The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium.
It was first proposed in 1872 by Wolfgang Sellmeier and was a development of the work of Augustin Cauchy on Cauchy's equation for modelling dispersion. [1]
In its original and the most general form, the Sellmeier equation is given as
where n is the refractive index, λ is the wavelength, and Bi and Ci are experimentally determined Sellmeier coefficients . These coefficients are usually quoted for λ in micrometres. Note that this λ is the vacuum wavelength, not that in the material itself, which is λ/n. A different form of the equation is sometimes used for certain types of materials, e.g. crystals.
Each term of the sum representing an absorption resonance of strength Bi at a wavelength √Ci. For example, the coefficients for BK7 below correspond to two absorption resonances in the ultraviolet, and one in the mid-infrared region. Close to each absorption peak, the equation gives non-physical values of n2 = ±∞, and in these wavelength regions a more precise model of dispersion such as Helmholtz's must be used.
If all terms are specified for a material, at long wavelengths far from the absorption peaks the value of n tends to
where εr is the relative permittivity of the medium.
For characterization of glasses the equation consisting of three terms is commonly used: [2] [3]
As an example, the coefficients for a common borosilicate crown glass known as BK7 are shown below:
| Coefficient | Value |
|---|---|
| B1 | 1.03961212 |
| B2 | 0.231792344 |
| B3 | 1.01046945 |
| C1 | 6.00069867×10−3 μm2 |
| C2 | 2.00179144×10−2 μm2 |
| C3 | 1.03560653×102 μm2 |
For common optical glasses, the refractive index calculated with the three-term Sellmeier equation deviates from the actual refractive index by less than 5×10−6 over the wavelengths' range [4] of 365 nm to 2.3 μm, which is of the order of the homogeneity of a glass sample. [5] Additional terms are sometimes added to make the calculation even more precise.
Sometimes the Sellmeier equation is used in two-term form: [6]
Here the coefficient A is an approximation of the short-wavelength (e.g., ultraviolet) absorption contributions to the refractive index at longer wavelengths. Other variants of the Sellmeier equation exist that can account for a material's refractive index change due to temperature, pressure, and other parameters.
| Material | B1 | B2 | B3 | C1, μm2 | C2, μm2 | C3, μm2 |
|---|---|---|---|---|---|---|
| borosilicate crown glass (known as BK7) | 1.03961212 | 0.231792344 | 1.01046945 | 6.00069867×10−3 | 2.00179144×10−2 | 103.560653 |
| sapphire (for ordinary wave) | 1.43134930 | 0.65054713 | 5.3414021 | 5.2799261×10−3 | 1.42382647×10−2 | 325.017834 |
| sapphire (for extraordinary wave) | 1.5039759 | 0.55069141 | 6.5927379 | 5.48041129×10−3 | 1.47994281×10−2 | 402.89514 |
| fused silica | 0.696166300 | 0.407942600 | 0.897479400 | 4.67914826×10−3 | 1.35120631×10−2 | 97.9340025 |
| Magnesium fluoride | 0.48755108 | 0.39875031 | 2.3120353 | 0.001882178 | 0.008951888 | 566.13559 |
In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is an approximate measure of the material's dispersion, with high values of V indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V-number should not be confused with the normalized frequency in fibers.
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.
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.
In optics and in wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium.
In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.
The laser diode rate equations model the electrical and optical performance of a laser diode. This system of ordinary differential equations relates the number or density of photons and charge carriers (electrons) in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain.
Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form. This differs from all other commercial glasses, such as soda-lime glass, lead glass, or borosilicate glass, in which other ingredients are added which change the glasses' optical and physical properties, such as lowering the melt temperature, the spectral transmission range, or the mechanical strength. Fused quartz, therefore, has high working and melting temperatures, making it difficult to form and less desirable for most common applications, but is much stronger, more chemically resistant, and exhibits lower thermal expansion, making it more suitable for many specialized uses such as lighting and scientific applications.
In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility.
A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. Hence a fiber Bragg grating can be used as an inline optical filter to block certain wavelengths, can be used for sensing applications, or it can be used as wavelength-specific reflector.
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy, who originally defined it in 1830 in his article "The refraction and reflection of light".
A glass code is a method of classifying glasses for optical use, such as the manufacture of lenses and prisms. There are many different types of glass with different compositions and optical properties, and a glass code is used to distinguish between them.
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.
Athermalization, in the field of optics, is the process of achieving optothermal stability in optomechanical systems. This is done by minimizing variations in optical performance over a range of temperatures.
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.
The refractive index of water at 20 °C for visible light is 1.33. The refractive index of normal ice is 1.31. In general, an index of refraction is a complex number with real and imaginary parts, where the latter indicates the strength of absorption loss at a particular wavelength. In the visible part of the electromagnetic spectrum, the imaginary part of the refractive index is very small. However, water and ice absorb in infrared and close the infrared atmospheric window, thereby contributing to the greenhouse effect.
When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:
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.
A compound prism is a set of multiple triangular prism elements placed in contact, and often cemented together to form a solid assembly. The use of multiple elements gives several advantages to an optical designer:
Wolfgang Sellmeier was a German theoretical physicist who made major contributions to the understanding of the interactions between light and matter. In 1872 he published his seminal work Ueber die durch die Aetherschwingungen erregten Mitschwingungen der Körpertheilchen und deren Rückwirkung auf die ersteren, besonders zur Erklärung der Dispersion und ihrer Anomalien. Before this publication, physicists tried to understand light as a periodic perturbation of an invisible substance that spanned the entire universe: the ether.
Optical glass refers to a quality of glass suitable for the manufacture of optical systems such as optical lenses, prisms or mirrors. Unlike window glass or crystal, whose formula is adapted to the desired aesthetic effect, optical glass contains additives designed to modify certain optical or mechanical properties of the glass: refractive index, dispersion, transmittance, thermal expansion and other parameters. Lenses produced for optical applications use a wide variety of materials, from silica and conventional borosilicates to elements such as germanium and fluorite, some of which are essential for glass transparency in areas other than the visible spectrum.
{{cite web}}: CS1 maint: archived copy as title (link)