Filter Properties and Film Design

Optical filters are core components of modern optical systems, and their core function is to selectively transmit or block light of specific wavelengths.This crucial function does not originate from the substrate material itself, but is determined by the optical thin film layer (film system) precisely deposited on its surface.The design, material selection, and manufacturing process of the filter layer directly determine the final transmittance profile of the filter. A deep understanding of this relationship is crucial for optical design, selection, and evaluation of filters.

I.The core of film layer function: light interference

The physical basis for wavelength selectivity in optical thin films is the interference effect of light. When light is incident on the surface of a thin film, it is reflected and refracted at various interfaces. By precisely controlling the thickness and refractive index of each film layer, light of the target wavelength (passband) can undergo constructive interference (enhanced transmission) in the transmission direction, while light of other wavelengths (stopband) can undergo destructive interference (enhanced reflection or absorption), thereby achieving the purpose of filtering.

II. How Film properties shape the transmittance curve

1. Film thickness

Key parameters: The optical thickness (physical thickness × refractive index) of the film is usually designed to be 1/4 of the target wavelength λ or an odd multiple thereof (λ/4, 3λ/4...) or 1/2 of the wavelength (λ/2).

Influence:

Center wavelength/cutoff wavelength positioning: The optical thickness directly determines the location of the strongest interference effect, that is, the center wavelength (bandpass) or cutoff wavelength (long pass/short pass) of the filter. For example, the reflection peak (corresponding to the transmission valley) of a high refractive index layer with an optical thickness of λ₀/4 is near λ₀.

Passband/Blockband Position: The combination of layers of different thicknesses in the entire film system determines the specific positions of the passband and blockband in the spectrum.

Precision Requirements: Extremely high precision is required for film thickness control; even slight deviations can lead to center wavelength shifts, decreased transmittance, or increased ripple.

2. Film material and refractive index:

Key characteristic: The refractive index (n) of thin film materials is the core parameter.

Influence:

Fundamentals of Reflectivity and Transmittance: The reflectivity of a single-layer film is determined by the refractive index difference between adjacent layers. The greater the refractive index difference, the stronger the reflection at the interface.

Design Freedom of Film Systems: The combination of high-refractive-index materials (such as TiO₂, Ta₂O₅, Si) and low-refractive-index materials (such as SiO₂, MgF₂) is the foundation for constructing highly efficient interference film systems. By alternately stacking high- and low-refractive-index layers (DBR - Distributed Bragg Mirror or Fabry-Perot Cavity), extremely high reflectivity (corresponding to low transmittance) can be achieved in specific wavelength bands, while high transmittance can be achieved in other wavelength bands.

Passband shape and steepness: The greater the contrast between high and low refractive index materials, the easier it is to design filters with steeper passband edges and better rectangularity (closer to the ideal square wave shape).

Absorption loss: The material must have low absorption in the target operating wavelength band. Any absorption will directly lead to a loss of transmittance (T<100%) in the target passband and heat generation in the filter. Material selection is particularly challenging in the ultraviolet band.

3. Number and structure of membrane layers:

Complexity: The higher the performance requirements of the filter (such as requiring a higher cutoff depth OD, a wider stopband, a steeper transition band, a flatter passband, and a narrower bandwidth), the more layers of film are usually required, and the more complex the structure (such as a multi-cavity structure).

Influence:

Cutoff depth (OD): To achieve extremely low transmittance (high optical density) in the stopband region, a sufficient number of layers are needed to enhance destructive interference.

Transition steepness: The steeper the transition from the passband to the stopband, the more layers are usually required, and the more sophisticated the design. 

Passband ripples: Within the passband, it is desirable to have the highest possible transmittance and the flattest surface (small ripples). Complex film designs (such as gradient refractive index layers and matching layers) can effectively suppress passband ripples.

Bandwidth: Narrowband filters (such as laser filters) typically employ a Fabry-Perot resonator structure (two mirrors sandwiching a spacer layer), and their bandwidth is determined by the reflectivity of the mirrors and the cavity length. Broadband filters, on the other hand, may require thicker layers or special designs.

4. Membrane interface and microstructure:

Manufacturing quality: In the actual coating process, the uniformity, density, roughness and interlayer diffusion of the film are crucial.

Influence:

Scattering loss: Rough interfaces or loose structures grown in columnar form can cause light scattering, deflecting the light that should be transmitted off course, resulting in decreased passband transmittance and unwanted stray light.

Increased absorption: Imperfect microstructures may increase the light absorption path, leading to increased absorption loss.

Stress and adhesion: affect the mechanical stability and environmental durability of the film.

Ⅲ.Actual Influencing Factors Beyond Design

Incident angle: When light is incident at an oblique angle, the effective optical thickness decreases, causing the entire spectral characteristics to shift towards shorter wavelengths (blue shift). The larger the angle, the more significant the shift. The angle must be considered during design.

Polarization: When incident at an oblique angle, S-polarized light and P-polarized light behave differently in the thin film, which may cause the transmittance curve to split. Therefore, it is necessary to design unpolarized filters or consider the effects of polarization.

Temperature: The refractive index and thickness of the film material and substrate change with temperature, causing a center wavelength shift (usually towards longer wavelengths, i.e., a redshift).

Substrate quality: The transmittance, surface smoothness, and cleanliness of the substrate itself are fundamental to the final performance of the filter. Substrate absorption limits the overall maximum transmittance.

The transmittance curve of a filter is a direct "fingerprint" of its film system. The thickness, refractive index, number of layers, and their combined structure of each thin film are precisely sculpted into the final spectral response through a delicate optical interference effect. From basic single-layer antireflective films to complex ultra-narrowband multi-cavity filters, film design is the core of optical thin-film technology. Understanding the four key relationships—film thickness determining wavelength positioning, refractive index difference affecting reflection and steepness, layer complexity increasing performance limits, and manufacturing processes and environmental factors influencing actual performance—is crucial for mastering the secrets of filter performance and making effective selections and applications. The development of light filters represents a perfect combination of the art and science of humankind precisely manipulating light using thin films.