physical coherence behavior.

Coherent Stack

All optical characteristics.

Incoherent Stack

R/T/A.

Hybrid (Mixed) Stack

R/T/A.

Algorithms

Explore FilmOptima's algorithm portfolio by category and jump to detailed documentation for each method.

Refinement

AdamW

Adaptive local refinement

Iteratively adjusts existing layer thicknesses using momentum and adaptive learning rates for stable, efficient convergence.

ClusterRefinement

Proprietary

Cluster-based candidate refinement

Enumerates clustered layer-thickness candidates and polishes each with AdamW to escape shallow local minima.

Synthesis

Needle

Zero-thickness synthesis

Builds designs by inserting zero-thickness layers at high-impact positions and refining the full stack after each insertion.

AnyNeedle

Proprietary

Finite-thickness synthesis

Extends Needle method by evaluating insertion depth and finite thickness candidates, then accepting the best refined stack.

Global Optimization

BranchAndBound

Bounded global search

Systematically partitions thickness space and prunes subregions using merit bounds to target globally superior solutions.

ParticleSwarmOptimization

Swarm-based exploration

Uses a population of particles that balance personal and social learning signals to discover high-quality regions.

Stochastic

Randomized global sampling

Performs repeated random initializations within bounds and refines each candidate to improve near-global search coverage.

How It Works

Datamanagement

FilmOptima employs a relational SQL database to ensure data integrity and efficient storage. Common entities like general targets or materials are stored only once and referenced across multiple user designs.

Flexible Optimization Control

Define your goals (e.g., max layers, max optimization duration) as stopping conditions, and hand-pick the algorithms to use. Our engine runs your chosen algorithms in round-robin manner.

Hands-Free Queue

Queue multiple designs for sequential processing, perfect for running long optimizations overnight or while you focus on other tasks.