Multilayer optical calculations
arXiv:1603.02720
Abstract
When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it are difficult to find explicitly and consistently worked out in the literature. Here, we derive the formulas underlying the transfer-matrix method of calculating the optical properties of these stacks, including oblique-angle incidence, absorption-vs-position profiles, and ellipsometry parameters. We discuss and explain some strange consequences of the formulas in the situation where the incident and/or final (semi-infinite) medium are absorptive, such as calculating in the absence of gain. We also discuss some implementation details like complex-plane branch cuts. Finally, we derive modified formulas for including one or more "incoherent" layers, i.e. very thick layers in which interference can be neglected. This document was written in conjunction with the "tmm" Python software package, which implements these calculations.
20 pages including appendices. Changed in version 5: Fixed one minor typo - "Layer 5" --> "Layer 6" in Figure 3
References in corpus (1)
Cited by in corpus (25)
- Temperature Dependent Thermal Boundary Conductance of Monolayer MoS by Raman Thermometry
- Temperature-independent thermal radiation
- Dry release transfer of graphene and few-layer h-BN by utilizing thermoplasticity of polypropylene carbonate for fabricating edge-contact-free van der Waals heterostructures
- TMM-Fast: A Transfer Matrix Computation Package for Multilayer Thin-Film Optimization
- Solcore: A multi-scale, python-based library for modelling solar cells and semiconductor materials
- Fast and anomalous exciton diffusion in two-dimensional hybrid perovskites
- Autoionization and dressing of excited excitons by free carriers in monolayer WSe2
- Dark exciton-exciton annihilation in monolayer WSe
- Time-dependent screening explains the ultrafast excitonic signal rise in 2D semiconductors
- Parameterized Reinforcement Learning for Optical System Optimization
- A New Optical Model for Photomultiplier Tubes
- Investigation of Magnetic Anisotropy and Heat Dissipation in Thin Films of Compensated Antiferromagnet CuMnAs by Pump-probe Experiment
- Non-destructive Characterization of Anti-Reflective Coatings on PV Modules
- Investigation of inverse design of multilayer thin-films with conditional invertible Neural Networks
- Active Control of Polariton-Enabled Long-Range Energy Transfer
- Ultra-low energy threshold engineering for all-optical switching of magnetization in dielectric-coated Co/Gd based synthetic-ferrimagnet
- Anti-reflection Coated Vacuum Window for the Primordial Inflation Polarization ExploreR (PIPER) balloon-borne instrument
- On performance of thin-film meso-structured perovskite solar cell through experimental analysis and device simulation
- A novel guided deep learning algorithm to design low-cost SPP films
- TMMax: High-performance modeling of multilayer thin-film structures using transfer matrix method with JAX
- Automated Optical Multi-layer Design via Deep Reinforcement Learning
- Photo-physics and electronic structure of lateral graphene/MoS2 and metal/MoS2 junctions
- Reconsidering the design of planar plasmonic lasers: gain, gap layers, and mode competition
- Increased formation of trions and charged biexcitons by above-gap excitation in single-layer
- Approximations used in the analysis of signals in pump-probe spectroscopy