Hubbry Logo
Dielectric mirrorDielectric mirrorMain
Open search
Dielectric mirror
Community hub
Dielectric mirror
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Dielectric mirror
Dielectric mirror
Dielectric mirror
View on Wikipedia
from Wikipedia
An infrared dielectric mirror in a mirror mount

A dielectric mirror, also known as a Bragg mirror, is a type of mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified reflectivity at different wavelengths of light. Dielectric mirrors are also used to produce ultra-high reflectivity mirrors: values of 99.999% or better over a narrow range of wavelengths can be produced using special techniques. Alternatively, they can be made to reflect a broad spectrum of light, such as the entire visible range or the spectrum of the Ti-sapphire laser.

Dielectric mirrors are very common in optics experiments, due to improved techniques that allow inexpensive manufacture of high-quality mirrors. Examples of their applications include laser cavity end mirrors, hot and cold mirrors, thin-film beamsplitters, high damage threshold mirrors, and the coatings on modern mirrorshades and some binoculars roof prism systems.

Mechanism

[edit]
Diagram of a dielectric mirror. Thin layers with a high refractive index n1 are interleaved with thicker layers with a lower refractive index n2. The path lengths lA and lB differ by exactly one wavelength, which leads to constructive interference.

The reflectivity of a dielectric mirror is based on the interference of light reflected from the different layers of a dielectric stack. This is the same principle used in multi-layer anti-reflection coatings, which are dielectric stacks which have been designed to minimize rather than maximize reflectivity. Simple dielectric mirrors function like one-dimensional photonic crystals, consisting of a stack of layers with a high refractive index interleaved with layers of a low refractive index (see diagram). The thicknesses of the layers are chosen such that the path-length differences for reflections from different high-index layers are integer multiples of the wavelength for which the mirror is designed. The reflections from the low-index layers have exactly half a wavelength in path length difference, but there is a 180-degree difference in phase shift at a low-to-high index boundary, compared to a high-to-low index boundary, which means that these reflections are also in phase. In the case of a mirror at normal incidence, the layers have a thickness of a quarter wavelength.

The color transmitted by the dielectric filters shifts when the angle of incident light changes.

Other designs have a more complicated structure generally produced by numerical optimization. In the latter case, the phase dispersion of the reflected light can also be controlled (a chirped mirror). In the design of dielectric mirrors, an optical transfer-matrix method can be used. A well-designed multilayer dielectric coating can provide a reflectivity of over 99% across the visible light spectrum.[1]

Dielectric mirrors exhibit retardance as a function of angle of incidence and mirror design.[2]

As shown in the GIF, the transmitted color shifts towards the blue with increasing angle of incidence. Regarding interference in the high reflective index medium this blueshift is given by the formula

,

where is any multiple of the transmitted wavelength and is the angle of incidence in the second medium. See thin-film interference for a derivation. However, there is also interference in the low refractive index medium. The best reflectivity will be at [3]

,

where is the transmitted wavelength under perpendicular angle of incidence and

.

Manufacturing

[edit]
An electron microscope image of an approximately 13 micrometre piece of dielectric mirror being cut from a larger substrate. Alternating layers of Ta2O5 and SiO2 are visible on the bottom edge.

The manufacturing techniques for dielectric mirrors are based on thin-film deposition methods. Common techniques are physical vapor deposition (which includes evaporative deposition and ion beam assisted deposition), chemical vapor deposition, ion beam deposition, molecular beam epitaxy, sputter deposition, and sol-gel deposition.[4] Common materials are magnesium fluoride (n = 1.37), silicon dioxide (n = 1.45), tantalum pentoxide (n = 2.28) , zinc sulfide (n = 2.32), and titanium dioxide (n = 2.4).

Polymeric dielectric mirrors are fabricated industrially via co-extrusion of melt polymers,[5] and by spin-coating[6] or dip-coating[7] on smaller scale.

See also

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Dielectric mirror

View on Grokipedia
from Grokipedia
A dielectric mirror is an optical component consisting of multiple thin layers of transparent dielectric materials with alternating refractive indices, engineered to achieve high reflectivity through constructive interference of light waves reflected at the interfaces between layers. These mirrors, also known as Bragg mirrors when designed with quarter-wavelength thicknesses, can reflect over 99.9% of incident light in specific wavelength ranges while exhibiting very low absorption and scattering losses, making them superior to metallic mirrors for applications requiring minimal heat generation. Common dielectric materials include silicon dioxide (SiO₂) for low refractive index layers and titanium dioxide (TiO₂) or tantalum pentoxide (Ta₂O₅) for high index layers, typically deposited on substrates such as fused silica or quartz via techniques like electron-beam evaporation or ion-beam sputtering. Dielectric mirrors are widely used in laser resonators to form high-finesse cavities, in interferometry for precise beam manipulation, and as cold mirrors to separate visible light from infrared heat in optical systems. They also find applications in ultrafast optics for dispersion control via chirped designs, in radiative cooling devices for passive thermal management, and in advanced imaging systems like telescopes and cameras to enhance reflectivity and durability.

Fundamentals

Definition and Principles

A dielectric mirror is an optical mirror composed of multiple thin layers of dielectric materials with alternating refractive indices, designed to achieve high reflectivity through constructive interference of light waves rather than metallic reflection. Unlike metallic mirrors, which rely on free-electron absorption and typically offer reflectivities below 99%, dielectric mirrors can exceed 99.9% reflectivity over specific wavelength bands by exploiting wave interference at dielectric interfaces. The foundational principles of dielectric mirrors stem from the interference of light waves reflected at multiple dielectric interfaces. Light incident on the multilayer stack undergoes partial reflection and transmission at each boundary, with the phase of reflected waves determined by the refractive indices of adjacent layers and the optical path lengths traversed. The refractive index nn governs the speed of light in each material, creating index contrasts (e.g., low-index SiO₂ with n≈1.45n \approx 1.45 and high-index TiO₂ with n≈2.4n \approx 2.4) that induce phase shifts upon reflection: a 180° shift occurs when light reflects from a higher-index medium, while no shift occurs from a lower-index one. For a single interface, the amplitude reflection coefficient at normal incidence is given by r=n1−n2n1+n2,r = \frac{n_1 - n_2}{n_1 + n_2}, where n1n_1 and n2n_2 are the refractive indices of the incident and transmitting media, respectively; this yields a reflectivity R=∣r∣2R = |r|^2 ranging from 0% (matched indices) to nearly 100% (large contrast). In a multilayer dielectric mirror, these reflections coherently add, and reflectivity is amplified by stacking many layers, with the overall response approaching that of an ideal reflector for wavelengths where constructive interference dominates. To maximize reflectivity at a target wavelength λ0\lambda_0, each layer is typically designed with a quarter-wave optical thickness, nd=λ0/4n d = \lambda_0 / 4, where dd is the physical thickness. This ensures that round-trip phase delays within layers align reflected waves in phase, promoting constructive interference and a high-reflectivity stopband. The concept evolved from early thin-film optics developed in the 1930s, with vacuum deposition techniques pioneered by John Strong at the California Institute of Technology for anti-reflection coatings, while the first multilayer high-reflectivity dielectric mirrors were invented in 1939 by Walter Geffcken at the Schott Glass company.

Reflection Mechanism

Dielectric mirrors achieve high reflectivity through the constructive interference of light waves reflected at multiple interfaces within a stack of alternating thin dielectric layers. Each layer typically has an optical thickness of one quarter wavelength (λ/4\lambda/4) at the design wavelength, ensuring that the path length difference for reflections from adjacent interfaces results in a phase difference of π\pi radians (180 degrees), aligning the reflected waves in phase to add constructively. This interference amplifies the total reflected amplitude, leading to near-total reflection within a specific wavelength range known as the stopband, where transmittance is minimized. The phase behavior at interfaces plays a critical role in this enhancement. When light reflects from a medium of lower refractive index to higher (low-to-high interface), it undergoes a π\pi radian phase shift, whereas reflection from higher to lower index (high-to-low) incurs no such shift. In a typical high-reflectivity stack starting with a high-index layer on a substrate, the alternating interfaces are arranged such that all major reflections experience effectively the same phase shift relative to the propagation delay, enabling coherent addition upon stacking multiple periods. This design maximizes the buildup of the electric field amplitude for the reflected wave. Spectral selectivity arises from the periodic structure, creating a photonic stopband analogous to a one-dimensional photonic bandgap, where wavelengths within the band are strongly reflected due to the Bragg condition being satisfied. Outside this stopband (passband), the phase mismatches lead to destructive interference for reflections or high transmission. The stopband width increases with greater refractive index contrast between layers, providing tailored reflectivity over desired spectral regions. The reflectivity RR of a multilayer stack can be rigorously derived using the characteristic matrix method, which models the propagation through each layer. For a single isotropic layer of thickness dd, refractive index nn, and wave number k0=2π/λ0k_0 = 2\pi / \lambda_0, the characteristic matrix is M=(cos⁡δ(i/η)sin⁡δiηsin⁡δcos⁡δ),M = \begin{pmatrix} \cos \delta & (i / \eta) \sin \delta \\ i \eta \sin \delta & \cos \delta \end{pmatrix}, where δ=k0ndcos⁡θ\delta = k_0 n d \cos \theta is the phase thickness, θ\theta is the refraction angle, and η=ncos⁡θ\eta = n \cos \theta (or n/cos⁡θn / \cos \theta for TE/TM polarizations) is the admittance (with vacuum admittance normalized to 1). For a stack of pp layers, the total matrix is the product M=MpMp−1⋯M1=(m11m12m21m22)M = M_p M_{p-1} \cdots M_1 = \begin{pmatrix} m_{11} & m_{12} \\ m_{21} & m_{22} \end{pmatrix}. The effective admittance seen from the incident side is Ym=(m21+m22Ys)/(m11+m12Ys)Y_m = (m_{21} + m_{22} Y_s) / (m_{11} + m_{12} Y_s), where Ys=nsY_s = n_s is the substrate admittance and nsn_s its index. The amplitude reflection coefficient is then r=(Y0−Ym)/(Y0+Ym)r = (Y_0 - Y_m) / (Y_0 + Y_m), with incident medium admittance Y0=n0Y_0 = n_0, yielding the power reflectivity R=∣n0−Ymn0+Ym∣2.R = \left| \frac{n_0 - Y_m}{n_0 + Y_m} \right|^2.
Add your contribution
Related Hubs
User Avatar
No comments yet.