Optical Coatings — Abridged Guide
Quick-reference equations, tables, and rules of thumb for thin-film optical coatings — AR, HR, beam splitter, and filter coatings plus materials, deposition methods, and LIDT scaling. For worked examples, SVG diagrams, and detailed theory, see the Comprehensive Guide.
1.Introduction
Optical coatings are thin-film layers (tens to hundreds of nanometers thick) deposited on optical surfaces to control reflection, transmission, and absorption through interference effects. They range from single-layer antireflection films to stacks of 100+ layers for precision filters.
Every uncoated glass surface loses ~4% of light. In multi-element systems, coatings are not optional — they are essential for usable throughput.
Coatings divide into dielectric (transparent interference films) and metallic (high intrinsic reflectivity). Most precision coatings combine both principles. The two main functions are reducing unwanted reflections (AR coatings) and maximizing reflections (HR coatings), with filters, beam splitters, and polarizers as specialized variants.
2.Fresnel Reflection
Normal-Incidence Reflectance
n₁, n₂ = refractive indices of the two media.
Each uncoated glass–air surface reflects about 4%. For a system with N surfaces, total transmission is (1 − R)ⁿ — a 20-surface system transmits only ~42% without coatings.
At oblique incidence, s-polarization always reflects more than p-polarization. Brewster's angle (θ_B = arctan(n₂/n₁)) is where p-polarization reflectance drops to zero.
| Surfaces | Uncoated (4.2%) | BBAR (0.5%) |
|---|---|---|
| 2 | 91.8% | 99.0% |
| 10 | 65.2% | 95.1% |
| 20 | 42.5% | 90.4% |
3.Thin-Film Interference Theory
Quarter-Wave Optical Thickness
n_f = film refractive index, d = physical thickness, λ = design wavelength.
A film whose optical thickness equals λ/4 creates destructive interference of reflected light at that wavelength. This is the fundamental building block of all interference coatings — both AR and HR.
For a single-layer AR coating to reach zero reflectance, the film index must equal √(n₁ · n_s). No common material reaches the ideal index for glass (~1.23), which is why multilayer designs are needed for R < 1%.
The transfer matrix method extends this to arbitrary layer counts: each layer is a 2×2 matrix, and the total system matrix is the product of all individual matrices. This is how all modern thin-film design software computes coating performance.
4.Antireflection (AR) Coatings
Single-Layer AR Residual Reflectance
n_f = film index, n₁ = incident medium, n_s = substrate index.
Single-layer MgF₂ on glass achieves ~1.3% R — adequate for many applications. V-coats achieve R < 0.25% over a narrow band. BBAR coatings achieve R_avg < 0.5% over hundreds of nanometers using 4–10 layers.
When comparing AR specs, check both R_avg and R_max. A coating with R_avg < 0.5% might have individual wavelengths above 1%.
| Type | Layers | Typical R_avg | Bandwidth |
|---|---|---|---|
| MgF₂ | 1 | 1.3% | ~100 nm |
| V-coat | 2–3 | < 0.25% | 10–30 nm |
| BBAR | 4–6 | < 0.5% | 300+ nm |
| Dual-band | 8–12 | < 0.5%/band | Two bands |
5.High-Reflection (HR) Coatings
Quarter-Wave Stack Reflectance
N = number of layer pairs, n_H/n_L = high/low refractive indices.
Dielectric HR stacks achieve R > 99.9% with 10+ layer pairs of TiO₂/SiO₂. Higher index contrast means fewer layers needed and wider bandwidth. Metallic mirrors are broader but have lower peak R due to absorption.
HR coatings blueshift at oblique incidence by approximately 3–5% at 45°. A coating designed for 1064 nm at 0° will peak near 1020 nm at 45°.
6.Partial Reflectors & Beam Splitters
Partial reflectors provide designed R/T ratios (50/50, 90/10, etc.) using fewer layer pairs or non-quarter-wave designs. Dichroic coatings separate wavelengths. Thin-film PBS coatings separate polarizations with extinction ratios of 100:1 to 1000:1.
PBS coatings are highly angle-sensitive — even 1–2° deviation from the design angle degrades extinction ratio. For extinction > 10,000:1, use crystal polarizers instead.
7.Filter Coatings
Fabry-Pérot Finesse
R = mirror reflectance. FWHM = λ₀ / (m · F), where m = spacer order.
Bandpass filters are Fabry-Pérot cavities between reflective stacks. Higher mirror reflectance produces narrower FWHM. Multi-cavity designs give squarer passbands. Notch filters block narrow bands to OD > 6.
Edge filter steepness scales with layer count. For transitions < 1% of edge wavelength, specify IBS deposition.
8.Materials & Deposition
High-index materials (TiO₂, Ta₂O₅, HfO₂) provide strong interference; low-index materials (SiO₂, MgF₂) provide contrast. The deposition method determines coating quality: e-beam (soft, porous) → IAD (semi-hard) → IBS (hard, densest, highest LIDT).
For laser applications requiring high LIDT, always specify IBS deposition. For cost-sensitive general lab optics, IAD provides the best quality-to-cost ratio.
| Method | Film Density | Moisture Shift | LIDT | Cost |
|---|---|---|---|---|
| E-beam | 90–95% | 1–2% | Baseline | Low |
| IAD | 95–99% | 0.1–0.5% | 1.5–2× | Medium |
| IBS | ~100% | < 0.05% | 2–5× | High |
9.Performance & Specifications
LIDT Scaling (ns regime)
λ = wavelength, τ = pulse duration. Valid only for nanosecond pulses.
Coating performance is fully described by R + T + A + S = 1. Loss (A + S) sets the performance ceiling. Optical density OD = −log₁₀(T) quantifies blocking: OD 4 = 0.01% transmission, OD 6 = 0.0001%.
LIDT scaling is approximate — apply a safety factor of 2–3× in practice. The scaling law breaks down for sub-nanosecond pulses.
→10.Coating Selection Workflow
Coating selection requires specifying: wavelength, AOI, polarization, power/energy level, environment, and substrate. Match these to coating type (AR, HR, filter, etc.) and deposition method (e-beam, IAD, IBS).
The three most common specification mistakes are: (1) omitting angle of incidence, (2) failing to specify polarization for oblique-incidence coatings, and (3) specifying only R_avg without an R_max limit.