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Normalized Frequency (fiber Optics)
In an optical fiber, the normalized frequency, (also called the V number), is given by V = \sqrt = \times NA, where is the core radius, is the wavelength in vacuum, is the maximum refractive index of the core, is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture . In multimode operation of an optical fiber having a power-law refractive index profile, the approximate number of bound modes (the mode volume), is given by \left( \right)\ , where is the profile parameter, and is the normalized frequency, which must be greater than 5 for the approximation to be valid. For a step-index fiber, the mode volume is given by . For single-mode operation, it is required that , the first root of the Bessel function . See also * Abbe number References *{{FS1037C MS188 Fiber optics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Fiber
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher Bandwidth (computing), bandwidths (data transfer rates) than electrical cables. Fibers are used instead of metal wires because signals travel along them with less Attenuation, loss and are immune to electromagnetic interference. Fibers are also used for illumination (lighting), illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, such as fiber optic sensors and fiber lasers. Glass optical fibers are typically made by Drawing (manufacturing), drawing, while plastic fibers can be made either by drawing or by extrusion. Optical fibers typically incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves), phase'' on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The multiplicative inverse, inverse of the wavelength is called the ''spatial frequency''. Wavelength is commonly designated by the Greek letter lambda (''λ''). For a modulated wave, ''wavelength'' may refer to the carrier wavelength of the signal. The term ''wavelength'' may also apply to the repeating envelope (mathematics), envelope of modulated waves or waves formed by Interference (wave propagation), interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed phase velocity, wave speed, wavelength is inversely proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface (e.g., a flat interface). The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an Objective (optics), objective (and hence its light-gathering ability and Optical resolution, resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it. General optics In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by \mathrm = n \sin \t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power-law Refractive Index Profile
For optical fibers, a power-law index profile is an index of refraction profile characterized by : n(r) = \begin n_1 \sqrt & r \le \alpha\\ n_1 \sqrt & r \ge \alpha \end where \Delta = , and n(r) is the nominal refractive index as a function of distance from the fiber axis, n_1 is the nominal refractive index on axis, n_2 is the refractive index of the cladding, which is taken to be homogeneous (n(r)=n_2 \mathrm r \ge \alpha), \alpha is the core radius, and g is a parameter that defines the shape of the profile. \alpha is often used in place of g. Hence, this is sometimes called an alpha profile. For this class of profiles, multimode distortion is smallest when g takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limit of infinite g, the profile becomes a step-index profile. See also *Graded-index fiber A graded-index fiber, or gradient-index fiber, is an optical fiber whose core has a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Volume
Mode volume may refer to figures of merit used either to characterise optical and microwave cavities or optical fibers. In electromagnetic cavities The mode volume (or modal volume) of an optical or microwave cavity is a measure of how concentrated the electromagnetic energy of a single cavity mode is in space, expressed as an effective volume in which most of the energy associated with an electromagentic mode is confined. Various expressions may be used to estimate this volume: * The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to its maximum value V_ = \frac \;\;\; \rm \;\;\; V_ = \frac * The volume over which the electromagnetic energy density exceeds some threshold (e.g., half the maximum energy density) V_ = \int \left(, E, ^ > \frac\right) dV * The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to a weighted average value that emphasises higher energy den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abbe Number
In optics and lens design, the Abbe number, also known as the Vd-number or constringence of a Transparency (optics), transparent material, is an approximate measure of the material's dispersion (optics), dispersion (change of refractive index versus wavelength), with high values of ''Vd'' indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term Vd-number should not be confused with the Normalized frequency (fiber optics), normalized frequency in fibers. The Abbe number, V_\mathsf d\ , of a material is defined as : V_\mathsf d \equiv \frac, where n_\mathsf C, n_\mathsf d, and n_\mathsf F are the refractive indices of the material at the wavelengths of the Fraunhofer lines, Fraunhofer's C, d, and F spectral lines (656.3 nanometre, nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the visible spectrum, human vision. Outside this range requires the use of different spectral lines. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
