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Normalized Frequency (fiber Optics)
In an optical fiber, the normalized frequency, ''V'' (also called the V number), is given by :V = \sqrt\quad = \mathrm, where ''a'' is the core radius, λ is the wavelength in vacuum, ''n''1 is the maximum refractive index of the core, ''n''2 is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture ''NA''. 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)\quad, where ''g'' is the profile parameter, and ''V'' 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 ''V''2/2. For single-mode operation, it is required that ''V'' < 2.4048, the first root of the ''J'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss; in addition, fibers are immune to electromagnetic interference, a problem from which metal wires suffer. Fibers are also used for 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, some of them being fiber optic sensors and fiber lasers. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiber Optics
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss; in addition, fibers are immune to electromagnetic interference, a problem from which metal wires suffer. Fibers are also used for 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, some of them being fiber optic sensors and fiber lasers. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter ''lambda'' (λ). The term ''wavelength'' is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. Wavelength depends on the medium (for example, vacuum, air, or water) that a wav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index 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 medium is , where ''Π... [...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, NA 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. 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 (and hence its light-gathering ability and 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 \theta, where is the index of refraction of the medium i ... [...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 or gradient-index fiber is an optical fiber whose core has a refractive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Volume
In fiber optics, mode volume is the number of bound modes that an optical fiber is capable of supporting. The mode volume ''M'' is approximately given by V^2 \over 2 and \left(\right), respectively for step-index and power-law index profile fibers, where ''g'' is the profile parameter, and ''V'' is the normalized frequency, ''which must be greater than 5 for this approximation to be valid''. See also *Equilibrium mode distribution *Mode scrambler *Mandrel wrapping In multimode fiber optics, mandrel wrapping is a technique used to preferentially attenuate high-order mode power of a propagating optical signal. Consequently, if the fibre is propagating substantial energy in affected modes, the modal distr ... References * Fiber optics {{optics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, 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, 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 the Helmholtz equation is solved in spherical coordinates. Applications of Bessel functions The Bessel function is a generalizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abbe Number
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 (change of refractive index versus wavelength), 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 Abbe number, ''Vd'', of a material is defined as :V_D = \frac, where ''n''C, ''n''d and ''n''F are the refractive indices of the material at the wavelengths of the Fraunhofer ''C'', ''d'', and ''F'' spectral lines (656.3 nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the visible spectrum. Outside this range requires the use of different spectral lines. For non-visible spectral lines the term V-number is more commonly used. The more general formulation defined as, :V = \frac, where ''n''short, ''n''cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
