What Are Extinction Coefficient, Transmittance, and Reflectance in Thin Films?
Optical thin films rely on key parameters to define their performance. Understanding refractive index (n), extinction coefficient (k), transmittance (T), and reflectance (R) is critical for designing functional optical components—from anti-reflection coatings to laser mirrors.
Refractive Index (n)
Refractive index describes the ratio of light speed in a vacuum to its speed in a material: n = c/v, where c is the speed of light in a vacuum and v is the speed in the material. Physically, it determines the refraction angle at an interface (Snell’s Law): n₁sinθ₁ = n₂sinθ₂. Multilayer thin film designs rely on combining layers with different refractive indices to achieve anti-reflection, high reflectivity, or filtering functions.
Extinction Coefficient (k)
The extinction coefficient quantifies light attenuation as it propagates through a material, linked to absorption. It is part of the complex refractive index: ñ = n + ik. The physical significance lies in the attenuation law of light intensity: I(z) = I₀e⁻⁴πkz/λ, where z is the propagation distance and λ is the wavelength. A k > 0 indicates light absorption by the material, such as semiconductors absorbing specific wavelengths.
Transmittance (T)
Transmittance is the ratio of transmitted light intensity (It) to incident light intensity (I₀): T = It/I₀. It is influenced by film thickness, n/k distributions, and interface reflection losses (e.g., anti-reflection coatings minimize T loss from reflection).
Reflectance (R)
Reflectance is the ratio of reflected light intensity (Ir) to incident light intensity (I₀): R = Ir/I₀. For a single interface, the Fresnel equation gives R = {(n₂ - n₁)/(n₂ + n₁)}², where n₁ and n₂ are the refractive indices of adjacent media.
Synergies Between Parameters
n and k: Balancing Performance
Take indium tin oxide (ITO) films—used in transparent conductors—for example. High conductivity (low resistance) requires high carrier concentration, but carriers cause near-infrared absorption (increasing k). The design challenge: maintain low k (k ≈ 0) in the visible range while allowing moderate absorption in the infrared.
T and R: Complementary Properties
In ideal lossless films: T + R + A = 1, where吸收率 A (absorptance) is determined by k. Anti-reflection (AR) coatings use destructive interference in multilayers to minimize R (R → 0), thereby increasing T (e.g., camera lenses with R < 0.5%). High-reflectivity films use periodic high-low n layers (e.g., TiO₂/SiO₂) to achieve R > 99% at specific wavelengths.
Key Performance Relationships & Examples
Transparent Conducting Oxides (TCOs) like ZnO:Al require visible T > 80% → low k values (<0.01@550 nm). High doping increases infrared absorption (k ↑), demanding a balance between conductivity and optical loss.
Passivation layers (e.g., SiNₓ) use high n (~2.0@600 nm) to optimize anti-reflection and enhance light absorption, with low k (<0.005) to reduce parasitic absorption—critical for solar cells.
Laser mirrors (damage threshold) rely on high-reflectivity designs: alternating high-n (HfO₂, n≈2.0) and low-n (SiO₂, n≈1.45) materials, each λ/4 thick. Extremely low k (<10⁻⁵) is required to avoid absorption-induced film damage from laser energy.
Optical filters (wavelength selectivity): Bandpass filters use periodic n/k modulation to transmit specific wavelengths (e.g., 532 nm). UV cut-off filters achieve high short-wavelength R using high-k materials.
Measuring & Optimizing Parameters
Ellipsometry measures n and k by analyzing the amplitude ratio (ψ) and phase difference (Δ) of reflected polarized light, fitting to obtain optical constants. It works for thicknesses from 0.1 nm to tens of microns.
Transmission/Reflection Spectroscopy directly measures T and R. Combined with Kramers-Kronig relations, it infers n and k dispersion curves (assuming k=0 or specific models).
Optical thin film design software (e.g., Essential Macleod, TFCalc) uses the Transfer Matrix Method (TMM) to simulate multilayer performance, optimizing n/k/thickness combinations.
Practical Design Considerations
For refractive index (n): High-n materials (e.g., TiO₂, n≈2.4) enable thinner films (e.g., thinner λ/4 layers) but may increase reflectivity. Low-n materials (e.g., SiO₂, n≈1.45) work well for anti-reflection layers but often require more layers to offset reflection.
For extinction coefficient (k): High k is needed for light-absorbing devices (e.g., photodetector active layers, k > 0.1@operating wavelength). Optical windows or transparent electrodes demand k approaching 0.
For T and R trade-offs: Energy devices (e.g., photovoltaics) prioritize high T, accepting lower R (though multi-layer AR designs can optimize both). Functional devices (e.g., mirrors) target high R, tolerating low T (e.g., metal mirrors with R > 95% and T ≈ 0).
Note: Practical applications require joint optimization of thickness, substrate matching, and process conditions (e.g., deposition temperature). Avoid over-reliance on single parameters—e.g., local high k in high-reflectivity films can cause thermal damage.
Need Help with Your Thin Film Design?
Whether you’re balancing n/k for a transparent conductor, optimizing T/R for an AR coating, or need a custom filter with precise parameters, OPTOStokes has you covered. We offer extensive stock thin films and tailored solutions—all meeting international quality standards with reliable lead times.
Share your performance requirements (wavelength range, T/R targets, or substrate specs) with our engineers at sales@optofilters.com or leave a message on our website. We’ll help you achieve the perfect parameter balance for your application.