Thin-Film Optical Coating Calculator
Calculate optical interference, reflectivity, and transmissivity for thin-film coatings
Calculate Thin-Film Optical Properties
Optical Geometry
Angle of incident light (0-90 degrees)
Physical thickness of the optical film
Light Properties
Wavelength of incident light
Material Properties
Incident medium (usually air)
Thin film coating material
Base substrate material
Optical Properties Results
Reflectivity
Transmissivity
OPD Formula: OPD = 2 × n₂ × d × cos(θ₂) = 2 × 1.380 × 0.0 × 1.000 nm
AR Coating: d_min = λ / (4 × n₂) = 550 / (4 × 1.380) = 99.64 nm
Coating Analysis
Example: Anti-Reflective Coating
MgF₂ Coating on Glass
System: Air → MgF₂ → Crown Glass
Refractive Indices: n₁ = 1.0, n₂ = 1.38, n₃ = 1.52
Wavelength: 550 nm (green light)
Purpose: Anti-reflective coating for camera lenses
Optimal Thickness Calculation
For destructive interference (AR coating):
d_min = λ / (4 × n₂) = 550 nm / (4 × 1.38) = 99.6 nm
This minimizes reflection at normal incidence
Common Materials
Applications
Camera lens anti-reflection coatings
Microscope and telescope optics
LED efficiency enhancement
Optical filters and mirrors
Solar panel coatings
Design Tips
For AR coatings: n₁ < n₂ < n₃ typically works best
Quarter-wave thickness minimizes reflection
Multi-layer coatings work across broader spectra
Consider angle of incidence for practical use
Balance s and p-polarized performance
Understanding Thin-Film Optical Coatings
How Thin-Film Interference Works
When light encounters a thin film, reflections occur at both the top and bottom surfaces. These reflected waves can interfere constructively or destructively, depending on the optical path difference and phase relationships.
Key Concepts
- •OPD: Optical path difference determines interference type
- •Phase change: Occurs when n₁ < n₂ at interface
- •Fresnel equations: Describe reflection and transmission
Main Formulas
OPD = 2 × n₂ × d × cos(θ₂)
d_min = λ / (4 × n₂)
R_s = |r₁₂ + r₂₃ × t₁₂ × e^(iδ)|²
Interference Conditions
Destructive: OPD = (m - ½)λ (for AR coatings)
Constructive: OPD = mλ (for mirrors)
Where: m = 0, 1, 2, 3... (order of interference)
Note: Phase changes at interfaces affect the interference conditions. Most practical AR coatings use the quarter-wave principle.
Types of Coatings
Anti-Reflective (AR)
Minimize reflection, maximize transmission
High-Reflective (HR)
Maximize reflection for mirrors
Bandpass Filters
Selective wavelength transmission
Design Considerations
Wavelength Selection
Choose design wavelength for optimal performance
Angle Dependence
Performance varies with incident angle
Polarization Effects
S and p-polarizations behave differently