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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 defined it in 1837.
The most general form of Cauchy's equation is
where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres.
Usually, it is sufficient to use a two-term form of the equation:
where the coefficients A and B are determined specifically for this form of the equation.
A table of coefficients for common optical materials is shown below:
| Material | A | B (μm2) |
|---|---|---|
| Fused silica | 1.4580 | 0.00354 |
| Borosilicate glass BK7 | 1.5046 | 0.00420 |
| Hard crown glass K5 | 1.5220 | 0.00459 |
| Barium crown glass BaK4 | 1.5690 | 0.00531 |
| Barium flint glass BaF10 | 1.6700 | 0.00743 |
| Dense flint glass SF10 | 1.7280 | 0.01342 |
The theory of light-matter interaction on which Cauchy based this equation was later found to be incorrect. In particular, the equation is only valid for regions of normal dispersion in the visible wavelength region. In the infrared, the equation becomes inaccurate, and it cannot represent regions of anomalous dispersion. Despite this, its mathematical simplicity makes it useful in some applications.
The Sellmeier equation is a later development of Cauchy's work that handles anomalously dispersive regions, and more accurately models a material's refractive index across the ultraviolet, visible, and infrared spectrum.
Cauchy's two-term equation for air, expanded by Lorentz to account for humidity, is as follows: [1]
where p is the air pressure in millibar, T is the temperature in kelvin, and v is the vapor pressure of water in millibar.
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.
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as
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.
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.
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.
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.
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 in which other ingredients are added which change the glasses' optical and physical properties, such as lowering the melt temperature. Fused quartz, therefore, has high working and melting temperatures, making it less desirable for most common applications.
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency-dependence of wave propagation and attenuation.
Self-phase modulation (SPM) is a nonlinear optical effect of light–matter interaction. An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect. This variation in refractive index will produce a phase shift in the pulse, leading to a change of the pulse's frequency spectrum.
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.
Lithium niobate is a synthetic salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other linear and non-linear optical applications. Lithium niobate is sometimes referred to by the brand name linobate.
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 ...
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.
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, either enhancing or reducing the reflected light. When the thickness of the film is an odd multiple of one quarter-wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other. Since the wave cannot be reflected, it is completely transmitted instead. When the thickness is a multiple of a half-wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission. Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are attenuated. Thin-film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses. If the thickness of the film is much larger than the coherence length of the incident light, then the interference pattern will be washed out due to the linewidth of the light source.
