Dielectric mirror

Last updated
An infrared dielectric mirror in a mirror mount Dielectric-mirror780 3.jpg
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.

Contents

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

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. Dielectric mirror diagram.svg
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. Dielectric filter tilted.gif
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

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. DBR SEM.jpg
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, and sputter deposition. 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, [4] and by spin-coating [5] or dip-coating [6] on smaller scale.

See also

Related Research Articles

<span class="mw-page-title-main">Fresnel equations</span> Equations of light transmission and reflection

The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.

<span class="mw-page-title-main">Refractive index</span> Ratio of the speed of light in vacuum to that in the medium

In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

<span class="mw-page-title-main">Rayleigh scattering</span> Light scattering by small particles

Rayleigh scattering, named after the 19th-century British physicist Lord Rayleigh, is the predominantly elastic scattering of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium, the amount of scattering is inversely proportional to the fourth power of the wavelength, e.g., a blue color is scattered much more than a red color as light propagates through air.

<span class="mw-page-title-main">Total internal reflection</span> Complete reflection of a wave

In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).

<span class="mw-page-title-main">Brewster's angle</span> Angle of incidence for which all reflected light will be polarized

Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. The angle is named after the Scottish physicist Sir David Brewster (1781–1868).

<span class="mw-page-title-main">Snell's law</span> Formula for refraction angles

Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.

In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.

<span class="mw-page-title-main">Optical coating</span> Material which alters light reflection or transmission on optics

An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in the field of optics. One type of optical coating is an anti-reflective coating, which reduces unwanted reflections from surfaces, and is commonly used on spectacle and camera lenses. Another type is the high-reflector coating, which can be used to produce mirrors that reflect greater than 99.99% of the light that falls on them. More complex optical coatings exhibit high reflection over some range of wavelengths, and anti-reflection over another range, allowing the production of dichroic thin-film filters.

<span class="mw-page-title-main">Anti-reflective coating</span> Optical coating that reduces reflection

An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses, other optical elements, and photovoltaic cells to reduce reflection. In typical imaging systems, this improves the efficiency since less light is lost due to reflection. In complex systems such as cameras, binoculars, telescopes, and microscopes the reduction in reflections also improves the contrast of the image by elimination of stray light. This is especially important in planetary astronomy. In other applications, the primary benefit is the elimination of the reflection itself, such as a coating on eyeglass lenses that makes the eyes of the wearer more visible to others, or a coating to reduce the glint from a covert viewer's binoculars or telescopic sight.

<span class="mw-page-title-main">Gires–Tournois etalon</span>

In optics, a Gires–Tournois etalon is a transparent plate with two reflecting surfaces, one of which has very high reflectivity, ideally unity. Due to multiple-beam interference, light incident on a Gires–Tournois etalon is (almost) completely reflected, but has an effective phase shift that depends strongly on the wavelength of the light.

<span class="mw-page-title-main">Distributed Bragg reflector</span> Structure used in waveguides

A distributed Bragg reflector (DBR) is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with different refractive index, or by periodic variation of some characteristic of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection and refraction of an optical wave. For waves whose vacuum wavelength is close to four times the optical thickness of the layers, the interaction between these beams generates constructive interference, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic stopband. Within this range of wavelengths, light is "forbidden" to propagate in the structure.

<span class="mw-page-title-main">X-ray reflectivity</span>

X-ray reflectivity is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers. It is a form of reflectometry based on the use of X-rays and is related to the techniques of neutron reflectometry and ellipsometry.

X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray diffraction, X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.

Fluorescence interference contrast (FLIC) microscopy is a microscopic technique developed to achieve z-resolution on the nanometer scale.

<span class="mw-page-title-main">Dispersive prism</span> Device used to disperse light

In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.

<span class="mw-page-title-main">Acousto-optics</span> The study of sound and light interaction

Acousto-optics is a branch of physics that studies the interactions between sound waves and light waves, especially the diffraction of laser light by ultrasound through an ultrasonic grating.

Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element.

<span class="mw-page-title-main">Transfer-matrix method (optics)</span>

The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors.

<span class="mw-page-title-main">Thin-film interference</span> Optical phenomenon

Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, increasing reflection at some wavelengths and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections.

<span class="mw-page-title-main">Rugate filter</span> Dielectric mirror that selectively reflects a particular wavelength range of light

A rugate filter, also known as a gradient-index filter, is an optical filter based on a dielectric mirror that selectively reflects specific wavelength ranges of light. This effect is achieved by a periodic, continuous change of the refractive index of the dielectric coating. The word "rugate" is derived from corrugated structures found in nature, which also selectively reflect certain wavelength ranges of light, for example the wings of the Morpho butterfly.

References

  1. Slaiby, ZenaE.; Turki, Saeed N. (November–December 2014). "Study the reflectance of dielectric coating for the visiblespectrum" (PDF). International Journal of Emerging Trends & Technology in Computer Science. 3 (6): 1–4. ISSN   2278-6856. Archived from the original (PDF) on 2022-11-28. Retrieved 2022-11-19.
  2. Apfel, J. H. (1982). "Phase retardance of periodic multilayer mirrors". Applied Optics. 21 (4): 733–738. Bibcode:1982ApOpt..21..733A. doi:10.1364/AO.21.000733. PMID   20372527.
  3. E, Huett (April 26, 2022). "Determination of 2D Plasma Parameters with Filtered Cameras. An Application to the X-Point Radiator Regime in ASDEX Upgrade". Max-Planck-Institut für Plasmaphysik. doi:10.17617/2.3379034.
  4. Comoretto, Davide, ed. (2015). Organic and Hybrid Photonic Crystals. doi:10.1007/978-3-319-16580-6. ISBN   978-3-319-16579-0. S2CID   139074878.
  5. Lova, Paola; Giusto, Paolo; Stasio, Francesco Di; Manfredi, Giovanni; Paternò, Giuseppe M.; Cortecchia, Daniele; Soci, Cesare; Comoretto, Davide (9 May 2019). "All-polymer methylammonium lead iodide perovskite microcavities". Nanoscale. 11 (18): 8978–8983. doi:10.1039/C9NR01422E. hdl: 11567/944564 . ISSN   2040-3372. PMID   31017152. S2CID   129943931.
  6. Russo, Manuela; Campoy‐Quiles, Mariano; Lacharmoise, Paul; Ferenczi, Toby A. M.; Garriga, Miquel; Caseri, Walter R.; Stingelin, Natalie (2012). "One-pot synthesis of polymer/inorganic hybrids: toward readily accessible, low-loss, and highly tunable refractive index materials and patterns". Journal of Polymer Science Part B: Polymer Physics. 50 (1): 65–74. Bibcode:2012JPoSB..50...65R. doi:10.1002/polb.22373. ISSN   1099-0488.