Omnidirectional Reflector

A dielectric omnidirectional reflector Authors: Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas Journal: Science 282(5394), 1679–1682 (1998) · Comparison target: Figure 4 https://doi.org/10.1126/science.282.5394.1679

Nine alternating layers of polystyrene and tellurium keep the entire 10–15 um band highly reflective across every incidence angle from 0° to 80° and in both polarizations — no alignment to a particular angle required.

This case builds that nine-layer stack from the published materials, thicknesses, and layer order, computes TE and TM reflectance at 0°, 45°, and 80°, and compares against all five panels of paper Figure 4.

Note

The published figure is not reproduced here: Figure 4 is copyright Science (AAAS) and commercial reuse permission has not been granted. Open the original through DOI 10.1126/science.282.5394.1679 to view it; access may require a subscription or institutional login. Every value labelled “paper” below is a data point read off the original independently; the figure itself is neither copied nor redrawn.

At normal incidence, 10–15 um already sits inside a continuous high-reflectance plateau.

Note

Prerequisite: complete Quick Start and become familiar with reflectance and polarization results in Basic Optical Results.

Background

An omnidirectional reflector is not defined by a single high-reflectance peak at one angle. The engineering requirement is a wavelength interval that stays highly reflective over a broad angular range and under both polarizations, so a device does not depend on precise single-angle alignment.

The published parameters map directly onto a one-dimensional stack: a PS-Te system, 9 layers alternating from Te, Te = 0.8 um and PS = 1.65 um, a target band of 10–15 um, and an angular range of 0°–80°.

Structure

Item	Model value	Reason
Incidence medium	Air	Consistent with the air-side reflectance measurement in the paper
Stack architecture	Te / (PS / Te) x 4	Nine layers total, equivalent to Te / PS / Te / PS / Te / PS / Te / PS / Te
Top Te layer	0.8 um	Published thickness
PS inside the repeated period	1.65 um	Published thickness
Te inside the repeated period	0.8 um	Published thickness
Te source	Two built-in Te entries, Caldwell-o and Sherman-o, merged	The merged file spans 6–15 um, matching the Figure 4 axis
PS source	The built-in polystyrene entry	Extends to 20 um and preserves mid-IR absorption features
Transmission medium	Air	Isolates the stop-band behaviour of the nine-layer film

Caution

The experimental sample is deposited on a real substrate, but this case uses the Air / PS-Te / Air free-film approximation so the angular stop-band behaviour of the nine-layer film can be checked directly. That affects absolute band-edge positions but not whether a broad angular high-reflectance band exists.

The repeated part of the stack is a four-fold period, which a Layer Group expresses more easily than eight manually duplicated layers. Keep the top single Te layer, set its thickness to 0.8 um, set its material to File and upload the merged Te data file; remove the leftover standalone substrate row; then add a Layer Group with a repeat count of 4 containing PS at 1.65 um and Te at 0.8 um.

The completed structure page, with the single Te Entrance on top and the repeated PS-Te Period below:

Open Edit Group to check the period unit — repeat count 4, with PS and Te inside:

Note

No single built-in Te entry covers the full 6–15 um axis of paper Figure 4, so this case takes one span from each of two database entries, merges them into one file, and loads it through the standard upload control.

Optical Settings

Setting	Value
Wavelength range	6000–15000 nm
Step	50 nm
Detector	Reflectance only
Angles	0°, 45°, 80°
Polarization	TE as pRatio = 0, TM as pRatio = 1

The result page uses nm on the horizontal axis, so the paper’s 10–15 um band appears as 10000–15000 nm.

Note

This case does not use Optimize. If a notice related only to Optimize appears at the bottom of the page, continue with Run.

Simulation Results and Comparison with Figure 4

The five comparisons follow the order of the paper’s sub-panels, one software result per condition; view the published panels in the original paper.

Normal incidence (0°):

TE, 45°:

TM, 45°:

TE, 80°:

TM, 80°:

Placed next to Figure 4, the comparison is straightforward:

• At normal incidence, the 10-15 um target interval already lies inside a continuous high-reflectance region.
• At 45°, both TE and TM remain broad plateau-like high-reflectance responses rather than collapsing into narrow resonances.
• At 80°, the TE branch still keeps a broad plateau, while the short-wavelength edge of TM shifts more strongly. That matches the paper’s physical interpretation that the more restrictive edge of the omnidirectional band is governed by the TM branch.
• The local dents visible in the platform are consistent with the mid-IR absorption of PS, which the paper also notes.

The central conclusion is therefore reproduced at the correct level of rigor for a first pass: the structure behaves as a broad angular high-reflectance band, not as a single resonance peak.

Deviation Notes

Both materials use published optical constants from the database rather than measurements of the 1998 samples, so absorption strength and fine structure will not match point by point. The Te file is merged from two database entries, which may leave a small line-shape kink near the handover around 9 um.

The model uses a free-film approximation with no real substrate, so absolute band-edge positions and local line shape are more idealized than a measurement. Process tolerances, interface roughness, and thickness drift are not included.

Going further

These tutorials cover the operating steps only. The physics behind them, the full parameter reference for each feature, how to read the results, and the algorithm validation all live on the documentation site:

• Transfer-Matrix Method — the physics and formulas behind these tutorials
• Feature Guide — complete reference for every screen and parameter
• Results — how to read each kind of output
• Open Dreapex TMM — build and simulate in the browser