[Paper Review] A quantitative first-order approach for the scattering of light by structured thin films

Slawa Lang, Lukas Maiwald+4 more|arXiv (Cornell University)|Feb 20, 2018

Photonic Crystals and Applications3 citations

TL;DR

This paper presents a quantitative first-order vectorial approach based on the Born approximation to model light scattering in structured thin films with low refractive index contrast. By leveraging the Ewald sphere geometry and normalization to a representative volume, it enables efficient and accurate prediction of scattering in disordered, low-contrast photonic structures, particularly those producing color effects via coherent scattering.

ABSTRACT

We present a full vectorial first-order approach to the scattering by arbitrary photonic structures with a low refractive index contrast. Our approach uses the first-order Born approximation and keeps the simple geometrical representation of the Ewald sphere construction. Via normalization to a representative sample volume, the approach can also predict the scattering by infinitely extended layers of scattering media. It can therefore be used to describe and efficiently calculate the scattering by structures where the linear first-order scattering terms dominate, e.g. in low index contrast disordered structures creating a color impression.

Motivation & Objective

• To develop a computationally efficient method for modeling light scattering in photonic structures with low refractive index contrast.
• To maintain the intuitive geometric framework of the Ewald sphere construction while enabling full vectorial treatment of scattering.
• To enable prediction of scattering from infinitely extended layers by normalizing to a representative sample volume.
• To describe and quantify scattering in disordered, low-contrast systems that produce visible color effects through coherent scattering.
• To provide a scalable and analytically tractable approach applicable to real-world photonic thin films with weak inhomogeneities.

Proposed method

• Applies the first-order Born approximation to model scattering from arbitrary photonic structures with low index contrast.
• Uses a full vectorial formulation to account for polarization and directionality of scattered light.
• Preserves the geometric intuition of the Ewald sphere construction for visualizing scattering wavevectors.
• Normalizes the scattering response to a representative unit cell volume to extrapolate to infinite, periodic or disordered layers.
• Enables efficient numerical computation by reducing the problem to a single scattering event per structure element.
• Treats the medium as a collection of weakly scattering inhomogeneities, valid when refractive index contrast is small.

Experimental results

Research questions

• RQ1 How can the scattering of light in low-index-contrast structured thin films be modeled efficiently with analytical rigor?
• RQ2 To what extent can the Ewald sphere construction be preserved in a full vectorial first-order scattering model?
• RQ3 Can a representative volume normalization accurately predict scattering from infinitely extended disordered media?
• RQ4 What is the role of vectorial effects in scattering when index contrast is low and structures are disordered?
• RQ5 How does this approach compare to more complex multiple-scattering models in terms of accuracy and computational cost?

Key findings

• The first-order Born approximation provides a valid and accurate description of scattering in low-index-contrast photonic structures.
• The method successfully retains the geometric simplicity of the Ewald sphere while incorporating full vectorial polarization effects.
• Normalization to a representative volume enables reliable prediction of scattering from macroscopic, infinitely extended layers.
• The approach efficiently models coherent scattering in disordered thin films that produce visible color effects.
• The model is computationally efficient and scalable, suitable for rapid design and analysis of photonic color structures.
• The framework is particularly effective for systems where linear first-order scattering dominates, such as in disordered photonic thin films with weak inhomogeneities.